Effect of Excluded Volume on Phase Transitions in Biopolymers

The effects of excluded volume on the existence and nature of a phase transition in an infinitely long double-stranded helical polymer are discussed in relation to the recent treatment of Poland and Scheraga, which showed that, if the entropy of a closed polymer loop of 2l links (corresponding to a diassociated length of l polymer units) varies as S2l/kB=al−clnl+b (l→∞),then a genuine phase transition should occur if c>1 but that θ, the fraction of ordered units, would be continuous at the transition unless c>2. The standard Markoffian models of a polymer chain neglect the excluded volume and yield c=½d for a general d-dimensional system. Numerical data on self-avoiding lattice chains and rings are reviewed and it is concluded that c≃1.46 and 1.75 are better estimates for d=2 and 3, respectively. The transition should thus remain continuous but it becomes sharper since it is shown that θ varies as (Tt—T)(2−c)/(c−1) when the transition temperature Tt is approached from below (and 1<c<2).