A Variational Field-Theoretical Approach to Control the Center-Of-Mass of Macromolecules

Trapping macromolecules is important for the study of their conformations, interactions, dynamics, and kinetic processes. Here, we develop a new theory using a Gaussian variational approach to confine the center-of-mass of polymers. It self-consistently introduces a mean force that controls the average position of the center-of-mass and a self-adjustable harmonic potential that counters the fluctuation of the center-of-mass position. The effectiveness and versatility of our theory are verified in three classical yet not fully understood problems in polymer science: (1) single-chain conformation in the whole regime of solvent quality, (2) globule-pearl necklace-coil transition of a polyelectrolyte, and (3) interchain interaction by simultaneously confining two polymers. The scaling relationships and θ behaviors are well captured. Conformations with large shape anisotropies appearing in charged polymers are clearly depicted. Being a field theoretical framework, our theory also facilitates visualization of the conformational response and kinetic process. Our theoretical prediction of the radius of gyration of poly(N-isopropylacrylamide) (PNIPAM) is in quantitative agreement with experimental results reported in the literature.