Polymethylene Chains and Rings on a Diamond Lattice with Atom Overlap Excluded

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Abstract
A study has been made of alkane‐type chains of N bonds on a diamond lattice with atom overlap (both carbon and hydrogen) excluded. An exact enumeration of all allowed chains and their end‐to‐end distances and numbers of trans bonds has been made for chains of up to 18 bonds. The allowed polymethylene rings have also been determined through 18 bonds. The results have been compared with those for the simple model in which only gauche—gauche prime sequences are disallowed. The number of configurations and the fraction of trans bonds do not appear to differ significantly for the two models. Definite conclusions regarding the mean‐square end‐to‐end distance cannot be drawn from the enumerations reported here, but the two models probably are not in serious disagreement if N is not more than a few thousand.