A Variational Field-theoretical Approach to Trap Macromolecules

Trapping macromolecules is important for the study of their conformations, interactions, dynamics and kinetic processes. Here, we develop a new theory using Gaussian variational approach to confine the center-of-mass of polymers. It self-consistently introduces a mean force that controls the average position of center-of-mass and a self-adjustable harmonic potential that counters the fluctuation of 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) inter-chain interaction by simultaneously confining two polymers. The scaling relationships and q behaviors are well captured. Conformations with large shape anisotropy 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. Furthermore, we apply our theory to a variety of biomacromolecular systems, for example, the fission/fusion of vesicles and the stabilization of RNA condensates in the presence of proteins.