Revisiting the Chain Behaviors of a Polymer at the Theta Point

As one of the key concepts in polymer solutions, the theta point is defined as the vanishing of the osmotic second virial coefficient, and it is highly relevant to many important topics such as the coil-globule transition and phase separation in polymer solutions. In spite of many theoretical and simulation studies, there is currently no consensus on the shift of the theta point and the chain size change (i.e., whether chains are expanded or contracted). Here, based on a discrete Gaussian chain model, we investigate the theta point and the chain behaviors using a four-parameter model, which includes the bare second and third virial coefficients as well as the square-gradient term accounting for the finite interaction range. Our model is free of the divergence problem commonly encountered in previous studies based on the continuous Gaussian chain model, and thus can give unambiguous predictions and clarify the discrepancies in the literature. We find that the sign of the chain size change relative to the ideal counterpart depends on the relative strength of the bare third coefficient and the coefficient of the square-gradient term.