MBMB--JASS 2006JASS 2006 ZelenogradZelenograd, , MoscowMoscow

NanobiotechnologyNanobiotechnology and Biosensorsand Biosensors

SolidSolidLiquidLiquid

InterfaceInterface

Alexander Mehlich

Content

I. Motivation

II. Introduction

III. Theoretical Approach

IV. Experiment

V. Simulation

VI. Application

VII. Review

Motivation

Understanding of Solid/Liquid-Interface is inevitable for applicationsin the field of Nanobiotechnology and Biosensors

• Biosensors – metal/electrolyte-contacte.g. ISFET:

• Nanotubes – solid tubes with liquid inside

• Electrokinetics & microfluidics

Introduction

• Structure: crystalline grid

• Smallest unit: unit cell → immobile • Structure: no particular order

• Smallest unit: atoms and molecules → mobile

Solid Liquid

• Dominant forces: covalent bonding

Conductance: electronicConductance: ionic

• Dominant forces: ionic and hydrogen bonds

• special: hydration, surface tension

Theoretical Approach Helmholtz layer

Concept of the „Electric double layer“

• The Helmholtz layer:charged surface

→ electric field→ attraction of counterions

→ arrangement of plate-capacitor with molecular size

Capacitance per unit area:

dC A

H0εε ⋅

= d - half diameter of solvated ionε - dielectric constant of water

Potential - Poisson equation (PE):

0

2

εερψ −=∇ linear potential drop

0=ρ

Theoretical Approach Gouy Chapman –Poisson-Boltzmann

• Gouy-Chapman Theory (GCT):

thermal fluctuations of charge carriers→ „diffuse electric double layer“

Boltzmann equation (BE):

⎟⎟⎠

⎞⎜⎜⎝

⎛ −⋅=

TkWccB

iii exp0 ( ) ( )

⎥⎦

⎤⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛−⋅=−= −+

Tkzyxe

Tkzyxeeccce

BB

,,exp,,exp)( 0ψψρ

use for local charge density

Poisson-Boltzmann equation (PBE = PB + BE):

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅=∇

−Tk

eTk

e

BB eeec ψψ

εεψ

0

02assumptions made:

• 1:1 salt; otherwise:• only electric work done

eze i ⋅→

Theoretical Approach Gouy Chapman – planar surface

Applying PBE to a planar surface:

→ series expansion

xzyx →,,

0→⇒<<Tk

eTke

BB

ψψ

•

•

simplifications:

ψεε

ψ⋅=

Tkec

dxd

B0

02

2 2result: → linearized PBE orDebye-Hückel approximation

boundary conditions

with:

∑=≡i

iiBB

zcTk

eTk

ec 20

0

2

0

202

εεεεκ

general casexe κψψ −⋅= 0

Theoretical Approach Gouy Chapman –planar surface II

xe κψψ −⋅= 0 Dλκ =−1 → decay length calledDebye length

• exponential drop of potential• increase of salt concentration→ steeper drop, shorter Dλ

reason: better screening of surface charge with more ions

Theoretical Approach Gouy Chapman –linear and full solution

Comparing linear and full solution of PBE:

⎟⎟⎠

⎞⎜⎜⎝

⎛−⋅=∇

−Tk

eTk

e

BB eeec ψψ

εεψ

0

02

xe κψψ −⋅= 0

xy

y

y

y

eee

ee κ−

ΥΥ

⋅+−

=+−

434213210

0

0

11

11

2/

2/

2/

2/

⎟⎟⎠

⎞⎜⎜⎝

⎛=

Tkey

B

ψ

20 mM monovalent salt

• small surface potential:good linear fit

• higher potentials:full solution has lower potentials+ steeper decay for x < λ/2

Theoretical Approach Gouy Chapman – capacity

Capacity of the diffuse electric double layer:

→ relation between surface charge and surface potential ?σ 0ψ

Grahame equation:

DBB Tk

eTkcdxλψεεψεερσ 000

000 2

sinh8... ≈⎟⎟⎠

⎞⎜⎜⎝

⎛⋅==⋅−= ∫

∞

Capacitance:

• low potentials: linear behaviour• high salt concentration:→ more surface charge required

for same potentialDBD

AGC Tk

eddC

λεεψ

λεε

ψσ 000

0 2cosh ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅==

⎟⎠⎞

⎜⎝⎛ =

dUdQC electric double layer like plate capacitor with d = !Dλ

Theoretical Approach Gouy Chapman – discussion

Discussion – limitations of GCT:

• finite size of ions neglected

• continuous charge distribution considered

• non-Coulombic interactions disregarded

• continuous solvent with constant permittivity ε

• flat surface assumed

• …

BUT - good predictions for symmetric electrolytes at: salt concentrations < 0.2 Mpotentials < 50-80 mV

