Nonequilibrium dynamics of polymer translocation and straightening

When a flexible polymer is sucked into a localized small hole, the chain can initially respond only locally and the sequential nonequilibrium processes follow in line with the propagation of the tensile force along the chain backbone. We analyze this dynamical process by taking the nonuniform stretching of the polymer into account both with and without hydrodynamics interactions. Earlier conjectures on the absorption time are criticized and formulas are proposed together with time evolutions of relevant dynamical variables.

Figure 1

(Color online) A dynamical response of a polymer initially at rest to the strong aspiration. A chain is pulled from the $(x<0)$ region to the aspiration spot located at the origin. Monomers in the gray region are under the influence of the tensile force, while monomers in the rear part are yet relaxed. The distance between the boundary (associated with tension propagation) and the origin and the size of the largest blob at the boundary are denoted as $R\left(t\right)$ and $y_R\left(t\right)$, respectively. Monomers are sequentially labeled as $1,2,\dots ,N_0$ from one end (arriving at the origin initially) to the other. $M\left(t\right)$ and $N\left(t\right)$ are, respectively, labels of the monomers residing at the origin and the boundary at time $t$. (Top) $N_0^{-\nu }<{\tilde{f}}_b<1$ and (bottom) $1<{\tilde{f}}_b<N_0^{\nu }$, in which the anterior part $[-l\left(t\right)<x<0]$ is completely stretched.

Figure 2

Time evolutions of number of absorbed monomers $M\left(t\right)$ at various forces for the chain length $N_0={10}^3$ under good solvent condition $(\nu =3∕5)$. Inflectionlike points mark the end of the tension propagation stage ($t={\tau }_1$ and $M=M_1$).

Figure 3

(Color online) Normalized time evolutions (double logarithmic scale) of number of absorbed monomers $M(t∕{\tau }_1)∕M_1$ at various scaled forces in the tension propagation stage under a good solvent condition $(\nu =3∕5)$.

Figure 4

(Color online) A dynamical response of a polymer initially at rest to the strong pulling by its one end $(N_0^{-\nu }<{\tilde{f}}_b<1)$. A coordinate is defined in such a way that the origin is the position of one chain end at time $t=0$ and that end is starting to be pulled to the right $(x>0)$ direction. Monomers in the gray region are under the influence of the tensile force, while monomers in the rear part are yet relaxed. The distance between the boundary (front of the tension propagation) and the origin and the size of the largest blob at the boundary are denoted as $R\left(t\right)$ and $y_R\left(t\right)$, respectively. Monomers are sequentially labeled as $1,2,\dots ,N_0$ from the pulled end to the other. $N\left(t\right)$ is the label of the monomer residing at the boundary at time $t$.