lukas felix michalek msc materials science felix_michalek... · 2020-02-02 · quantifying...
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QUANTIFYING MACROMOLECULAR
GROWTH AND HIERARCHICAL
STRUCTURING ON INTERFACES
Lukas Felix Michalek
MSc Materials Science
Submitted in fulfilment of the requirements for the degree of
Doctor of Philosophy
School of Chemistry, Physics and Mechanical Engineering
Science and Engineering Faculty
Queensland University of Technology
2020
To create is to live twice.
- Albert Camus
Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces i
Abstract
For the development of the next generation of soft matter based functional
surfaces it is critical to obtain an in-depth molecular understanding of the processes
that govern the functionalization. There exists a multidisciplinary need for advanced
surface performance ranging from wear/chemical resistance to biomedical
applications. Especially the interplay between theoretical and experimental
assessments is of substantial value for generating an encompassing picture of the
macromolecular functionalisation process on the molecular level.
In the present thesis, the current methods for determining quantitative grafting
densities are critically assessed and a user's guide is provided to estimate maximum
chain coverage. More importantly, the most frequently employed approaches for
determining grafting densities, i.e., dry thickness measurements, gravimetric
assessment, and swelling experiments are examined. An estimation of the reliability
of these determination methods is provided via carefully evaluating the underpinning
assumptions, their simplicity as well as the stability of the deriving equations. The
assessment is concluded with a perspective on the development of advanced
approaches for determination of grafting density.
By functionalisation of a quartz crystal microbalance sensor via the ‘grafting-
to’ approach of poly(methyl methacrylate) (PMMA), one of the proposed possibilities
of precise grafting density determination was experimentally assessed. By virtue of
this experimental approach, it was demonstrated that grafting a distribution of polymer
chains onto a surface critically affects the shape of the distribution, with shorter chains
being preferentially attached. The preferred surface attachment of shorter chains was
unambiguously underpinned by single-molecule force spectroscopy measurements,
establishing a preferential grafting factor. The preferential grafting factor allows to
predict the molar mass distribution of polymers on the surfaces compared to the initial
distribution in solution. These findings not only have serious consequences for
functional polymer interface design, yet also for the commonly employed methods of
grafting density estimation.
Furthermore, the reaction conditions were found to influence the resulting
grafting density and molar mass distribution when grafting polymers onto surfaces.
Theoretically and experimentally the application of poor solvents is proven to be
beneficial for the ‘grafting-to’ approach. The effect is demonstrated by grafting
PMMA chains on silica nanoparticles in different solvents and comparison of the
molar mass distributions via size exclusion chromatography. The shorter polymer
chains are preferentially grafted onto the surface, leading to a distortion effect between
the molar mass distribution in solution and on surfaces. The molecular weight
distortion effect is significantly higher for better solvent quality than for poor solvents.
In summary, the current thesis is exploring theoretical and experimental
aspects of functionalising surfaces with macromolecules, focusing on the precise
determination of grafting densities. Especially for the ‘grafting-to’ approach novel
procedures of surface characterisations were introduced, enabling an advanced
understanding of the grafting procedure on the molecular level. The gained
information result in the introduction of a preferential grafting factor, which can be
used in any further investigation of surface grafting by the ‘grafting-to’ method.
ii Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces
Published Papers Included in this PhD
Research Program
Chapter 2:
L. Michalek, L. Barner, C. Barner-Kowollik, Polymer on Top: Current Limits
and Future Perspectives of Quantitatively Evaluating Surface Grafting, Advanced
Materials, 2018, 30, 1706321(1-18). DOI:10.1002/adma.201706321 (IF = 25.809)
Chapter 3:
L. Michalek, K. Mundsinger, C. Barner-Kowollik, L. Barner, The Long and the
Short of Polymer Grafting, Polymer Chemistry, 2019, 10, 54-59.
DOI:10.1039/c8py01470a (IF = 4.760)
Chapter 4:
L. Michalek, K. Mundsinger, L. Barner, C. Barner-Kowollik, Quantifying
Solvent Effects on Polymer Surface Grafting, ACS Macro Letters, 2019, 8, 800-805.
DOI:10.1021/acsmacrolett.9b00336 (IF = 5.775)
The signed Statement of Contribution of Co-Authors for Thesis by Published
Papers for the three publications included in this PhD Thesis (as mentioned above) is
attached as Appendix A.
Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces iii
Additional publications during candidature
M. M. Zieger, P. Müller, E. Blasco, C. Petit, V. Hahn, L. Michalek, H. Mutlu,
M. Wegener, C. Barner-Kowollik, A Substractive Photoresist Platform for Micro- and
Macroscopic 3D Printed Structures, Advanced Functional Materials, 2018, 28,
18014059(1-7). DOI:10.1002/adfm.201801405 (IF = 15.621)
B.T. Tuten, F.R. Bloesser, D. Marshall, L. Michalek, C.W. Schmitt, S.J.
Blanksby, C. Barner-Kowollik, Polyselenoureas via Multicomponent Polymerizations
Using Elemental Selenium as Monomer, ACS Macro Letters, 2018, 7, 898-903.
DOI:10.1021/acsmacrolett.8b00428 (IF = 5.775)
H. Woehlk, J. Steinkönig, C. Lang, L. Michalek, V. Trouillet, P. Krolla, A.S.
Goldmann, L. Barner, J.P. Blinco, C. Barner-Kowollik, K.E. Fairfull-Smith,
Engineering Nitroxide Functional Surfaces Using Bioinspired Adhesion, Langmuir,
2018, 34, 3264-3274. DOI:10.1021/acs.langmuir.7b03755 (IF = 3.683)
S. Bialas, L. Michalek, D.E. Marschner, T. Krappitz, M. Wegener, J. Blinco, E.
Blasco, H. Frisch, C. Barner-Kowollik, Access to Disparate Soft Matter Materials by
Curing with Two Colors of Light, Advanced Materials, 2019, 31, 1807288(1-5).
DOI:10.1002/adma.201807288 (IF = 25.809)
A.S. Goldmann, N.R. Boase, L. Michalek, J.P. Blinco, A. Welle, C. Barner-
Kowollik, Adaptable and Reprogrammable Surfaces. Manuscript in press Advanced
Materials, 2019, (IF = 25.809)
iv Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces
Conference Contributions
L. Michalek, L. Barner, C. Barner-Kowollik, (November 2017) Polymer on
Top: Current Limits and Future Perspectives of Quantitatively Evaluating Surface
Grafting - Talk, Queensland-Annual-Chemistry-Symposium (QACS) 2017, QUT
Brisbane, Australia.
L. Michalek, K. Mundsinger, L. Barner, C. Barner-Kowollik, (July 2018) The
Limits of Grafting Processes - Talk, World Polymer Congress (MACRO) 2018, Cairns
Convention Centre, Australia.
L. Michalek, K. Mundsinger, L. Barner, H. Frisch C. Barner-Kowollik,
(September 2018) Investigating Light Gated Folding and Limits of Grafting Processes
via AFM - Poster, International Microscopy Congress (IMC) 2018, International
Convention Centre Sydney, Australia.
L. Michalek, L. Barner, C. Barner-Kowollik, (November 2018) Exploring the
Limits of Surface Grafting - Talk, Queensland-Annual-Chemistry-Symposium (QACS)
2018, Griffith University Brisbane, Australia.
Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces v
Awards and Grant Funding Resulting from the
PhD Research Program
L. Michalek (2017-2019) QUT Postgraduate Research Award ($26,688 p.a.).
L. Michalek (November 2017), Excellent Student Presentation at Queensland-
Annual-Chemistry-Symposium (QACS) 2017.
L. Michalek (July 2018), MACRO Travel Bursary for World Polymer Congress
(MACRO) 2018.
L. Michalek (November 2018), Best Student Presentation at Queensland-
Annual-Chemistry-Symposium (QACS) 2018.
L. Michalek (April 2019), High Achiever Award from the Faculty of Science
and Engineering for outstanding PhD work.
C. Barner-Kowollik, L. Barner, H. Frisch, L. Michalek (2019-2020) Merck 350
Year Anniversary Grant for Photochemistry in Mechanical Fields: The Next Frontier
in Dynamic Material Design ($320,000) as co-investigator.
vi Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces
Table of Contents
Abstract ..................................................................................................................................... i
Published Papers Included in this PhD Research Program ...................................................... ii
Additional publications during candidature ............................................................................ iii
Conference Contributions........................................................................................................ iv
Awards and Grant Funding Resulting from the PhD Research Program ................................. v
Table of Contents .................................................................................................................... vi
List of Figures ....................................................................................................................... viii
List of Tables ........................................................................................................................... ix
List of Abbreviations ................................................................................................................ x
Statement of Original Authorship ........................................................................................... xi
Acknowledgements ................................................................................................................ xii
Chapter 1: Introduction ...................................................................................... 1
1.1 Surface functionalisation ................................................................................................ 3
1.2 Polymers on Surfaces ..................................................................................................... 5
1.3 Surface Characterisation ................................................................................................ 7
1.4 Thesis Outline .............................................................................................................. 11
Chapter 2: Current Limits and Future Perspectives of Quantitatively
Evaluating Surface Grafting ......................................................... 13
2.1 Abstract ........................................................................................................................ 13
2.2 Introduction .................................................................................................................. 13
2.3 Recapping the Theory of Polymer Brushes ................................................................. 15
2.4 Characterization of Grafting Densities ......................................................................... 26
2.5 Conclusion and future Perspectives ............................................................................. 40
Chapter 3: The Long and the Short of Polymer Grafting .............................. 45
3.1 Abstract ........................................................................................................................ 45
3.2 Introduction .................................................................................................................. 45
3.3 Grafting Densities evaluated via QCM ........................................................................ 46
3.4 Preferantial Surface Grafting ....................................................................................... 49
3.5 Conclusion ................................................................................................................... 53
Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting ........ 55
4.1 Abstract ........................................................................................................................ 55
4.2 Introduction .................................................................................................................. 56
4.3 Theoretical evaluation of MMDs on Surface Grafting ................................................. 57
4.4 Experimental Solvent Effects on Polymer Grafting ..................................................... 60
Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces vii
4.5 Conculsion ....................................................................................................................62
Chapter 5: General Discussion ......................................................................... 65
5.1 Summary of Studies and Key Outcomes ......................................................................65
5.2 Future Direction ............................................................................................................67
5.3 Conclusions ..................................................................................................................69
Bibliography ............................................................................................................. 73
Appendices ................................................................................................................ 89
Appendix A Statements of Contribution of Co-Authors for Thesis by Published Paper ........89
Appendix B Supporting Information Chapter 2 ......................................................................93
Appendix C Supporting Information Chapter 3 ....................................................................104
Appendix D Supporting Information Chapter 4 ...................................................................115
Appendix E Calculations of MMDs and grafting densities for surface grafting via dry
thickness method. ..................................................................................................................123
viii Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces
List of Figures
Figure 1: Schematic representation on AFM based SMFS measurements of surface
grafted polymer chains.
Figure 2: Streamline of PhD thesis.
Figure 3: Density profiles (box like-like and parabolic brush) of polymer brushes
using AG or SCF theory.
Figure 4: Thickness vs. grafting density, scaling behaviour in all grafting regimes.
Figure 5: Schematic representation for crystalline polymer brush confirmation for
maximum grafting density calculation.
Figure 6: Maximum grafting density in dependency of C-atoms in side chain and
molecular weight for poly--olefines.
Figure 7: Scheme for grafting density limitations of polymer functionalised
surfaces via ‘grafting-to’ approach.
Figure 8: Grafting density limitations for ‘grafting-to’ approach as a function of
radius of gyration and degree of polymerisation.
Figure 9: Schematic illustration of the three most common grafting‐density
determination methods.
Figure 10: Grafting density as a function of the dry thickness of a polymer brush
determined via the dry thickness approach.
Figure 11: Grafting‐density dependency of the polymer weight fraction of a polymer
brush calculated via the gravimetric assessment.
Figure 12: Grafting‐density dependency of the swelling ratio of a polymer brush
evaluated via swelling experiments.
Figure 13: MMDs of PMMA polymer library and grafting densities determined via
in-situ QCM experiments.
Figure 14: Experimental and calculated time dependent frequency change for
polymer mixtures.
Figure 15: Mass weighted, number weighted and predicted surface MMDs and
rupture length determined via SMFS.
Figure 16: Simplified presentation of the preferred attachment of shorter PMMA
polymer chains onto SiO2 nanoparticles.
Figure 17: Calculated shift of MMD on surface depending on solvent quality
Figure 18: Deconvoluted peak for MMD calculations with calculated shift of MMD
on surface and solution depending on solvent quality.
Figure 19: Experimentally observed shifts in DMAc and EA with percentage
difference of Mw on surface and solution after grafting.
Figure 20: Difference of grafting density in dependency of solvent quality for a
polymer graft evaluated via dry thickness method.
Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces ix
List of Tables
Table 1: Literature values for estimated grafting densities of polymer systems
characterized by dry thickness analysis.
Table 2: Determined maximal grafting densities for polymers considered here.
Table 3: Literature values for estimated grafting densities of polymer systems
characterized by gravimetric measurements.
Table 4: Literature values for estimated grafting densities of polymer systems
characterized by the swelling method.
Table 5: Literature values for estimated grafting densities of polymer systems for
less‐used characterization methods
Table 6: Samples used to investigate grafting bias, their composition, theoretical
Mn in solution Mnsol and on the surface Mn
sur with calculated preferential
grafting factor.
x Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces
List of Abbreviations
acronyms name acronyms name
AFM atomic force microscope PMMA poly(methyl
methacrylate)
AG Alexander–de Gennes theory PS polystyrene
ALD atomic layer deposition PVD physical vapour
deposition
BET Brunauer–Emmett–Teller QCM quartz crystal
microbalance
C14 tetradecane RAFT
reversible addition
fragmentation chain
transfer
CTA chain transfer agent RDRP reversible deactivation
radical polymerization
CVD chemical vapour deposition SAM self-assembled
monolayers
DMAc N,N-dimethylacetamide SCF self‐consistent field
approximation
DP degree of polymerisation SEC size exclusion
chromatography
EA ethyl acetate SEM scanning electron
microscopy
FJC freely jointed chain SERS surface-enhanced Raman
spectroscopy
FRC freely rotating chain SIMS secondary ion mass
spectroscopy
GPC gel permeation chromatography SMFS single molecule force
spectroscopy
IR infrared spectroscopy SPM scanning probe
microscope
LEED low-energy electron diffraction STM scanning tunnelling
microscope
LFM lateral-force measurements TEM transmission electron
microscopy
MMD molar mass distribution TERS tip-enhanced Raman
spectroscopy
MS microsphere THF tetrahydrofuran
NP nanoparticle ToF time‐of‐flight
NR neutron reflectivity UHV ultra-high vacuum
PDMAEMA poly(2‐(diemethylamino)ethyl
methacrylate) UPS
ultraviolet photoelectron
spectroscopy
PEG poly(ethylene glycol) WLC worm-like chain
PEO poly(ethylene oxide) XPS x-ray photoelectron
spectroscopy
PHEMA poly(2‐hydroxyethylmethacrylate)
XRR X‐ray reflectivity
PIBA poly(isobornyl acrylate)
Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces xi
Statement of Original Authorship
The work contained in this thesis has not been previously submitted to meet
requirements for an award at this or any other higher education institution. To the best
of my knowledge and belief, the thesis contains no material previously published or
written by another person except where due reference is made.
QUT Verified Signature
xii Quantifying Macromolecular Growth and Hierarchical Structuring on Interfaces
Acknowledgements
First, I want to thank my principle supervisor Prof. Dr. Christopher Barner-Kowollik
for the possibility of undertaking my PhD studies in his Soft Matter Materials Lab at
the Queensland University of Technology. Giving me – a material scientist with
previous focus on materials physics – the opportunity to do research in his polymer
chemistry group is a perfect example of how Christopher welcomes any new
researcher sincerely and is open to any scientific idea. The constant support and trust
he shows towards my research is incredible and means a lot to me. Furthermore, he
gave me the possibilities of being part of new research proposals, which resulted
successfully in the Merck 350 Year Anniversary Grant.
A special thanks goes to my secondary supervisor Prof. Dr. Leonie Barner also from
the Soft Matter Materials Lab at the Queensland University of Technology. She gave
me always constructive feedback to my research and had always time to discuss the
latest results of my work. I especially want to thank her for giving me the opportunity
of conducting QCM measurements by organizing an instrument on which I could carry
out the experiments.
I especially want to acknowledge the support by the QUTPRA PhD scholarship.
Another thanks go to Kai Mundsinger who did most of the synthetic work included in
this PhD thesis. Even though he has his own research topics he finds always the time
to help me out and collaborate on additional projects. Without the help of Kai
Mundsinger I wouldn’t have been able to progress successfully through my PhD
research in the same time frame. I want to thank the whole Macroarc team for the
special atmosphere and working conditions. The collaborative environment and spirit
of helping each other is impressive. Here I especially want to name Dr. Hendrik Frisch,
Dr. Tim Krappitz and Sabrina Bialas for amazing collaborative work and
companionship.
Last but not least, I want to thank my whole family and friends for supporting me
during the time of research in Australia. Even though it was tough being apart from
my family for such a long time, I could still feel their support at any moment of my
journey. Without them it would have been never possible to perform my research in
such a way.
Chapter 1: Introduction 1
Chapter 1: Introduction
Surfaces are the part of any matter we perceive and interact with constantly.
However, the precise definition and analysis of such surfaces is a rather complex task.
From the early beginnings of philosophy to the introduction of modern science,
philosophers vigorously debated the precise definition of matter and its interactions
with its environment.1 One of the founders of modern science, René Descartes, defined
matter – “essence” of a material substance – as the extension in length, breadth, and
depth which constitutes the space occupied by a body, is exactly the same as that which
constitutes the body.2 In other words, the sole fundamental property of a body/matter
is its three-dimensional expansion – which is essentially the surface of matter. This
rather simple and fundamental explanation of matter was revised in the early 1970ies
by the Bulgarian philosopher Panayot Butchvarov, addressing the perception of
surfaces and bodies in his book The Concept of Knowledge. Butchvarov implies that
the surface of a body and the inside are not the same and have no direct correlation
necessarily.3 For being able to understand the properties of matter the surface and the
inside (bulk) have to be investigated separately. Transferred to the field of surface
science, the concept of Butvhvarov can be compared to the often significant
differences in surface and bulk properties of materials and the need of separately
investigating each.
The pioneers in the field of surface science were Paul Sabatier (Nobel Laureate
Chemistry 1912) and Fritz Haber (Nobel Laureate Chemistry 1918), who established
the principles of heterogeneous catalysis.4-5 In both cases, metals were employed to
catalyse high temperature and high pressure chemical reactions for making them
industrially relevant. Today, the Haber-Bosch process generates multi-million tons of
ammonia every year, which is primarily used as fertilizer.6 A further important founder
of the field of surface science is Irving Langmuir (Nobel Laureate Chemistry 1932),
who introduced the concept of mono(molecular) layers.7 The asymmetry of chemical
binding at surfaces – compared to the inner bulk of a material – lead to the conclusion
that the surface atoms (and their properties) have to be different. The work of Langmuir
redefined our understanding of surfaces and interfaces, thus his name stands for the
2 Chapter 1: Introduction
American Chemical Society journal Langmuir, which focus on the research areas of
surface chemistry and surface characterisation.
