Lectures: 20 h - Preceptorship: 6 h

Objectives

This course deals with the statistical physics approach to the study of polymers properties with an emphasis on strengthening intuitive understanding. The aim is to offer the students a good intuition for the system, the length scales, and the time scales.

Syllabus

We focus on the ideas, mechanisms, driving forces, understanding of competing interactions. Then, we develop simple calculations which are almost always compared to experiments for verification.

1. Entropy of polymer chains (in relation with the Statistical mechanics module)
   
   
   • Intrinsic dimensions of a polymer chain (ideal/real, stretched/confined, measurement of size by scattering
     
   • Polymer blend and polymer solution (free energy of a binary mixture: entropy vs enthalpy, exclude volume concept for polymer solutions: chain size and correlation length in good solvent)
     
   • Rubber elasticity (affine network model and its limits, swelling properties of a polymer
   
   
2. Dynamics of conformational changes
   
   
   • Thermal energy /energy of weak interactions (van der Waals, H bonds...)
     
   • Time of measurement/ time of conformational changes
     
   • Different length scales: i) chain diffusion : motions of an entangled chain (example of the reptation) ; ii) glass transition: motions at length scales from the Kühn segment to the entanglement distance ; iii) characteristic times of chain rearrangement & mechanical perturbation: temperature and time dependence of the modulus E*(T, w) , viscoelasticity and time temperature equivalence, WLF law.

Preceptorship

• Dimensions of a chain: conformations and properties in solution
  
• Vitreous transition
  
• Rubber elasticity

Links to other course modules

The concepts are presented in relation to other courses: Statistical mechanics, Optics, Mechanics of solids and materials II and Crystalline materials.

Requirements : Stress-strain response of visco-elastic solids ; thermodynamics : entropy, internal enregy, statistic of a random walk ; short range interactions : Van der Waals, H bond, etc. ; thermodynamics of binary mixtures ; conformations and configurations of a polymer chain.

Evaluation mechanism : Exam written in English in 2 parts (answers in English or French allowed): part I, 10 concept questions; part II, 5 short problems.

Last Modification : Thursday 7 September 2017