ENAS 606 : Polymer Physics
Professor
Chinedum Osuji
302 Mason Lab, 432-4357, chinedum.osuji@yale.edu
   
Description
This course covers the static and dynamic properties of polymers in solution, melt and surface adsorbed states and their relevance in industrial polymer processing, nanotechnology, materials science and biophysics. Starting from basic considerations of polymerization mechanisms, control of chain architecture and a survey of polymer morphology, the course also addresses experimental methods for the study of structure and dynamics via various scattering (light, x-ray, neutron) and spectroscopic (rheology, photon correlation spectrscopy) methods as an integral component of polymer physics.
   
Course Topics
Polymerization basics
Polymer morphology
Static properties - Chain statistics and structure
Solution and melt thermodynamics
Scattering and rheology as tools in polymer physics
Lab characterization of structure, thermodynamics and dynamics
Gelation and network formation
Polymer dynamics
   
TA
TBD, if required
   
Prerequisite
Undergraduate courses in physical chemistry, thermodynamics and basic physics, or the permission of the instructor
   
Class
Tuesdays and Thursdays, 11:35a-12:50p, 104 ML
   
Office Hours
As required
   

Textbook(s)
“Polymer Physics” by M. Rubinstein and R. H. Colby
   
Additional reading
“Scaling Concepts in Polymer Physics” by P. G. de Gennes
   
“Principles of Polymer Chemistry” by P. J. Flory
   
“The Theory of Polymer Dynamics” by M. Doi and S. F. Edwards
   
“Introduction to Polymers” by R. J. Young and P. A. Lovell
   
“The Structure and Rheology of Complex Fluids” by R. G. Larson
   
“Principles of Polymerization” by G. Odian
   
“Methods of X-ray and Neutron Scattering in Polymer Science” by R-J. Roe
   
Exams
There will be 3 exams, incremental in nature, based on material covered during lectures and on problem sets.
   
Homework
There will be periodic homework assignments throughout the semester (≈ 5) which should be submitted at the start of class on their due date. Students are permitted to work cooperatively on assignments, but each person must submit his or her own individually prepared results.
   
Lab assignment
There will be three topics for laboratory investigation. Students will be assigned in groups to one topic each and will submit a lab report of their work.
   
In class discussion
In addition to general in-class participation, each student will give one 20 minute presentation of a seminal paper or recent publication of interest during the course of the semester.
   
Grading - a rough guideExam I 20 points
   
Exam II 20 points
   
Exam III 20 points
   
Graded Homework20 points
   
Lab assignment 10 points
   
In class discussion 10 points
   
Total 100 points
   

Lecture Schedule (subject to change!)

Lecture #Date Lecture Topic Chapter(s)
    
