Theoretical Studies of Polymer Dynamics in Confined Spaces

Abstract

The growing use of micro- and nano-fabricated devices to study complex biological processes has made it increasingly important to understand the effects of confinement on macromolecular behaviour. In this thesis, I will discuss how theoretical models of polymer dynamics in small spaces or crowded environments can provide useful insights into the dynamics of real systems. To this end, I consider the application of various statistical mechanical methodologies to the following illustrative many-body problems: (i) the shear-induced stretching of ideal flexible chains in narrow capillaries, (ii) the relaxational dynamics of Gaussian polymers in rectangular slits, (iii) the cyclization kinetics of long polymers in spherical cavities and in viscoelastic media, and (iv) the reactivity of the terminal groups of surface-tethered self-avoiding walks. Among other results, I find that geometrical constraints can screen out hydrodynamic effects and produce free-draining behavior, introduce logarithmic corrections to the bulk scaling of diffusion coefficients and relaxation times, and modify the molecular weight dependence of chain reactivity. These results highlight the significant part that can be played by confinement on chain dynamics.