Sequence length distributions and entropy of stereoregularity in homopolymers of finite molecular weight

Abstract

Equations are derived for the mean sequence length, the sequence length distribution and the entropy associated with the rearrangement of these sequences in tactic homopolymers or binary copolymers of finite molecular weight. The treatment requires that each addition be described by a single probability factor, and that the degree of polymerization is more than six times the mean sequence length. It is found that the mean sequence length is rather insensitive to molecular weight, but that the number fraction of sequences of length m and the entropy of sequence rearrangement are appreciably dependent on molecular weight when the polymer contains less than a thousand monomer units. Errors in the limiting [infinite degree of polymerization] equations for these two quantities are particularly important for isotactic polymers. Numerical values of the entropy, designated the entropy of stereoregularity when applied to the case of a tactic homopolymer, are reported over a range of degrees of polymerization, 2 000 to 20.