Configurational statistics

Volkenstein, M. V. Configurational statistics of polymer chains. New York Interscience 1963... 

M.V. Volkenstein, Configurational Statistics of Polymeric Chains, Interscience, New York, 1963. 

The statistical basis of diffusion requires arguments that may be familiar from kinetic molecular theory. Elementary concepts from the theory of random walks and its relation to diffusion form the third topic, which is covered in Section 2.6. As is well known, the random walk statistics can also be used for describing configurational statistics of macromolecules under some simplifying assumptions this is outlined in Section 2.7. 

Response of the mean square dipole moment, < J2>, to excluded volume is evaluated for several chains via Monte-Carlo methods. The chains differ in the manner in which dipolar moment vectors are attached to the local coordinate systems for the skeletal bonds. In the unperturbed state, configurational statistics are those specified by the usual RIS model for linear PE chains. Excluded volume is introduced by requiring chain atoms participating in long-range interactions to behave as hard spheres. 

The influence of the chain expansion produced by excluded volume on the mean-square optical anisotropy is studied in six types of polymers (PE, PVC, PVB, PS, polylp-chlorostyrene), polylp-bromostyrenel. RIS models are used for the configuration statistics of the unperturbed chains. The mean-square optical anisotropy of PE is found to be insensitive to excluded volume. The mean-square optical anisotropy of the five other polymers, on the other hand, is sensitive to the imposition of the excluded volume if the stereochemical composition is exclusively racemic. Much smaller effects are seen in meso chains and in chains with Bernoullian statistics and an equal probability for meso and racemic diads. 

A comparison is presented between the behavior of unperturbed stars of finite size whose configurational statistics are evaluated by R1S theory and the Kratky-Porod wormlike chain model. Emphasis Is placed on the initial slopes of the characteristic ratio, C, or g when plotted as a function of the reciprocal of the number of bonds, n. 

N 020 "Conformational Energies and Configurational Statistics of Copolypeptides containing L-Proline"... 

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Configurational Statistics of Polysaccharide Chains. Part I. Amylose"... 

Dobson, G. R., and M. Gordon Configurational statistics of highly branched polymer systems. J. Chem. Phys. 41, 2389 (1964). 

Here NA and NK are the concentrations of molecules A and B on the surface, N0 is the number of elementary cells per unit surface, FA, FB and FA,B. are the non-configurational statistical sums of molecules A and B and of activated complex A B, z is the number of neighbouring cells (for a square cell z = 4), PAB i is the probability of two neighbouring cells being occupied by the AB pair and for this pair to have the environment marked by the index i, Ea is the energy difference between the pair AB and the activated complex A B provided that the cells that are nearer to both AB and A B are not occupied, and Ae is the energy difference between the interactions of both A B and AB with the environment. It is assumed that molecules A and B occupy one elementary cell and the activated complex occupies two of them. 

U P. J. Flory, Principles of Polymer Chemistry, Cornell University Press, Ithaca, New York, 1953. [121 M. V. Volkenstein, Configurational Statistics of Polymer Chains, Wiley, New York, 1963. 

Volkenstein, M. V. Configurational statistics of polymeric chains (in-Russian). Moscow and Leningrad Academy of Sciences. USSR. 1959. An English translation by S. Timasheff is in preparation (Interscience Publishers). 

Equation (40) may help to convert the examples presented in Figs. 7-9 to other cases of physical interest. Equation (40) makes it clear once more that the present mean field theory is too crude to describe the interplay between the configurational statistics of flexible polymers and surface enrichment in thin films ... 

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