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Register a new userDriven Anomalous Diffusion: An example from Polymer Stretching
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The way tension propagates along a chain is a key to govern many of anomalous dynamics in macromolecular systems. After introducing the weak and the strong force regimes of the tension propagation, we focus on the latter, in which the dynamical fluctuations of a segment in a long polymer during its stretching process is investigated. We show that the response, i.e., average drift, is anomalous, which is characterized by the nonlinear memory kernel, and its relation to the fluctuation is nontrivial. These features are discussed on the basis of the generalized Langevin equation, in which the role of the temporal change in spring constant due to the stress hardening is pinpointed. We carried out the molecular dynamics simulation, which supports our theory.
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The translocation dynamics of a polymer chain through a nanopore in the absence of an external driving force is analyzed by means of scaling arguments, fractional calculus, and computer simulations. The problem at hand is mapped on a one dimensional {em anomalous} diffusion process in terms of reaction coordinate $s$ (i.e. the translocated number of segments at time $t$) and shown to be governed by an universal exponent $alpha = 2/(2 u+2-gamma_1)$ whose value is nearly the same in two- and three-dimensions. The process is described by a {em fractional} diffusion equation which is solved exactly in the interval $0 <s < N$ with appropriate boundary and initial conditions. The solution gives the probability distribution of translocation times as well as the variation with time of the statistical moments: $<s(t)>$, and $<s^2(t)> - < s(t)>^2$ which provide full description of the diffusion process. The comparison of the analytic results with data derived from extensive Monte Carlo (MC) simulations reveals very good agreement and proves that the diffusion dynamics of unbiased translocation through a nanopore is anomalous in its nature.
We present a comprehensive investigation of polymer diffusion in the semidilute regime by fluorescence correlation spectroscopy (FCS) and dynamic light scattering (DLS). Using single-labeled polystyrene chains, FCS leads to the self-diffusion coefficient while DLS gives the cooperative diffusion coefficient for exactly the same molecular weights and concentrations. Using FCS we observe a new fast mode in the semidilute entangled concentration regime beyond the slower mode which is due to self-diffusion. Comparison of FCS data with data obtained by DLS on the same polymers shows that the second mode observed in FCS is identical to the cooperative diffusion coefficient measured with DLS. An in-depth analysis and a comparison with current theoretical models demonstrates that the new cooperative mode observed in FCS is due to the effective long-range interaction of the chains through the transient entanglement network.
We study the translocation dynamics of a polymer chain threaded through a nanopore by an external force. By means of diverse methods (scaling arguments, fractional calculus and Monte Carlo simulation) we show that the relevant dynamic variable, the translocated number of segments $s(t)$, displays an {em anomalous} diffusive behavior even in the {em presence} of an external force. The anomalous dynamics of the translocation process is governed by the same universal exponent $alpha = 2/(2 u +2 - gamma_1)$, where $ u$ is the Flory exponent and $gamma_1$ - the surface exponent, which was established recently for the case of non-driven polymer chain threading through a nanopore. A closed analytic expression for the probability distribution function $W(s, t)$, which follows from the relevant {em fractional} Fokker - Planck equation, is derived in terms of the polymer chain length $N$ and the applied drag force $f$. It is found that the average translocation time scales as $tau propto f^{-1}N^{frac{2}{alpha} -1}$. Also the corresponding time dependent statistical moments, $< s(t) > propto t^{alpha}$ and $< s(t)^2 > propto t^{2alpha}$ reveal unambiguously the anomalous nature of the translocation dynamics and permit direct measurement of $alpha$ in experiments. These findings are tested and found to be in perfect agreement with extensive Monte Carlo (MC) simulations.
This article focuses on a preaveraging description of polymer nonequilibrium stretching, where a single polymer undergoes a transient process from equilibrium to nonequilibrium steady state by pulling one chain end. The preaveraging method combined with mode analysis reduces the original Langevin equation to a simplified form for both a stretched steady state and an equilibrium state, even in the presence of self-avoiding repulsive interactions spanning a long range. However, the transient stretching process exhibits evolution of a hierarchal regime structure, which means a qualitative temporal change in probabilistic distributions assumed in preaveraging. We investigate the preaveraging method for evolution of the regime structure with consideration of the nonequilibrium work relations and deviations from the fluctuation-dissipation relation.
Using Langevin dynamics simulations, we investigate the dynamics of a flexible polymer translocation into a confined area under a driving force through a nanopore. We choose an ellipsoidal shape for the confinement and consider the dependence of the asymmetry of the ellipsoid measured by the aspect ratio on the translocation time. Compared with an isotropic confinement (sphere), an anisotropic confinement (ellipsoid) with the same volume slows down the translocation, and the translocation time increases with increasing the aspect ratio of the ellipsoid. We further find that it takes different time for polymer translocation into the same ellipsoid through major-axis and minor-axis directions, depending on the average density of the whole chain in the ellipsoid, $phi$. For $phi$ lower than a critical value $phi_c$, the translocation through minor axis is faster, and vice versa. These complicated behaviors are interpreted by the degree of the confinement and anisotropic confinement induced folding of the translocated chain.
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