proceedings

FORUM PROCEEDINGS
ments. A molecule can therefore exist in very many different
configurations, and as a consequence has high
entropy. On stretching, the molecules become less random,
and the chains tend to become parallel. The decrease in
entropy is responsible for the strong force in a piece of
stretched rubber which attempts to contract it to its original
state of maximum randomness. Clearly the force, and
hence the modulus of elasticity of a plastic made of long
chain molecules, could be calculated if we could enumerate
the possible configurations of such an assembly of chains.
This can be done in a simple way and leads to results in
rough agreement with experiments, at least for highly
elastic substances. The simple theory has a number of defects,
principally the fact the molecules have volume and
can only occupy the same volume of space once. The problem
of this effect of "excluded volume" on the number of
configurations is a topological one of great difficulty. We
have set out to solve this topological problem by a straightforward
enumeration of the configurations of chains. In
essence, we have investigated the famous "random walk"
problem, in a tetrahedral lattice accounting for the effect
of excluded volume.
This, then, is an example of the use of punched cards in
sampling a Gibbsian ensemble, in which each system is
described appropriately on a set of cards. The required
statistical averages can be very readily made by arithmetical
means by conventional processing of these samples
on cards.
RBI