Chain dimensions near the critical point

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Abstract
We calculate the average end-to-end distance 〈R2〉 of a polymer in a semidilute solution that is near the temperature Tc at which phase separation occurs. The calculation is carried out within the usual canonical partition function formalism, the Hamiltonian of the system being taken to comprise a reference term, in which the chains are represented as collapsed coils, and a perturbation, which originates in repulsive excluded volume interactions between different monomers. The description of the reference state employs the fractional Brownian walk approach developed in an earlier paper, while the perturbation is modeled by delta function pseudopotentials. The treatment of excluded volume follows the methods developed by Edwards, Singh, and Jeffers, which make use of the equations derived for an effective step length and an effective monomer–monomer potential to determine various polymer properties. In this way, we find that near Tc, R scales with chain length N as N0.462.

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