A Variational\nField-Theoretical Approach to Control\nthe Center-Of-Mass of Macromolecules

Trapping macromolecules is important for the study of\ntheir conformations,\ninteractions, dynamics, and kinetic processes. Here, we develop a\nnew theory using a Gaussian variational approach to confine the center-of-mass\nof polymers. It self-consistently introduces a mean force that controls\nthe average position of the center-of-mass and a self-adjustable harmonic\npotential that counters the fluctuation of the center-of-mass position.\nThe effectiveness and versatility of our theory are verified in three\nclassical yet not fully understood problems in polymer science: (1)\nsingle-chain conformation in the whole regime of solvent quality,\n(2) globule-pearl necklace-coil transition of a polyelectrolyte, and\n(3) interchain interaction by simultaneously confining two polymers.\nThe scaling relationships and θ behaviors are well captured.\nConformations with large shape anisotropies appearing in charged polymers\nare clearly depicted. Being a field theoretical framework, our theory\nalso facilitates visualization of the conformational response and\nkinetic process. Our theoretical prediction of the radius of gyration\nof poly(<i>N</i>-isopropylacrylamide) (PNIPAM) is in quantitative\nagreement with experimental results reported in the literature.