The disparity of the surface atoms to the bulk atoms – specifically their impact
on the properties of a material – is enhanced by miniaturising feature sizes of matter.
The increased impact of the surface atoms can be explained by the example of the
surface to volume ratio of a spherical particle, which is increasing asymptotically by
decreasing the radius of a particle. In 1959, the renowned physicist Richard Feynman
(Nobel Laureate Physics 1965) gave his seminal lecture Plenty of Room at the Bottom
at the American Physical Society annual meeting, in which he explored the large
potential of miniaturization.8 His vision is the foundation of modern nanotechnology
and a perspective for the direct manipulation of atoms. One of the defining
characteristics of nanotechnology is the nanometre magnitude (at least in one
dimension) of feature size of a material/component. The increased amount of surface
to volume is changing the properties and performance of the material and therefore has
to be characterised thoroughly.
One of the major breakthroughs in the emerging field of nanotechnology was the
development of the scanning tunnelling microscope (STM) by Gerd Binnig and
Heinrich Rohrer (Nobel Laureates Physics 1986).9 In addition, precise imaging of
surfaces (atomic resolution for conducting materials), and accurate manipulation of
atoms arose with the invention of the STM. Further development steps from Binnig
resulted in the design of an atomic force microscope (AFM) which could also image
non-conductive materials to a resolution of a few angstroms.10 In addition,
(interaction) forces between a sample and a nano-sized probe could be recorded. The
development of both scanning probe microscopes (SPM) enabled an entirely new level
of understanding of surfaces and the concomitant design of precision functional
surfaces.
Gerhardt Ertl (Nobel Laureate Chemistry 2007) reformed the field of surface
science by establishing the in-depth characterisation of surface chemical reactions.11
His teaching redefined our understanding of heterogeneous catalysis and revealed the
nature of surface chemical bonds.12-13 The elucidation of fundamental principles of
chemical reaction on surfaces was feasible due to advanced surface characterisation
tools i.e. low-energy electron diffraction (LEED), ultraviolet photoelectron
spectroscopy (UPS) and STM. Additional surface characterisation techniques
including surface-enhanced Raman spectroscopy (SERS) and tip-enhanced Raman
Chapter 1: Introduction 3
spectroscopy (TERS) were frequently employed by Gerhardt Ertl.14-15 With such
techniques, the resolution of chemical imaging was considerably improved and
therefore revised our knowledge of surface chemistry and surface properties.
A further recent advance in the application of surface science is the topological
insulator (Nobel Prize Physics 2016), which is a material that behaves like an insulator
in bulk (interior), yet is conductive on the surface. Early calculations predicted time-
reversal symmetry-protected surface states which are leading to a surface conductive
behaviour of insulating binary compounds (containing bismuth).16-17 The first
experimental proof of such symmetry-protected surface states was carried out by
Hasan and co-workers, investigating Bi0.9Sb0.1 bulk material.18 Further studies show
that the concept of a topological insulator could be employed in low-power-
consumption electronics, which may be adopted in quantum computing.19 The
difference between the surface and bulk properties of the topological insulator is a
good example for how far (surface) science has progressed and how important it is to
investigate and tailor surfaces with precise material properties.
An advanced way to tailor surface properties of a material is by decorating the
surface with atoms or (macro)molecules, which include a specific function.20-21 In this
scenario the bulk material is merely a substrate (structural element) and the surface
properties are defined by the attached functionality. The design and characterisation
of such a functional surface is critical for many application fields of (soft matter)
materials. After all, the surface/interface is the most crucial point of interaction
between matter.
In the next three subchapters a short introduction into Surface Functionalisation,
Polymers on Surfaces and Surface Characterisation is provided, followed by a Thesis
Outline to position the progress of the present PhD project in the field of surface
science. The research which was conducted in this PhD thesis is exclusively focusing
on the functionalisation and characterisation of solid surfaces with polymers.
Therefore, no deeper introduction into any kind of liquid or gaseous interfaces will be
provided.
1.1 SURFACE FUNCTIONALISATION
For the majority of materials and their applications, their surface possesses
particular and well-defined functions. The surface can feature functionalities ranging
from wear resistance for structural materials,22 conductive or insulating layers for
4 Chapter 1: Introduction
micro-electronics,23 wettability,24 release of small molecules for drug delivery
systems,25 chemical resistance up to biocompatibility for medical devices26-27. The
surface decoration with specific functionalities can be achieved by attaching atoms,
ions, molecules or macromolecules on surfaces via adsorption processes, which are
commonly subdivided into chemisorption and physisorption.28 Both processes can be
defined by the interaction forces between the substrate and the adsorbent. Nevertheless
it is rather complex to define the difference between both processes, similar to the
separation between chemical and physical interactions in general. For the
chemisorption the substrate and the adsorbent encounter strong interaction forces
comparable to chemical valence forces (analogous to the ones in forming chemical
compounds). Therefore, also strong hydrogen bonding of the adsorbent to the surface
is called chemisorption by IUPAC definition.29 In contrast, no significant change in
the electronic orbital pattern occurs in physisorption, where the interaction forces are
van der Waals forces and significantly lower.30
One of the simplest forms of designing surfaces with defined properties is by
depositing a layer on top of a substrate. The thickness of the deposited layer can range
from a monolayer (a few Ångstrom) to several micro-meters.31 Generally, the
deposition methods are divided into two major categories, the physical- and the
chemical-deposition. In the later approach, a precursor is subject to a chemical change
at a solid substrate surface, whereas for the physical deposition, the deposition occurs
via physical impacts such as mechanical or thermodynamical processes.32 It is
important to note that the nature of the deposition method (chemical or physical
deposition) does not have to be necessary the same as the adsorption phenomenon
(chemisorption or physisorption). In other words, films which are deposited via
chemical methods (i.e. spin coating) can be adsorbed via physisorption and vice versa
(i.e. physical vapour deposition (PVD) sputtering techniques). Common techniques
for the chemical deposition include chemical solution deposition (sol-gel method),33
spin/dip coating (polymer coating),34-35 chemical vapour deposition (CVD)36 and
atomic layer deposition (ALD).37 Examples for the physical deposition involve
thermal evaportation,38 molecular beam epitaxy,39 sputtering techniques (PVD),40 and
electro-hydrodynamic deposition.41 The aim of the aforementioned deposition
methods is to form uniform (thin) films on top of a substrate with a precisely desired
function. For guaranteeing reliable surface properties, the attachment of the film to the
substrate has to be ensured. The macroscopic interaction between the film and the
Chapter 1: Introduction 5
substrate is defined as adhesion and is often a mixture between chemisorption and
physisorption on the microscopic scale. Adhesion is defined as the tendency of a
substance to attach to the surface of another substance – a process that requires energy
(adhesion energy), which can come either from physical and/or chemical linkage.42
There are primarily five mechanisms to describe the phenomenon of two materials
adhering: mechanically by mechanical interlocking (velcro principle),43 dispersive by
intermolecular van der Waals forces (Keesom and London forces),44-45
electrostatically by difference in electric charge,46 diffusive by inter-diffusion between
both materials (interdigitating chains on polymer surfaces)47 and chemically by
covalent bond formation (chemisorption).
The functionalisation of a surface by chemical adhesion is especially durable due
to the strong interaction forces between surface and substance. Nowadays
sophisticated chemical procedures allow to equip almost any surface with any kind of
function/property on the nanoscale domain, which makes this process highly
versatile.48 One way to achieve such uniform chemical surface modification is through
formation of self-assembled monolayers (SAM).49-50 The functional group of the
chemisorbed molecules – often small organic molecules with a head and tail structure
– have a strong chemical affinity to the surface. The driving force for the SAM
formation is the minimization of surface energy from the substrate, which occurs in
three phases defined by the density of the self-organized layer (low – intermediate –
high density).51 In addition, the tail of the SAM molecule can be equipped with specific
chemical end-groups for further functionalisation of the surface, for example by
surface initiating polymerisation groups.52 Functionalisation of the surfaces with
polymers rather than small organic molecules is increasing the range of accessible
surface properties even further.
1.2 POLYMERS ON SURFACES
Since the advent of polymer science and the macromolecular hypothesis by
Hermann Staudinger53 (Nobel Laureate Chemistry 1953), the fields of polymer
chemistry, physics and technology are vibrantly growing research areas. The need for
polymeric materials in almost any application field is increasing and therefore the
production is at an all-time high.54 Even though a large amount (by mass) of polymeric
material is still employed in the area of packaging, fields of more advanced
applications i.e. surface modification are growing to a great extent. Covering materials
6 Chapter 1: Introduction
surfaces with polymers is of fundamental interest in many application fields.55 As
described already briefly in the previous Sub-Chapter 1.1, there are in general two
ways to attach polymers to surfaces by weak physisorption (e.g. via processes such as
spin/dip coating)56 or via chemically tethering polymer chains onto surfaces. The later
approach is leading to strongly durable long living surface functionalisation and can
be achieved either by ‘grafting-to’ or ‘grafting-from’ approach.57 The process of
covalently attaching polymers on surfaces is referred to as (polymer) grafting and will
be explained in greater detail in Chapter 2 of the current PhD thesis. The current sub-
chapter is focusing on the properties of polymers on surfaces.
The properties of polymers on surfaces can be divided into single chain and
densely grafted chain properties. In the latter case, the interaction between many
polymer chains are resulting in specific properties of a polymer graft. For the possible
inter-molecular interaction of polymer chains on a surface, the single chains have to
be tethered sufficiently dense. The polymer is then typically referred to as polymer
brush.58 A further explanation of polymer brushes and how to define different grafting
density regimes can be found in Chapter 2 of the current thesis. Other ‘many’ chain
properties are the thickness, and the density profile of the formed polymer graft, which
depend strongly on the grafting density and the contour length of the single polymer
chains. The length of a single polymer chain is defined by the product of the monomer
size and the degree of polymerisation. Nota bene that the degree of polymerization and
therefore the length of the polymer chains are not the same for each single chain. The
dispersity describes the extent of dissimilarity between all degrees of polymerizations
and can be calculated by dividing the weight averaged molecular weight with the
number weighted averaged molecular weight.59 Especially for the ‘grafting-to’
approach the effect of dispersity on the formed polymer graft is critical and is
investigated in detail in Chapters 3 and 4.60-61 A further important property of a
polymer chain on a surface is the chain elasticity, which describes the flexibility of the
polymer backbone. Depending on the model used for describing the physics of a
polymer chain, the chain elasticity is defined as persistence length (worm-like chain
(WLC) model), Kuhn length (freely jointed chain (FJC) model) or rotating unit (freely
rotating chain (FRC) model).62 The determination of all above mentioned properties is
important for the performance of a polymer graft. To be able to tailor the performance
of such functionalized surfaces, an in-depth understanding of the polymers on the
surface has to be achieved.
Chapter 1: Introduction 7
1.3 SURFACE CHARACTERISATION
For understanding growth processes and hierarchical structuring of grafted
polymers on surfaces – specifically at the molecular level – in-depth characterisation
methods have to be employed. As already mentioned in previous subchapters, such
knowledge is the essential key for designing and tailoring surfaces with specific
properties. Surface characterisation can be grouped into three major categories,
chemical characterisation, surface imaging and physical properties.63 All three
categories will be introduced in the following paragraphs, focusing on the techniques
applied in the experimental work of the current PhD thesis.
1.3.1 Chemical Characterisation of Surfaces
There are several characterization techniques available for analysing the
chemical composition of surfaces i.e. x-ray photoelectron spectroscopy (XPS), Raman
Spectroscopy, secondary ion mass spectroscopy (SIMS), infrared spectroscopy (IR)
and many more.64 Nevertheless, samples prepared in the current work were solely
analysed via XPS, due to the conclusive results achieved with this method. In XPS,
the sample are irradiated with soft X-rays in an ultra-high vacuum (UHV) chamber.65
The x-ray irradiation leads to the emission of core electrons (photoelectrons) with
specific (measureable) kinetic energy, which can be used for the calculation of the
binding energy. For each element the binding energy of a photoelectron is
characteristic. Therefore, the signal intensity (usually given in counts of photoelectrons
per seconds) can be correlated to the elemental composition of the sample.65
Additional slight shifts (a few eV) of the binding energy can give insights into the
chemical vicinity and/or the oxidation states of the element. The possibility of not only
obtaining a quantitative result for the elemental composition but also a quantitative
result for chemical moieties (chemical shifts) is of specific interest for chemical
characterization of organic molecules and polymers on surfaces.56, 66 An additional
benefit of chemical characterisation via XPS – which is commonly mentioned – is the
non-destructive nature of the method. However, there are reported cases of x-ray
damaging samples, implying that care should be taken when conducting such
experiments.67-68 Standard x-ray photoelectron spectrometers are averaging over an
area of a few square millimetres, which allows representative chemical analysis of the
surface even if microscopic inhomogeneities are present. New developments in
spectrometer design allow XPS mapping (chemical imaging) of a surface with a lateral
8 Chapter 1: Introduction
resolution of roughly 50 m. XPS mapping not only offers the possibility to
chemically analyse the average surface composition, yet also provides spatial
resolution (limited to a few ms) to the chemical information.69 It is important to
mention that even though the ratio of elemental composition and binding energies of
specific elements can be readily determined quantitatively via XPS, a quantitative
correlation with the exact amount of atoms or (macro)molecules is challenging.
Therefore, a direct determination (calculation) of grafting densities via standard XPS
measurements is not feasible.
1.3.2 Imaging of Surfaces
There are many imaging tools which can spatially resolve surfaces/interfaces
such as confocal microscopy, scanning electron microscopy (SEM), transmission
electron microscopy (TEM), scanning probe microscopy (SPM) and many more.64, 70
Most of these characterisation methods can investigate additional material/surface
properties or the chemical composition. The imaging method of choice is mainly
depending on the material properties of the substrate and surface layer. For example,
in the case of STM the surface and the measurement probe have to be conductive for
being able to measure a tunnelling current.71 The samples in the present work are solely
investigated via AFM due to the unique flexibility of the measurement procedure.
Samples can be characterized via the tip surface interaction in environments ranging
from ambient to harsh conditions (even in organic solvents) along with a minimal
effort in sample preparation. Via AFM, unmatched quantitative atomic resolution in
lateral direction (z-height profile) can be achieved,72 although the resolution in the x-
y-plane is restricted by the extent of the tip radius of the employed cantilever. The
shape and uniformity of the tip can critically affect the resolution/quality of the
recorded surface topography, which can lead to artefacts such as shadowing effects,
broadening of surface features and double imaging.73 In addition to recording the
surface topography, AFM can investigate other materials’ characteristics including
electronic properties, magnetism, thermal conductivity or nano-mechanical properties
(storage/loss modulus, friction, adhesion and stiffness).74 Further chemical contrast
(qualitative) in AFM imaging can be achieved by phase contrast via operating the
AFM with an oscillating cantilever (commonly mentioned as ‘tapping-mode’) in either
non- or semi-contact mode. Depending on the chemical interaction between the sample
and the AFM cantilever tip the phase will vary with a resolution down to a few nm.75
Chapter 1: Introduction 9
One way to reach quantitative chemical surface imaging with an AFM is by coupling
it with additional spectroscopic methods including IR (AFM-IR) or Raman
spectroscopy (TERS). For the latter example, the Raman scattering is enhanced by a
metallic AFM tip which leads to quantitative chemical analysis. The spatial resolution
in the chemical imaging is limited by the AFM tip radius and can be as low as a few
nm (single dye molecule ~ 15nm).76-77
1.3.3 Physical Properties of Surfaces
When discussing physical properties of surfaces or surface coatings, literature
often refers to mechanical properties (i.e. stiffness, hardness and viscoelastic
behaviour). Although other properties including wettability, conductivity, density and
layer thickness are equally important for the performance of materials surfaces.
Investigation of the underlying samples in the current work – with respect to their
physical properties – was performed via AFM, quartz crystal microbalance (QCM)
and Ellipsometry. As already mentioned in the previous Sub-Chapter 1.3.2, AFM can
be used to map the nano-mechanical properties of a surface.74 The force modulation
via nano-mechanical imaging can be used for the precise distinction between disparate
soft matter materials on surfaces.56 An alternative way to characterize these physical
properties is via force spectroscopy. The term ‘force spectroscopy’ describes all
measurements on the response of a material to an externally applied mechanical force.
There exist several ways to perform force spectroscopic measurements, e.g. single
molecule force spectroscopy (SMFS),78 lateral-force measurements (LFM),79 or
colloidal probe measurements.80 For SMFS, the force response of a single polymer
chain to an applied pulling event is recorded. SMFS measurements on single chains
can be conducted using optical tweezers, magnetic tweezers and AFM.78 Nevertheless,
these methods are all based on the same principle of stretching a molecule – which is
tethered with one end to a substrate – by attaching the free end of the chain to a probe
and applying a force (pulling). One of the most common techniques is AFM based
SMFS.81-83 The measurement process can be divided into four stages, which are
illustrated in Figure 1. The process commences with pressing the AFM cantilever on
the surface (Figure 1 A) with a specific trigger force and dwell time. During stage (A)
a polymer can attach to the tip of the cantilever. By retracting the cantilever from the
surface with a specific velocity (Figure 1 B), the chain starts to uncoil. If the distance
between the substrate and the cantilever tip is further increased, the polymer is
10 Chapter 1: Introduction
stretched. This can be seen as an increase of the force (Figure 1 C) in the force distance-
curve, due to the change in deflection of the cantilever beam. When reaching a force
exceeding the rupture force, the attachment of the chain to the cantilever cleaves and
the force will decrease immediately to zero (see Figure 1 D). With the data acquired
from the third stage, it is possible to determine the length and elasticity of a single
chain quantitatively by fitting the data to a physical model of the polymer chain.62 The
precision of force recording is in the low pico-Newton range and can even detect the
conformational change between cis to trans isomers of alkenes in polymers.84 Even
though the SMFS shows high precision in investigating single chain properties, the
method becomes exponentially difficult in high grafting density regimes when
multiple chains are attached to the cantilever. A direct quantitative correlation of
grafting density by counting the amount of rupture events cannot be achieved.
Figure 1: Measured deflection versus Z position of the cantilever and calculated force-distance
curve of a force measurement on a single molecule chain. Sketches of the four stages of
the experiments: (A) pressing the tip of cantilever onto the sample, (B) retraction from
the surface, (C) stretching of the polymer chain and (D) rupture of the chain.
Another important analytical technique for precise quantitative surface
characterisation – addressing the number of tethered molecules – is QCM where
surface mass uptake can be recorded by the change of resonance frequency of an
oscillating quartz crystal. The strengths of a QCM setup is the high (mass) sensitivity,
in-situ operation and straightforward quantification.85-87 The analysed surface area is
in the range of several square millimetres up to centimetres, therefore inhomogeneities
are not greatly affecting results with regard to their statistical reproducibility.
Combined with the determination of the thickness of the surface layer (e.g.
ellipsometry), further calculation of densities can give a complete picture of the
dimensions and densities of a polymer functionalised surface.
Chapter 1: Introduction 11
1.4 THESIS OUTLINE
As the title – Quantifying Macromolecular Growth and Hierarchical Structuring
on Interfaces – of the current PhD thesis implies, a precise quantification of
macromolecules (polymers) attached onto interfaces (surfaces) is targeted as the final
goal. As outlined in the introduction, there is a multidisciplinary need for surface
functionalisation especially by tethering polymers covalently onto solid substrates. To
enable the design of new advanced functional surfaces, the understanding of the
processes governing surface attachment at the molecular level is critical.
