Time Correlation Functions Of Fluctuations Research Articles

Viscoelasticity of a Stretched Semiflexible Polymer Chain with Fixed Ends

Regularities of the decay of time correlation functions of fluctuations of the microscopic stress tensor characterizing viscoelastic properties for statically stretched chains composed of elastic units with bending stiffness are studied by molecular dynamics and analytically. Chains with the persistent length smaller than the contour length at degrees of extension up to break are considered. In the region of high extensions, where distortions of the local structure of a chain appear, the decay of correlation functions can be described by the modified Rouse model consisting of subchains with anisotropic rigidities depending on the equilibrium chain extension. This makes it possible to determine the relaxation times and moduli of strongly stretched chains, which is necessary in studying the strength of polymer networks. For correlation functions, the analytical relation is formulated that takes into account the contribution of transverse bending fluctuations and agrees with the results of computer simulation at low extensions. A change in the correlation functions with the extension of long semiflexible chains is qualitatively similar to that for flexible chains, but quantitatively is appreciably different.

Distribution of transverse chain fluctuations in harmonically confined semiflexible polymers

Two different experimental studies of polymer dynamics based on single-molecule fluorescence imaging have recently found evidence of heterogeneities in the widths of the putative tubes that surround filaments of F-actin during their motion in concentrated solution. In one [J. Glaser, D. Chakraborty, K. Kroy, I. Lauter, M. Degawa, N. Kirchesner, B. Hoffmann, R. Merkel, and M. Giesen, Phys. Rev. Lett. 105, 037801 (2010)], the observations were explained in terms of the statistics of a worm-like chain confined to a potential determined self-consistently by a binary collision approximation, and in the other [B. Wang, J. Guan, S. M. Anthony, S. C. Bae, K. S. Schweizer, and S. Granick, Phys. Rev. Lett. 104, 118301 (2010)], they were explained in terms of the scaling properties of a random fluid of thin rods. In this paper, we show, using an exact path integral calculation, that the distribution of the length-averaged transverse fluctuations of a harmonically confined weakly bendable rod (one possible realization of a semiflexible chain in a tube), is in good qualitative agreement with the experimental data, although it is qualitatively different in analytic structure from the earlier theoretical predictions. We also show that similar path integral techniques can be used to obtain an exact expression for the time correlation function of fluctuations in the tube cross section.

Viscoelasticity of stretched polymer chains: Analytical theory and computer-aided simulation

The viscoelasticity of stretched polymer chains has been studied by the method of collisional dynamics. To this end, time correlation functions of the fluctuations of the microscopic stress tensor are modeled and relaxation moduli are expressed. Before, for stretched polymer networks, correlation functions used to be calculated in terms of an approximate theory that allowed one to estimate the strain dependences of loss modulus. The calculated dependences are shown to agree qualitatively with the results of measurements performed over a wide interval of strains, including prefracture strains. This theory is verified by comparing the time correlation functions of stress tensor fluctuations for a single stretched chain; these functions are found by computer-aided simulation and calculated on the basis of the existing analytical theory. In this case, a simple theory is adopted according to which a polymer molecule represents a chain composed of N atoms connected by freely jointed elastic bonds. The first and Nth atoms of this chain are attached by harmonic springs to immobile points located at a fixed distance. The decay of time correlation functions under study can be resolved into three stages. After a short initial interval provided by local motions, one can observe a region of power-law decay, which is followed by monoexponential decay at long times. The results of computer-aided simulation generally agree with the predictions of analytical theory. Certain discrepancies primarily concern the dependences of the exponent of power-law relaxation on the degree of chain stretching.

Computer simulation studies of solvent effect on electron transfer in acetonitrile solutions

The Molecular Dynamics method of computer simulation has been applied to evaluate the statistical distribution of the electrostatic potential difference eΔV between donor and acceptor sites immersed in acetonitrile solvent. By using this distribution the electron transfer rate constant for considered molecular systems has been calculated as a function of the free energy change of the reaction, ΔG. This dependence has been compared with the corresponding result calculated on the basis of the dielectric continuum model. It appears that a molecular model of solvent causes the shift of the inverted region for the charge separation reaction towards more negative values of ΔG. Consequently, the inverted region starts in the range of ΔG which is not accessible by experimental measurements. An estimation of the quantum correction to the potential difference distribution has been also performed. The correction calculated using the time correlation function of fluctuations in eΔV is found negligible.

The Mode-Coupling Theory for the Nematic Mesophase near the Clearing Point

A general kinetic equation is derived for the probability distribution function of critical fluctuations in a nematic liquid crystal below a clearing point using Kawasaki's formulation of the mode·mode coupling theory. Two kinds of variables, i.e., local momentum density and transverse components of the local director are chosen as gross variables. Discussion of the dynamic scaling reveals predominance of orientational relaxation processes in dynamic behavior of critical nematics. A simplified version of the kinetic equation determines timecorrelation functions of fluctuations which relate the shear viscosity to the decay rate of director fluctuations to indicate an apparent logarithmic divergence of the critical part of the shear viscosity.

Contributions to Statistical Mechanics Far from Equilibrium. III: Non-Perturbative Method for Steady States

The systematic perturbation scheme for solving stochastic equations for the distribution function of gross variables described in earlier publications of this series is used to develop a non-perturbative self-consistent method for obtaining average values of the gross variables, time correlation functions of fluctuations, non-equilibrium steady state distribution function and the response function to an external disturbance. The analogy of the present problem with that of condensed Bose systems is found to be helpful, and the method requires two kinds of renormalized propagators and three kinds of renormalized vertices to be determined self-consistently. The formalism of Martin, Rose and Siggia on the same problem comes out rather naturally in our approach without introducing their unfamiliar operator. The problem can be simplified so that only one type of propagators and one type of vertices appear if the steady state distribution function is Gaussian.