Internal transition in an infinitely long polymer chain

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Abstract
The existence of an internal transition (collapse) in a long polymer chain is investigated as follows: a chain of n segments is simulated by a self-avoiding walk of n-1 steps on a simple cubic lattice, an energy- epsilon being associated with each pair of neighbouring segments, and the distribution of the zeros of the partition function in the complex plane associated with the variable x=exp( epsilon /kT) is studied for increasing n values. A tentative conclusion is that a line of roots cuts the real positive axis in xc approximately=1.74(kTc/ epsilon approximately=1.82) in the limit n to infinity , supporting the occurrence of a transition in this model.