1 T Jan 13 Polymerization basics –
    
2 R Jan 15 Polymerization basics; Polymer Morphology –
    
Structure
    
3 T Jan 20 Ideal, Gaussian conformations 2
    
4 R Jan 22 Models for coil structure 2
    
5 T Jan 27 Entropic free energy 2
    
6 R Jan 29 Non-ideal chains I 3
    
7 T Feb 03 Non-ideal chains II 3
    
8 R Feb 05 Adsorption and confinement effects 3
    
9 T Feb 10 Intro to Scattering Methods –
    
R Feb 12 Literature discussion I –
    
T Feb 17
Exam I
    
Thermodynamics+
    
10 R Feb 19 Lattice models, Flory-Huggins theory 4
    
11 T Feb 24 Stability and Demixing 4
    
12 R Feb 26 Microphase separation in block copolymers –
    
13 T Mar 03Osmotic Pressure; Solvency 4,5
    
14 R Mar 05Polymer Brush Theory –
    
F Mar 06
New England Complex Fluids Workshop@Yale
    
T Mar 10
Spring recess
    
R Mar 12
Spring recess
    
T Mar 17
Spring recess
    
R Mar 19
Spring recess
    
T Mar 24Literature discussion II –
    
15 R Mar 26Gelation and Network Formation 6
    
16 T Apr 1 Rubber Elasticity and Linear Viscoelasticity 7
    
17 R Apr 3 Intro to Rheological Methods –
    
T Apr 8
Exam II
    
Dynamics
    
18 R Apr 10 Unentangled Dynamics I 8
    
19 T Apr 15 Unentanged Dynamics II 8
    
20 R Apr 17 Glassy Dynamics; Tg –
    
21 T Apr 22 Entangled Dynamics I 9
    
22 R Apr 24 Entangled Dynamics II 9
    
23 T Apr 29 Literature discussion III –
    
24 R May 1 TBD –
    
~ May 10
Exam III
    

Course Topics - Detail

  1. Principles of Polymerization [1-2 lectures]
    1. Step growth and chain growth mechanisms
    2. Anionic, radical and modern living chain polymerizations
    3. Molecular weight distributions; characterization by osmotic pressure, light scattering, intrinsic viscosity
  2. Polymer Morphology [1-2 lectures]
    1. Crystalline and semi-crystalline polymers; Liquid crystalline polymers
    2. Self-assembly by microphase separation of block copolymers
    3. Morphology of polymer thin films vs. bulk - surface influence
  3. Static Properties of Polymers [4-5 lectures]
    1. Conformations of Ideal Chains
      1. Freely rotating, worm-like, hindered rotation and rotational isomeric state chain models
      2. Random walk statistics, radius of gyration, end-to-end distance distributions
      3. Free energy of an ideal chain
      4. Measurement of single chain structure by scattering
    2. Conformations of Real Chains
      1. Excluded volume and self-avoiding random walks
      2. Flory theory of polymers in good solvents
      3. Deformation of real chains by tension and compression
      4. Adsorption of single chains
      5. Temperature effects on real chains
        1. Temperature dependence of coil size
        2. Flory theory of polymers in poor solvents
        3. Second virial coefficient
      6. Dilute solution scattering
  4. Thermodynamics of Blends and Solutions [2-3 lectures]
    1. Flory interaction parameter; Flory-Huggins/lattice models for polymer mixing
    2. Experimental investigations of binary mixtures; determination of interaction parameters
    3. Osmotic pressure and osmotic compressibility
    4. Spinodal and binodal decomposition; critical phenomena
    5. Dilute and semi-dilute regimes
    6. Measuring chain conformations in semi-dilute regime
    7. Polymer brushes and multi-chain adsoprtion
  5. Gelation and Network Formation [3 lectures]
    1. Percolation models of gelation
    2. Mean-field and scaling models for gelation
    3. Rubber elasticity - entangled and unentangled systems
      1. Edwards and Mooney-Rivlin models
    4. Linear viscoelasticity
      1. Maxwell and Voigt models
      2. Stress relaxation; Creep and creep recovery
      3. Boltzmann superposition
      4. Oscillatory shear and steady shear deformation
  6. Introduction to Scattering and Rheological Methods [2-3 lectures]
    1. Structure and Dynamics via Scattering
      1. Elastic and inelastic scattering
      2. Rayleigh ratios and mass determination; Zimm plots
      3. Structure factors and form factors; Debye function
      4. Guinier and Porod/fractal regimes
      5. Time-correlation spectroscopies
    2. Dynamics via Rheology
      1. Linear and non-linear regimes
      2. Zero-shear viscosity; Einstein viscosity for hard spheres in solution
      3. Frequency dependent viscoelasticity
  7. Unentangled Polymer Dynamics [4 lectures]
    1. Rouse and Zimm models
    2. Intrinsic viscosity
    3. Relaxation modes
    4. Semi-flexible chain modes
      1. Bending energy and dynamics
      2. Tensile modulus and stress relaxation
    5. Temperature dependence of dynamics
      1. Time-temperature superposition
      2. Glassy dynamics
    6. Dynamic scattering
  8. Entangled Polymer Dynamics [4 lectures]
    1. Entanglements and reptation in polymer melts
      1. Relaxation times and diffusion
      2. Stress relaxation and viscosity
    2. Reptation in semi-dilute solutions
    3. Dynamics of a single entangled chain
    4. Many chain effects - constraint release
    5. Entanglement in worm-like micelles