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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]

This paper presents a theoretical analysis of the closure kinetics of a polymer with hydrodynamic interactions. This analysis, which takes into account the non-Markovian dynamics of the end-to-end vector and relies on the preaveraging of the mobility tensor (Zimm dynamics), is shown to reproduce very accurately the results of numerical simulations of the complete nonlinear dynamics. It is found that Markovian treatments based on a Wilemski-Fixman approximation significantly overestimate cyclization times (up to a factor 2), showing the importance of memory effects in the dynamics. In addition, this analysis provides scaling laws of the mean first cyclization time (MFCT) with the polymer size N and capture radius b, which are identical in both Markovian and non-Markovian approaches. In particular, it is found that the scaling of the MFCT for large N is given by T - N3/2ln(N/b²), which differs from the case of the Rouse dynamics where T - N². The extension to the case of the reaction kinetics of a monomer of a Zimm polymer with an external target in a confined volume is also presented. [ABSTRACT FROM AUTHOR]

We use the two solvation potentials discussed in the previous paper and polymer reference interaction-site model (PRISM) theory to calculate the mutually consistent single-molecule conformation and liquid structure of model linear flexible nonpolar polymers. We focus on the mean end-to-end distance R2 and radius of gyration Rg of the single chain as functions of polymer density. Our calculations are compared to computer simulations to assess their accuracy, and some aspects of the general trends with density predicted are discussed. Two methods of calculating the conformation of the single chain in the solvation potential are used, one is Monte Carlo simulation, the other, introduced in this paper, employs a generating functional. We cannot unambiguously confirm the accuracy of one solvation potential over the other; at low density they give identical results, and the exact values are too few at high density. However, we are inclined to question the accuracy of the hypernetted-chain (HNC) style potential at high densities because it seems to predict a strong contraction of the polymer chain that is not seen experimentally in real polymer melts. [ABSTRACT FROM AUTHOR]

This paper is the first in a series of papers in which polymer adsorption on a surface is studied by computer simulation using the ‘‘scanning method.’’ This method is especially efficient to handle chain systems with finite interactions and geometrical constraints. Here we test the method by applying it to models of a single random walk (without excluded volume) on a simple cubic lattice, which are solved analytically; in the immediately following paper a self-avoiding walk model is treated. The scanning method is found to be extremely efficient, where walks of up to N=105 steps can be simulated reliably, leading thereby to very precise estimates of transition temperatures and critical exponents. In particular we test carefully for a lattice model the range of validity of scaling functions developed by Eisenrigler, Kremer and Binder [J. Chem. Phys. 77, 6296 (1982)] for a continuous model. We pay a special attention to corrections to scaling and demonstrate that they are strong above the transition temperature for ⊥, the perpendicular part of the mean-square end-to-end distance and for ρ(z), the monomer concentration profile. We show that at T=∞, the asymptotic regime, in which these corrections become negligible, is obtained for N≊40 000 for ⊥ but a significantly larger N is required for ρ(z). This means that this regime corresponds to a real polymer length that is not realized experimentally. [ABSTRACT FROM AUTHOR]

Obtaining a rigorous and reliable method for linking computer simulations of polymer blends and composites at different length scales of interest is a highly desirable goal in soft matter physics. In this paper a multiscale modeling procedure is presented for the efficient calculation of the static structural properties of binary homopolymer blends. The procedure combines computer simulations of polymer chains on two different length scales, using a united atom representation for the finer structure and a highly coarse-grained approach on the mesoscale, where chains are represented as soft colloidal particles interacting through an effective potential. A method for combining the structural information by inverse mapping is discussed, allowing for the efficient calculation of partial correlation functions, which are compared with results from full united atom simulations. The structure of several polymer mixtures is obtained in an efficient manner for several mixtures in the homogeneous region of the phase diagram. The method is then extended to incorporate thermal fluctuations through an effective χ parameter. Since the approach is analytical, it is fully transferable to numerous systems. [ABSTRACT FROM AUTHOR]

