Single polymer dynamics offers a powerful approach to study molecular-level interactions and dynamic microstructure in materials. Direct visualization of single polymer chains has uncovered new ideas regarding the rheology and nonequilibrium dynamics of macromolecules, including the importance of molecular individualism, dynamic heterogeneity, and molecular subpopulations in governing macroscopic behavior. In recent years, the field of single polymer dynamics has been extended to new materials, including architecturally complex polymers such as combs, bottlebrushes, and ring polymers and entangled solutions of long chain polymers in flow. Single molecule visualization, complemented by modeling and simulation techniques such as Brownian dynamics and Monte Carlo methods, allow for unparalleled access to the molecular-scale dynamics of polymeric materials. In this review, recent progress in the field of single polymer dynamics is examined by highlighting major developments and new physics to emerge from thes...

https://sor.scitation.org/doi/pdf/10.1122/1.5013246

Single polymer dynamics for molecular rheology

Single polymer dynamics offers a powerful approach to study molecular-level interactions and dynamic microstructure in materials. Direct visualization of single chain dynamics has uncovered new ideas regarding the rheology and non-equilibrium dynamics of macromolecules, including the importance of molecular individualism, dynamic heterogeneity, and molecular sub-populations that govern macroscale behavior. In recent years, the field of single polymer dynamics has been extended to increasingly complex materials, including architecturally complex polymers such as combs, bottlebrushes, and ring polymers and entangled solutions of long chain polymers in flow. Single molecule visualization, complemented by modeling and simulation techniques such as Brownian dynamics and Monte Carlo methods, allow for unparalleled access to the molecular-scale dynamics of polymeric materials. In this review, recent progress in the field of single polymer dynamics is examined by highlighting major developments and new physics to emerge from these techniques. The molecular properties of DNA as a model polymer are examined, including the role of flexibility, excluded volume interactions, and hydrodynamic interactions in governing behavior. Recent developments in studying polymer dynamics in time-dependent flows, new chemistries and new molecular topologies, and the role of intermolecular interactions in concentrated solutions are considered. Moreover, cutting-edge methods in simulation techniques are further reviewed as an ideal complementary method to single polymer experiments. Future work aimed at extending the field of single polymer dynamics to new materials promises to uncover original and unexpected information regarding the flow dynamics of polymeric systems.

Single Polymer Dynamics for Molecular Rheology

Time-dependent fluctuations in the distance x(t) between two segments along a polymer are one measure of its overall conformational dynamics. The dynamics of x(t), modeled as the coordinate of a particle moving in a one-dimensional potential well in thermal contact with a reservoir, is treated with a generalized Langevin equation whose memory kernel K(t) can be calculated from the time-correlation function of distance fluctuations C(t)≡⟨x(0)x(t)⟩. We compute C(t) for a semiflexible continuum model of the polymer and use it to determine K(t) via the GLE. The calculations demonstrate that C(t) is well approximated by a Mittag-Leffler function and K(t) by a power-law decay on time scales of several decades. Both functions depend on a number of parameters characterizing the polymer, including chain length, degree of stiffness, and the number of intervening residues between the two segments. The calculations are compared with the recent observation of a nonexponential C(t) and a power law K(t) in the conformat...

Multiple time scale dynamics of distance fluctuations in a semiflexible polymer: A one-dimensional generalized Langevin equation treatment

We present exact and analytically accurate results for the problem of a flexible polymer chain in shear flow. Under such a flow the polymer tumbles, and the probability distribution of the tumbling times $\ensuremath{\tau}$ of the polymer decays exponentially as $\ensuremath{\sim}\mathrm{exp}﻿(\ensuremath{-}\ensuremath{\alpha}\ensuremath{\tau}/{\ensuremath{\tau}}_{0})$ (where ${\ensuremath{\tau}}_{0}$ is the longest relaxation time). We show that for a Rouse chain this nontrivial constant $\ensuremath{\alpha}$ can be calculated in the limit of a large Weissenberg number (high shear rate) and is in excellent agreement with our simulation result of $\ensuremath{\alpha}\ensuremath{\simeq}0.324$. We also derive exactly the distribution functions for the length and the orientational angles of the end-to-end vector $\mathbit{R}$ of the polymer.

http://dspace.rri.res.in/bitstream/2289/3723/1/2008%20PRL_V101_188301.pdf

Accurate statistics of a flexible polymer chain in shear flow.

