Polymers in confinement: Free energy scaling and folding transitions

Geometric confinement of a polymer chain results in loss of conformational entropy. For an athermal polymer the associated free energy increase is expected to exhibit power law scaling with an exponent that depends on confinement dimensionality. For a chain that can fold into a compact native state, confinement primarily reduces the number of possible unfolded states, thereby providing entropic stabilization of the folded state and allowing for the possibility of confinement driven folding [1]. Here we investigate these confinement effects for flexible hard-sphere (HS) and square-well (SW) sphere chains (where the latter exhibit all-or-none folding characteristic of many small proteins [2]). We use a Wang-Landau simulation approach to construct the partition function for a polymer confined within a hard-wall slit, a cylindrical pore, and both a cylindrical and spherical cavity. Scaling analysis of the HS-chains shows significant finite size effects. For the confined SW-chain, isothermal reduction of the confinement dimension can induce folding, unfolding, or crystallite restructuring. Scaling results and phase diagrams will be presented. [1] Taylor, Macromolecules 50, 6967 (2017); [2] Taylor, Paul, and Binder, J. Chem. Phys. 145, 174903 (2016).