| Lecture 1: | Read up on history of polymers (handout, Pt3 Major Option "Struc.-Prop. Cond. Mat.", preface to the books by Strobl, de Gennes...) A very interesting "popular" book is by Herbert Morawetz: Polymers: the origins and growth of a science |
| Lecture 2: | Clarify the physical differences and approximations involved in each different model of polymer chain
Slides 11-12: follow the derivation, especially the role of N>>1 in permitting the expansion at small (kb) |
| Lecture 3: | Slide 13: revise Pt2 "Therm. Stat. Phys." handout/examples 2; complete the derivation of
P(Rx); reproduce the 3D version of P(R)
Revise Pt2 "Therm. Stat. Phys." handout/examples 2 on the definition and forms of partition function Z; Revise (or find/read up) the diffusion equation and its solution (e.g. Pt2 TP1 option handout) Revise Pt1B "Quantum Mech. I" for Schrodinger eq. in general and sec.5-1 for free particle between reflecting walls |
| Lecture 4: | Revise "Electromagnetism" for characteristics of plane and spherical waves (also
radiation);
Go through and try connecting together all forms of structure factor S(q) you've seen so far; Reproduce the derivation of Rg and S(q) on slides 23-24, plot the Debye scattering function; |
| Lecture 5: | Revise Pt2 "Therm. Stat. Phys." handout/examples 3 on the virial expansion and 2nd virial coefficient B2 (also the question 1.8 on v.d.Waals gas expansion) |
| Lecture 6: | Follow the calculation and plot spinodal and binodal phase boundaries for a Flory-Huggins
model of phase separation with one component a polymer of length N=20, say.
Read up (e.g. Strobl, Chapter 3) on nucleation-growth and spinodal-decomposition mechanisms of phase separation |
| Lecture 7: | Study the suggested review article by F.S. Bates |
| Lecture 8: | Reproduce the Flory-style estimate of the brush height and relate it to the
expression for excluded-volume potantial and the Flory's estimate of the chain size in good
solvent, R~N3/5. Study the suggested review article by S.T. Milner |
| Lecture 9: | Revise the portion of Pt3. Major-option course "Structure and properties of Cond. Mat." related to glass and crystallisation of polymers; cf. the current handout on this topic |
| Lecture 10: | Follow the calculation of the average rubber-elastic free energy density, in particular the
quenched averaging procedure. Try obtaining your own crude estimate for the rubber modulus m = cx kT of a network with strands, say, 100 monomers long (at room-T). |
| Lecture 11: | Definitions of different response kinds, time vs. frequency dependence. Compare the "Linear response" and "Fluctuation-dissipation" arguments with their form used in Thermal and Statistical Physics |
| Lecture 12: | Single-relaxation time maths: derive the time- and the frequency dependent response
functions. On Langevin Equation - see how it arises in different systems, the role of thermal noise, the limit of "overdamped" motion (compare with short-time "inertial or "ballistic" motion). |
| Lecture 13: | Make clear the concept of Fourier transformation from the chain arc length variable
(monomer number) to a set of collective modes; clarify the role of boundary condition on
free chain ends. Verify how the "zero" Rouse mode becomes a free diffusion, while all others correspond to a diffusion under a spring force (role of non-local interaction of a given monomer with its neighbours, leading to the square-gradient and p2-terms. List increasing Rouse modes and their decreasing relaxation times; be able to change between "spring constant" k/kBT and "step length" b forms of writing - why are they equivalent? |
| Lecture 14: | Make a connection between the tube model concept and the (unrestricted) Rouse modes
with high-p (of small groups of monomers) - what is Ne and
te. How do all relaxation times depend on overall chain length and "why"? Colloids: what is the role of particle polydispersity and shape anisotropy? |
| Lecture 15: | Try plotting the sum of the three potentials in DLVO approximation against r (take v.d.Waals as 1/r and then 1/r6 and take Debye length 1/k=2 and then ~10; for particle radius a=1) to see how the change of parameters generates different minima and maxima. |