Abstract
We investigated the statistical behaviors of semiflexible polymer chains, which were simultaneously subjected to force stretching and rectangular tube confinement. Based on the wormlike chain model and Odijk deflection theory, we derived a new deflection length, by using which new compact formulas were obtained for the confinement free energy and force–confinement–extension relations. These newly derived formulas were justified by numerical solutions of the eigenvalue problem associated with the Fokker–Planck governing equation and extensive Brownian dynamics simulations based on the so-called generalized bead-rod (GBR) model. We found that, compared to classical deflection theory, these new formulas were valid for a much more extended range of the confinement size/persistence length ratio and had no adjustable fitting parameters for sufficiently long semiflexible chains in the whole deflection regime.
Highlights
Statistical physics properties of single polymer chains can be significantly influenced or even determined by geometrical confinements and applied external forces [1,2,3,4]
We will present numerical calculations based on the eigenvalue technique developed by Chen and coworkers [19,31,32] and Brownian dynamics simulations in terms of the generalized bead-rod (GBR) model [30,33,34] to justify our theoretical predictions
For a tightly confined polymer in a channel with a rectangular cross-section, Burkhardt and Yang et al [16,19] have derived that the confinement free energy of the polymer chain can be scaled by the average length of the tube occupied by the polymer, which is the average extension of the polymer chain, as follows: F
Summary
Statistical physics properties of single polymer chains can be significantly influenced or even determined by geometrical confinements and applied external forces [1,2,3,4]. For the confinement of a rectangular tube with height and width Hh and Hw , the deflection length associated with the free energy calculation has been suggested as [15,16]. For semiflexible polymer chains confined in rectangular tubes and slits, we derived a modified deflection length, which was expected to be valid for a more extended range than the classical Odijk deflection length. This extended deflection length was directly used to quantitatively formulate both energy and extension. We will present numerical calculations based on the eigenvalue technique developed by Chen and coworkers [19,31,32] and Brownian dynamics simulations in terms of the generalized bead-rod (GBR) model [30,33,34] to justify our theoretical predictions
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