Mechanical Principles of Biological Nanocomposites

Greg Orlicz Introduction / Fracture MechanicsGeorge Keller Mechanics employed by nature / Role of “nano”Anthony Salvagno Biological examples / Hierarchy in natureJingshu Zhu Characterization / Fabrication of synthetic materials

What can we learn from biological materials?

• Biological materials (e.g. bone, tooth, shell, and wood) -- excellent mechanical properties: strength, toughness, and resistance to fracture

• Much is attributed to nanostructure

• Want to understand what factors attribute to strength and toughness by understanding the mechanical forces that result due to the structure

• Perhaps we can synthesize materials to meet and surpass the same robustness of biological materials (biomimicking)

• Emphasis is material strength and resistance to fracture – fracture mechanics

Setting the foundation for fracture mechanics…

Strain energy – energy stored in plate like a spring during elastic deformation (can return to same position) (like pushing fist into car door)

Stress: σ = F/A

Strain: ε = ΔL/L0 Young’s Modulus (Stiffness): E = Tensile Stress/Tensile Strain =

related by Hooke’s Law: σ = E ε

LA

L F 0

Analog to spring force: Fs= -kx

* When material is unloaded, the strain energy can do work

ΔL

L0

AF

• Plastic deformation - if stress is high enough, material is strained beyond elastic approximation

- internally damaged and deformation is irrecoverable (like punching car door – denting)

- linear relationship between stress and strain is lost

• Yield Stress = stress under which material no longer deforms elastically (deforms plastically – irrecoverable)• Ultimate Tensile Strength = max stress that material can withstand

What is plasticity?

Extensometer

• Stress-Strain relationship determined by tensile test

Strength – how much stress a material can support without failure (usually defined as σUTS = max stress on stress-strain curve)

Toughness – amount of energy per unit volume a material can absorb before rupturing

Toughness vs. Strength

df

0volume

energy toughness

σ

ε

A very close look at elastic fracture

Arrive at critical stress:

Considering all bonds per unit area, Pc σc; k E (Young’s modulus) :Surface energy – energy required to break a plane of atomic bonds to create two free surfaces (energy per surface area):

Bond energy:

Approximate force as half of sine wave:

For small displacements:

k is analogous to spring constant:

Pc

E

Cracks and defects in a material magnify the local stress

Stress concentration at crack tip – stress is higher at crack tip than externally applied stressStress intensity factor k = σA/σ

Materials do not begin to fail at yield stress (theoretical strength of material) – fail at lower values because flaws create higher local stresses

da Vinci – strength of iron wires varied inversely to the wire length -- flaws

Location, A

Recall:

Bonds break when σA=σc

Highest local stress

(describes crack nucleation)

Griffith’s Energy Balance – describes crack propagationGriffith, Irwin, and Orowan Energy balance criteria

0

dA

dW

dA

d

dA

dE s

R is the energy required to break atomic bonds with further crack extension (create two new surfaces). It is a measure of the toughness of a material.E

a

dA

dG

2

The total energy must remain the same for a given increase in crack size (strain energy in plate plus work input)

Therefore,

=

G is called the Energy Release Rate, which is thought of as the driving force trying to extend the crack

So if the driving force equals the resistance (G=R), then the crack will grow.

E

Ba22

0

potential energy due to strain energy

ss aBW 4 work that goes into creating two new surfaces

ss

dA

dWR 2

* Modification substitute psfw for plasticity effects(more energy)

i.e.

R-curves help predict fracture resistance and material toughness• R-curves are studied in literature so we can predict:

(1) the conditions under which a crack will extend(2) if crack growth occurs whether it will result in failure of the

material (unstable growth)

• R-curves can take on different shapes and values, depending on the material, its microstructure, geometry, temperature etc…

A flat R-curve indicates a brittle material.R is ideally an invariant material property.(e.g. glass)

A rising R-curve indicates materials that undergo plastic deformation. (e.g. ductile metals)

Testing resistance to fracture

• Test specimens are used to determine resistance to fracture of various materials

• A stress intensity factor is associated with each kind of specimen• Usually use displacement control• Arrive at the fracture toughness (how much stress is needed for the crack to grow)

Both are Mode I loading(load is normal to crack)

Nature has found a way to improve the strength of materials

Biological materials can have greater mechanical properties than the individual components that make them up (strength, toughness, fracture resistance)

We want to understand nature’s approach to material structuring!

