A Monte Carlo study of the excluded‐volume effect on the amylosic chain conformation

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Abstract
A Monte Carlo procedure was used to determine the effect of excluded volume on the conformational dimensions of amylosic chains. The excluded volume was introduced into the model by assuming that hard spheres, which cannot overlap each other, exist at the center of mass of each glucose unit in the chain sequence. Monte Carlo chains, which were generated to be distributed consistent with the potential energy of nonbonded nearest‐neighbor interactions, underwent self‐intersections, and the attrition rate in the generation of self‐avoiding chains was found to obey an exponential decay law with increasing chain length x. Thus, in order to generate effectively a large number of self‐avoiding chains with long sequences, we used the Wall–Erpenbeck s‐p method of chain enrichment [F. T. Wall and J. J. Erpenbeck (1959) J. Chem. Phys. 30, 634–637]. By examination of the radial distribution of the end‐to‐end distance and the chain‐length dependence of the quantity 〈r2〉/xl2 (〈r2〉 is the mean square end‐to‐end distance and l is the virtual bond length), it was found that unperturbed amylosic chains change in overall conformation from a non‐Gaussian chain having a helical character to Gaussian as x is increased, whereas perturbed chains do not show Gaussian behavior even at x = 500. For the perturbed chains, 〈r2〉 can be expressed by the equation 〈r2〉 = axb in the range of 100 ≤ x ≤ 500, where a and b > 1 are constants. From comparisons of the persistence vectors and perspective drawings of representative unperturbed and perturbed chains, we felt the local conformation of the amylosic chains, i.e., the local helical character, is also affected by the long‐range excluded‐volume interaction.