Abstract
A two-stage model is developed in order to understand the scaling behaviors of single polymers ejecting from a spherical cavity through a nanopore. The dynamics of ejection is derived by balancing the free energy change with the energy dissipation during a process. The ejection velocity is found to vary with the number of monomers in the cavity, m, as at the confined stage, and it turns to be at the non-confined stage, where N is the chain length and D the cavity diameter. The exponents are shown to be , and , with being the Flory exponent. The profile of the velocity is carefully verified by performing Langevin dynamics simulations. The simulations further reveal that, at the starting point, the decreasing of m can be stalled for a good moment. It suggests the existence of a pre-stage that can be explained by using the concept of a classical nucleation theory. By trimming the pre-stage, the ejection time are properly studied by varying N, D, and (the initial volume fraction). The scaling properties of the nucleation time are also analyzed. The results fully support the predictions of the theory. The physical pictures are given for various ejection conditions that cover the entire parameter space.
Highlights
The ejection of polymer is a process concerning a polymer being ejected from a confined space into a non-confined space through a small pore
A well-known example can be found in a bacteriophage, a virus that is able to infect a bacterial cell by injecting its genetic materials that are encapsulated in the capsid head into the cell through a channel tail [1,2]
In the ejection problem, the condition of a process is controlled by the three main parameters: the chain length N, the cavity diameter D, and the initial volume fraction φ0
Summary
The ejection of polymer is a process concerning a polymer being ejected from a confined space into a non-confined space through a small pore. In order to verify the conjecture, we have recently developed a scaling theory to explain polymer ejection from a cavity through a small pore [47]. With a good knowledge of the primitive model we are able to go further to assess the impacts that are brought in by the other effects, such as the chain stiffness, hydrodynamics, electrostatics, etc., in order to gain a better understanding of a real ejection process that happened in nature and the applications. The studied topics include the scaling of the ejection velocity (Section 4.1) and the time evolution of the number of monomers in a cavity (Section 4.2). The scaling behaviors for the nucleation time and the following ejection time will be properly investigated by systematically varying the chain length, the cavity size, and the initial packing fraction (Section 4.3).
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