Simulation of polymer chains on a tetrahedral lattice

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Abstract
A thorough analysis of partially restricted random walks on a tetrahedral lattice has been carried out to demonstrate the validity of Wall’s recent theory of polymer chain configurations. Tetrahedral lattice walks of order six (those for which ring closures corresponding to polygons of six of fewer vertices are forbidden) were studied both analytically and numerically. A set of forty-one different five-step configurations suffices for the numerical analysis; the total numbers of the configurations, together with the corresponding first and second moments, have all been determined with great accuracy. With increasing contour chain lengths, the dimensional distributions for all configurations become Gaussian and their mean square end-to-end separations, 〈r2〉n, become linear in the number of steps, n. As predicted by theory, the derivative of 〈r2〉n with respect to n becomes independent of the kind of configuration as n→∞. All parameters have been determined precisely and the results are interpreted in the light of their asymptotic trends.