One of the main challenges which commonly arises after grafting polymers on
surfaces relates to the question of how many polymer chains are attached to the surface
over a certain area? Or in other words, how dense are the chains tethered on the
surface? The physical quantitative measure is the grafting density. The frequent
employed procedures of grafting density determination are often flawed.
Reproducibility and statistical significance of such methods are questionable.
Critically, for most of the common evaluation methods physical assumptions are
invoked which influence the quality of quantitative determination significantly. For
understanding existing characterization procedures and their physical limitations, a
comprehensive assessment of existing procedures was undertaken resulting in the first
major publication of the current thesis – Chapter 2: Current Limits and Future
Perspectives of Quantitatively Evaluating Surface Grafting. In Chapter 2, not only a
precise investigation of existing methods is carried out, but also calculations for
physical limitations of the grafting process are shown. Furthermore, future
perspectives on the quantitative evaluation of grafting densities are provided.
One of the proposed evaluation methods is the evaluation via QCM
measurements. As mentioned in the previous Sub-Chapter 1.3.3, a QCM is able to
detect the amount of surface grafted polymers via the frequency change of an
oscillating crystal with highly reproducible precision. Therefore, QCM was selected
as a precise method of characterising surface grafting, resulting in the second major
publication of the current thesis – Chapter 3: The Long and the Short of Polymer
Grafting. By grafting PMMA chains (with different molecular weight) on a silica
QCM sensor via the ‘grafting-to’ process, the grafting density limitations could be
correlated to the radius of gyration. Additional ratio experiments detected the effect of
12 Chapter 1: Introduction
preferential surface grafting of shorter polymers chains on surfaces allowing the
introduction of the preferential grafting factor.
Further investigations of solvent effects on the change (shift) of molar mass
distribution on surfaces compared to solutions resulted in the third major publication
– Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting. By
calculations and experiments, the significance of solvent quality on the preferential
surface grafting was investigated. The experimental results (and calculations) are
suggesting the use of poor solvents for grafting via the ‘grafting-to’ method.
The graphical representation of the streamline/outline of present PhD thesis can
be found in Figure 2.
Figure 2: Streamline of PhD thesis with three major outcomes (publications) for quantifying
macromolecular growth and hierarchical structuring on interfaces.
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 13
Chapter 2: Current Limits and Future
Perspectives of Quantitatively
Evaluating Surface Grafting
2.1 ABSTRACT
Well‐defined polymer strands covalently tethered onto solid substrates
determine the properties of the resulting functional interface. Herein, the current
approaches to determine quantitative grafting densities are assessed. Based on a brief
introduction into the key theories describing polymer brush regimes, a user's guide is
provided to estimate maximum chain coverage and — importantly — examine the
most frequently employed approaches for determining grafting densities, i.e., dry
thickness measurements, gravimetric assessment, and swelling experiments. An
estimation of the reliability of these determination methods is provided via carefully
evaluating their assumptions and assessing the stability of the underpinning equations.
A practical access guide for comparatively and quantitatively evaluating the reliability
of a given approach is thus provided, enabling the field to critically judge
experimentally determined grafting densities and to avoid the reporting of grafting
densities that fall outside the physically realistic parameter space. The assessment is
concluded with a perspective on the development of advanced approaches for
determination of grafting density, in particular, on single‐chain methodologies.
2.2 INTRODUCTION
The design of functional interfaces is critical for almost every application, as the
majority of materials' interface with their environment.88 In particular, interfaces
decorated with (functional) macromolecules fulfill critical functions in a range of
devices and applications, covering areas from medical implants,89-90 3D cell
scaffolds,91-92 optoelectronics,93 and sensors94 to coatings.95-97 The functionality of the
interface and its interactions with the environment are critically determined by the type
of polymer and, critically, the density with which the strands are tethered to the surface.
Thus, the modification of surfaces with synthetic—and to some extent natural—
polymers has been, and is, currently a highly active research field.98 The covalent
modification of surfaces with polymers has been significantly affected by the advent
14 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
of polymerization methods that afford fine control over the polymer length and the
dispersity of the resulting molecular weight distribution. These advanced synthetic
methods, which have been developed over the last two decades, include reversible
deactivation radical polymerization (RDRP) processes,99-101 yet also advanced cationic
and anionic macromolecular growth mechanisms.102-103 For the first time, the length
of a synthetic polymer chain ensemble can be effectively controlled for a wide array
of functional monomers, presenting notable opportunities for surface modification.103
The process of growing chains from a surface, termed “grafting‐from” and discussed
in the following sections in more detail, exploits covalently tethered small‐molecule
initiation sites on the surface. Of similar impact on the field of covalent surface
modification has been the development of mild and efficient ligation protocols not
only for the construction of complex macromolecules in solution by linking
prefabricated polymer strands, but also the covalent attachment of such strands onto a
rich array of surfaces. Some of these linkage protocols adhere to the stringent click
chemistry criteria pioneered by Sharpless and co‐workers104 and refined in the context
of polymer chemistry by Barner‐Kowollik et al.105 The postattachment approach is
often termed “grafting‐to.” The chemistry of the employed polymers has been explored
in substantial depth, and a plethora of studies has been devoted to assess the resulting
surface properties, both on the macroscopic and molecular levels. For example, the
ability to protect surfaces from biological impact,26, 106-107 the fine control over surface
hydrophilicity and hydrophobicity,108-109 the possibility of releasing small
molecules,110-111 the fluorescence, as well as emission properties112 and tribological
behavior113-114 have been studied. On the molecular level, e.g., probing the surface
chemistry with photoelectron emission spectroscopy115 or time‐of‐flight secondary‐
ion mass spectrometry (ToF‐SIMS)116-117 has been explored in depth. However, one
property‐defining characteristic is typically not as critically examined, the grafting
density. Nearly all published studies recognize the importance of the chain grafting
density, and an array of methods and models on how polymer chains behave on
surfaces has been published.118-119 Despite this progress, the literature abounds with
grafting densities that challenge physical limits or that have been assessed based on
incorrect assumptions and thus feature limited accuracy. Thus, we herein provide—
after a concise overview of the most important polymer brush models—a discussion
on the limits of physical grafting densities by applying a simple model. More
importantly, however, we examine the three most employed methods for
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 15
experimentally estimating grafting densities, i.e., dry thickness measurements,
gravimetric assessment, and swelling experiments. Critically, we provide for each of
these a clear explanation of the inherent assumptions and assess the stability of the
underlying equations for each method by mathematical error propagation. We
demonstrate that key methods used for accessing grafting densities have inherent
weaknesses that lead to considerable errors, which, in some cases, can be minimized
by selecting the correct experimental assessment, while some methods are
nonapplicable in certain grafting regimes. Finally, we make recommendations on how
determinations of grafting density should ideally be carried out and provide a
perspective into future methods. We hope that this work will serve as a blueprint and
a reference guide for future measurements of grafting density, while concomitantly
serving as a user's guide for estimating the expected errors.
2.3 RECAPPING THE THEORY OF POLYMER BRUSHES
By tethering one end of a polymer chain to a surface or interface, a polymeric
brush surface can be constructed. The term “polymer brush”, if used correctly (to
describe the brush regime) describes a sufficiently dense (covalent) attachment of
polymer chains. Nevertheless, polymer systems with a lower‐ or a higher‐grafting‐
density conformation are also often denoted as “polymer brush” in the literature.58
Here, this term will also be used to refer to the different dense grafting conformations.
In the brush regime, the polymer chains interact with each other so that a stretched
configuration of the polymer chains (in the absence of an external field) is present. The
behaviour of a stretched configuration differs significantly to that of free polymers in
the random‐walk configuration.119 The behaviour of polymer chains in low‐density
brushes is also significantly different to that of free polymers in solution.120
While there exists a variety of possible polymer brush configurations, such as
polymer micelles,121 adsorbed (co)polymers (on solid or liquid–liquid interface),122-123
diblock copolymer melts,124 and covalently grafted polymers on a solid surface, here,
we will exclusively address the latter: end‐grafted polymers on a solid substrate. As
noted in the introduction, polymer brushes are accessible by two main approaches, i.e.,
“grafting‐to” and “grafting‐from” methods. In addition, some surfaces are modified by
“grafting‐through” approaches.125 As also noted, the synthetic process of grafting
polymers on surfaces is well established and summarized in an abundant number of
excellent reviews.52, 119, 126-128 Nonetheless, a brief reiteration—focusing on some
16 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
critical points—of these approaches is crucial for our current report. As the “grafting‐
to” and “grafting‐from” approaches are the primary methods for covalently attaching
polymers on solid surfaces, we will solely focus on these mechanisms.
In the case of “grafting‐to”, an end‐functionalized polymer chain is tethered
covalently to a suitable substrate by undergoing a chemical reaction under appropriate
conditions.99 The key advantage of the “grafting‐to” approach is that polymer chains
can be synthesized with a narrow molecular weight distribution incorporating the
desired functionalities before the attachment to the surface. Critically, the degree of
polymerization can be determined before tethering the polymer on the surface.
Knowledge of the chain length of the polymer is important for several polymer brush
characterization methods, which we will assess in depth in the following sections. A
prefunctionalization (by self‐assembled monolayers (SAMs) or coupling agents) of the
substrate surface is necessary for introducing functional groups that can react with the
end‐functionalized polymer chain. An often‐suggested general disadvantage of the
“grafting‐to” approach is that only a smaller number of chains can be attached per unit
area, due to slow diffusion of macromolecules.119 To reach a reactive site on the
surface, a polymer chain has to diffuse through the previously attached polymer coils.
If the thickness of the polymer layer is increasing, this barrier will become more and
more significant. Therefore, the grafting density and the thickness of a polymer brush
with the “grafting‐to” approach should be limited. The “grafting‐from” method can
circumvent these drawbacks.
During “grafting from”, a polymer chain is synthesized in situ on a surface‐
functionalized substrate.128 Surface‐confined macromolecular growth is achieved by
immobilization of a polymerization initiator onto the surface by covalent ligation.
Most of the known polymer syntheses can be carried out with this grafting mechanism.
In addition, controlled growth can be achieved, for example, via surface‐initiated
RDRP.129-130 As the polymer chain is constructed starting from the surface of the
substrate, only a monomer, and not an entire macromolecule, has to diffuse to the
active site, which is a much faster process. Therefore, thicker polymer brushes and
higher grafting densities may be accessible. The major disadvantage of the “grafting‐
from” approach is that the degree of polymerization, N, the number average molecular
weight, Mn, and the dispersity, Đ, of the polymers at the surface are unknown, posing
a significant challenge for quantitative brush surface characterization, as we will
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 17
discuss in the following sections. To determine the unknown characteristics of the
polymer chains, the polymers have to be either cleaved after synthesis or a sacrificial
initiator has to be added into the polymerization solution during synthesis.131-132
Cleaving of the polymer is a rather complicated and laborious task because a
sufficiently large surface area must be coated to obtain sufficient polymer chains for
common characterization methods such as size‐exclusion chromatography. On the
other hand, by adding a sacrificial initiator to the polymerization mixture and
determining the unknown characteristics of the polymer by measuring the free
polymers synthesized in solution, only a weak and indirect link to the polymers on the
surface is available. In the literature, the correlation between free polymer in solution
and on the surface is a controversially discussed topic and no clear statement regarding
the quality of the correlation can be made.133-134 In this context, we note a recent study
of Spencer and co‐workers, who investigated the influence of the grafting density on
the polymer growth rate on surfaces and solution, concluding that the difference
between the surface and solution‐generated molecular weight is a function of the
grafting density.135
In addition to the intramolecular properties such as the degree of polymerization,
N, and molecular weight, the critical properties such as the grafting density, σ (amount
of polymer chains per certain surface area), brush thickness, h, and density profile,
Φ(h) (progression of segment density perpendicular to the surface) determine the
properties of a polymer brush.136 These parameters are a result of the interactions of
the polymer chains with each other, the solvent and the surface. To obtain a clearer
picture of the distinctive properties of a polymer brush, several notable theoretical
models have been introduced in the past, which we will briefly review.119, 137-151
The simplest description of a polymer brush rests on free‐energy‐balance
arguments. In general, there are two counteracting driving forces affecting the polymer
chain: the maximization of the configurational entropy, achieved by a random‐walk
configuration, and the tendency for a polymer chain to be surrounded by solvent. With
increasing grafting density, the polymer brush has to balance the increase of Helmholtz
free energy, A, due to a reduction of configurational entropy and the overlapping of
neighbouring polymer chains (excluded volume effect).119 One of the first models
providing an elaborate analytical description of the polymer brush properties on solid
planar surfaces is the Alexander–de Gennes (AG) theory,137-139 for which several
assumptions are made. First, the segment density profile of the polymer brush
18 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
perpendicular to the surface is a step‐like function, featuring a constant value for the
monomer concentration through the entire brush with each chain behaving in the exact
same manner. The step‐like density profile and the corresponding integral are shown
in Figure 3 with black solid lines. Second, all free ends of the tethered polymer chains
are placed in one single plane with the distance, h (brush thickness), parallel to the
planar substrate surface. The “Flory approximation” is invoked to give an explicit
expression for the free energy of the polymer brush in the AG theory.140 This
approximation evaluates the reduction in configurational entropy caused by the
constraint of not being an ideal random‐walk polymer in solution and instead being
tethered on a surface with the free‐end of the polymer situated at the brush thickness,
h. As a result, the equilibrium brush thickness h for a polymer brush in a good solvent
can be obtained by Equation 1
ℎ ≈ 𝑁𝑎4 3⁄ 𝜎1 3⁄ (1)
with the degree of polymerization N, the monomer size a, and the grafting density .
In contrast to a free random‐walk polymer, where the dimension of the polymer (radius
of gyration) is scaling in an 𝑅g ~ 𝑁3 5⁄ relation, the dimension of the polymer brush
scales linearly with the degree of polymerization (ℎ ~ 𝑁), leading to the conclusion
that the densely grafted polymer chains are deformed (in comparison to the random‐
walk polymers). The linear scaling behaviour is also valid for poor solvents.119
Figure 3: Density profile of a box‐like brush (AG theory, in black solid lines) and a parabolic brush
(analytical SCF theory, in red dashed lines) with the corresponding integral of the segment
density.
As noted, the AG theory is only applicable for planar samples. For a theoretical
model of a polymer brush on a curved substrate (e.g., a nanoparticle (NP) or a
microsphere (MS)), the AG theory has to be adapted.143-144 Daoud and Cotton
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 19
implemented the radial distance dependency of the excluded volume effect into the
AG theory, leading to a more accurate description of polymer brushes on curved
substrates.143 Their extension is a simple geometrical calculation having a smaller
excluded volume (more space for polymer chains and, therefore, higher
configurational entropy), the further away the polymer is from the surface. The theory
of Daoud and Cotton was elaborated for star‐shaped polymers, yet can also be directly
used for polymer brushes on curved surfaces.
In a numerical study of Hirz (using a self‐consistent field (SCF)
approximation), their simulations show a quite different behaviour with regard to the
density profile of a polymer brush, in comparison to the AG theory (no step‐like
profile).145-146 Thus, a more accurate description of a polymer brush was suggested by
Milner et al.147-149 based on the idea that the free‐chain ends can be located anywhere
in the polymer brush. Specifically, an analytical approximation to solve an SCF theory
of polymer brushes in an external potential is invoked. The external potential in this
approximation is generated by replacing the monomer interactions with a position‐
dependent monomer chemical potential originating from the self‐consistent segment
density profile. For the calculations of the aforementioned potential, the excluded‐
volume effect is balanced with the decrease of configurational entropy. In the SCF
theory suggested by Milner et al., the self‐consistent field for equal length polymer
chains is a parabolic potential and is therefore called the “parabolic field”
approximation. The density profile and the corresponding integral are depicted in
Figure 3 by the red dashed lines. The key difference in comparison with the AG theory
manifests itself in the overall brush thickness, h. For the AG theory, the predicted value
is an underestimation for polymer brushes with similar grafting density, although an
exact value is needed for the quantitative determination of the grafting densities. The
underestimation of grafting densities is problematic for the different characterization
methods and will be examined comprehensively below.
In general, it should be noted that the parabolic density profile of the SCF
theory affords a better description of moderately densely grafted polymer brushes in a
good solvent. In an experimental result by Field et al., the measured density profile of
a polystyrene (PS)–poly(ethylene oxide) (PEO) brush was well described by a
parabolic profile (SCF theory).152 The step‐like profile of the AG theory seems to fit
better for strongly stretched (high‐grafting‐density) polymer chains on surfaces.
20 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
Nevertheless, both theories are failing in their description of polymer brushes with
very low or very high grafting densities.141 For a more accurate description of a
polymer brush, numerical calculations and simulations have to be adopted, including
Monte Carlo methods,150 molecular dynamic simulations,151 Brownian dynamics, or
numerical SCF calculations.153
The polymer brush architecture (conformation) is strongly influenced by the
grafting density of the polymer brush, as indicated earlier. By solvent interactions the
effect of grafting density on brush conformation can be even more pronounced, with a
good solvent leading to a swollen state, whereas a poor solvent will cause a collapse
of the polymer brush.154 Depending on the grafting density, the conformation of a
polymer brush can be subdivided into four different groups, i.e., the pancake‐,
mushroom‐, brush‐, and high‐density brush regime.120, 155-156 A schematic
representation of their analogous scaling law (thickness vs grafting density predicted
by AG theory) is presented in Figure 4. Here the effect of increasing grafting density,
σ, on brush thickness, h, for polymer chains with the same constant length in a good
polymer solvent is shown. The thickness, h, is proportional to the grafting density, σ,
to the power of the exponent n, which is dependent on the spacing, d, between the
chains (usually, σ = d−2). If the distance d is far larger than the radius of gyration Rg
(radius of polymer in random‐walk conformation) of the polymer chains, no
interaction between the chains will occur. Therefore, brush conformations can either
result in a pancake or mushroom conformation (Regime I in Figure 4) and an increase
of the grafting density σ will result in a constant brush thickness h (n = 0 for very low
grafting densities). The substrate–polymer interaction defines if the chain is flat
(attractive interaction between substrate and polymer) or erect (repulsive interaction
between substrate and polymer) on the substrates surface. By further increasing the
grafting density, σ, the distance between the chains, d, becomes smaller than twice the
radius of gyration, Rg, and the chains start to interact with each other, which is also
known as the moderate‐density brush (Regime II in Figure 4).155 Here, an increase of
the polymer thickness, h, by increasing the grafting density σ takes place (n = 1/3, see
also Equation 1). The high‐density brush regime (Regime III in Figure 4) is reached
by increasing the grafting density σ even more, which drives the thickness h to an even
steeper increase (n > 1/3 for very high grafting densities).156
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 21
Figure 4: Schematic representation of the different grafting regimes (pancake, mushroom, brush,
and high‐density brush) and their scaling laws for the brush thickness depending on the
grafting density in a good solvent.
