Search

The purpose of this paper is to investigate several analytical methods of solving first passage (FP) problem for the Rouse model, a simplest model of a polymer chain. We show that this problem has to be treated as a multi-dimensional Kramers' problem, which presents rich and unexpected behavior. We first perform direct and forward-flux sampling (FFS) simulations and measure the mean first-passage time t(z) for the free end to reach a certain distance z away from the origin. The results show that the mean FP time is getting faster if the Rouse chain is represented by more beads. Two scaling regimes of t(z) are observed, with transition between them varying as a function of chain length. We use these simulation results to test two theoretical approaches. One is a well known asymptotic theory valid in the limit of zero temperature. We show that this limit corresponds to fully extended chain when each chain segment is stretched, which is not particularly realistic. A new theory based on the well known Freidlin-Wentzell theory is proposed, where dynamics is projected onto the minimal action path. The new theory predicts both scaling regimes correctly, but fails to get the correct numerical prefactor in the first regime. Combining our theory with the FFS simulations leads us to a simple analytical expression valid for all extensions and chain lengths. One of the applications of polymer FP problem occurs in the context of branched polymer rheology. In this paper, we consider the arm-retraction mechanism in the tube model, which maps exactly on the model we have solved. The results are compared to the Milner-McLeish theory without constraint release, which is found to overestimate FP time by a factor of 10 or more. [ABSTRACT FROM AUTHOR]

Understanding the interfacial organization of heteropolymers near solid surfaces is an issue of fundamental interest that is relevant for many technological and biological applications. In this paper we address several questions pertaining to the surface-induced ordering and the adsorption–desorption phase behavior of a dilute solution of two-letter random heteropolymers interacting with a solid surface. Our analysis is based on a statistical field theoretic formulation of the propagator for the problem of interest. We employ the replica trick to alleviate analytical difficulties which arise when considering averaging over the sequence distribution of the A and the B units. In order to highlight the effects of the surface, we consider the situation wherein the intersegment interactions are of the excluded volume type while the segment–surface interactions of the A and B segments are arbitrarily different. Within the replica symmetric solution, we show that proper coarse-graining of the interaction potentials leads to exact analytical expressions for the self-consistent propagator of the heteropolymer at theta conditions and for the case where excluded volume interactions prevail. One of our interesting findings is that heteropolymers undergo an adsorption–desorption transition in the vicinity of a surface that interacts with the different types of segments in arbitrarily different ways. This is consistent with our previous numerical findings for much more restricted circumstances.We explicitly analyze the influence of the fluctuations in the sequence distribution on the conformational organization of the adsorbed chains and obtain the scaling behavior of properties of interest in the vicinity of the adsorption–desorption threshold with respect to the disorder strength and other polymer interaction parameters. Specifically, invoking the Ehrenfest theorem we find that the adsorption–desorption transition at theta conditions is... [ABSTRACT FROM AUTHOR]

We present a self-consistent-field structure for the thermodynamic description of concentrated solutions of liquid-crystal polymers. The polymers are assumed to be locally stiff but capable of curvature over large distances. The formulation of the chain geometry is that of a wormlike polymer, but the final analysis is simpler than the Kratky–Porod form. The phase behavior is analyzed for a cylindrically symmetric mean-field nematic ordering interaction. As expected, in two dimensions the system undergoes a second-order phase transition and in three dimensions the nematic transition is first-order uniaxial. The three relevant physical parameters which describe the phase behavior of the polymers are the molecular mass of the polymers, a measure of the chain stiffness and strength of the nematic interaction. The formulation in this paper is for infinitely long polymers. If the chain stiffness is measured by the bending energy ε, with u as the strength of the hardcore repulsion and U that of the soft interactions, we find the following relationship at the isotropic-nematic transition: ccβcε(u+Uβc)=6. cc is the critical concentration and βc=1/kBTc is the inverse critical temperature. At the transition we find that the order parameter has a universal value of 0.25. We present universal plots for the order parameter and free energy of the system as a function of polymer concentration and temperature. [ABSTRACT FROM AUTHOR]

In this paper we study the stability of steady state solutions to Doi’s kinetic equation for rigid rod-like polymers in an arbitrary flow field. It is found that for a certain range of concentration, the addition of flow to an isotropic phase can induce a transition to the nematic phase, if the flow rate exceeds a certain critical value. This critical flow rate decreases as concentration is increased. For phase transitions occurring in weak flow, exact solutions to this problem are calculated. Unlike the ‘‘free energy’’ approach, these calculations are not restricted to potential flows. [ABSTRACT FROM AUTHOR]

The flow-induced coil-stretch transition of high molecular weight polymers has generally been held to be of first order. But evidence of significant slowing down in the rate at which the polymers relax to equilibrium in the vicinity of the transition suggests that the thermodynamic character of the transition may be less clear-cut. The above slowing down effect is actually characteristic of a second-order transition, and it points to the existence of a broad spectrum of conformational states in the transition region, analogous to the existence of fluctuations of all length scales at a critical point. In this paper, using a path integral approach based on a free-draining finitely extensible chain model, we calculate various polymer properties as a function of elongational flow as a way of exploring different statistical mechanical details of the coil-stretch transition. These properties include the molecular weight dependence of the flow-extension curve of the polymer, the distribution of its steady-state end-to-end distances, and the characteristic relaxation time τR of these distances. Among other findings, our calculations indicate that the coil-stretch transition is discontinuous in the N → ∞ limit, that the effective free energy of the chain is unimodal at all values of the flow, becoming broad and flat in the immediate vicinity of the transition, and that the ratio of τR to the Rouse relaxation time increases abruptly at the transition before eventually reaching a plateau value at large flow strengths. These aspects of the coil-stretch transition place it among a larger class of unconventional nominally first-order single chain transitions that include the adsorption transition of surface-tethered polymers and the escape transition of compressed polymers. [ABSTRACT FROM AUTHOR]