Abstract
To obtain an expression for the entropy S of a polymer network at volume V, the assumption is made that a volume V~0~ can be defined a which the distribution of end‐to‐end distances is the same as in a solution of freely dispersed chains and is Gaussian, and that the distribution of end‐to‐end distances at the volume V is likewise Gaussian. Although these assumptions are the same as those made by Flory, the formula obtained differs from Flory's. The results is
where n is the number of solvent molecules, ϕ the volume fraction of polymer, G the number of chains (i. e., chain portions between crosslinks), and Ω the factor by which the structural pattern of the network reduces the number of accessible configurations. The customary assumption is made that Ω is volume independent. The consequences of the result obtained for S are discussed. Flory's method was to calculated the “entropy of crosslinking” by considering the probability that in a polymer solution certain segments are found in each other's vicinity. The error in the calculation lies in the assumption that the probability for two arbitrary segments to be in each other's vicinity is independent of whether other pairs of segments are or not. If this error is avoided, Flory's result becomes identical with the one derived in the present article. Arguments are given to show that the distribution of end‐to‐end distances assumed by Guth and James is erroneous. A consideration of the equilibrium between the network and a polymer solution proves that their formula must be rejected also on experimental grounds.