One essential question associated with the schematic representation of the
scaling laws in Figure 4 is how far the grafting density can be increased and where the
theoretical maximum lies. To address this issue, a rather simple approach can be
followed for deriving an absolute theoretical limit for grafting densities. The
theoretical limit has to be the brush conformation where the polymer chains are aligned
perfectly and as densely as possible, resembling a crystalline polymer brush
(physically no higher density is possible). In this case, the brush thickness, h, would
be exactly the contour length, lc, of the polymer chains, and the distance, d, between
the nearest neighbouring polymer is constant and periodical throughout the entire
brush. Such a crystalline brush conformation is illustrated in Figure 5. The chains in
the shown case are perfectly aligned as a simple cubic crystal in plane (top view) and
perpendicular (side view) to the substrates interface. When the crystalline cross‐
section Axtal (red squares in Figure 5) of a polymer chain is known, the maximum
grafting density, σmax, can be calculated by
𝜎max =1
𝐴xtal≈
1
𝑑2 (2)
which gives the maximum amount of polymer chains per certain surface area (usually
denoted as chains per nm2).
22 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
Figure 5: Simplified representation of a crystalline polymer‐brush conformation in the side‐ and
top views and the related crystal cross‐sectional area of a polymer chain within the red
squares.
The size of the side groups of a polymer chain mainly influences the size of the
crystal cross‐sectional area. With the literature‐known crystal cross‐sectional areas of
several poly‐α‐olefins (refer to Table S1 in the Supporting Information), a perfect
linear dependency (R2 = 0.998) of the crystal cross‐sectional area to the length of side
groups (the number of carbon atoms in linear side chain NC,SC) is observed (Figure 6,
left‐hand side inner small graph). The literature values of the crystal cross‐sectional
area are represented by the black dots in the graph.157 Using Equation 2, this fit can be
converted into a prediction of the maximum grafting density 𝜎maxfit = (0.1579𝑁C,SC +
0.1526)−1
chains·nm−2, indicating that already for polybutylene a maximum grafting
density of 𝜎max ≈ 2 chains·nm−2 cannot be exceeded. For longer and, therefore, more
sterically demanding side chains, the maximum grafting density decays exponentially.
Furthermore, the crystal cross‐sectional area is plotted against the monomer molecular
weight m0 (Figure 6, right‐hand side small graph). A good linear fit of the crystal
cross‐sectional area to the monomer molecular weight can readily be explained by the
linear mass increase by adding more and more carbons in the side chain. Analogous to
the length of the side group, the maximum grafting density as a function of the
monomer molecular weight is plotted (Figure 6, right‐hand side). Here, the maximum
grafting density for poly(methyl methacrylate) (PMMA) and PS (based on the same
literature values),157 marked with a green and a blue star, respectively, and calculated
in the same way as for the polyolefins is shown, and deviates from the maximum
grafting‐density prediction of poly‐α‐olefins. This deviation demonstrates that side
chains can be heavier but not as sterically demanding as the linear chain (benzene ring
or methacrylate group). Thus, the prediction of the maximum grafting density by the
monomer molecular weight (for polymers different than polyolefins) is only an
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 23
estimation. For a more reliable determination of the maximum grafting density, the
length of the side chain (longest linear chain of atoms, NSC) has to be compared to the
length of the linear side chains of the polyolefins. If, for instance, the length of the side
chain of PMMA is compared to the length of the linear chain of a polyolefin
(methacrylate group of similar length to side chain of 1‐pentene), the actual maximum
grafting density 𝜎max ≈ 1.57 chains·nm−2 is certainly close to the predicted value of
𝜎maxfit = 1.60 ± 0.16 chains·nm−2.
Figure 6: Crystal cross‐sectional area as a function of the length of side groups (number of carbon
atoms in the linear side chain, NC, SC) and monomer molecular weight m0 with a linear fit
provided by the red dashed line for several poly‐α‐olefins in the inset graphs. Prediction
of the maximum grafting density in the main graphs with additional values for PMMA
and PS (green/blue stars).
Assuming perfect synthetic processes and thus full surface coverage of initiators
on the surface, as well as perfectly controlled polymerization (no chain termination
and a perfect monodisperse polymer weight distribution), it may be possible to reach
this maximum grafting density for “grafting‐from” polymer brushes. However, note
that the polymer brush has to be in a crystalline conformation, which is testable with
common characterization methods such as X‐ray diffraction.
The maximum grafting‐density limit suggested above is too high for the
“grafting‐to” approach and has to be lower. The maximum grafting density for the
“grafting‐to” approach is strongly dependent on the degree of polymerization—or
more accurately on the radius of gyration Rg —which is the degree of polymerization
scaled by the solvent conditions. By applying a simple geometrical model of filling the
surface with polymer coils of the size of the radius of gyration (𝑅g = 𝑁3 5⁄ random‐
walk polymer in coil),119 a first limit for grafting densities can be derived. A simplified
sketch of this model is depicted in Figure 7.
24 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
Figure 7: Representation of polymer coils filled densely on a planar surface for a “grafting‐to”
polymer brush. The small red circles represent the active centres of the polymer chain for
the surface reaction.
The grafting density can be calculated by
𝜎 ≈1
𝐴coil=
1
𝜋𝑅g2
=1
𝜋(𝑏𝑁𝑛)2 (3)
with the area of the polymer coil covering the surface Acoil, the radius of gyration Rg,
the smallest freely rotating unit in the polymer chain b (chain elasticity), the degree of
polymerization N, and the exponent n, which describes the scaling law (depending on
the solvent quality).119, 155-156 The results of Equation 3 are depicted in Figure 8. For
the graphs showing the degree of polymerization, a chain elasticity of b = 0.153 nm
(length of a C–C bond as smallest possible freely rotating unit) and exponent of n =
1/3 (for poor solvents) leads to the smallest possible polymer coil for a given degree
of polymerization. The data in Figure 6 show a rapid exponential decay; for a radius
of gyration of Rg = 1 nm, the grafting density is merely σ = 0.32 ± 0.6 chains·nm−2
(Figure 8, left) and for a degree of polymerization of N = 100 just
σ = 0.63 ± 0.33 chains·nm−2 (Figure 8, right).
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 25
Figure 8: Grafting density as a function of the radius of gyration Rg (left) and degree of
polymerization N (right) (with b = 0.153 nm and n = 1/3 for a smallest possible polymer
coil) in linear and double‐logarithmic scales.
The limit of the grafting density is a rather rough estimation of the maximum
grafting density (more specifically, the description of transition between Regimes I
and II in Figure 4).155 For a more accurate calculation, several effects have to be
included in the model: i.e., those effects that favour a higher grafting density. Like, a
reduction of the total energy in the system by binding the active centre of the polymer
chain to the surface, due to the lower energy in the binding state. The decrease of total
energy has to be balanced with the decrease of configurational entropy by stretching
the polymer chain in order to get higher grafting densities. Furthermore, a high
dispersity, Đ, favours a higher grafting density. Here, a variety of different radii of
gyration are possible, leading to the possibility of filling smaller spaces with smaller
polymers, which merge into a polymer brush with higher grafting densities. On the
other hand, there are effects that drive the polymer brush to even lower grafting
densities. The diffusion of the polymer coil to an empty unfilled spot on the surface is
one effect, which is a diffusion‐controlled process leading to a lower grafting density
if the surface reaction merely takes place over a certain period of time. In addition, the
probability that a polymer chain (polymer coil) does not bind covalently but instead
adsorbs onto the substrate surface will lower the grafting density. For attaching the
polymer covalently to the surface, the active group of the polymer chain must be at the
surface. As the polymer coil is a 3D object, there is the possibility that this coil
approaches the surface with the active group far away from a position close to the
surface. Therefore, the polymer coil could be attached only via van der Waals
interactions and may be washed away afterward, leading to a significant decrease of
the grafting density. The balance of all these effects will give an accurate picture of
26 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
the polymer brush on the surface. The values given by Equation 3 serve as a guideline.
If grafting densities that are far higher than these values were obtained experimentally,
the results have to be critically questioned and an appropriate explanation has to be
found.
A critical assessment of the common characterization methods for grafting
densities must consider the above theoretical descriptions of end‐grafted polymer
brushes on solid surfaces. The aim here is to combine the theory, calculations, physical
limitations, and error determination and use them to judge the accuracy of the
commonly used characterization methods for grafting densities. Thus, a prediction for
novel and more accurate quantitative characterization methods can be made.
2.4 CHARACTERIZATION OF GRAFTING DENSITIES
The quantitative characterization of grafting densities of polymer brushes is a
rather challenging process, which is exemplified by the large amount of diverse
experimental methods, and attempts that have been made to solve this issue.
Nevertheless, three major characterization methods have been firmly established for
determining grafting densities on solid substrates. These three established methods are
dry thickness measurements (by invoking the dry thickness, hdry; density, ρ0; and the
number‐average molecular weight, Mn),58, 134, 158-180 gravimetric assessment (by
knowing the amount of polymer on the substrate, wpoly, and the number‐average
molecular weight, Mn),172, 181-190 and swelling experiments (applying the thickness ratio
of dry and swollen polymer brushes, αSR).162, 191-196 Therefore, we will focus on the
aforementioned characterization methods. A schematic illustration of these three
determination methods is depicted in Figure 9.
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 27
Figure 9: Illustration of the three most common grafting‐density determination methods: dry
thickness, gravimetric measurements, and swelling experiments.
In the discussion of each method, we commence our exploration with a
derivation of the underpinning equations. This entails a discussion of the assumptions
that affect each equation. In the following, we will illustrate how these methods, via
their governing equations, are affected by errors in the input parameters. Here, our
approach is not focused on using individually determined errors for each input
parameter, but to provide the user with (i) a quantitative tool (i.e., equations) for
accurately reporting errors using their own individual errors and (ii) demonstrate that
even with relative modest errors in the input parameters, the stability of the
underpinning equations is limited. The error calculations are carried out via series
expansion of measurement errors of the independent input variables xi in the following
way
𝜎 = 𝜎(𝑥𝑖) → ∆𝜎 = ∑ |𝛿𝜎
𝛿𝑥𝑖| ∆𝑥𝑖
𝑛
𝑖=0 (4)
with the error of grafting density Δσ calculated by the sum of the derivative of the
grafting density to the input variables xi multiplied by the individual errors of the input
parameters Δxi. To be able to compare the different characterization methods, the
individual input parameter errors were chosen to be identical for all calculations. As
modest example errors, we assume a 4% (black error bars and lines in all following
graphs) and 10% (red error bars and lines in all following graphs) global value for the
input variables for the error propagation calculation. Note that the errors for an
individual example will be different from the herein employed 4% and 10%, and –
importantly – in most cases larger. As we will discuss in the following sections, for
28 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
one method (dry thickness) at least, one of the input parameters (the bulk polymer
density) is only valid for a certain grafting‐density regime and the method's outside
use of this regime leads to very high errors as it is no longer applicable. The derived
equation for the error propagation can be found in Appendix B Supporting Information
(Equation S1 – S6).
2.4.1 Dry thickness
In the first method we scrutinize, i.e., determination by dry thickness, the
grafting density is calculated based on the AG theory, which provides the relation
between thickness, h, of the polymer brush and the distance, d, between the polymer
chains. 58, 134, 158-180 As the name already implies, the thickness of a dry polymer brush
is invoked in the calculations and is measured, e.g., with ellipsometry, X‐ray
reflectivity (XRR), or neutron reflectivity (NR). A polymer brush in the dry states
behaves similar to the one in a poor solvent (collapse of polymer chains) with regard
to the scaling laws. Thus, the following equation for calculating the grafting density
holds
ℎdry𝑑2 = 𝑁𝑎3 (5)
𝜎 =1
𝑑2=
ℎdry
𝑁𝑎3 (6)
𝜌0 =1
𝑎3≈
𝜌𝑏𝑁A
𝑚0 (7)
𝜎 =ℎdry𝜌𝑏𝑁A
𝑚0𝑁=
ℎdry𝜌𝑏𝑁A
𝑀n (8)
with the thickness of the collapsed polymer brush hdry, the average distance d between
two polymer chains, the degree of polymerization N, the size of the monomer a (mesh
size in the lattice model of AG theory, based on Flory–Huggins theory), the grafting
density σ, the segment density ρ0, the bulk density ρb of the corresponding polymer,
the Avogadro constant (NA = 6.022 × 1023 mol−1), the molecular mass of the monomer
m0, and the number‐average molecular weight, Mn, of the polymer chain. For
Equation 5, the scaling behaviour of the dry thickness within the brush regime based
on the AG theory is implemented. In other words, Equation 5 describes the volume of
a polymer chain calculated in two ways. The volume of the polymer chain calculated
by the dry thickness, hdry, times the square of the distance, d, is equal to the degree of
polymerization, N, times the cube of the monomer size, a. By transforming Equation 5
and noting that σ = d−2, Equation 6 can be derived. Based on the assumption
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 29
(Equation 7) that the segment density, ρ0, can be approximated by the bulk density, ρb,
and the monomer molecular weight, m0, of the corresponding polymer, the final
equation (Equation 8) results. For calculating the grafting density with this method,
the dry thickness, hdry, the bulk density, ρb, and the number‐average molecular weight,
Mn, of the polymer chain must be known. The dependency of dry thickness on grafting
density for a polymer brush with Mn = 100 kg·mol−1 and ρb = 1.15 g·cm−3 is illustrated
in Figure 10. A linear increase of thickness with increasing grafting density is depicted
in the left graph. The percentage error (calculated as previously described and
illustrated on the right‐hand side of Figure 10) appears to be constant and independent
of the value of the grafting density. The same graphical representation of the
dependency between number‐average molecular weight, Mn, and grafting density can
be made and is shown in Figure S1 in Appendix B.
Figure 10: Dry thickness approach: grafting density as a function of the dry thickness of a polymer
brush with Mn = 100 kg mol−1 and ρb = 1.15 g cm−3 on the left‐hand side. Absolute and
percentage errors for these grafting densities on the right‐hand side. An error of 4% (black
error bars and lines) as well as 10% (red error bars and lines) of the value for the input
variables is used for the error propagation calculation as example values to illustrate the
stability of the method.
Although the percentage error of this characterization method appears low and
stable compared to the other methods (refer to the following sections) merely based on
a mathematical analysis, the method entails several critical disadvantages that
jeopardize is general applicability. The key drawback is the assumptions invoked in
Equation 7, which equates the segment density, ρ0, with the bulk density, ρb, of the
polymer. As noted in the section on error calculation, by deducing the grafting density
via the dry thickness method an already preset density is used, even though the density
in the polymer brush can be significantly lower than in a bulk polymer. Thus, even the
assumption of 10% error for the bulk density is certainly too low for cases where the
30 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
grafting density is low, and the surface does not display a brush regime. A similar high
error, yet in the other direction, is possible in the high‐density brush regime.
Furthermore, the bulk density assumption implies that the segment density is equal at
any position of the entire brush (AG theory), although we have already discussed in
the previous section that the density profile, especially for lower grafting densities, can
vary rather strongly (SCF theory). In addition, the absolute brush thickness is different
for the AG and SCF theories. Thus, an incorrect estimation of the grafting density can
result, as the observed polymer brush would be correctly described by the SCF theory,
yet the calculations are based on the AG theory, which lead to an overestimation of the
grafting density. Critically, a prefactor to relate the SCF brush height, hSCF, to the AG
theory, hAG, can be calculated with hSCF = (4/3)·hAG.196 Another critical point
concerning the dry thickness characterization method is that the number‐average
molecular weight, Mn, or the degree of the polymerization, N, of the polymer chains
must be known to calculate the grafting density. In the case of the “grafting‐to”
approach, this is easily possible, as the polymer chains are presynthesized and can
therefore be readily characterized. However, for the “grafting‐from” approach, this is
a rather complicated issue, as described in the theory section here.
The determination of grafting density via the dry thickness approach is by far the
most commonly used quantitative characterization method. It is used for the “grafting‐
to” as well as for the “grafting‐from” approach. A selection of several polymer systems
with a large variety of determined grafting densities is collated in Table 1. An even
more detailed description of these polymer systems and additional explanations for all
acronyms can be found in Table S2 and Table S3 of the Supporting Information in
Appendix B.
Table 1: Literature values for estimated grafting densities of several polymer systems
characterized by dry thickness analysis.
Ref. grafting mechanism Substrate polymer ℎdry
[nm]
𝑀n [kg mol‒1]
𝜎 [chains nm‒2]
158 from ATRP Si PAAm 0 - 3.5 17 0.06 - 0.2
159 from ATRP Si (100) PDMAEMA 68 39 0.84
160 from ATRP Si PHEMA 2 - 7 --- 0.26
161 from ATRP Si (100) PMAA 8 - 20 106 0.01 - 0.12
162 from ATRP Si (100) PMMA 13 - 71 38 - 151 0.23 - 0.31
160 from ATRP Si PMMA 2 - 5 --- 0.19
163 from ATRP Si (111) PMMA 5 - 28 8 - 35 0.43 - 0.61
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 31
Ref. grafting mechanism Substrate polymer ℎdry
[nm]
𝑀n [kg mol‒1]
𝜎 [chains nm‒2]
179 from ATRP Si PMMA 12 - 102 23 - 171 0.4
164 from ATRP Si / SiO2 PMMA 5 - 55 57 0.07 - 0.70
58 from ATRP Si PMMA 40 - 140 50 - 200 0.517±0.012
160 from ATRP Si PMPC 4 - 10 --- 0.17
178 from ATRP Si PMPC 6 - 18 13 - 34 0.28 - 0.32
165 from ATRP Si (111) PMPC 9 - 39 29 - 140 0.22
166 from ATRP Au PNIPAM --- 33 - 152 0.063
166 from ATRP Si PNIPAM
--- 52 - 230 0.08 - 0.21
167 from ATRP Si / quartz PS 10 - 32 15 - 44 0.40 - 049
168 from NMP Si PS 10 - 47 12 - 28 0.55 - 1.10
134 from NMP Si PS 8 - 30 15 - 16 0.3 - 1.2
169 from free radical LASFN9 PS 134 500 - 1,000 0.11 - 0.25
170 from ATRP Si PS 25 - 29 34 - 38 0.44 - 0.49
171 from free radical LASFN9 PVP 23 - 170 1,100 0.11 - 0.25
171 from free radical LASFN9 (Me)PVP 15 - 557 1,800 - 2,500 0.005 - 0.261
172 to thiol - Au Au on Si (110) C14 1.5 0.2 3.3
173 to GPS+
carboxyl Si (100) PBA
0.58 -
0.94 6.5 0.048 - 0.075
173 to GPS+
carboxyl Si (100) PBA + PS
1.95 -
3.61 6.5 + 4.2 / 9.7 0.26 - 0.43
174 to SAM Si (100) PDMS 0.8 - 14 11 0.046 - 0.79
172 to thiol - Au Au on Si (110) PEO45 2.5 2.1 0.9
174 to SAM Si (100) PPG/PEG 6 - 10 2 2.41 - 4.01
180 to GPS+
carboxyl Si PS 1 - 7 17 0.14 - 0.22
175 to GPS+
carboxyl Si PS --- 3 - 75 0.045 - 0.24
176 to GPS+
carboxyl Si PS 5 48 0.062
174 to SAM Si (100) PS 6 - 12 8 0.071 - 0.14
177 to disulfide Au PS 0.6 12 - 17 0.005
172 to thiol - Au Au on Si (110) PS19 1.8 2.0 0.6
172 to thiol - Au Au on Si (110) PS125 0.9 13.3 0.04
180 to GPS+
carboxyl Si PS + PVP 5 - 8 17 + 39 0.021 - 0.06
32 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
Ref. grafting mechanism Substrate polymer ℎdry
[nm]
𝑀n [kg mol‒1]
𝜎 [chains nm‒2]
176 to GPS+
carboxyl Si PS + PVP 6 - 7 --- 0.092
175 to GPS+
carboxyl Si PVP --- 42 0.030 - 0.053
176 to GPS+
carboxyl Si PVP 5 41 0.075
Most of the grafting densities determined above (Table 1) are within the limit of
the physically possible (maximum) grafting densities. The calculated maximum
grafting density for each of the polymer systems is given in Table 2. Even though the
grafting‐density values of tetradecane (C14)172 and poly(ethylene glycol) (PEG)174
seem to be high, the grafting densities may even be higher, as for these “polymer
chains” no sterically demanding side chains are present within the molecule.
