Conformation of Adsorbed Polymeric Chain. IV

概要

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In order to develop further the theoretical treatment of a polymeric chain adsorbed at an interface, a random walk model, in which each step has the same probability except that no step can retrace the preceding one on a simple cubic lattice, has been used. The average number of adsorbed segments \barν, the average number of trains \barm, and the mean square end-to-end distance \barr2 are calculated as functions of the adsorption energy of segment ε and the number of segments n when n is infinitely large. The average numbers of segments in a train and a loop, \bark′ and \bark′, are also calculated. Through the increment in the value of critical adsorption energy εc, prohibition of immediate reversal for the random walk fairly influences the average properties of adsorbed polymeric ,chain. The decrease in \barm and the increase in \bark′ with ε⁄kT at its large values are remarkable in comparison with those of the symmetric random walk, which may be accounted for by the diminution of the chance of making loops. It is shown that \barr2 is equivalent to the mean square two-dimensional end-to-end distance of a restricted random walk without immediate reversals on a simple cubic lattice at εc⁄kT and approaches that on a simple square lattice in the limit ε⁄kT→∞.
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