BE 450 – Biomaterials & Biocompatibility: Defects, Crystallinity, and Thermal Transitions

Biomaterial Design ↔ Biocompatibility

• Bulk material properties are the bridge between material design and biological response.
  • What engineers manipulate (micro-/nano-structure, processing) ultimately governs biocompatibility.
  • Iterative loop: Material ➜ Analysis ⇄ Biocompatibility.

Physical Properties of Polycrystalline Materials

• Polycrystalline property set emerges from the interaction of many crystals (grains).
• Four defect classes dictate behaviour:
  1. Point (0-D)
  2. Line / Dislocations (1-D)
  3. Planar / Interfaces (2-D)
  4. Volume (3-D)
• Defect presence and density are processing-controlled (thermal history, mechanical working, surface treatment).
  • Quantification tools: electron microscopy, X-ray diffraction.

Point Defects & Atomic Diffusion

• Empty or misplaced lattice sites change electrical / mechanical response.
• Diffusion view = sequence of atomic jumps.
  • Jump requirements:
  • Adjacent empty site.
  • Sufficient activation energy (fraction ↑ with temperature).
• Modes of diffusion:
  • Vacancy diffusion (metals): atom ↔ vacancy exchange.
  • Net flux opposite to vacancy flux.
  • Interstitial diffusion (metals): small atoms (H, C, N, O) migrate between interstitials; faster than vacancy.
  • Ceramics: simultaneous movement of ions + vacancies to retain electroneutrality.
• Fick’s First Law (steady state): J = \frac{1}{A}\frac{dM}{dt} = -D \frac{dC}{dx} D = D_0 e^{\frac{-Q}{RT}}
  • Q = activation energy; R = 8.314\,\text{J·mol}^{-1}\text{K}^{-1}; T = absolute temperature.

Linear Defects (Dislocations)

• Created mainly by plastic deformation during fabrication.
• Categories & notation (Burger vector b, dislocation line \ell):
  • Edge (⊥): extra half-plane terminates; b ⟂ \ell.
  • Screw (∏): shear creates helical ramp; b ∥ \ell.
  • Mixed: orientation of b w.r.t \ell varies along line.
• Burger circuit: closed atomic loop used to measure b (magnitude & direction invariant for a given defect).
• Fundamental characteristics:
  1. Produce local compressive/tensile strains.
  2. Cannot terminate inside a perfect lattice – must end at surface, another dislocation, or form a loop.
  3. Glide (slip) plane contains b and \ell; high atomic-density planes.
• Mechanical implications:
  • Dislocation motion = mechanism for plastic deformation.
  • Even low dislocation densities drastically lower the yield stress required for slip.

Slip Planes & Slip Systems

• Slip = plastic deformation via dislocation glide.
• Slip system = slip plane family + slip directions.
  • Body-Centered Cubic (BCC): {110} planes, 6 \times 2 = 12 systems (e.g., α-Fe, Mo).
  • Face-Centered Cubic (FCC): {111} planes, 4 \times 3 = 12 systems (Al, Cu, γ-Fe).
  • Hexagonal Close-Packed (HCP): {0001} basal, 1 \times 3 = 3 systems (Mg, α-Ti) ➜ limited slip, more brittleness.
• Ceramics: longer b, slip not on highest-density planes due to charge neutrality ⇒ less plasticity, brittle fracture.

Planar Defects – Surfaces & Grain Boundaries

• Surface atoms have unsatisfied bonds ⇒ high surface free energy (γ). Systems minimise γ via reactions, adsorption.
• Grain boundaries (GBs): interface mismatch between differently oriented grains.
  • Atoms there have lower coordination, high energy.
  • Larger grains ↓ total GB area ↓ corrosion susceptibility.

Types of Grain Boundaries

• Low-angle (LABG): θ < 11^\circ
  • Composed of aligned arrays of dislocations.
  • Examples:
  • Tilt boundary: rotation about axis in boundary plane (edge dislocation array).
  • Twist boundary: rotation about axis ⟂ boundary plane (screw array).
• High-angle (HABG): severe misorientation, higher energy ➜ preferred corrosion sites.
• Twin boundary: mirror image across plane; can strengthen materials (block dislocation motion).

Volume Defects – Porosity & Precipitates

• 3-D zones where long-range order lost.
  • Precipitates: clusters of impurities.
  • Voids/pores: vacancy aggregates; intentional via porogens in biomaterials.