• Hard, brittle mineral crystals embedded in soft, elastic protein matrix

• The load transfer is accomplished largely by the shearing of the protein matrix between the long sides of mineral platelets

• The TSC can be regarded as the primary structure of biological materials

• Affects the mechanical properties of the nanostructure such as, load transfer, stiffness, strength and elastic stability

• Large ratios make up for softness in the protein matrix

• Aspect ratio cannot be infinitely large

h

• Why is the structure of biological materials always at the nanoscale?

• Length Scale:

• When mineral exceeds the length scale material is sensitive to crack-like flaws

• When mineral drops below the length scale failure is governed by the theoretical strength of material

• Protein effectively stabilizes mineral crystals

• At a given volume concentration of protein, the critical stress approaches a constant limited value as the aspect ratio becomes sufficiently large

• Buckling stress in composite nanostructure is proportional to the geometric means of Young’s moduli of protein and mineral

• For nanocomposites, as the mineral bits have nanoscale size, the protein-mineral interfacial area can be enormous

• Interface strength depends on both size and geometry

• The chain structure of proteins is a crucial factor for the strength of the protein-mineral interfaceFigure. Atomistic modeling of protein-mineral

interface strength showing the mechanical behavior of chain molecules and their interaction with the substrate during interface failure.

Whether or not a bone splits or breaks depends on how efficiently short cracks can be prevented from growing into longer ones

Role of micro cracks Crack deflection and crack bridging

5X greater toughness in the transverse orientation compared to the longitudinal orientation

http://www.lbl.gov/publicinfo/newscenter/features/assets/img/MSD-bone-tough/Bone-Transverse-Koester.mov

• hierarchy is inherent in natureo DNA, proteins, cells,

organisms, ecosystems, planets, etc.

• differing structures at the meso, micro, and nano scales all play a role

Example: Crab Exoskeleton-layers of brittle mineral rods organized in a helix-each rod is made of softer protein which are comprised of smaller fibrils

hierarchy of crab exoskeleton

• fractal-bone modelo self-similar layers repeated

N times• bottom-up design process

o design lowest level structure first

o next level structure determined from current level and characteristics wanted

• strengtho by combining different compounds,

shapes, and structures in a material, strength limitations can be exceeded

• toughnesso shielding of crack initiation and

propagation• flaw-tolerance

o lots of small structures handle flaws better than one large structure

•  stiffnesso more hierarchy leads to higher

stiffness• effects of more levels of hierarchy:

o decrease in strengtho increase in fracture energy and flaw-

tolerance

Bone•  platelets in protein matrix

 Wood• complexity from cellular

construction  Seashell (Nacre)• layers of tiles in brick-and-

mortar fashion Tendon• tightly packed arrays of

collagen

bone

wood

nacre

Mechanical Properties• multifunctional material• compact bone for strength and

toughness (structural support for body)

• spongy bone for bone marrow and living cells; also allows for compression in other bone types

• can withstand crack-like flaws at many levels of hierarchy

Hierarchical Organization• compact bone exterior; spongy

interior• osteons are concentric rings of

mineral and collagen • each ring has parallel sheets of fibrils

and mineral plates• tropocollagen forms larger fibrils that

act as a protein matrix• nanocrystals mineralize into plate-

like structures

Mechanical Properties• high strength due to brick-like arrangement• high resilience due to organic

matrix• toughness similar to silicon

o addition of water enhances toughness

• low crack propagation• can undergo microbuckling

Hierarchy• staggered-tile structure• mineral "bricks" in an

organic "mortar"• organic matrix made up of

thin layers of elastic biopolymers

Hierarchy• cellulose packed into microfibrils• bundles of microfibrils packed into

larger macrofibrilso contains regions of crystalline

structure and amorphous regions • large fibrils supported by amorphous

matrix of lignin and hemicellulose• these fibers organize into a number

of cell walls surrounding a given cell

Mechanical Properties• specific stiffness and strength

comparable to steel• microfibril angle plays a large part in

the strength and stiffnesso young trees are more flexible and

have larger angleso older trees have small MFA and

thus stiffer trunks• high toughness similar to nacre

o cracks don't easily propagate perpendicularly

Hierarchy• similar to bone's organization• repeat layers of larger and larger

structures• collagen molecules self assemble

into fibrils• fibrils decorated with proteoglycans

and grouped to form fascicles

Mechanical Properties• connects muscle to bone• has elastic properties• stiffness increases with strain• up to 300x stronger than muscle

o allows for small sizes• fibers provide flexibility

Spider Silk• in nature, needs to absorb high momentum without recoil

and endure high stress from impact• high toughness and extensibility(ability to endure strain

without failure)• strength comparable to steel

Teeth• two layers of protection: enamel and dentin• enamel has high hardness (hardest material in vertibrates)• dentin (similar in design to bone) has high toughness