Theoretical Approach Stern‘s Modification

Tuning GCT:

0ψ

βψ

dψ

βσ

dσ

0σ

IHP OHP

diffuse layer

Stern layer

potential characteristics:

capacitance:( )Tke

dCCC B

DA

GCAH

Atot 2/cosh

111

000 ψεελ

εε ⋅+=+=

- - - - - - - - - - - - - - - - - - - - - - - solid surface - - - - - - - - - - - - - - - - - - - - - - -

Stern layer – bound layer of adsorbed ions, immobile: IHP – specific adsorbtionOHP – nonspecific adsorb.

- - - - - - - - - - - - - - - - - - - - - - - - ζ-potential - - - - - - - - - - - - - - - - - - - - - - - -

Gouy-Chapman layer – diffuse layer, mobile

- - - - - - - - - - - - - - - - - - - - - - - - bulk water - - - - - - - - - - - - - - - - - - - - - - - - x

Content

I. Motivation

II. Introduction

III. Theoretical Approach

IV. Experiment

V. Simulation

VI. Application

VII. Review

Experiment Adsorption – mercury drop

Adsorbtion at the Interface:

→ experiment: mercury drop in electrolytecharge density at interface?

AG∂∂

=γ • p, T - const• formation of surface unfavourable

special: surface tension -

Gibbs Adsorption Equation:

0,

1

0,

1

1

0

=+++− ∑∑−=

=

−=

=kj

Kk

kkj

Jj

jS dndQdAdpVdTS µεγ σσσσ

σ – surface related, ε – overall potential diff.n – # of charge carriers on surface, µ- chem. potential

∑=−i

ii dA

nd µγσ

→ p, T const: - Gibbs Adsorption isotherm

dEd Mσγ =−AnF eM −=σ

- electrocapillary equation

- excess charge

Experiment Adsorption – mercury drop II

⎟⎠⎞

⎜⎝⎛−=

dEdM γσ

repelling excess charge carriers → lowering of γ- excess charge

Def.: point of zero charge (pzc) ≡ no charge within the metal

expectation for γ over potential?

pzc

asymmetric! → coulombic + specific adsorption

here anions specifically adsorb, cations not

Experiment Specific Adsorption – parameters

Parameters influencing specific adsorption:

• Charge density on solid surface

specific adsorption of ion ↑↔ opposite charge within solid ↑

note:anions can be adsorbed at negative charge (see graph)

• Ion Size Effectsize of ion ↑→ specific adsorption ↑

( hydration weaker…)

• IonTypeanions have greater tendencyto spec. adsorb than cations

(for metals observed…)

Experiment Specific Adsorption – parameters II

• Hydration

strong primary hydration sheath → little specific adsorption

Anion F(-) Cl(-) Br(-) I(-)Ion-Solvent Interaction [kcal/mol] -20.6 -13.6 -12.2 -10.7

• Concentration Changehigher concentration → higher specific adsorption

• Temperature

increase of temperature→ decrease of

specific adsorption

Experiment (Specific) Adsorption – general parameters

of general importance is:

• type of the solid→ type of “docking stations” for adsorbates (surface texture)

• solvent-solid interaction→ solvation of surface + desorption for creating vacancies

• solvent-adsorbate interaction→ hydration sheath

…

Experiment Limits of Observation

Problem:• many influences can be measured directly, others cannot

• there are experimental results striking the so far developed theory

• complexity of parameters to be considered is rising

→ no “all-describing”-theory found yet!

Way out:developing models for simulation +

comparing results with real experiment

Simulation Four State Model - idea

special property of water:DIPOLE

Four state model (1975):experimental data –capacity over excess charge:

explanation?

idea: dipoles cause extra potential drop → influence on capacitance

assumption: no specific adsorption→ first adsorbed layer only water→ four states to be differed

Simulation Four State Model - model

Monolayer of water with single molecules + clusters of molecules – 2 dipole directions

cN +

cN −

N +

N −

cµ

µ → 4 statesN – # molecules of certain state in monolayerµ – dipole moment

Energies:

solvent molecule in cluster -

monolayer permittivity

}/c cµ σ ε+ = −U

{/c cµ σ ε− =U

charge on metal

/ bUµσ ε += − ++U

{/ bUµσ ε −= +-U

due to different bonding

free solvent molecule -

Potential drop across inner layer:}

{0

free charge

dipoles Cσφ ψ χ∆ = + = + χ / / / /c c c cN N N Nχ µ ε µ ε µ ε µ ε+ − + −= − + − +→

idea: Boltzmann for N + varying parameters

Simulation Four State Model - results

Total capacitance:

