Extension of the Zimm and Rouse model to a polymer chain confined by a harmonic potential in θ-solvent conditions

Abstract

We consider a polymer chain confined by a harmonic potential in θ solvents using the Zimm and Rouse model to elucidate the chain relaxation behavior in weak and strong fields, respectively. We investigate a case in which the center of the field is tuned to match the center of mass of the polymer at the instant when the field is switched on. The closed-form expressions are obtained for these models. When the field strength is weak enough so that the chain conformation is close to ideal Gaussian, the Zimm model predicts that the chain molecule would fluctuate within the confined space induced by the applied field. Moreover, the molecular rotation relaxes faster than the translational motion of the center of mass of the polymer molecule. However, under a strong field, the polymer molecule contracts continuously from a random coil to a collapsed conformation after the field is switched on. The Rouse model makes predictions that the center of mass of the confined polymer molecule would achieve its equilibrium state first. After the relaxation of the center of mass, the polymer molecule reaches the equilibrium chain conformation, followed by the molecular rotation. Furthermore, the Rouse model also predicts that in the presence of a strong field, the Rouse time is predominated by the field strength only.