In this work, we develop a new algorithm for nonequilibrium molecular dynamics of fluids under planar mixed flow, a linear combination of planar elongational flow and planar Couette flow. To date, the only way of simulating mixed flow using nonequilibrium molecular dynamics techniques was to impose onto the simulation box irreversible transformations. This would bring the simulation to an end as soon as the minimum lattice space requirements were violated. In practical terms, this meant repeating the short simulations to improve statistics and extending the box dimensions to increase the total simulation time. Our method, similar to what has already been done for pure elongational flow, allows a cuboid box to deform in time following the streamlines of the mixed flow and, after a period of time determined by the elongational field, to be mapped back and recover its initial shape. No discontinuity in physical properties is present during the mapping and the simulation can, in this way, be extended indefinitely. We also show that the most general form of mixed flow, in which the angle between the expanding (or contracting) direction and the velocity gradient axis varies, can be cast in a so-called canonical form, in which the angle assumes values that are multiples of π (when a mixed flow exists), by an appropriate choice of the field parameters.

https://researchbank.swinburne.edu.au/file/d864a6aa-7a70-4f19-bb04-59449079adde/1/PDF (Published version).pdf

A new algorithm for extended nonequilibrium molecular dynamics simulations of mixed flow.

Recent simulations by Chu et al. [Phys. Rev. E 66, 011915 (2002)] on the behavior of bead–spring and bead–rod models of polymers in linear mixed flows (flows with unequal amounts of extension and rotation) are compared with the predictions of a finitely extensible Rouse model that was used earlier [J. Chem. Phys. 112, 8707 (2000)] to describe the behavior of long flexible molecules of \lambda-phage DNA in simple shear. The model is a generalization of the continuum Rouse model in which the "spring constant" of the bonds connecting near neighbor segments is allowed to become nonlinearly flow-dependent through a term involving the initially unknown mean square size of the chain, [R2]. A self-consistent equation for this quantity is derived by using the flow-modified Hamiltonian to calculate it from its statistical mechanical definition. After solving this equation numerically, the mean fractional extension of the chain x can be obtained as a function of the Weissenberg number Wi and a mixing parameter \alpha. The results compare favorably with data from the simulations of Chu et al., and suggest the existence of a scaling variable Wieff = \sqrt{\alpha} Wi in terms of which separate curves of x versus Wi fall more or less on a single universal curve.

/pdf/polymer-dynamics-in-linear-mixed-flow-ja8lcsdrw0.pdf

Polymer dynamics in linear mixed flow

The dynamics of an ideal polymer ring enclosing a constant algebraic area is studied. The constraint of a constant area is found to couple the dynamics of the two Cartesian components of the position vector of the polymer ring through the Lagrange multiplier function which is time dependent. The time dependence of the Lagrange multiplier is evaluated in a closed form both at short and long times. At long times, the time dependence is weak, and is mainly governed by the inverse of the first mode of the area. The presence of the constraint changes the nature of the relaxation of the internal modes. The time correlation of the position vectors of the ring is found to be dominated by the first Rouse mode which does not relax even at very long times. The mean square displacement of the radius vector is found to be diffusive, which is associated with the rotational diffusion of the ring.

Constrained dynamics of a polymer ring enclosing a constant area.

Summary: The conformational behavior of a polymer in a critical binary solvent confined in a porous medium is studied. The size of the polymer in bulk, which is mainly governed by the correlation length of the solvent density fluctuations, depends on the proximity to the critical point of the binary mixture. We find that in contrast to the bulk behavior, the conformational properties of the polymer in a porous medium depends strongly on the pore size. The latter controls the correlation length of the solvent density fluctuations and thus determines the polymer size.

Arti Dua

Papers

Polymer dynamics in linear mixed flow

Constrained dynamics of a polymer ring enclosing a constant area.

Chains in Critical Fluids and Nanopores