Nevertheless, the grafting densities for the poly(2‐(diemethylamino)ethyl
methacrylate) (PDMAEMA)159 (σ = 0.84 nm−2 to 𝜎maxfit = 0.91 nm−2) and PS134, 168 (σ
= 1.2 nm−2 to 𝜎maxfit = 1.28 nm−2 or σmax = 1.43 nm−2) system shown in Table 1 are
close to the maximum grafting density (given in Table 2). If for the maximum grafting
density, 𝜎maxfit , a perfect crystalline polymer is expected, the degree of crystallinity, D,
of the polymer brush may be provided by the ratio 𝜎 𝜎maxfit⁄ , leading to the finding that
the degree of crystallinity of the polymer brush for PDMAEMA159 is D ≈ 89% and for
PS134 is D ≈ 94%. These calculated degrees of crystallinity are unusually high, and
therefore the accuracy of the determined grafting densities is questionable.
Table 2: Determined maximal grafting densities for several polymers considered here.
Polymer Ref. 𝑁SC
𝜎maxfit
[chains nm‒2]
C14 172, 184 0 6.55
PAA 185 2 2.14
PAAm 158 2 2.14
PAEA 185 5 1.06
PBA 173 6 0.91
PDHA 185 6 0.91
PDMAEMA 159 6 0.91
PDMS 174 2 2.14
PEMA 192-193 4 1.28
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 33
Polymer Ref. 𝑁SC
𝜎maxfit
[chains nm‒2]
PEO/PEG 172, 174, 181, 184,
186-187 0 6.55
PFOEMA 192 12 0.49
PHEMA 182 5 1.06
PHFMA 192 6 0.91
PIBA 188 6 0.91
PMAA 161 2 2.14
PMMA 160, 162-164, 194 3 1.60
PMPC 165, 178 12 0.49
PNIPAM 166, 185 4 1.28
PPG 174 1 3.22
PS
134, 167-170, 172,
174-176, 180, 188-
189, 195-196
4 1.28
PTFMA 192-193 4 1.28
PVP 171, 175, 180 4 1.28
(Me)PVP 171 5 1.06
2.4.2 Gravimetric Measurements
For determining the grafting density via gravimetric measurements, the grafting
density is calculated by the ratio of mass between polymer brush and substrate. 172, 181-
190 The method rests on the idea that the total number of chains and surface area can
be estimated, and accordingly the grafting density (Equation 9). The amount of
polymer is determined either via thermogravimetric analysis, elemental analysis, or
“before and after” weighing of the substrate covered with the polymer brush. In
addition, to track the weight increase or decrease due to the formation or
decomposition of the polymer brush at the substrate's surface, a certain amount of
polymer has to be present. Therefore, the gravimetric measurements are only
applicable for polymer films on NPs, MSs, and highly porous materials, due to the
high surface area and the thereby trackable amount of polymer. The surface area can
be determined via, for example, electron microscopy or N2 adsorption isotherms
(Brunauer–Emmett–Teller (BET)). For the calculation of the grafting density, the
following equations then hold
34 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
𝜎 =𝑁chains
𝐴sub (9)
𝑁chains =𝑚poly𝑁A
𝑀n (10)
𝑚poly = (𝑤poly
𝑤sub) 𝑚sub = (
𝑤poly
100 − 𝑤poly) 𝑚sub (11)
𝑚sub = 𝜌sub𝑉sub (12)
𝜎 =
(𝑤poly
100 − 𝑤poly) 𝜌sub𝑉sub𝑁A
𝑀n𝐴sub
(13)
with the grafting density σ, total amount of chains on the substrate Nchains, surface area
of the substrate Asub, absolute mass of the polymer mpoly, the Avogadro constant NA,
the number‐average molecular weight of the polymer chain Mn, the polymer weight
fraction wpoly, the weight fraction of substrate material in system wsub, the absolute
mass of the substrate msub, the density of the substrate ρsub, and the volume of the
substrate Vsub.
For the calculation of the grafting density, the total number of chains on a
substrate with a certain surface area, Asub, must be determined (see Equation 9). The
number of chains can be calculated via Equation 10, which equates the absolute mass
of the polymer divided by the number‐average molecular weight with the total number
of polymer chains, Nchains. The absolute mass of the polymer can be expressed by the
percentage amount of polymer in the system and the substrate density and volume
(Equations 11 and 12). By combining Equations 9–12, the final term for calculating
the grafting densities can be derived (Equation 13). For calculating the grafting density
with the gravimetric measurement method, the percentage amount of polymer in the
system wpoly, the substrate density ρsub, area Asub, and volume Vsub, as well as the
number‐average molecular weight, Mn, of the polymer chain must be known. An
additional simplification of Equation 13 for spherical particles can be invoked by
𝜎 =
(𝑤poly
100 − 𝑤poly) 𝜌sub𝑟sub𝑁A
3𝑀n
(14)
with the radius of a spherical particle as a substrate rsub. The dependency of the
percentage amount of polymer on the grafting density for a polymer brush with
Mn = 10 kg·mol−1 and rsub = 3.5 nm is described in Figure 11. The increase of polymer
weight fraction with increasing grafting density is depicted on the left‐hand side of
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 35
Figure 11. The percentage error (calculated as previously described and illustrated on
the right‐hand side of Figure 11) increases drastically with increasing grafting density.
Note that in a real experiment, the error of the input parameters, such as of the polymer
weight fraction, is not necessarily constant. The same graphical representation of the
dependency of number‐average molecular weight, Mn, and particle radius, rsub, to
grafting density is shown in Figures S2 and S3 in Appendix B.
The nature of the equation underpinning the gravimetric assessment leads to a
very strong increase of the percentage error with increasing grafting densities. Under
our scenario, for instance, grafting densities exceeding a value of σ > 2 chains·nm−2
have a percentage error of Δσ > 65% by assuming a general input value error of
Δxi = 10%. However, an advantage of this characterization approach is its overall
assumption‐free nature. The gravimetric measurement method is only based on a
simple mass balance. Nevertheless, the number‐average molecular weight, Mn, of the
grafted polymer chains must be known. As described earlier, for the “grafting‐to”
approach this is a straightforward task, whereas for the “grafting‐from” approach,
evaluating the number‐average molecular weight, Mn, is challenging.
The determination of grafting density via gravimetric measurements is most
commonly adapted for polymer brushes on NPs, MSs, or other nanostructures and
applied to the “grafting‐to” as well as the “grafting‐from” approach. A list of selected
polymer systems on different substrates is shown in Table 3. A more detailed
description and definitions for all acronyms can be found in Table S2 and Table S3 of
the Supporting Information in Appendix B.
Table 3: Literature values for estimated grafting densities of several polymer systems
characterized by gravimetric measurements.
Ref. grafting mechanism substrate polymer ℎdry
[nm]
𝑀n
[kg mol‒1]
𝜎
[chains nm‒2]
181 from anionic DVB MS PEO 7 -
10 14 1.65 - 2.09
182 from RAFT IIPs PHEMA --- 16 - 19 1.06 - 1.43
183 from ATRP PS latex PNIPAM --- 47 - 838 0.027 - 0.079
172, 184 to thiol - Au Au NPs C14 --- 0.2 4.35
185 to thio bromo, alkoxysilane Si NPs PAA --- 1.4 0.50
185 to thio bromo, alkoxysilane Si NPs PAEA --- 2.1 0.23 - 0.65
185 to thio bromo, alkoxysilane Si NPs PDHA --- 3.4 0.41
186 to melt grafting Fe3O4 NPs PEG --- 5 3.5
185 to thio bromo, alkoxysilane Si NPs PEG(MA) --- 3.8 0.31
36 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
Ref. grafting mechanism substrate polymer ℎdry
[nm]
𝑀n
[kg mol‒1]
𝜎
[chains nm‒2]
187 to silane silica NPs PEO --- 5 0.58 - 1.18
172, 184 to thiol - Au Au NPs PEO45 --- 2 1.15
188 to cycloaddition DVB MS PIBA --- 6 - 26 3.6 - 7.3
185 to thio bromo, alkoxysilane Si NPs PNIPAM --- 1.7 0.30 - 0.58
189 to nitroxides Ag NPs PS --- 13 - 14 2.0 - 5.9
188 to cycloaddition DVB MS PS --- 4 31.1
190 to SAM Silica NPs PS --- 17 - 272 0.01 – 0.1
172, 184 to thiol - Au Au NPs PS19 --- 2 3.45
172, 184 to thiol - Au Au NPs PS125 --- 13.3 0.94
Applying the gravimetric measurement method, several calculated grafting
densities for different polymer systems (Table 3) exceed the limits of the physically
possible maximum grafting density. The estimated maximum grafting‐density limit
for each of the polymer systems is given in Table 2. For poly(2‐
hydroxyethylmethacrylate) (PHEMA)182 (σ = 1.43 nm−2 to 𝜎maxfit = 1.06 nm−2),
PS19172, 184 (σ = 3.45 nm−2 to 𝜎max
fit = 1.28 nm−2), PS189 (σ = 5.9 nm-2 to 𝜎maxfit = 1.28
nm−2), poly(isobornyl acrylate) (PIBA)188 (σ = 7.3 nm−2 to 𝜎maxfit = 0.91 nm−2), as well
as PS188 (σ = 31.1 nm−2 to 𝜎maxfit = 1.28 nm−2), the limit is massively exceeded. As
already mentioned by Barner‐Kowollik and co‐workers,188 these unfeasible high
values for grafting density may be caused by the incorrect determination
(underestimation) of the surface area of the substrate. In addition, the inaccuracy of
the method increases with increasing grafting densities based on the nature of the
equation underpinning the method (Figure 11, right‐hand side), thus compounding the
uncertainty in these values. Although the grafting densities of C14172, 184 and PEO181,
186 seem to be high, the maximum grafting density is not exceeded and can be
theoretically even higher, since for these “polymer chains”, no sterically demanding
side chain is present, as mentioned before.
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 37
Figure 11: Gravimetry: grafting‐density dependency of the polymer weight fraction of a polymer
brush with Mn = 10 kg mol−1 and rsub = 3.5 nm on the left‐hand side. Absolute and
percentage errors for these grafting densities on the right‐hand side. An error of 4% (black
error bars and lines) as well as 10% (red error bars and lines) of the value for the input
variables is used for the error propagation calculation as example values to illustrate the
stability of the method
2.4.3 Swelling Experiments
In the case of the swelling experiments, the grafting density is determined by
measuring the thickness ratio of the polymer film in the dry, hdry, and swollen state,
hswell.162, 191-196 The thickness of the polymer brush is measured, for example, by
ellipsometry, XRR, or NR. From this thickness ratio, a direct estimation of the grafting
density is possible by knowing the monomer size, a, and the scaling exponent, n, of
the swollen brush. Generally, the ratio of the dry, hdry, to the swollen state, hswell, is the
ratio of the polymer brush described by two different scaling laws, as the polymer
brush in the dry states behaves similar to the one in a poor solvent. The characterization
method is consequently also based on the AG theory and can be established by the
following procedure
ℎdry =𝑁𝑎3
𝑑2 (15)
ℎswell = 𝑛blob𝐷blob =𝑁
𝑔𝐷blob (16)
𝐷blob = 𝑎𝑔𝑛 ≈ 𝑑 (17)
𝛼SR =ℎswell
ℎdry=
𝑁 (𝑑𝑎)
−1 𝑛⁄
𝑑
𝑁𝑎3
𝑑2
= (𝑑
𝑎)
3−1 𝑛⁄
(18)
𝜎 =1
𝑑2= 𝑎−2𝛼SR
2𝑛1−3𝑛 (19)
38 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
with the dry thickness of the polymer brush hdry, the degree of polymerization N, the
size of the monomer a, the average distance between two tethering sites d, swollen
brush thickness in solvent hswell, number of blobs per polymer chain nblob, blob size
(diameter) Dblob, number of monomer units in a blob g, the exponent n (which describe
the solvent quality) and the swelling ratio of the polymer brush αSR. Equation 15
describes the scaling law of the dry thickness based on the AG theory and is a
rearrangement of Equation 5. In the AG theory, the swollen polymer brush is described
by a sequence of blobs, in which the polymer behaves like a free polymer in a solvent
(Equation 17). By the number of blobs per polymer chain, nblob, multiplied by the blob
size, Dblob, the swollen thickness can be calculated (see Equation 16). For calculating
the grafting density, the diameter of a blob, Dblob, and the distance, d, between two
tethering sites are assumed to be equal (approximation), which is provided by Equation
17. By combining Equations 15–17 to afford the swelling ratio, αSR, and transforming
Equation 18, the grafting density can be calculated as a function of the swelling ratio
αSR, the monomer size a, and the scaling exponent n (Equation 19). The exponential
decay of the swelling ratio by increasing the grafting density for a polymer brush with
a = 5 Å and n = 0.5 is depicted in Figure 12. The percentage error (calculated as
previously described and illustrated on the right‐hand side of Figure 12) drastically
increases for decreasing grafting densities, merely based on the mathematical nature
of the equation.
Figure 12: Swelling experiments: grafting‐density dependency of the swelling ratio of a polymer
brush with a = 0.5 nm and n = 0.5 on the left‐hand side. Absolute and percentage errors
for these grafting densities on the right‐hand side. An error of 4% (black error bars and
lines) as well as 10% (red error bars and lines) of the value for the input variables is used
for the error propagation calculation as example values to illustrate the stability of the
method.
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 39
The exponential decay of the percentage error with increasing grafting densities
leads to an enormous uncertainty for low grafting densities within our scenario. For a
grafting density of a value lower than σ < 0.5 chains·nm−2, the percentage error already
exceeds Δσ > 80% based on the assumption of a general input value error of Δxi = 10%.
Similar to the dry thickness measurements, the same approximations were made for
the swelling experiments, as the AG theory was used as well. Therefore, an advantage
of the swelling experiments is that the wrong estimation of the brush thickness (due to
incorrect use of the AG theory) can be neglected because the prefactor is eliminated
by the calculation of the ratio. Another benefit of the characterization method is that
the molecular weight of the polymer chain is not required for the evaluation of the
grafting density, which therefore makes it a suitable method for the “grafting‐from”
approach.
A selection of several polymer systems produced via the “grafting‐from”
approach with a variety of determined grafting densities by swelling experiments is
collated in Table 4. A more detailed description and definitions for all acronyms can
be found in Table S2 and Table S3 of the Supporting Information section of
Appendix B.
Table 4: Literature values for estimated grafting densities of several polymer systems
characterized by the swelling method.
Ref. grafting mechanism substrate solvent polymer ℎdry
[nm]
𝑀n
[kg mol‒1]
𝜎
[chains nm‒2]
191 from ATRP mica water PNIPAM 10 - 215 475 0.02 - 0.42
192 from ATRP Si (111) acetone, HFP,
NFE, FC-40 PEMA 75 74 - 94 0.53 - 0.68
193 from ATRP Si (111) acetone PEMA 6 - 206 26 - 167 0.16 - 0.82
192 from ATRP Si (111) acetone, HFP,
NFE, FC-40 PFOEMA 80 360 - 1,140 0.09 - 0.22
192 from ATRP Si (111) acetone, HFP,
NFE, FC-40 PHFMA 78 115 - 330 0.19 - 0.55
194 from PMPP Si THF PMMA 7 - 110 341 - 631 0.033 - 0.13
162 from ATRP Si (100)
methanol,
(cyclo)hexane,
acetone,
ethyl acetate,
THF, toluene
PMMA 13 - 71 38 - 151 0.24 - 0.35
195 from anionic glass toluene PS 16.6 - 18 40 - 41 0.28 - 0.31
196 from ATRP Si (100) toluene PS 31 - 116 147 - 420 0.16 - 0.19
192 from ATRP Si (111) acetone, HFP,
NFE, FC-40 PTFEMA 80 74 - 100 0.57 - 0.69
193 from ATRP Si (111) acetone PTFEMA 9 - 140 69 - 137 0.09 - 0.73
40 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
All of the mentioned grafting densities in Table 4 are within the physical limit
of the maximum grafting density (Table 2). Nevertheless, all of the given values are in
a rather low‐grafting‐density regime. As explained above, the accuracy of low grafting
densities determined from swelling experiments may be questionable. However, the
concept of the swelling method is based on a direct measurement of one property
(swelling ratio), which is in a direct relation to the polymer brush.
The estimated maximum grafting densities of the polymer systems used here are
listed in Table 2 and are determined by comparing the length of the side chains of the
polymer to the length of the linear side chains of poly‐α‐olefins NSC. The procedure is
described in more detail in the previous theory section.
2.5 CONCLUSION AND FUTURE PERSPECTIVES
To assess which of the previously mentioned methods is most accurate and in
which range of grafting densities they are applicable, all three characterization
methods have to be compared with regard to their inherent assumptions, simplicity
(direct or indirect measure of grafting density), and error propagation. With regard to
a priori assumptions, the dry thickness and swelling experiments are based on the AG
theory and therefore all assumptions that are used in this theory also apply to these
characterization methods. In the case of dry thickness measurements, the additional
assumption of using a preset density (bulk density ρb of the polymer) for describing
the polymer brush introduces significant uncertainties. Only for the gravimetric
measurements, no general assumption is made, as the grafting density is solely
calculated by the mass change and the surface area. However, the molecular weight of
the polymer chains has to be known for the calculation by gravimetric measurements,
which is a critical disadvantage. The simplicity of a method is directly correlated with
the number of additionally required input parameters. For dry thickness and
gravimetric measurements, several parameters have to be known, including the dry
thickness, hdry, the number‐average molecular weight, Mn, the surface area (surface
volume), and mass change, wpoly. All of these values have to be estimated via different
experiments, leading to a high inaccuracy of these methods. Especially the problem of
access to exact number‐average molecular weights for polymer brushes generated via
“grafting‐from” increases this error. In the case of swelling experiments, only the ratio
of swelling (ratio between dry hdry and hswell) has to be measured, which can be
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 41
achieved by in situ swelling experiments. Nevertheless, the swelling experiments are
merely a “semidirect” characterization method, because the exponent n must still be
known. However, this exponent is mostly well established for a large number of
polymer solvents/systems in the literature.197 Based on a purely mathematical analysis
of the nature of the underpinning equations and a constant error of the input variables,
close inspection of Figures 8-10 (right hand side) indicates that the propagating error
is constant and lowest for the dry thickness method, whereas the error increases with
increasing grafting density for the gravimetric measurements, and increases with
decreasing grafting density for the swelling experiments. However, it is very important
to note that this merely reflects the mathematical behaviour of the methods and that
considerable additional uncertainties are introduced when operating the method
outside its application regime. This is particularly true for the often‐hailed dry
thickness method, where an a priori determination of the grafting regime – confirming
its brush nature – is essentially required before the bulk polymer density is inserted
into the equation. However, such an approach cannot be found in the literature.
