Materials & Polymer Chemistry

Why real materials behave nothing like their ideal crystals

About this course

How structure sets properties in solids and polymers — defects and interfaces, chain statistics and polymerisation, the glass transition and crystallinity, mechanical behaviour, electronic materials and soft matter, and the role of processing history.

What you will be able to do

  • Explain how point defects, doping and interfaces control the properties of a crystal
  • Calculate molecular-weight averages and relate them to the polymerisation that produced them
  • Use chain statistics to explain rubber elasticity, the glass transition and partial crystallinity
  • Apply elasticity, Griffith fracture, time-temperature superposition and the rule of mixtures
  • Describe how band gaps, doping and self-assembly give electronic and soft materials their function

What this course covers

  • Theoretical shear strength bound from bonding
  • The factor of ~10,000 and the whisker experiment
  • Dislocation mechanism and the Peierls–Nabarro formula
  • Non-monotonic strength vs. defect density
  • Hall–Petch law and its self-announced limit
  • Defect-controlled vs. ideal-structure properties: course framework
  • Random walk model of polymer size
  • Gaussian end-to-end distance distribution
  • Real chain stiffness and the Kuhn segment
  • Polymer coil emptiness and entanglement
  • Entropic origin of rubber elasticity
  • Gaussian model's limits and derivative-sensitivity
  • Polyethylene crystal anisotropy and stiffness
  • Voigt and Reuss bounds for two-phase stiffness
  • Orientation as the dominant stiffness loss mechanism
  • Linearity: strain-dependent secant modulus
  • Isotropy: flow-induced orientation in molded parts
  • Three qualifiers of modulus and the snap-fit worked case
  • Origin of electronic bands in solids
  • Band gap as an exponent, not a category boundary
  • Polyethylene as a perfect insulator — and why real insulators fail
  • Doping and the hydrogen-atom coincidence
  • Real reason for doping: composition control over temperature dependence
  • Doping in polymers vs. crystals — mechanism transfer warning
  • Step-Growth Polymerization and the Carothers Equation
  • The Flory–Schulz Distribution and Dispersity of Step-Growth
  • Stoichiometric Imbalance: The Ceiling You Cannot Outrun
  • Chain-Growth Polymerization and the Poisson Distribution
  • Forging the Fingerprint: Blending Two Uniform Polymers
  • Synthesis: Mechanism as Specification
  • Peierls Instability and the Band Gap of Polyacetylene
  • Doping in Conducting Polymers as a Redox Reaction
  • Record vs. Usable Material: Polyacetylene vs. PEDOT:PSS
  • Decomposing the Conductivity Gap to Copper: Carriers vs. Mobility
  • Disorder as the Design Variable: Orientation and Conjugation Length
  • Worked Case: Specification-Driven Doping Level for Antistatic Coatings
  • Necking instability and Considère's condition
  • Neck stabilization by strain hardening in polymers
  • Neck propagation, natural draw ratio, and toughness
  • Inglis stress concentration and the Griffith flaw theory
  • Breakdown of Griffith's surface energy in polymers
  • Rate dependence of toughness and slow crack growth
  • Thermodynamic Inevitability of Point Defects
  • Point vs. Line Defects: Thermodynamic vs. Historical
  • Bulk-Average vs. State-Based Properties
  • Nine-Nines Purity as Arithmetic
  • Color as a Defect-Controlled Property
  • The Defect as the Device: Yttria-Stabilised Zirconia
  • Glass transition vs. first-order phase transition
  • Ehrenfest classification and the Prigogine-Defay ratio
  • Measured Prigogine-Defay ratios and the glassy state as history-dependent
  • TG as a timescale crossing and the WLF equation
  • Cooperative relaxation and fragility classification
  • Window-pane myth: bounding an unknown quantity
  • Modulus as a function of time
  • Relaxation spectrum vs. single relaxation time
  • Time–temperature superposition and the WLF shift factor
  • Identity of the 3.14 K/decade number across two lectures
  • Boltzmann superposition and power-law recovery
  • Ceiling of time–temperature superposition
  • Entropic crystallization of hard spheres
  • The hydrophobic effect as entropy of the solvent
  • The packing parameter and morphology prediction
  • Onsager's excluded-volume theory for rod alignment
  • Unifying principle: entropy of the unobserved degree of freedom
  • Course context: self-assembly vs. imposed structure, and the road to kinetics
  • Salt-induced sphere-to-cylinder transition (worked formulation case)
  • Polymer molecular weight as a distribution
  • Most probable distribution in step-growth polymerization
  • Living polymerization and Poisson chain-length distribution
  • Same MN, tenfold difference in melt viscosity
  • One subpopulation counted two ways: the factor-of-eleven mechanism
  • Dispersity as a design variable: blending and bimodal grades
  • Matching the right average to the right property
  • Why polymer crystallization cannot finish
  • Chain folding, tie molecules, and partial crystallinity
  • Crystallinity as a controlled process variable
  • Gibbs–Thomson equation and melting point as a process variable
  • Model-dependent crystallinity and the rigid amorphous fraction
  • Worked case: quench vs. slow-cool HDPE moulding
  • Phase contrast as the determinant of bound usefulness
  • Bounds ratio as a function of contrast alone
  • Physical meaning of Voigt and Reuss bounds
  • Critical fiber length and load-transfer efficiency
  • Halpin–Tsai equations and the fitted-parameter problem
  • Arrangement over chemistry: module synthesis and reverse composites
  • Interface geometry and atom fraction
  • Temper embrittlement: mechanism and reversibility
  • McLean isotherm and boundary segregation
  • Why purity barely helps: the 'nearly free' arithmetic
  • Free-surface segregation and catalysis/sintering
  • Two correct measurements, one specification principle
  • The Deborah Number: Material Clock vs. Process Time
  • The Freezing Line: Where a Process Loses Contact with the Material
  • WLF Constants as Physical Theory: Free Volume Prediction
  • Differential Free Volume and Residual Stress in Moulded Parts
  • Four Frozen-In Structural Variables and Their Timescales
  • Composition as Permission Slip: Course Synthesis

Syllabus

  1. Defects, Distributions and Interfaces

    1. L1 · Ideal Crystals and Real Materials: the Factor of a Thousand
    2. L2 · Defects Are Not Flaws: Point Defects, Doping and Colour
    3. L3 · Distributions, Not Averages: Molecular Weight and Why the Mean Lies
    4. L4 · Interfaces: Grain Boundaries, Surfaces, and Where Materials Fail

  2. Polymer Structure

    1. L5 · Chain Statistics: the Random Walk That Predicts Rubber
    2. L6 · Polymerisation: How the Distribution Is Made
    3. L7 · The Glass Transition: a Transition That Is Not One
    4. L8 · Crystallinity in Polymers: Why Nothing Is Fully Crystalline

  3. Mechanical Behaviour

    1. L9 · Elasticity, and the Assumption Inside a Modulus
    2. L10 · Yield, Fracture, and Griffith's Crack
    3. L11 · Viscoelasticity: Time and Temperature Are the Same Variable
    4. L12 · Composites, the Rule of Mixtures, and Where It Fails

  4. Electronic Materials, Soft Matter and Processing

    1. L13 · Bands, Gaps and Doping: One Atom in a Million
    2. L14 · Conducting Polymers: Disorder as the Design Variable
    3. L15 · Soft Matter: Self-Assembly, Colloids and Liquid Crystals
    4. L16 · Processing History: the Same Composition, Two Materials