Porogens (Creating Controlled Porosity)

1. Solid (NaCl, gelatin, wax):
   • Embed ➜ fabricate ➜ leach or melt out.
   • Amount dictates porosity; particle shape controls pore geometry.
2. Gaseous (N₂, CO₂):
   • Gas evolution during polymerisation; bubble foaming.
   • Timing/flow alter size & interconnectivity.
3. Fibre meshes (metals/polymers):
   • Draw fibres ➜ weave/bond ➜ dissolve/etch fibres post-processing.

Advantages of pores

• Fluid/gas exchange, tissue in-growth, density reduction.
  Drawbacks
• Lower mechanical strength, altered degradation/corrosion profiles.

Physical Properties of Semicrystalline Materials

• Polymers exhibit wide crystallinity range due to complex chains.
• Degree of crystallinity influences mechanical & degradative behaviour.

Factors Governing Percent Crystallinity

• Side group size: bulky substituents hinder chain packing.
• Chain branching: branches hinder alignment.
• Tacticity: atactic < isotactic/syndiotactic for ordering.
• Copolymer mer regularity: more regular ➜ easier crystallisation.

Chain-Folded Lamella & Spherulites

• Lamella: basic crystalline plate; multiple chains fold back & forth.
• Spherulite: 3-D radial aggregate of lamellae separated by amorphous regions (chain folds, tie molecules).

Defects in Polymer Crystals

• Dislocations exist but b long; slip mainly along chain axis; minimal role in polymer deformation (rubbery flow dominates).
• Planar/volume defects analogous to metals: spherulite boundaries act like GBs; porosity engineered with porogens.

Thermal Transitions

• Deformation in non-crystalline solids = viscous flow obeying
  \tau = \eta \dot{\gamma}

Metals & Crystalline Ceramics

• Sharp melting point Tm: above which lattice order collapses → viscous flow; below Tm: rigid solid.

Amorphous Ceramics (Glasses)

• No distinct T_m; viscosity rises progressively.
• Glass transition temperature T_g: below this, glassy & brittle; above, bond clusters of ‘broken bonds’ enable flow.

Polymers – General Behaviour

• Depending on crystallinity and temperature, polymer can be glassy, rubbery, or liquid.

Crystalline Polymers

• Possess T_m analogous to metals.
• Influencing variables:
  • Secondary bonding (↑ bonds ⇒ ↑ T_m).
  • Percent crystallinity (↑ crystallinity ⇒ ↑ T_m).
  • Branching (↑ branching ⇒ ↓ T_m).
  • Molecular weight (↑ MW ⇒ ↑ T_m – fewer chain ends).

Amorphous & Semicrystalline Polymers – Glass Transition T_g

• Below T_g: glassy, brittle.
• Above T_g: chains mobile → rubbery.
• Factors raising T_g (reduce chain mobility):
  • Rigid backbone (C-C vs. flexible C-O).
  • Bulky side groups (steric hindrance).
  • Polar side groups (inter-chain attraction).
  • High molecular weight (entanglement).
  • Cross-linking.
• Example methacrylate series:
  • Poly(methyl methacrylate) T_g \approx 100$–$120^{\circ}\text{C} > ethyl (65 °C) > propyl (35 °C) > butyl (20 °C).

Molecular Weight Effects on Tm & Tg

• Fewer chain ends at high MW ⇒ more cooperative motion required ⇒ higher transition temps.
• Branching lowers T_m by reducing van der Waals/hydrogen bonds.

Semicrystalline Polymers – Crystallisation Temperature T_c

• On cooling, chains have enough mobility above Tg to organise into lamellae at Tc (exothermic).
• Annealing protocol: heat to T_c, hold for time t, slow cool.
• Degree of crystallinity evolution (Avrami): X(t) = 1 - e^{-kt^{n}}
  • n indicates nucleation/growth mode (1 D rods, 2 D discs, 3 D spheres, etc.).

Thermal Analysis Techniques

• Determine transition temps, composition, degradation.
  1. Thermogravimetric Analysis (TGA): mass vs. T; reveals decomposition, solvent loss, filler content.
  2. Differential Scanning Calorimetry (DSC): heat flow vs. T; detects Tg, Tm, T_c, crystallinity (% area under peaks).

Practical / Ethical / Biological Implications

• Tailoring defects allows engineers to:
  • Optimise strength-to-weight (orthopaedic implants, stents).
  • Promote tissue integration via controlled porosity while balancing mechanical integrity.
  • Control degradation rate (e.g., Mg alloys, biodegradable polymers).
• High-energy GBs & surfaces are preferential corrosion / protein adsorption sites – crucial for long-term biocompatibility.
• Thermal properties guide sterilisation methods (steam vs. gamma), storage, and in-vivo performance (e.g., shape-memory polymers operating between T_g and body temperature).