Critically, the grafting densities have to be reported with an appropriate uncertainty
(error), which has to be calculated, as we have demonstrated above. For most of the
literature‐known values, no error is reported at all (see Table S2 in the Supporting
Information in Appendix B).
It is mandatory to note that several other (uncommon) methods exist for the
quantitative characterization of grafting densities.80, 171, 198-203 A few examples are
listed in Table 5. Some of these characterization methods are even more indirect and
inaccurate, such as estimating the grafting density by the assumption that only 10% of
the initiator grafted on the surface will result in a grafted polymer chain198 or the
determination of the grafting density via decomposition kinetics of an azo‐initiator
grafted on the surface.171, 199-200 However, some other methods measure the grafting
density in a more direct fashion, such as the fluorescamine‐ and ninhydrine‐based
assay labeling201 or colloidal probe measurements.80 For instance, a colloidal probe
experiment measures the force response of polymer brush by compressing it, which
can be directly converted into the grafting density by fitting the measured force–
distance curve.
42 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
Table 5: Literature values for estimated grafting densities of several polymer systems for less‐used
characterization methods
Ref. grafting mechanism substrate polymer ℎdry
[nm]
𝑀n
[kg mol‒1]
𝜎
[chains nm‒2] method
96 from ATRP Si (100) PDMA 176 - 339 815 0.29 10% of init.
density
96 from ATRP Si (100) PHMA 44 - 113 272 0.29 10% of init.
density
199 from free
radical
Si,
LASFN9 PMAA 144 1,500 0.056
initiator
decomposition
kinetics
200 from free
radical
Si,
LASFN9 PMAA 23 - 160 177 - 3.733 0.005 - 0.16
initiator
decomposition
kinetics
80 from ATRP Si PMAA 60 - 100 --- 0.053 colloidal probe
measurements
202 from ATRP
porous
glass filter
s
PMMA --- 5 - 40 0.6 BET - FTIR
96 from ATRP Si (100) POMA 86 - 207 498 0.29 10% of init.
density
171 from free
radical LASFN9 PVP 23 - 170 1,100 0.015 - 0.105
initiator
decomposition
kinetics
171 from free
radical LASFN9 (Me)PVP 15 - 557
1,800 –
2,500 0.007 - 0.216
initiator
decomposition
kinetics
201 to ligand
exchange
Au
nanostruct
ure
PEG --- 3 - 20 0.14 - 2.21
fluorescamine-
and ninhydrine
assay
203 to SAM glass
PDMAEMA -
b-
PTMSPMA
--- --- 0.01 - 0.05 QA - method
For obtaining reproducible and comparable values for grafting densities, the
method must be direct and ideally entail no assumptions. As noted, the first attempts
of developing such determination procedures have been made. Such a method has to
either measure a property of the polymer brush that is directly related to the value of
grafting density, or the number of the single polymer chains has to be
counted/determined, and the exact surface area has to be known. In the following
section, we explore five possible approaches for developing a more precise and direct
way to quantitatively establish grafting densities. These methods have not yet been
developed into functioning approaches, yet hold – in our view – the potential to
significantly increase the accuracy and precision of grafting‐density determination.
While some of the following approaches are currently “science fiction”, all of them
Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting 43
have the potential to be viable and powerful avenues to an accurate grafting‐density
determination.
(i) The quantitative determination of the grafting density via advanced atomic
force microscopy (AFM) is a viable option. AFM is frequently adopted for the precise
evaluation of intramolecular chain properties, including contour length, rupture force,
and chain elasticity via single‐molecule force spectroscopy (SMFS), which is an
already well‐established technique.81, 204-205 By exploiting the SMFS experimental
concept and expanding the method from measuring single polymer chains to multiple
polymer chains (multiple‐molecule force spectroscopy)206, the exact number of chains
bound to the AFM cantilever can be determined. By knowing the exact area of indent
(depending on radius of the AFM cantilever) and the number of polymer chains bound
to the cantilever, the grafting density can be calculated in a direct and exact manner.
By scanning over a defined area of the surface (force map), even the spatial distribution
of the grafting density should be accessible. For this experimental approach, advanced
characterization methods and calculation protocols have to be developed.
(ii) An alternative possibility for an even more accurate process for quantitative
grafting‐density determination is the combination of the previously mentioned
colloidal probe measurements with swelling experiments. The colloidal probe
measurement already provides a direct relation of the force response to the grafting
density by compressing the polymer brush.80 By an additional variation of the solvent
(different brush conformations, poor solvent for collapsed, and good solvent for
swollen conformation) and adjustment of the calculation procedure, the grafting
density for several different brush conformations can be evaluated. The grafting
density of each of the different brush conformations has to be identical. If the values
of the grafting density are nonidentical, an adjustment of the calculation protocols must
be carried out. This gives a good measure for the accuracy of the characterization
method and would improve the concept of simple colloidal probe measurements of a
single brush conformation.
(iii) An alternative method can be realized by labelling each of the polymer
chains in a polymer brush with a distinctive marker. Using spectroscopic
characterization methods (such as X‐ray photoelectron spectroscopy and ToF‐SIMS),
which can detect the marker molecules, the number of chains can be estimated by
simple counting.207-208 In addition, the exact scanning area (analysed using a
spectrometer) is needed for the quantitative characterization of the grafting density.
44 Chapter 2: Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting
For this method, the precision of the spectroscopic characterization tools must be of
highest standard.
(iv) In a rather unconventional suggestion, the process of grafting polymer
chains (synthesis of polymer brushes) on a surface could be investigated in situ,
especially for the “grafting‐from” approach. In this context, “in situ” implies that the
polymer brush growth is monitored “live” without any disruption of, or interference
with, the grafting process. Such an approach may become possible by following the
changes in mass, energy, or thickness of a growing polymer brush traced over time,
starting from time t0 until the final state of growth.209-211 With either an extrapolation
of the data to the starting point or the possibility of directly measuring the initial step
of brush growth, the value of the grafting density should be accessible, if the exact
surface area is known.
(v) Finally, a visionary concept for determining grafting densities can be realized
by using laser‐assisted atom probe tomography (APT).212-214 APT is a characterization
tool mainly used for conductive materials where atoms are field evaporated (from a
sharp tip r < 100 nm) and accelerated to a time‐of‐flight detector. Using the recorded
information by the detector, a complete 3D reconstruction of the tip can be simulated.
The recent progress toward laser‐assisted APT allows the characterization of
nonconductive material.215-216 With a further development of this technique, the
imaging of polymers grafted on such sharp tips could be realized.217 Thus, a 3D
reconstruction of the polymer brush can potentially be established and based on this
image, the grafting density may be determined.
We hope to have demonstrated that for the reliable, comparable, and quantitative
determination of grafting densities, a substantial number of problems have to be
addressed. We further submit that the herein‐reported first‐time comprehensive
quantitative assessment of the limits and errors of the most popular methods to
determine grafting densities will, on the one hand, lead to a critical revaluation of
literature‐reported densities, as well as—importantly—accelerate the development of
methods that are more powerful than the existing ones, possibly along the above
outlined lines. At stake is nothing less than the precision design of one of the most
critical points in any device resting on soft matter technology, the interface.
Chapter 3: The Long and the Short of Polymer Grafting 45
Chapter 3: The Long and the Short of
Polymer Grafting
The need for novel techniques for reliable grafting density estimation was
demonstrated in Chapter 2. Five possible ways of approaching the problem of grafting
density estimation were proposed. For demonstrating that these approaches can lead
to an improved precise quantitative evaluation of surface grafting the 4th approach was
chosen as a proof of concept. However, instead of measuring in-situ the growth of a
polymer brush via the ‘grafting-from’ method a ‘grafting-to’ polymer graft was
investigated with a flow QCM setup. In addition to the precise quantification of the
grafting density, a preferential grafting of short polymer chains could be observed.
3.1 ABSTRACT
We demonstrate that grafting a distribution of polymer chains onto an interface
critically affects the shape of the distribution, with shorter chains being preferentially
attached. This distortion effect is herein quantified for the first time, exploiting a quartz
crystal microbalance – underpinned by single-molecule force spectroscopy – on the
example of grafted poly(methyl methacrylate) (PMMA) chain distributions of
different molar mass. ‘Grafting-to’ of different ratios of number average molecular
weight of PMMA distributions unambiguously establishes the preferred surface
grafting of shorter polymers, which can be correlated to their smaller radius of
gyration. Our findings allow to establish a preferential grafting factor, 𝜅, which allows
to predict the molar mass distribution of polymers on the surfaces compared to the
initial distribution in solution. Our findings not only have serious consequences for
functional polymer interface design, yet also for the commonly employed methods of
grafting density estimation.
3.2 INTRODUCTION
Polymers covalently attached to surfaces can exhibit different confirmations,
primarily depending on the distance amongst tethering sites described by the grafting
density σ.119 For densely grafted polymers, also referred to as ‘polymer brushes’,155
the interactions between the individual polymer chains are influencing essential
46 Chapter 3: The Long and the Short of Polymer Grafting
surface properties including wettability,108 adhesion,218 tribological behaviour114 and
biocompatibility.219 For surface functionalization, two main methods can be
employed, i.e. the ‘grafting-to’ and the ‘grafting-from’ approach. The latter method is
generally suggested to lead to higher grafting densities as polymers are grown in situ
from the surface in a process driven by monomer diffusion.128 Thus, surface induced
reversible deactivation radical polymerization (RDRP) techniques can yield dense
polymer brushes.135, 220-221 Nevertheless, the ‘grafting-from’ method suffers from lack
of information about the degree of polymerisation (DP) and molar mass distribution
(MMD) of the grafted polymer. In the ‘grafting-to’ approach, pre-fabricated polymers
with suitable end-groups are tethered onto a surface.99 A critical advantage of the
‘grafting-to’ approach is that the bulk polymers can be characterized post-synthesis,
prior to their surface attachment.222 Assuming the properties determined in solution,
the DP and MMD, accurately reflect the properties of the surface-tethered polymers,
‘grafting-to’ provides comprehensive knowledge about the functionalized surface.119
However, this general assumption has never been experimentally tested and is
questionable, as the preferential attachment of shorter over longer polymer chains
appears possible due to diffusion, probability and geometrical effects.223
3.3 GRAFTING DENSITIES EVALUATED VIA QCM
In the current study, we scrutinize this hypothesis by conducting quartz crystal
microbalance (QCM) measurements of ‘grafting-to’ experiments and corroborate the
results by atomic force microscopy (AFM) based single-molecule force spectroscopy
(SMFS). QCM measurements enable the investigation of surface mass uptake by
recording the frequency change of an oscillating piezo-electric quartz crystal induced
by a mass change in the crystal's mass (attachment of polymer chains). These
measurements can be performed with high precision, even in liquid environments.85-87
Most of the conducted QCM studies on polymer systems investigated grafting
kinetics209, 211, 224-227 or conformational changes in the polymer brush228-229 with
additional dissipation energy recording. The current work solely focuses on the overall
mass uptake resulting from ‘grafting-to’ of end-functionalised poly(methyl
methacrylate) PMMA chains on a silicon dioxide (SiO2) coated QCM sensor. The
mass uptake Δm on a QCM sensor for rigid thin films in vacuum and air can be
calculated by the measured change of resonance frequency Δf using the Sauerbrey
Equation 20,230
Chapter 3: The Long and the Short of Polymer Grafting 47
∆𝑚 = −𝐶QCM
∆𝑓
𝑛 (20)
with the mass sensitivity constant CQCM = 17.7 ng·cm−2·Hz−1 (for an AT cut sensor
with f0 = 5 MHz), defined by the fundamental frequency f0, thickness and density of
the piezo crystal,87 and the overtone number n (= 1, 3, …). In the case of grafting
polymers to a QCM sensor from solution, two additional effects are influencing the
frequency change, i.e. the frequency change induced by the solvent and the additional
damping of the frequency due to viscoelasticity of the attached film. Both effects are
not covered by the Sauerbrey equation, Equation 20. To account for the effect of
frequency change induced by the solvent covering the sensor, the baseline can be
directly recorded in the solvent and used as reference for frequency changes.226
However, compensating the effect of a viscoelastic film is more challenging, yet it can
be achieved with rather complex models.231 Nevertheless, the work of Höök et al.
shows by theoretical simulations that for films less than 100 nm, no overestimation of
mass uptake was noticed using the Sauerbrey relation (the film thickness in our study
was approximately 8 nm, Table S10 in Appendix C).87 Therefore, the calculations of
the mass uptake are herein based on the Sauerbrey equation, Equation 20.
A reversible addition fragmentation chain transfer (RAFT) polymerization
agent (CTA) functionalized with a silyl ether (refer to the Supporting Information in
Appendix C CTA1)232 was employed to synthesize polymers P1 to P5 via RAFT
polymerization (Supporting Information in Appendix C P1–P5).233 The hydrolysis
sensitive end group allowed tethering of the polymers to SiO2 coated QCM sensors
under mild conditions. The attachment takes place via the R-group of the CTA,
ensuring (almost) all chains carry the silane function. RAFT was employed to establish
control over the molar mass and MMD as well as a high end group fidelity, rendering
the need for post-functionalization obsolete. For the current study, polymers with five
different number average molar masses Mn were synthesized (P1: Mn = 8,240 g·mol−1,
P2: Mn = 48,000 g·mol−1, P3: Mn = 106,000 g·mol−1, P4: Mn = 133,900 g·mol−1 and
P5: Mn = 216,100 g·mol−1, the MMD are depicted in Figure 13 A).
48 Chapter 3: The Long and the Short of Polymer Grafting
Figure 13: (A) Normalised weight MMD of P1 (black), P2 (red), P3 (blue), P4 (green) and P5 (grey).
(B) Time dependent grafting density σ of samples P1–P5 calculated by normalising the
mass uptake. Mass uptake Δm was determined from Δf for n = 9 via Equation 20. The
small non-linearity in the black curve is due a gas bubble that formed during the
experiment. A plateau in the grafting density was reached after 60 min and no change was
subsequently observed. (C) Grafting density σ in dependency of the number averaged
molecular weight Mn plotted in a double logarithmic graph and fitted to a power law. The
exponent of the power law (slope in double logarithmic graph) can be related to the
solvent interaction parameter n* (for PMMA in toluene at 50 °C).57
The polymer samples were dissolved in toluene and introduced into a QSense
QCM flow cell with a flow rate of 15 μl·min−1. The flow cell temperature was
controlled to 50 °C and flushed with pure toluene to record a stable baseline. The
frequency change associated with grafting of the polymer distributions onto the QCM
sensor was recorded for all overtones n = 1, 3, 5, 7, 9, 11 and 13. However, the
fundamental frequency (n = 1) was not taken into account for further evaluation, due
to the insufficient energy trapping. Subsequent calculation of the absolute mass change
Δm was performed according to Equation 20. Further normalization of the mass
change by the respective number average molecular weight Mn of each polymer
resulted in the grafting density σ = Δm/Mn. The resulting time dependent grafting
density σ for each polymer sample (P1–P5) at an overtone number of n = 9 is shown
Chapter 3: The Long and the Short of Polymer Grafting 49
in Figure 13 B. Before comparing the different grafting densities of P1 to P5, it is
important to note that for our system and conditions the surface saturation results in
one single plateau (regime) after approximately one hour. This is in contrast to
literature results, which suggest the existence of up to four different regimes in the
grafting kinetics.234 Such single regime kinetics occur at high temperatures and
concentrations, when the energy barrier is sufficiently small to directly form a densely
grafted layer in one step, as also observed in other studies.224
The quantitative comparison of the grafting densities for polymer samples P1 to
P5 sizes is depicted in Figure 13 C. The grafting densities estimated from overtones 3
to 13 (after 5,000 s) were averaged and plotted vs. the number average molar mass Mn.
The calculated data was subsequently fitted to a power-law. Thus, the slope represents
the scaling behaviour ν of the grafting density as a function of the number averaged
molar mass Mn. In a recent publication, we demonstrated that the grafting density σ for
the ‘grafting-to’ approach is likely related to the radius of gyration Rg,57
𝜎 ~1
𝑅g2 ~
1
(DP𝑛𝑛∗
)2 ~𝑀n
−2𝑛∗ (21)
with the degree of polymerisation DP and the solvent interaction exponent n*, which
describes the polymer solvent interaction at a given temperature (here PMMA in
toluene at 50 °C). The almost perfect fit of the measured data to the power law with a
solvent interaction parameter of n* = 0.47 ± 0.02 evidences the previously postulated
relation of grafting density σ to the radius of gyration Rg.57 Nevertheless, this result
merely suggests that a higher grafting density is achieved by grafting shorter polymers
– as already demonstrated235-236 – and no information on the preferential grafting of
shorter polymers within a given distribution are provided. P1, for instance, comprises
– despite its Mn of 8,240 g·mol−1 and narrow dispersity of 1.06 – chains ranging from
approximately 3,500 g·mol−1 to almost 17,400 g·mol−1.
3.4 PREFERANTIAL SURFACE GRAFTING
To elucidate the bias towards lower molar mass chains during ‘grafting-to’,
defined mixtures of polymers were immobilized on QCM sensors. By comparison of
the molar ratio of the polymer samples in solution with the ratio of the polymers on
the surface, we establish and quantify this bias. The aforementioned mixtures were
prepared from polymers P1 (Mn = 8,240 g·mol−1) and P3 (Mn = 106,000 g·mol−1) as
their MMDs do not overlap (Figure 13 A). The ratios chosen for the mixtures are
50 Chapter 3: The Long and the Short of Polymer Grafting
R1 = 1 : 0 (P1 : P3), R2 = 1 : 1, R3 = 1 : 4, R4 = 1 : 9 and R5 = 0 : 1 (in molar
equivalents). The evaluation of the ratios R2 to R4 is not as trivial as for the individual
polymer solutions, where the frequency change (or mass uptake) was simply
normalized by their number averaged molar mass in solution 𝑀nsol. If the frequency
change is normalized by a hypothetical average molar mass calculated according to
the employed ratios from the solution, the results show disparate ratios of short to long
polymers on the surface compared to the solution. Figure 14 A shows the progress of
the normalized frequency of the mixed samples. The black (R1) and grey (R5) curve
represent the lower and upper limit for the normalized frequency changes for all other
ratios as they represent the grafting of solely short and long chains, respectively. R3
(blue) and R4 (green) exceed these boundaries, indicating that the Mn in solution does
not reflect the average molar mass of the grafted polymer. Instead, the Mn on the
surface (𝑀nsur) is substantially lower than in solution, which clearly demonstrates that
shorter chains are preferentially grafted.
Figure 14: (A) Time dependent frequency change for polymer mixtures R1 to R5 normalized by
their average molar mass in solution 𝑀nsol. (B) Time dependent frequency change for R1
to R5 normalized by 𝑀nsur to match expected frequency behaviour.
