Effect of residual interactions on polymer properties near the theta point

Abstract

Perturbation calculations are performed for 〈R2〉, 〈S2〉, 〈RH〉, A2, and A3 for polymers near the theta point using a continuous curve representation of the three-parameter theory of Yamakawa. Both dimensional regularization and cut-off schemes are employed, but only the latter method is shown to be in accord with observed polymer properties, demonstrating the necessity of retaining a cut-off (or its equivalent) when ternary interactions are incorporated into the three dimensional model. An effective binary interaction parameter is defined to vanish along with the second virial coefficient under theta conditions. Renormalization group calculations are then combined with the perturbation expansions to extend the predictions for these polymer properties to larger ternary interactions while still remaining in the vicinity of the theta point where the effective binary interaction is small. A comparison of calculated values of A3 and the ratios 〈S2〉1/2/RH and 〈R2〉/〈S2〉 with data from experiment and computer simulations provides a self-consistent estimate of 𝒪(10−3) for the magnitude of the three body interaction term. The ternary effect is found to be small but not negligible for flexible linear polymers. Ternary interactions are, however, expected to be more substantial for branched polymers. The cut-off theory of theta point polymers accounts satisfactorily for the shift in the theta temperature observed, but previously unexplained, in numerical studies of lattice polymers. Our calculations also reconcile many contradictory conclusions of earlier calculations on theta point polymer properties.