We present theoretical studies for the conformational behavior of isolated polymers under an external field in good solvents. We assume the monomers of the polymer chain are subject to a three-dimensional external field, which is modeled as a spherical harmonic potential, and monomers interact via hard-core repulsions. We begin with Monte Carlo simulations to investigate the effects of the external field. The chain conformation changes insignificantly if the external field is weak. When the strength of the external field is increased, the chain contracts drastically. A first-order perturbation theory (with ideal-chain reference system) is proposed, with the hard-core repulsion modeled as a perturbation. This approach yields good agreement with the simulations, but with the discrepancy between these two approaches becoming pronounced for strong external field. The perturbation theory makes the prediction that the size of a polymer chain contracts approximately one order of magnitude before collapsing to its globular conformation. Further, to account for behavior under strong fields, a theory of mean-field type is developed, which predicts 〈R2〉∼(N/k)2/5 (where k denotes field strength), consistent with the simulations. These studies are of importance in understanding supercoiled long chain DNA in a tiny cellular nucleus, and deformation of polymer materials under external fields.

Articles you may be interested inDiffusion assisted end-to-end relaxation of a flexible Rouse polymer chain: Fluorescence quenching through a model energy transfer Density functional studies of solvation forces in hard sphere polymer solutions confined between adsorbing walls. I. Solvent effects and dependence on surface potential range Effect of solvent quality on the conformation and relaxation of polymers via dissipative particle dynamicsWe consider a polymer chain confined by a harmonic potential in 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.

We investigate the dynamics of a copolymer molecule in a θ-solvent under a weak alternating field using the Zimm model. We first consider a diblock copolymer with two blocks of same force constant, where the monomers on the two different blocks interact with the applied field differently. The theory predicts that the center-of-mass and the chain conformation of copolymer molecules oscillate in response to the sinusoidal electric field. For the center-of-mass, the oscillation becomes more pronounced as the charge fraction is increased. However, the oscillation of chain conformation is not observed for neutral or fully charged homopolymers, but is enhanced when the fraction of the two blocks becomes equal. In highly viscous solutions, the strength of the oscillation of the center-of-mass and conformation is weakened, and the phase of oscillation is shifted. Moreover, the oscillatory behavior diminishes at higher frequencies. For comparison, we also study a special copolymer model where the two monomers alternate along the polymer backbone. Again the oscillation emerges for the molecular motion and conformation, but the oscillation of chain properties becomes much weaker than diblock copolymers. These results disclose the effect of the chemical architectures of copolymers on their chain dynamic behavior under an alternating field.