We present a computer simulation model of polymer melts representing each chain as one single particle. Besides the position coordinate of each particle, we introduce a parameter nij for each pair of particles i and j within a specified distance from each other. These numbers, called entanglement numbers, describe the deviation of the system of ignored coordinates from its equilibrium state for the given configuration of the centers of mass of the polymers. The deviations of the entanglement numbers from their equilibrium values give rise to transient forces, which, together with the conservative forces derived from the potential of mean force, govern the displacements of the particles. We have applied our model to a melt of C800H1602 chains at 450 K and have found good agreement with experiments and more detailed simulations. Properties addressed in this paper are radial distribution functions, dynamic structure factors, and linear as well as nonlinear rheological properties. [ABSTRACT FROM AUTHOR]

It has been suggested that, due to topological constraints, rings in the melt may assume a more compact shape than Gaussian chains. In this paper, we exploit the availability of narrow fractions of perdeuterated linear and cyclic polydimethylsiloxane (PDMS) and, through the analysis of the small angle neutron scattering (SANS) profiles, demonstrate the difference in scattering properties of linear and cyclic PDMS molecules. As expected for Gaussian chains, for the H/D linear PDMS samples, log-log plots of the scattered intensity versus scattering vector Q display a Q(-2) dependence. However, for H/D cyclic blends, the scaling exponent is higher than 2, as predicted by computer simulations reported in the literature. We show that cyclic molecules in bulk display the characteristic maximum in plots of scattered intensity versus Q(-2) that is expected on the basis of Monte Carlo calculations and from the Casassa equation [E. F. Casassa, J. Polym. Sci. A 3, 605 (1965)]. It is also shown that, for rings, the Debye equation [P. Debye, J. Appl. Phys. 15, 338 (1944)] is no longer appropriate to describe the SANS profiles of H/D cyclic blends, at least up to Mw≈10 000. For these samples, the Casassa form factor gives a better representation of the SANS data and we show that this function which was developed for monodisperse cyclics is still adequate to describe our slightly polydisperse samples. Deviations from all above observations are noted for Mw>11 000 and are attributed to partial contamination of cyclic samples with linear chains. The failure of both the Debye and the Casassa form factors could be due to contamination of the cyclic fractions by linear polymers or to a real conformational change. [ABSTRACT FROM AUTHOR]

In this paper, we present computer simulation results concerning interdiffusion of fully compatible components in symmetric binary (AB) polymer mixtures in solutions. The simulation is performed in two dimensions using the algorithm based on the dynamic lattice liquid model. The solvent molecules are taken into account explicitly. The evolution of the concentration profiles in time at an interface is studied for chain lengths N=2,4,8,16 for three polymer concentrations [lowercase_phi_synonym]=0.1,0.5,0.9. The tracer diffusion coefficients for polymer chains and for the solvent are obtained by monitoring the mean square displacements of their center of mass. The relationships between coefficients of interdiffusion and self-diffusion are tested. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

The dynamics of protein folding result from both enthalpic and entropic contributions to the free energy. In this paper we focus on entropic volume exclusion effects. We carry out computer simulations using a model that allows us to independently change the size or biochemical properties of amino acid residues. To determine the importance of excluded volume effects, we investigate the effects of changing the size of side chains on the unfolding dynamics of a model four-helix bundle protein. In addition, we also investigate the effects of changing the thickness of the chain’s backbone. This has relevance to the behavior of synthetic polymers where the size of the constituent units can be varied. We find that entropic excluded volume effects are crucially important for stabilizing the organized native state relative to the molten globule. © 2004 American Institute of Physics. [ABSTRACT FROM AUTHOR]

Estimates are evaluated for all constants in the theory of polymer dynamics developed in the preceding paper. These theoretical estimates are employed in calculations on the many chain systems simulated previously by Kremer and Grest and by Paul and co-workers. The agreement between the theoretical calculations and the simulations of Kremer and Grest is found to be very good for the bead mean squared displacement. The theoretically evaluated center of mass mean squared displacement is in good qualitative agreement with the Kremer–Grest simulations, although there are quantitative differences. Good qualitative agreement with the simulations of Paul and co-workers is also obtained. It is shown that quantitative agreement can be obtained with modest changes in the theoretical estimates of a few of the constants in the theory. © 1996 American Institute of Physics. [ABSTRACT FROM AUTHOR]