While this finding provides a qualitative description of the size bias in ‘grafting-
to’, we also quantitatively establish to which extent shorter chains are preferentially
grafted. If the molar mass – or rather the radius of gyration – influences the grafting
density as demonstrated above, an equimolar mixture of two polymer samples should
ideally result in an averaged grafting density of the individual polymer samples. The
same should be true for mixtures of different ratios, i.e. the grafting density of a
mixture should be the weighted average based on the molar ratio of its components.
We introduce the value 𝑀nsur (Table 6) to describe the molar mass average of
the polymers on the surface to establish the expected grafting densities (Figure 14 B).
The molar mass averages of the surface attached polymers are well below their known
Chapter 3: The Long and the Short of Polymer Grafting 51
corresponding mass averages in solution 𝑀nsol (Table 6). Thus conclusively indicating
a preferential attachment of shorter chains. When we compare the ratio of the surface
mass average to the mass average in solution obtaining a preferential grafting factor
κ = 3.36 ± 0.58, we demonstrate that P1 (Mn = 8,240 g·mol−1) is grafted preferentially
to the surface compared to the P3 (Mn = 106,000 g·mol−1) sample. Interestingly, the
experimentally established preferential grafting factor κ is in excellent agreement with
the polymer samples’ ratio of their radii of gyration of 3.32 Equation 21, establishing
a comprehensive physical explanation for the grafting bias.
𝑅gP3
𝑅gP1
= (𝑀n
P3
𝑀nP1
)
𝑛∗
= (106
8.24)
0.47
= 3.32 (21)
with n* = 0.47 as determined above (Fig. 11C). Further defined mixture experiments
with P2 and P3 (Fig. S10 in the Supporting Information in Appendix C) were
conducted and resulted in a preferential grafting factor of κ = 1.40 ± 0.10, which
corresponds to an Rg ratio of 1.45, in excellent agreement with the above results. These
findings provide clear evidence that the ‘grafting-to’ method is heavily biased towards
lower molar masses, which is a result of their smaller radius of gyration. Thus, they
exhibit greater mobility and faster diffusion. A smaller Rg also increases the probability
of the end group to be located on the surface of the polymer coil, which critically
enhances the likelihood of a surface attachment. Finally smaller polymers simply
occupy less space and can therefore realize higher grafting densities.
Table 6: Samples used to investigate grafting bias, their composition, theoretical Mn in solution
Mnsol and on the surface Mn
sur with calculated preferential grafting factor.
Sample Composition
[P1:P3]
Norm. Mnsol
[g·mol-1]
Norm. Mnsur
[g·mol-1] adjustment factor
R1 1:0 8,240 8,240 ---
R2 1:1 57,100 17,500 3.26 ± 0.39
R3 1:4 86,400 20,200 4.29 ± 0.96
R4 1:9 96,200 37,900 2.54 ± 0.38
R5 0:1 106,000 106,000 ---
avg.: 3.36 ± 0.58
The short-chain grafting preference, however, is not merely relevant when samples of
different molar masses are to be grafted. It is just as important when well-defined
narrow disperse polymers are grafted. Even the most sophisticated contemporary
polymerization methods yield dispersities far from unity. Thus, polymer chemists
52 Chapter 3: The Long and the Short of Polymer Grafting
effectively always employ mixtures of polymers with different molar masses, in fact
even in a fairly narrow MMD, such as P1, only approximately 1.5% of the polymer
chains correspond to the Mn of 8,240 g·mol−1 and the chains within the sample cover
a range of molar masses from 3,500 g·mol−1 to 17,400 g·mol−1. Based on our current
results, we can now quantitatively predict how the MMD is affected upon
immobilization onto the substrate, taking the ratios of Rg within a given polymer
sample into account. The preferential grafting factor κ expresses by how much the
molar mass of interest Mi is preferred or unfavoured over the molar mass average Mn
of the sample.
𝜅 = (𝑀n
𝑀i)
𝑛∗
(21)
with the number averaged molecular weight Mn, the single molar mass Mi of the
polymer distribution, scaled by the solvent interaction parameter n*. Exemplary
preferential grafting factor κ curves for different number averaged molar masses are
shown in Appendix B Fig. S11.†
To predict the grafting behaviour of a polymer sample, it is necessary to know
the number weighted molar mass distribution MMDn of the sample, which can be
obtained by size exclusion chromatography (SEC) employing concentration sensitive
detectors (Fig. S3–S7 in the Supporting Information in Appendix C).
The number and mass weighted distributions of P1, P3 and P5 are depicted in
Figure 15 A/B. One important observation in the MMDn is that the majority of chains
(62%) for sample P5 (Figure 15 B) is below the Mn, which is not obvious when
inspecting the mass weighted distribution.
To estimate the molar mass distribution on the surface, the MMDn in solution is
multiplied with κ, which shifts the distribution further towards lower molar masses
(Figure 15 C) – under the provision that each chain in the distribution has a reactive
end group. For rather small polymers below 100,000 g·mol−1 this shift is almost
negligible, however for large polymers it is substantial. For P1, for instance, κ is 1.5
at 3,500 g·mol−1 and 0.7 at 17,500 g·mol−1 implying that the lower end of the
distributions is approximately twice as likely to be grafted as its upper end. For P5, κ
is 2.6 at 28,000 g·mol−1 and 0.4 at 1,240,000 g·mol−1, implying the lower end is more
than six times probable to be grafted than the upper end of the distribution. ‘Grafting-
to’ with high molar mass samples therefore requires special attention to address the
mismatch of the SEC derived molar mass distribution with the actually grafted chain
Chapter 3: The Long and the Short of Polymer Grafting 53
distribution (see Figure 15 D shift of solid to dotted line). To confirm the prediction of
preferential surface grafting of shorter polymer chains, AFM based SMFS
measurements were conducted. The normalized Gaussian distributions of the recorded
rupture length lR are depicted in Figure 15 E for sample P1 (lR = 26 ± 3 nm),
P3 (lR = 150 ± 9 nm) and P5 (lR = 154 ± 15 nm). The expected shift from different
peak maxima in solution (see Fig. 13A) to the same peak maximum on a surface of P3
and P5 (see Figure 15 C) is confirmed by the same average rupture length. A detailed
description of these experiments can be found in the Supporting Information in
Appendix C.
Figure 15: (A) Normalized mass weighted distribution in solution 𝑀𝑀𝐷wsol, (B) normalized number
weighted distribution in solution 𝑀𝑀𝐷nsol and (C) normalized number weighted
distribution on surfaces 𝑀𝑀𝐷𝑛surfor P1 (black curves), P3 (blue curves) and P5 (grey
curves). (D) Shift of the molar mass distributions 𝑀𝑀𝐷wsol (solid line), 𝑀𝑀𝐷n
sol (dashed
line) and 𝑀𝑀𝐷𝑛sur (dotted line) of P5. (E) Normalized Gaussian distribution of the rupture
length determined via SMFS experiments from sample P1, P2 and P3.
3.5 CONCLUSION
In summary, we demonstrate and quantify to which extent a polymer distribution
is distorted when grafted from solution onto a surface. We furthermore evidence that
this distortion can be quantitatively related to the radius of gyration, thereby providing
a physical explanation for the phenomenon. These results will critically affect methods
for the determination of the grafting density that rely on information of the number
average molecular weight of the grafted polymers, including the ‘dry thickness’
54 Chapter 3: The Long and the Short of Polymer Grafting
method or ‘gravimetric measurements’.57 We suggest a simple, yet quantitative
measure, κ, to predict the likelihood of certain polymer masses within a sample to be
grafted. The preferential grafting factor κ allows for the prediction of the grafted
distribution, effectively enabling quantitative access to grafted chain size distribution.
Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting 55
Chapter 4: Quantifying Solvent Effects on
Polymer Surface Grafting
As demonstrated in the previous chapter, shorter polymer chains are
preferentially attached to surfacers, and a preferential grafting factor, was
introduced. The observed shift of MMD could be correlated to the radius of gyration
of different-size polymer chains. Via SMFS the surfaces were investigated and a
drastic difference between surface and solution MMD for larger molecular weights
was detected. The result of this strong surface shift raised the question if the shift can
be minimized by ideal reaction conditions. By grafting PMMA chains on silica NPs
the difference between solution distributions after grafting and surface distribution can
be investigating. With theoretical calculations and experimental results the effect of
solvent quality on the shift of the surface distribution was investigated.
4.1 ABSTRACT
When grafting polymers onto surfaces, the reaction conditions critically
influence the resulting interface properties including the grafting density and molar
mass distribution (MMD) on the surface. Herein, we show theoretically and
experimentally that application of poor solvents is beneficial for the ‘grafting-to’
approach. We demonstrate the effect by grafting poly(methyl methacrylate) (PMMA)
chains on silica nanoparticles (NPs) in different solvents and comparison of the MMD
of the polymer in solution before and after grafting via size exclusion chromatography
(SEC). The shorter polymer chains are preferentially grafted onto the surface, leading
to a distortion effect between the MMD in solution and on surfaces. The molecular
weight distortion effect is significantly higher for ethyl acetate (better solvent quality,
difference in Mw surface to solution 14%) than for N,N-dimethylacetamide (poor
solvent quality, 6%). The difference in MMD on the surface to the solution
significantly affects both the surface properties (e.g. the grafting densities) and their
determination.
56 Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting
4.2 INTRODUCTION
Designing and tailoring functional surfaces is one of the key endeavours in soft
matter materials science. Applications for functional interfaces range from 3D cell
scaffolds,91-92 optoelectronics237-239 and coatings96, 240-241 to sensors.94, 242-243 One way
to tailor properties such as hydrophobicity,109, 244-245 tribology114, 246 or anti-
biofouling26, 97, 106, 247-249 is to covalently tether polymers onto surfaces. The surface
attached polymers can be additionally equipped with specific functional groups to fine-
tune the desired surface properties.108, 250 Two important properties of surface grafted
polymers are the grafting density (tethering distance between individual polymeric
chains) and the molar mass distribution (MMD) of the surface attached polymers, as
these determine the surface performance. The main approaches to achieve polymer
functionalized surfaces are the ‘grafting-to’ and ‘grafting-from’ method.52, 119, 126-127,
130, 251 In the latter approach, the polymers are synthesized in-situ, growing from the
surface, and giving access to high grafting densities. The ‘grafting-to’ approach uses
polymer chains which are synthesized prior to grafting and are equipped with
endgroups which easily react with the surface generally leading to lower grafting
densities compared to the ‘grafting-from’ approach.128 However, the ‘grafting-to’
method allows for a plethora of characterization methods of the polymer chains to be
applied prior to surface attachment. Polymer properties determined as such are often
assumed to reflect the polymer properties on the surface and are even used as factual
data in further characterization.119, 222 Recently, we demonstrated this assumption to
be incorrect.60 Due to a preferred attachment of shorter polymer chains, a significant
shift of the MMDs to lower molar masses was observed on the surface. A schematic
representation of the preferred attachment of short polymer chains on surfaces is
depicted in Figure 16 on the example of silica nanoparticles, which we based the
herein introduced method on. This method allows for the simple and instrumentally
non-demanding determination of MMD shifts during grafting-to of polymers.
Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting 57
Figure 16: Schematic and simplified presentation of the preferred attachment of shorter PMMA
polymer chains onto SiO2 nanoparticles (NPs). The coloured lines represent the short
(red) and long (blue) polymer chains.
4.3 THEORETICAL EVALUATION OF MMDS ON SURFACE GRAFTING
Earlier, the preferred attachment of shorter polymer chains was quantified via
quartz crystal microbalance (QCM) measurements and correlated with the difference
in radius of gyration, Rg. The quantification of this shift, corroborated by atomic force
microscopy (AFM) based single-molecule force spectroscopy (SMFS) measurements,
led to the establishment of a preferential grafting factor, κ. The preferential grafting
factor applied on a number based molar mass distribution predicts the shift of the
distribution upon surface attachment. The shift is more pronounced for higher molar
masses and broad distributions.60 In addition, a solvent dependency of the shift is
expected due to the power law of the preferential grafting factor, κ, with the solvent
interaction exponent, n*,
𝜅 = (𝑀n
𝑀i)
𝑛∗
(21)
and the ratio of number average molecular weight, Mn, and single molar mass, Mi, at a
certain point of the polymer distribution. In the case of n* = 0.5 (θ-conditions) the
polymer chain behaves like an ideal chain following a random walk. At θ-conditions,
the polymer-polymer interactions are energetically equal to polymer-solvent
interactions, and therefore the excess energy of mixing is zero. In good solvents
58 Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting
(n* > 0.5), the polymer-solvent interactions are advantageous, causing the chain to
expand. Whereas for bad solvents (n* < 0.5) the polymer chain contracts due to
favourable polymer-polymer interactions.252
To evaluate and quantify the effect of preferred surface attachment (difference
of MMDs from solution to surface) with varying solvent quality, we herein conduct a
calculation, showing a larger difference for good solvents. Symmetrical Gaussian
distributions are employed as approximation for MMDs to simplify the calculations.
Furthermore, the distributions employed in the calculations are considerably narrow
(dispersity of Ɖ = 1.05 for a number average molar mass of Mn = 5.00·105 g·mol-1) to
illustrate the relevance for polymers synthesized via controlled polymerization
techniques. The prediction of the MMD on a surface are conducted by multiplying the
preferential grafting factor (Equation 21), κ, with the MMD in solution. The calculated
shifts of MMD on surfaces for the described distribution with a solvent interaction
parameter from n* = 0.1 (very poor solvent) to n* = 1.0 (very good solvent) are
depicted in Figure 17.The dotted lines in Figure 17 A show the normalized MMD of
the calculated surface distributions. An increase of the solvent quality results in a
stronger shift of the MMD towards lower molar masses (difference in percentage of
Mn plotted in Figure 17 B) whereas bad solvents show a negligible shift. The difference
in radius of gyration, Rg, of polymer coils – with low versus high molar mass – is
distinctly lower for contracted chains. In a good solvent, the increased size difference
of the expanded polymer coils results in a preferred attachment of the lower molar
mass fraction of the MMD and therefore results in a more pronounced shift of the
distribution. For an increase of the solvent quality the impact on the surface
distribution is noticeably stronger, suggesting that preferably poor solvents should be
employed for the ‘grafting-to’ approach to guarantee a similar surface MMD in
comparison to the solution MMD. We herein demonstrate this effect.
Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting 59
Figure 17: (A) Calculated shift of normalized MMD on surfaces (dotted lines) for different solvent
interaction parameters, n* (ranging from 0.1 ‘poor solvent’, over 0.5 ‘θ-condition’, to 1.0
‘good solvent’). Starting with a narrow Gaussian MMD (Ɖ = 1.05) with a number and
weight average molecular weight of Mn = 5.00·105 g·mol-1 and Mw = 5.24·105 g·mol-1
(solid black line). (B) Percentage shift of Mn on surface MMD depending on the solvent
quality extracted from the MMDs in Figure 17A.
A shift in MMD from higher to lower molar masses on the surface implies that a
shift of the same magnitude but towards higher molar masses has to occur in the
solution. The sum of the shifted MMD on the surface and the MMD of the remaining
reaction solution has to be equal to the distribution of the starting reaction solution
(principle of mass conservation). The above raises a critical question: Why are there
no reports for such MMD shifts of the reaction solution? Typically in the ‘grafting-to’
approach, a large excess of polymer chains to reactive surface sites is employed to
drive the reactions to high grafting densities.180, 253 Especially for smooth planar
substrates the excess is commonly several orders of magnitude. In the case of our
previous QCM study, the experiments were conducted in a flow setup (very high
excess of end-functionalized polymers) to insure homogenous and full coverage of the
surface.60 The enormous excess of polymer guaranteed exclusion of any concentration
related effects on the grafting density, however, it is also the reason why a shift in the
MMD of the remaining reaction solution cannot be detected. The change in the
polymer concentration is therefore infinitesimal small and thus virtually non-
observable. To be able to detect a change in the MMD of the remaining polymer
concentration either the number of endfunctionalized polymers in the reaction solution
has to be strongly decreased or the number of reactive surface sites has to be
sufficiently high. In an ideal case, the concentration of polymer chains in the reaction
solution will be reduced by fifty percent after grafting. In other words, half of the total
amount of polymers is tethered to the surface and the other half remains in solution.
60 Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting
The sum of the two MMDs must result in the distribution of the reaction solution before
grafting. For a symmetrical Gaussian distribution (same as in Figure 17 with a solvent
interaction parameter of n* = 0.9) the surface and solution MMD would look like the
deconvoluted peak in Figure 18 A. The area of the surface distribution (red curve) and
the remaining reaction solution distribution (blue curve) is equal and the sum is
resulting in the start solution distribution (black curve). The different shape of the two
distributions can be explained by the power law relation (see Equation 21) of the
preferential grafting factor, κ. The increased weighting of smaller molar masses will
lead to slight peak broadening of the surface distribution. In Figure 18 B, the
normalized MMDs on surfaces (red curves) and in solution (blue curves) for varying
solvent quality can be seen. The sum of the surface and remaining reaction solution
distribution always results in the solution distribution before grafting (black curve).
Figure 18: (A) Deconvoluted peak for a starting reaction solution MMD (reduction in polymer
concentration of 50%) with the surface distribution (red curve) and solution distribution).
(B) Calculated shift of normalized MMD on surfaces (red dotted lines) and solutions (blue
dotted lines) for different solvent interaction parameters, n* (ranging from 0.1 ‘poor
solvent’, over 0.5 ‘θ-condition’, to 1.0 ‘good solvent’). Starting with a narrow Gaussian
MMD (Ɖ = 1.05) with a number and weight average molecular weight of
Mn = 5.00·105 g·mol-1 and Mw = 5.24·105 g·mol-1 (solid black line)
4.4 EXPERIMENTAL SOLVENT EFFECTS ON POLYMER GRAFTING
To elucidate the complementary shift of MMD in solution, a sufficient amount
of polymer must be tethered to the surface to induce measurable changes in the
remaining reaction solution. Theoretically, this may be achieved by very low sample
concentrations, yet in practice one would have to use such low concentrations that
most characterization methods would not yield meaningful data. Instead, we chose to
Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting 61
use common procedures and instruments. A concentration of 2 mg·mL-1 of polymer is
common and can be readily analyzed via SEC. To observe a change in this solution,
sufficient polymer must be removed from the solution, requiring a large surface for
grafting-onto.
Spherical nanoparticles (NPs) are ideal substrates due to their ratio of surface to
volume that increases with decreasing particle size. Poly(methyl methacrylate)s with
hydrolysable silane end groups were used as this enables the application of silica
nanoparticles as substrate. The minimal nanoparticle size is limited by the radius of
gyration of the grafted polymers. The particles diameter needs to be large enough to
rule out excluded volume effects.144 Therefore, a difference between the diameter of a
silica NP before and after grafting should be as low as possible. With a radius of
gyration of Rg ≈ 7.1 nm (refer to the Supplementary Information in Appendix D), the
difference between a 460 nm silica NP before and after grafting is less than 3%. Silica
NPs of 460 nm diameter were synthesized according to a published procedure.254 The
next consideration is the amount of NPs to be used as substrate, ideally 50 % of the
polymer in solution should be immobilized. In our hands solutions containing
4 mg·mL-1 polymer and dispersions containing 400 mg·mL-1 silica particles result in
the desired 50 % reduction. The solutions were prepared in different solvents (S1 Ethyl
acetate (EA), S2 N,N-dimethylacetamide (DMAc) containing 0.08 wt.-% LiBr).