0

1 1

i

d dC d C d

φ χσ σ∆

= = +

achieved plots:simulation

experiment

Simulation Four State Model - results II

results from adapting the parameters:

10 0 -10 -20 -30 -40

0.0

0.2

0.4

0.6

0.8

1.0

NC+

NC_

N+

N_

mol

ecul

es /

NT

charge density (µC/cm2)

• asymmetry, because of different stability of 2 orientations of free molecules

• 3 water molecules per cluster

• total dipole moment of cluster approxsame as dipole moment of free molecule→ ring groupings of water possible:

• maxima + minima are deduced ashigh or low switching-possibilitiesof the dipole orientation:

0, , , ,c b bU U Cε µ + −

Simulation Diffuse Layer Capacitance

Diffuse Layer Capacitance:

Influence of diffuse layer around pzcstrong for low concentrations:More experimental capacitance-data:

DBD

AGC Tk

eddC

λεεψ

λεε

ψσ 000

0 2cosh ≈⎟⎟

⎠

⎞⎜⎜⎝

⎛⋅==

Huge minimum at very low concentrations

Simulation Adsorption Capacitance

Adsorption Capacitance:

• Assume absorbed charged moleculesRTFzRTGb

iii eea //0

1φ

θθ −∆−=−

→ Adsorption isotherm – here: Langmuir isotherm:

• Surface charge:

-10 -5 0 5 10

0.0

0.5

1.0

Surfa

ce c

over

age,

θ

∆G/kT-10 -5 0 5 10

0.00

0.05

0.10

0.15

0.20

0.25

dθ/d∆G

= C

apac

itanc

e

∆G/kT

θ⋅= iSadsp qQ

→ Capacitance due to adsorbed molecules = ( ) ( )θθφθ

φ−== 1RTFzq

ddq

ddQ

iiiSadsp

(θ – surface coverage)

Simulation Molecular Dynamics Simulations –model, results

Molecular Dynamics Simulations (MDS) of water at hydrophobic substrates:(2004)

• Aim: water density depending on - curvature (spherical, planar)- temperature- pressure

• Model: for interactions used models

simulation cell: cubic box filled with ~ 1000 – 3000 water moleculesperiodic boundary conditions

- Lennard-Jones + Coulomb potential- Buckingham potential

I: spherical solute in box• Results

- increased density for small solute- water depletion for large solute

- Temperature increase causesdecrease of density

- Same pressure dependenceas at Results II

Simulation Molecular Dynamics Simulations – results II

• Results II: planar surface in box

64 alkane molecules + 2781 water molecules

- water depletion at interface→ layer thickness ~ 2.5 A

- high pressure reduces depletion layer

- layerthickness rises with Temperature

- potential drop at interface→ caused by dipoles→ top water layer oriented

Simulation Molecular Dynamics Simulations –facing reality

Experiments on depletion (2003):Experimental data also gives reason to a depletion layer of water onhydrophobic substrates:

Neutron Reflectivity Measurements&

Atomic Force Microscopy

• Layer thickness:2-5nm

20nm

• Oberserved interface:

on ahydrophobic plane

OD2

• memory-effect observed

3D-plot

AFM: tapping mode topology image of„nanobubbles“

NRM: Kiessig oszillations due to gas layer

Content

I. Motivation

II. Introduction

III. Theoretical Approach

IV. Experiment

V. Simulation

VI. Application

VII. Review

Application Electrokinetics – zeta potential

Electrokinetics:

• due to strong electrostatic forcesions in the inner layer are immobile• under pressure driven flow (pdf)

ions of the diffuse layer are able tomove → shear plane is formed

zeta-potential:

( ) ( )bulkshear xx ψψζ −=

Application Electrokinetics –stream current & potential

fluid in a (micro)tube:

• zeta-potential ≠ 0 grants movablenet charges in diffuse layer

• pdf induces a stream of chargesin a capillary:

DσDν

( ) ( ) { DDA

Dstream rdArrI νρπρν 2== ∫ - drift velocitiy in diffuse layer- charge densitiy in diffuse layer

capillary radius

• depletion and accumulation of charges at ends of capillary respectively:

krl

CiU DD

stream ⋅==

νσ2l

krC2π

=

(k = specific conductivity of solution)

- conductanceOhm‘s law

Application Electrokinetic Measurements on Adsorption -idea

Analysing charge density of the inner layer using electrokinetic measurements:(2001)

ζ-potential separates immobile and mobile layer

basic idea:sign of ζ-potential reveals sign of totalcharge within the inner layer

electrokinetic values measured:streaming potential & current

correlation with ζ-potential:

( )dpdI

bhLI S

rS εε

ηζ0

=( )dp

dUKU S

r

BS εε

ηζ0

= experimental setup

Application Electrokinetic Measurements on Adsorption -plots

Obtained data:

conclusions:

• HCl:

• pure water: +− +↔ OHOHOH 322→ negative ζ-potential

• KOH:

• KCl:

- first H-ions preferred → sign reversal- then: double layer compression

- first OH-ions preferred, afterwards:- compression of the double layer→ increasing surface charge compensation

already within inner layer (screening…)- only double layer compression

Application Electrokinetic Measurements on Adsorption -results

Conclusions:+−+− =>>> KClOHOH 3preferential adsorption:

IEP

• pH-dependence:→ low IEP proves result above

important factors for adsorption:

• structure of hydration shell important(OH-ion known to have less stable hydrationstructures → escapes more easily and buildsup hydrogen bonds with interfacial water)

• capability to bind interfacial water via hydrogen bonds

• another experiment using pH-Dependant Force Spectroscopy leads to conclusion:

- immobilized interfacial water acting as template for hydroxyl adsorption- density of molecular units of water building networks on the surface crucial

Application Electroosmosis – what it is

Electroosmosis:

• Applying electric field along capillary→ movement of liquid relative to stationary charged surface

• electric field induces force on net chargein diffuse layer

• diffuse layer displacement leads todragging of bulk fluid

drift velocity of fluid:

xEηεςνς = - Helmholtz-Smoluchowski

cµ - osmotic mobility

Application Electroosmosis – properties

the way to have laminar flow in microfluidicsat low Reynold‘s numbers

• advantage of electroosmosis:

- ζ-potential = -100mV- electric field = 2.5 x 10³V/m

• example:

time development after switching on the e-field → dragging → laminar flow

sm /200µνς =

Review

44444 344444 21

?1.

2.3.

4.Theory

HelmholtzGouy-ChapmanStern

ExperimentAdsorption &its parameters,AFM, NRM…

ApplicationElectrokinetics, microfluidics…

Simulation4 state model, MDS…

References

•! Hans Juergen Butt, Karlheinz Graf, Michael Kappl, Physics and Chemistry ofInterfaces, Wiley-VCH Verlag & Co. KGaA, 2003• S. Roy Morrison, Electrochemistry at Semiconductor and Oxidized Metal Electrodes,Plenum Press, New York 1980• Horst Kuchling, Taschenbuch der Physik, 17. Auflage, Fachbuchverlag Leipzig imCarl Hanser Verlag, München Wien 2001• J. O‘M. Bockris, Brian E. Conway, Ernest Yeager, Comprehensive Treatise ofElectrochemistry - Volume 1: The Double Layer, Plenum Press, New York and London1975+• Roger Parsons, A Primitive Four State Model for Solvent at the Electrode-SolutionInterface, printed in Electroanalytical Chemistry and Interfacial Electrochemistry, 59,229-237, Elsevier Sequoia S.A., Lausanne - printed in Netherlands 1975•! Rolando Guidelli, Wolfgang Schmickler, Recent Developments in Models for theInterface between a Metal and an Aqueous Solution, printed in Electrochimica Acta, 45,2317-2338, Elsevier Science Ltd., 2000

References

• Ralf Zimmermann, Stanislav Dukhin, Carsten Werner, Electrokinetic MeasurementsReveal Interfacial Charge at Polymer Films Caused by Simple Electrolyte Ions, printedin J. Phys. Chem., 105, 8544-8549, American Chemical Society, on web 2001• Christian Dicke, Georg Haehner, pH-Dependent Force Spectroscopy ofTri(ethylene Glycol)- and Methyl-Terminated Self-Assembled Monolayers Adsorbedon Gold, JACS articles, 124, 12619-12625, American Chemical Society, on web 2002• Roland Steitz, …, Nanobubbles and Their Precursor Layer at the Interface of WaterAgainst a Hydrophobic Substrate, Langmuir, 19, 2409- 2418, American ChemicalSociety, on web 2003• Roland R. Netz, Shavkat I. Mamatkulov, Pulat K. Khabibullaev, Water at HydrophobicSubstrates: Curvature, Pressure and Temperature Effects, Langmuir, 20 , 4756-4763, American Chemical Society, on web 2004

0 20

30

14 2

5.315 /

0.31

0.28 1.4 10

7 10c

tot

C F cmd nm d

Cm

N cm

ε ε ε µ

µ µ −

−

= ⋅ ⎫= ≈⎬= ⎭

= ⋅ = ⋅

= ⋅

Qualitative: