Cubic Lattice Model Chain

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Abstract
The partition functions for conditions of constant force Zf or fixed displacement length Z̃r are derived for the three‐dimensional cubic lattice model chain having two possible positions of different energy for each link. The problem can be set up so that it reduces to a one‐dimensional Markov chain, thus Zf can be obtained in closed form. The network treatment of Wang and Guth for non‐Gaussian chains is used to obtain the partition function for a network of cubic lattice chains. Qualitative comparison with experiment indicates that most of the deviations from Gaussian behavior which have been observed for cross‐linked natural rubber at low relative elongations may be ascribed to intramolecular rotational energy effects.

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