Feathers• require stiffness and flexibility to endure flight • hollow shaft reinforced with "foam" structure• very light but strong

Chemical properties behind biomimicking nanocomposites

Method to fabricate nanocomposites

Characterization Techniques for Nanocomposites

Limitations

The structure-function harmony of nacre and other hard biological tissues has inspired a large class of biomimetic advanced materials and organic/inorganic composites.

The addition of inorganic components, such as clays, to organic polymers noticely improves the mechanical, barrier and thermal properties of polymers and rubbers.

Finding a synthetic pathway to artificial analogs of nacre and bones represents a fundamental milestone in the development of composite materials.

In the case of organic-inorganic nanocomposites, the strength or level of interaction between the organic and inorganic phases is an important issue.

1. hydrogen bonding, van der Waals forces covalent or ionic-covalent bond

2. polarity, molecular weight, hydrophobicity, reactive groups, and so on of the polymer

3. type of solvent and clay mineral type

Extensive coiling of the polyelectrolyte leads to the formation of loops with macromolecular segments linked together by van der Waals and ionic interactions.

One surface charge on clay can attract positive headgroups from different parts of the chain resulting in loops. Gradually, the polyelectrolyte molecules become significantly deformed due to sliding of the clay platelets over each other to involve ionic bonds.

Chemistry Properties behind nanocomposites

More generally, molecular self-assembly seeks to use concepts of supramolecular chemistry and molecular recognition in particular, to cause single-molecule components to automatically arrange themselves into some useful conformation.

Photograph of the inner side of a green abalone (Haliotis fulgens) shell, showing the iridescent nacre. Shell diameter is ~20 cm.

Ease of preparation

Versatility

Capability of incorporating high loadings of different types of biomolecules in the films

Fine control over the materials’ structure

Robustness of the products under ambient and physiological conditions

Biomimetics

Biosensors

Drug delivery

Protein and cell adhesion

Mediation of cellular functions

Implantable materials

Schematic view of the interface bottom-up synthesis method of crystalline rubeanic acid copper.

Layer-by-layer assembly and supramolecular chemistry were used to create an ultrathin-film platform technology for small-molecule delivery using a hydrolytically degradable polyion (see picture, blue waves) and a polymeric cyclodextrin (see picture, red cups).

The layered organic-inorganic composites were made from montmorillonite clay platelets (C) and polyelectrolytes (P) by the well-established technique of sequential adsorption of organic and inorganic dispersion, often called layer-by-layer assembly (LBL). The general film structure can be represented by the schematic in Fig. 1c.

In nacre, mineral platelets, which are a fewhundreds of nanometers in thickness, interlock to form sheets that are stacked on top of each other in a staggered formation.

Atomic force microscope (AFM)

Scanning electron microscopy (SEM)

Transmission electron microscopy (TEM)

Wide-angle X-ray diffraction (WAXD)

Small-angle X-ray scattering (SAXS)

a, Phase-contrast AFM image of a (P/C) film on Si substrate.b, Enlarged portion of the film in a showing overlapping clay platelets marked by arrows.

e and f,Topographic AFM images of PDDA molecules adsorbed between the clay platelets. Elevated areas of irregular shape represent PDDA coils adsorbed to montmorillonite platelets. Arrows track the partially decoiled macromolecules stretched between the clay platelets. poly(diallyldimethylammonium chloride) (PDDA)

Scanning electron microscopy (SEM) examination (a) of the (P/C)100 film cross-section revealed a layered structure which was conceptually similar to that of nacre.The film was dense and uniform in thickness.

Scanning process and image formationIn a typical SEM, an electron beam is thermionicallyemitted from an electron gunelectron fitted with a tungsten filament cathode.

TEM images showed that the film remained continuous and retained its integrity even when local stress had torn away the epoxy resin serving as an embedding media (b). Perpendicular sectioning slightly expanded the multilayers (c).

Challenging problems in the biomimicking synthesis:

Control the size

Geometry

Alignment of nanostructure

Higher levels of hierarchy