Prerequisites: MATE 202 or MATE 235, MATH 231 or MATH 335
Course Description: Structure property relations are developed. Types of microstructures discussed and
unusual aspects of polymer properties presented. Topics covered are viscoelasticity;
bio- and synthetic polymers; statistics as an explanation of nature; gelation; molecular
weight distributions; condensation and addition synthesis; chemical kinetics; random
walks; chain statistics; viscosity; prions; diffusion; friction; reptation; glass
transition.
Required Textbooks:The Structural Basis of Polymer Properties by J. McCoy; Biophysics DeMYSTiFied by Goldfarb..
Recommended Textbooks: Introduction to Polymers by Young and Lovell; Introduction to Physical Polymer Science by Sperling
Course Topics
1. Proteins, Polymers and Soap Films
Meaning of structure in polymeric systems, comparison of biopolymer and synthetic
polymers; self assembled materials (soap films, Langmuir films, cell membrane)
2. Mechanical Properties of Spider Silk and Other Polymers
Meaning of stress and strain; Young’s modulus; stress strain of spider webs; comparison
of mechanical properties of polymers and metals; common fibers (nylon, Kevlar); rubber
elasticity; viscoelasticity; Lennard-Jones to calculate yield and Young’s modulus.
Use of statistics to explain nature; Quetelet’s average man; average from probability
distribution; number average; weight average; polydispersity index
5. Synthesis: Condensation Reactions
Example of condensation reactions (nylon, glucose); role of glucose in biology; extent
of reaction; analysis of cond. reactions for average chain; Carother’s formula; Flory/Stockmayer
formula; Walker analysis
6. Gelation and Fractals
Viscoelastic effects (open siphon and Weissenberg); scaling theory; gels; hydrogels;
use of Carother’s and Flory/Stockmayer theories to predict gel point
7. Kinetics and Predator-Prey Equations
Introduction of chemical kinetics using predator-prey equations; kinetics of condensation
reactions; time dependence of extent of reaction; role of catalyst
8. Synthesis: Addition (Free Radical) Reactions
Free radicals in biology and polymers; mitochondria; enzyme as catalyst; analysis
of molecular weight from kinetics
9. Single Chain Statistics and Random Walks
Structure of chains; scaling theory; dilute to semi-dilute crossover; liquid-liquid
phase separation; random walks; Brownian motion; self-avoiding random walks; traveling
salesman problem
10. Chain Entropy and the Nature of Time
Entropy as measure of forward direction of time; entropy from heat flow or diffusion;
chain end to end distribution from thermodynamics, statistical mechanics and Hooke’s
Law
11. Elasticity, Free Energy and Prions
Prions to introduce single chain force-extension; relation between force-extension
and free-energy; free energy description of rubber elasticity; viscoelasticity in
peel test; time-temperature superposition; Vogel-Fulcher description of glass transition;
Kuhn mapping to Gaussian chain
12. Free Energy, Viscosity and the Surface-Volume Ratio
Surface volume ratio in biology and materials science; Free energy surface volume
relations; Flory analysis of scaling of chain in good solvent; formal treatment of
viscosity; non-Newtonian liquids; Krieger-Dougherty treatment of effect of filler
on viscosity; Einstein viscosity equation; Mark-Houwink analysis of effect of chain
length on viscosity
13. Diffusion, Friction, Drag and Reptation
Inertial and viscous drag forces; Reynolds Number; Fick’s Law; Stokes-Einstein relation
between diffusion coefficient and drag coefficient; stochastic treatment of diffusion;
Rouse and Zimm models; reptation treatment of polymer viscosity
14. The Glass Transition
Divergence of viscosity; Vogel-Fulcher equation; Doolittle equation; Free volume;
velocity autocorrelation function; caged particles; mode-coupling theory; energy landscape.