Exact enumeration of selfavoiding walks on the cubic lattice terminally attached to an interface Self-avoiding walks on a lattice with m inner contacts are investigated as a model of a polymer chain in solutions for different solvents. Values of several critical exponents are estimated from the exact enumeration data for up to 22 and 20 steps on the square and tetrahedral lattices, respectively. The values of v and r estimated for neighbor-avoiding walks (m = 0) are in good agreement with those for self-avoiding walks. However, such agreement is not found in ~, the exponent for the end-distance distribution; it suggests a possibility that ~ is ruled out from the hypothesis that self-and neighbor-avoiding walks are in same class of universality in contrast to v and r. The limiting value of average m per step q is proposed as a parameter to describe the compactness of self-avoiding lattice walks.

The behaviour of the Zimm model for flexible chain dynamics is illustrated by the dielectric response for arbitrary field strength and by a calculation of the intrinsic viscosity from an appropriate tinie correlation function. The stochastic dynamics of a chain with constant bond Iengths and weak correlations between adjacent bond directions are developed and applied to the dielectric experiment. Introduction of rotational diffusion in parallel to local conformational changes appears to offer a useful approach to the problem of internal viscosity.* supported by a grant from the U.S. National Science Foundation 182 i3flat = -VT fvo + VT(kT/()H [Vf + f VUJkT+ 3b-2fAr],

The excluded-volume effect in a randomly ooiled polymer is investigated by the method of cumulants. The spatial expansion factor a 2 of a polymer chain is expanded in a power series:where z is the usual excluded-volume parameter, and a general formula for Cn is given. By means of a "ladder" approximation C. is calculated to be 1.3438. Contributions of small and giant clusters in a polymer chain to a 2 are discussed. The above power series is predicted in the ladder approximation to converge for O~z~N, where N is the total number of segments constituting the polymer chain. We are unable, however, to dispose of the possibility that in general C .. for 5~n«N includes a term proportional to Nl/2 logN.

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The development of the molecular theory of configurational relaxation phenomena in polymers is briefly reviewed with the emphasis on the method of generalized diffusion equation and Rouse's model.Various dispersion phenomena in polymeric systems such as of dynamic viscosity, of dynamic Young's modulus and of dynamic bulk modulus are elucidated on the basis of the model theory. The present theoretical situation of the dispersion phenomena in crystalline polymers is also discussed. at University of Pennsylvania Library on April 12, 2015 http://ptps.oxfordjournals.org/ Downloaded from * More precisely [71] = kM(Y, (0.5