Dynamics of Polymer Decompression: Expansion, Unfolding, and Ejection

The dynamics of polymer decompression from a compact state to swollen conformation can be formally described as nonlinear diffusion. We discuss two basic examples: (i) the expansion, or unfolding from a compact state, and (ii) the ejection of a compressed polymer through a pore. The problem can be solved exactly for case (i), but not for case (ii). Even in such situations, a scheme called uniform approximation is shown to be useful to get a physical insight involved. Its application to case (ii) is able to account for conflicting numerical data in a consistent way.

Figure 1

Schematics of expansion and ejection processes.

Figure 2

Solutions of nonlinear diffusion equation (solid lines) (with $\nu =3/5$) together with numerical results for initial condition of step distributions (points).

Figure 3

Comparison of predicted ejection time with that obtained from previous numerical experiments. (a) Double logarithm plot of ${\tau }_{\mathrm{ej}}$ as a function of $R_0$ for various system sizes. (b) Scaling plot of ${\tau }_{\mathrm{ej}}$ vs ${\tau }_D$ for small systems. (c) Scaling plot of ${\tau }_{\mathrm{ej}}$ vs ${\tau }_{1,2}+{\tau }_D$ for intermediate systems. Numerical data of ${\tau }_{\mathrm{ej}}$ in  b) and (c) were extracted from 20, 21, respectively.