Subsequently, 2.5 mL of polymer solution and 2.5 mL of nanoparticle dispersion were
combined and stirred for 7 d at 50 °C. The particles were separated via centrifugation
and washed twice with THF to remove physisorbed polymer. Prior to SEC analysis,
the supernatants were combined and the solvent evaporated under reduced pressure.
The SEC traces before and after grafting indicate a change in concentration of
50 ± 3 % (peak area), which is the desired range and equal to the shift assumed in the
calculated data (see Figure 18 A). DMAc and EA were chosen as they represent a near
θ-solvent (DMAc) and a good solvent (EA) under the current conditions. The
difference in the apparent hydrodynamic radii was determined via dynamic light
scattering to be 0.3 nm (7.3 nm in DMAc, 7.6 nm in EA, see Figure S7 in the
Supplementary Information in Appendix D). All SEC samples were run multiple times
to exclude errors due to shifts in retention volume caused by potential fluctuations in
temperature or eluent composition. Retention volumes were referenced to an internal
standard. Per sample three virtually identical traces were averaged to simplify the
further calculations. Figure 19 illustrates the shift of the MMD in solution from the
62 Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting
dissolved polymer before grafting in black (solution start) to the MMD after grafting
(solution DMAc/EA) in blue and the complementary MMD on the particle surface in
red (Surface DMAc/EA). The surface distributions were calculated by the difference
of the MMD in solution before and after grafting (principle of mass conservation).
Clearly evident is a distinct difference in the observed shift depending on the solvent
quality, with the shift being significantly larger for good solvents. Especially for the
higher molar mass region this effect is clearly visible. The distortion effect results in a
difference of the weight averaged molar mass Mw between in solution (after grafting)
and on surfaces of 14% for EA and 6% for DMAc (shown in Figure 19 B). Using
DMAc, the impact on the preferential grafting of shorter polymer chains on surfaces
was reduced and therefore the MMD on the surface is closer to the MMD in solution.
Figure 19: A) Experimentally observed shift of normalized MMD – recorded via SEC – on surfaces
(red curves) and solutions (blue curves) for grafting in DMAc (dashed lines) and EA
(dotted line). B) Weight averaged molecular weight Mw of the MMD and the difference
between surface and solution for DMAc and EA functionalization.
4.5 CONCULSION
Why are these information of relevance and how does the preferential grafting
change the properties of the functionalised surface? For an accurate calculation of
grafting densities (tethering density of polymer chains on surfaces), a precise
knowledge of the molar mass and MMD on the surface is critical. The general used
procedures for such grafting density calculations are the dry thickness method, the
gravimetric assessment and swelling experiments. The precise knowledge of MMD on
the surface is significantly increasing the exact quantification of surface grafting for
the first two methods.57 By changing from good solvents to θ-conditions, the precision
of these quantification methods can be improved and the error of the calculated value
can be reduced by a factor of two (difference in molecular weight in Figure 19 B).
Additionally, previous studies conducted via XPS and AFM showed that the grafting
Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting 63
density itself can be improved by decreasing the solvent quality,255 showing that a
decrease in solvent quality (by changing the ratio of a bad and good solvent in a binary
solvent mixture) is increasing the grafting densities.
In summary, we demonstrate that solvent-polymer interaction has a critical
impact on the resulting surface functionalization via the ‘grafting-to’ approach. Using
DMAc (near θ-condition) instead of EA (good solvent), the preferential grafting of
shorter polymer chains was reduced by a factor of two. If surfaces with a similar MMD
in solution and on surface are desired, a rather poor solvent must be employed,
accompanied by a concomitant increase of the grafting density.255 The choice of a poor
solvent is in contrast to the usual choice of good solvents for surface functionalization,
because the polymer must remain soluble to achieve surface functionalization. Solvent
systems with low solvent interaction parameters (n* << 0.5) are unable to sufficiently
solvate the polymer and can lead to agglomeration and precipitation. The ideal
conditions of surface grafting by the ‘grafting-to’ approach are therefore close to
θ-conditions, as demonstrated by the grafting of PMMA chains on silica NPs in DMAc
at 50°C. We submit that the herein introduced simple nanoparticle and SEC based
method for determining shifts in MMDs during surface grafting is applicable to other
polymer-solvent systems.
64 Chapter 4: Quantifying Solvent Effects on Polymer Surface Grafting
Chapter 5: General Discussion 65
Chapter 5: General Discussion
Throughout the entire PhD thesis, the need of in-depth surface characterisation
for designing interfaces with defined functions was pointed out multiple times. As
knowledge is the key for tailoring and designing advanced surface properties, a precise
understanding of the molecular processes which govern surface functionalisation has
to be established. Especially functionalisation of surfaces with molecular chain
structure serves a multidisciplinary need as described in Chapter 1. By evaluating the
covalent attachment of polymer chains on solid surfaces theoretically and
experimentally, this current study specifically establishes the molecular process of
tethering macromolecules via the ‘grafting-to’ approach. The study resulted in three
peer-reviewed publications, which are all showing the importance of a detailed
quantitative characterisation. In subsequent subchapters the key outcomes and future
directions of the current research work are summarized, followed by a general
conclusion of the PhD thesis.
5.1 SUMMARY OF STUDIES AND KEY OUTCOMES
Before any experimental work was conducted, a careful evaluation of existing
quantification methods was carried out. In the process of assessing the commonly used
grafting density characterisation methods – dry thickness method, gravimetric
assessment and swelling experiments – disadvantages concerning the quality of each
of the determination methods were identified. The assessment was divided into three
areas: (i) number of assumptions invoked in determining grafting densities (ii)
simplicity of determination (how many separate measurements have to be undertaken)
and (iii) stability in error propagation. Especially for the most frequently employed
determination method – the dry thickness method – questionable assumptions are
made, which critically influence the quality of the determined results. One can
conclude that all of the commonly used methods have their disadvantages with
approximately 12% of the reported values above or close to the physical limitations
introduced in Chapter 2. However, most strikingly, only around 6% of the reported
grafting densities (included in the current PhD thesis) conducted proper error
estimations for their grafting density calculations. For future research in this area, a
guide for precise error analysis is given, which will critically aid to judge the quality
66 Chapter 5: General Discussion
of the quantitatively determined value. Physical limitations of maximum grafting
densities are provided for both grafting approaches and should be used as a guide for
researchers employing any kind of grafting density determination. In cases for
calculated grafting densities close to – or even exceeding – the physical limitations,
the choice of determination method has to be reviewed and additional evidence for
such high grafting densities has to be provided. Alternative routes for a reliable
evaluation of grafting densities are proposed at the end of Chapter 2. For improving
the quality and precision of grafting density determination a simple direct assumption
free method has to be employed.
One of the proposed methods is the evaluation via in-situ QCM measurements
of the surface grafting. The experimental work resulted in the exact evaluation of
surface grafting densities on a library of different sized macromolecules (all PMMA
based) on a silica QCM sensor, which are in good agreement with the theoretical
calculations. The grafting density scales with the size of the polymer, with higher
grafting densities achieved with shorter polymer chains. It is important to note that in
the conducted experiments the QCM was operated in a flow setup, which implies that
always fresh polymer solution is streaming over the sensor surface. Unreacted polymer
chains are flushed away in this scenario, leading to a static ultimate state (no change
in resonance frequency of the quartz crystal and therefore no further mass uptake) of
maximum grafting density for applied conditions. The final state of polymer graft is
likely driven by the diffusion kinetics of the polymer coil, with faster diffusivity of
smaller macromolecules towards the surface. Further investigations via ratio
experiments demonstrated that shorter polymer chains are preferentially grafted (in
comparison to longer polymer chains) onto surfaces. The observed phenomenon of
preferential surface grafting can be physically explained by the difference in the ratio
of gyration, establishing a preferential grafting factor. Additional AFM based SMFS
measurements are congruent with the QCM observed phenomenon of preferential
surface grafting. A significant shift of MMD on surfaces in comparison to solution
distributions was discovered. The difference of MMD is especially crucial for any
process which involves surface functionalisation with high molecular weight polymers
via the ‘grafting-to’ approach.
Further investigations of functionalizing silica NP surfaces were conducted to
investigate the effect of solvent quality on the shift of MMD. Instead of examining the
surface MMD directly on the substrate, the large surface area of the NPs was employed
Chapter 5: General Discussion 67
to alter the distribution of the polymer solution after polymer grafting (easy SEC
readout). It is important to note that the amount of surface had to be significantly high
to observe a preferential surface grafting of shorter polymers without grafting the
entire concentration of polymer onto the NPs. For investigating the shift of MMDs
before and after grafting, a change of 50% of polymer concentration was targeted. The
effect of solvent quality on the shift of the MMD on the surface was investigated by
calculations and experimentally. The experiments were conducted over a reaction time
of 7 days (slow stirring for minimal shearing of polymer chains between NPs) to
achieve a similar static ultimate state comparable to the QCM experiments. For surface
functionalisation via the ‘grafting-to’ approach, the choice of a rather poor solvent
results in a less pronounced shift of MMD on the surface and in solution, which implies
to choose poor or theta conditions for surface functionalisation via the ‘grafting-to’
approach if similar surface to solution MMDs are desired. The application of poor
solvents will additionally result in a higher grafting density due to the decreased radius
of gyration.
5.2 FUTURE DIRECTION
As already proposed in Chapter 2, there are numerous possibilities of increasing
the quality of quantitative evaluation of grafting densities. In the current PhD thesis
the approach via in-situ QCM flow measurements was employed for grafting
macromolecules on silica surfaces by the ‘grafting-to’ method. The high sensitivity of
mass detection is an ideal tool for determining the mass increase per area due to the
surface functionalisation. The QCM additionally gave even more detailed insights into
the grafting process and allowed the implementation of a preferential grafting factor.
The experiments conducted in throughout the entire PhD thesis focused on
understanding a static ultimate state of surface grafting. For a full understanding of the
process of surface grafting via the ‘grafting-to’ approach a precise investigation on the
energetic and kinetic contributions has to be investigated. One way to investigate the
kinetic equilibrium of adsorption/desorption process (physisorption) on a QCM sensor
surface can be achieved by employing polymers without reactive end groups. The size
difference on the sorption behaviour will drive the kinetic equilibrium in either static
or flow (with varying flow rate) experiments and can be recorded via the difference in
frequency change. A variation of the reaction temperature for the surface grafting
process (chemisorption) will provide additional insights into the energetic contribution
68 Chapter 5: General Discussion
to the static ultimate state of the surface graft. Additional variation of the chemistry
employed in the chemisorption process (varying surface reactions) can increase or
decrease the energetic contribution and will change the thermodynamic effects on the
ultimate static state of the polymer brush. Another approach to increase the precision
of the performed QCM experiments – especially for the performed ratio experiments
– is by employing monodisperse macromolecules. The preferred attachment of shorter
polymers inside a distribution gives an additional distortion effect on the results, which
can be prevent by using i.e. monodisperse DNA. In particular the application of
monodisperse macromolecules could ease the determination of kinetic and energetic
contribution on surface grafting via the ‘grafting-to’ approach.
In a next step, the evaluation of grafting densities via QCM for the ‘grafting-
from’ approach has to be investigated. The evaluation of the data is not as straight
forward as for the ‘grafting-to’ method and has to be modelled to growth kinetics of
the polymer brush. Extrapolation towards the starting point of the polymer growth
should result in an accurate value of the grafting density. The investigation of changing
segment density inside the in-situ growing brush will give additional insights into
polymer growth kinetics of the brush and initiator efficiency. It is important to note
that especially for dense polymer layers which exceed a certain thickness, the simple
correlation between frequency change and mass uptake (refer to Equation 20 in
Chapter 3.3) cannot be employed. In the case of strong visco-elastic behaviour of the
polymer brush elaborate calculations have to be conducted, which take dissipation of
the surface grafts into account. By combining the QCM experiments with other surface
characterisation techniques e.g. neutron reflectometry (density profile in Z-direction)
an absolute understanding of the polymer brush – down to the molecular level – can
be achieved.
The grafting of PMMA chains onto silica NPs resulted in a significant change of
the MMD of the solution after grafting (in comparison to the initial solution). The shift
to higher molecular masses in solution after surface grafting is in accordance with the
preferential surface grafting of shorter polymer chains on surfaces observed via QCM
and AFM based SMFS. The performed experiments could only be conducted in a
narrow condition window (solvent, polymer concentration and NP concentration) due
to the fact that all components had to be soluble/disperse in the reaction solution. By
using rather highly porous membranes or monoliths (large surface area) the problems
of NP aggregation can be overcome and the condition window can be extended. The
Chapter 5: General Discussion 69
simple SEC readout of the solution after grafting provides a new opportunity in
determining the polymer solvent interaction. The shift in MMD between starting
solution and solution after grafting can be translated into the solvent interaction
parameter, possibly developing into a new and easy read out method for determining
the solvent interaction parameter of specifically challenging solvent polymer systems.
A further promising proposed method for high precision grafting density
evaluation is via AFM based colloidal probe measurements, as already mentioned at
the end of Chapter 2. Instead of trying to directly counting the polymers on a surface
via multiple rupture events recorded in a force spectroscopic measurement, the force
response of the polymer brush upon compression with a colloidal probe can be related
to the grafting density of the surface graft. Especially by using the effect of different
force responses of the polymer brush in varying solvents, the grafting density can be
directly related. The accuracy in load/force determination in AFM is high and can even
determine the grafting densities in low density regimes. Due to the possibility of
recording a large amount of single force spectroscopic measurements, the statistical
significance of the captured data is high. AFM therefore is one of the most ideal
methods for the precise quantitative evaluation of polymer surface functionalisation.
5.3 CONCLUSIONS
As a general conclusion, the interplay of theoretical/computational work and
experiments resulted in the detailed understanding of surface functionalisation with
polymers via the ‘grafting-to’ approach. The interplay of theoretical and experimental
research is the only way for successfully understanding processes at the molecular
level. By investigating the process of grafting PMMA chains onto silica surfaces (via
QCM), for the first time quantitatively the preferential surface grafting of short
polymer chains was observed. The observed phenomenon resulted in the
implementation of a preferential grafting factor, with a huge impact on how to design
functional surfaces with surface attached polymers. To design and tailor specific
surface functionalities a precise control over every aspect of the grafting procedure is
needed. By controlling the solvent quality in which the grafting process takes place,
the distribution of polymers on the surface can be controlled. The drastic effects the
preferential surface grafting has on the commonly used determination methods for
grafting densities and the following understanding of application performance can be
comprehend by the following example.
70 Chapter 5: General Discussion
In the case of grafting a polymer distribution with a number average molar mass
of Mn = 17,000 g·mol-1 and a broad distribution of Ɖ = 1.63 (comparable to reference
180) a dry thickness of hdry ~ 7 nm can be determined. Using the most commonly
employed dry thickness method for evaluating the grafting density (see Equation 8 in
Chapter 2.4.1), a value of σ = 0.22 chains·nm-2 is estimated using the number average
molar mass from solution. If now a preferential grafting of shorter polymer chains on
the surface would be taken to account, the number averaged molar mass would be
shifted to a lower value, which will result in a shift to higher grafting densities. For
increased solvent qualities (n* = 1), the shift can exceed 60% difference in grafting
density value, resulting in a value of σ = 0.36 chains·nm-2 (example from above). The
influence on the percentage difference on the grafting densities as a function of the
solvent interaction exponent is illustrated in Figure 20. The green and red area show
the regimes of where the polymer can be grafted (soluble – green area) or will be
precipitated (insoluble – red area). The complete calculations can be found in
Appendix E. If such a surface graft should be applied for the release of small
molecules (small molecule attached to the polymer at the free end-group) in a drug
discovery application, a miss calculation of the released small molecule concentration
from the surface (of up to 60 % difference in shown example) could lead to false
interpretation of the resulting performance.
Figure 20: Difference of grafting density in dependency of solvent quality for a polymer distribution
with Mn = 17,000 g·mol-1 and Ɖ = 1.63, evaluated via the dry thickness method
(comparable to reference 180).
Chapter 5: General Discussion 71
The results of the current thesis highlight the necessity of investigating processes
at the molecular level. Especially for processes in the field of surface functionalisation
with polymers a full understanding of the grafting process must be achieved. Further
investigations and application of discovered molecular effects (e.g. solvent interaction)
are crucial for the design of novel surface with unique surface properties. The surface
of any material is nothing less than the point of interaction in everyone’s daily life.
Therefore, it should be one of our highest aims to fully understand this crucial aspect
of matter.
72 Chapter 5: General Discussion
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Appendices 89
Appendices
Appendix A
Statements of Contribution of Co-Authors for Thesis by Published Paper
The signed Statement of Contribution of Co-Authors for Thesis by Published Papers
for:
Chapter 2: L. Michalek, L. Barner, C. Barner-Kowollik, Polymer on Top:
Current Limits and Future Perspectives of Quantitatively Evaluating Surface Grafting,
Advanced Materials, 2018, 30, 1706321(1-18).
Chapter 3: L. Michalek, K. Mundsinger, C. Barner-Kowollik, L. Barner, The
Long and the Short of Polymer Grafting, Polymer Chemistry, 2019, 10, 54-59.
Chapter 4: L. Michalek, K. Mundsinger, L. Barner, C. Barner-Kowollik,
Quantifying Solvent Effects on Polymer Surface Grafting, ACS Macro Letters, 2019,
8, 800-805.
90 Appendices
QUT Verified Signature
Appendices 91
QUT Verified Signature
92 Appendices
QUT Verified Signature
Appendices 93
Appendix B
Supporting Information Chapter 2
94 Appendices
Appendices 95
96 Appendices
Appendices 97
98 Appendices
Appendices 99
100 Appendices
Appendices 101
102 Appendices
Appendices 103
104 Appendices
Appendix C
Supporting Information Chapter 3
Appendices 105
106 Appendices
Appendices 107
108 Appendices
Appendices 109
110 Appendices
Appendices 111
112 Appendices
Appendices 113
114 Appendices
Appendices 115
Appendix D
Supporting Information Chapter 4
116 Appendices
Appendices 117
118 Appendices
Appendices 119
120 Appendices
Appendices 121
122 Appendices
Appendices 123
Appendix E
Calculations of MMDs and grafting densities for surface grafting via dry
thickness method.
For the simulations of the MMD in solution (comparable to Reference 180 with
Mn = 17,000 g·mol-1 and Ɖ = 1.63) a log-normal distribution with tailing to higher
molecular weight was used:
𝐼 =1
𝑥𝜎√2𝜋exp (−
(ln 𝑥−𝜇)
2𝜎2
2) with 𝜎 = 0.7 and 𝜇 = 9.5
Figure A1: MMD of polymer in solution (black curve) and polytmer on surface (red curve – for an
solvent interaction parameter of n* = 1)
The shifted surface distributions where calculated by multiplying the upper
distribution with κ from Equation 21. For different solvent interaction parameter
following grafting densities can be calculated via the dry thickness approach (Equation
8):
n* Mn [g·mol-1] σ [chains·nm-2]
1 10,457 0.36
0.9 10,982 0.35
0.8 11,533 0.33
0.7 12,113 0.31
0.6 12,721 0.30
0.5 13,360 0.28
0.4 14,031 0.27
0.3 14,735 0.26
0.2 15,475 0.25
0.1 16,252 0.23
1000 10000 100000
norm
. M
MD
Molar Mass / g mol-1