Monte Carlo studies of two-dimensional polymer–solvent systems

Polymer, 2002

Cubic lattice Monte Carlo simulation studies were conducted to examine the effect of con®nement on dilute and non-dilute solutions of polymer chains in a channel with a square cross section. In dilute solutions, the partition coef®cient K c with channels of different widths d followed the scaling-law prediction, and was close to the square of the partition coef®cient K s with a slit of the same d. The chain with its bulk radius of gyration greater than ,d/2 adopted a conformation extending along the channel and, with a decreasing channel width, the chain ends were forced to face outside. The chain conformation in broader channels was a compressed random coil. The K c increased with an increasing polymer concentration f E in the exterior solution equilibrated with the channel. In a weak con®nement, K c closely followed K s 2 of the same f E and d. The chains contracted at higher concentrations as they did in the bulk solutions. In a strong con®nement, K c was smaller than K s 2 at the same f E in the semidilute regime, and, at higher concentrations, sharply increased to the value close to K s 2 . q

Colloids and Surfaces A: Physicochemical and Engineering Aspects, 2002

Monomer density profile of polymer chains in the good solvent condition near an impenetrable wall was examined in lattice Monte Carlo simulation. It was found that a positive penetration depth k is necessary for the density profile to follow the prediction of the scaling theory. In dilute solutions, k was 0.13-0.22 of the lattice unit from a weak confinement to a strong confinement. With an increasing concentration, k increased gradually to a value close to 0.36. These findings corroborate our hypothesis that the need of the positive k and a greater k at higher concentrations result from non-even chain transport due to a large difference in site occupancy, especially at higher concentrations.

Physical Review E, 1998

A discrete-to-continuum approach is introduced to study the static and dynamic properties of polymer chain systems with a bead-spring chain model in two dimensions. A finitely extensible nonlinear elastic potential is used for the bond between the consecutive beads with the Lennard-Jones ͑LJ͒ potential with smaller (R c ϭ2 1/6 ϭ0.95) and larger (R c ϭ2.5ϭ2.1) values of the upper cutoff for the nonbonding interaction among the neighboring beads. We find that chains segregate at temperature Tϭ1.0 with R c ϭ2.1 and remain desegregated with R c ϭ0.95. At low temperature (Tϭ0.2), chains become folded, in a ribbonlike conformation, unlike random and self-avoiding walk conformations at Tϭ1.0. The power-law dependence of the rms displacements of the center of mass (R c.m.) of the chains and their center node (R cn) with time are nonuniversal, with the range of exponents 1 Ӎ0.45Ϫ0.25 and 2 Ӎ0.30Ϫ0.10, respectively. Both radius of gyration (R g) and average bond length (͗l͘) decrease on increasing the range of interaction (R c), consistent with the extended state in good solvent to collapsed state in poor solvent description of the polymer chains. Analysis of the radial distribution function supports these observations. ͓S1063-651X͑98͒11205-9͔

Journal of Computer-Aided Materials Design, 1996

Using a bead spring model of flexible polymer chains, the density profiles and chain configurational properties of polymer solutions confined between parallel plates were studied. A wide range of density ~, chain length N, and strength e of a short-range attractive wall potential was investigated. Both a temperature T in the good solvent regime (T > 0, 0 being the Theta temperature where a chain in unconfined bulk three-dimensional solution would behave ideally) and a temperature in the bad solvent regime (T < 0) were considered. It is shown that phase separation in a polymer-rich and polymer-poor solution in the slit competes with polymer adsorption at the walls. A qualitative connection to the wetting behavior of semiinfinite polymer solutions is drawn. The acceptance rate for monomer motions was studied for various conditions, and profiles of monomer mobility across the slit were recorded. Also, average chain relaxation times were extracted from the time dependence of mean-square displacements. Although with increasing density the chain radii (at T > e) show a crossover from two-dimensional excluded volume behavior (Re ~ N 2v with v = 3/4) to ideal random walk behavior (v = 1/2), the relaxation times show effective exponents Zef f (I: ~: N zeff) that clearly deviate from the Rouse prediction in concentrated confined solutions.

Macromolecular Theory and Simulations, 1997

We have explored the performance of a simulation model for Gaussian chains at different concentrations in a good solvent. The Gaussian statistics for the distances between contiguous beads in the model is directly implemented in the individual moves of a Monte Carlo algorithm. When the results of conformational properties for the Gaussian model are compared with those provided by a freely jointed model in the same conditions, significant differences arise at finite concentrations. The modeled Gaussian chain yields incorrect results for the quadratic average dimensions (R2) and (S') at high concentrations, but correctly reproduces the results for the scaled end-to-end distance distribution function at any concentration, showing the effects of the screening of excluded volume when concentration increases. The reason for the wrong behavior of the simulated Gaussian model comes from a strong distortion of the "bond distance" distribution as a result of the concentration increase. We conclude that this model can only be safely applied to infinitely dilute solutions.

The Journal of chemical physics, 1998

We investigate by means of a number of different dynamical Monte Carlo simulation methods the self-assembly of equilibrium polymers in dilute, semidilute and concentrated solutions under good-solvent conditions. In our simulations, both linear chains and closed loops compete for the monomers, expanding on earlier work in which loop formation was disallowed. Our findings show that the conformational properties of the linear chains, as well as the shape of their size distribution function, are not altered by the formation of rings. Rings only seem to deplete material from the solution available to the linear chains. In agreement with scaling theory, the rings obey an algebraic size distribution, whereas the linear chains conform to a Schultz-Zimm type of distribution in dilute solution, and to an exponentional distribution in semidilute and concentrated solution. A diagram presenting different states of aggregation, including monomer-, ring-and chain-dominated regimes, is given. The relevance of our work in the context of experiment is discussed.

The Journal of Chemical Physics, 2009

We present a comparative study of two computer simulation methods to obtain static and dynamic properties of dilute polymer solutions. The first approach is a recently established hybrid algorithm based upon dissipative coupling between Molecular Dynamics and lattice Boltzmann (LB), while the second is standard Brownian Dynamics (BD) with fluctuating hydrodynamic interactions. Applying these methods to the same physical system (a single polymer chain in a good solvent in thermal equilibrium) allows us to draw a detailed and quantitative comparison in terms of both accuracy and efficiency. It is found that the static conformations of the LB model are distorted when the box length L is too small compared to the chain size. Furthermore, some dynamic properties of the LB model are subject to an L −1 finite size effect, while the BD model directly reproduces the asymptotic L → ∞ behavior. Apart from these finite size effects, it is also found that in order to obtain the correct dynamic properties for the LB simulations, it is crucial to properly thermalize all the kinetic modes. Only in this case, the results are in excellent agreement with each other, as expected. Moreover, Brownian Dynamics is found to be much more efficient than lattice Boltzmann as long as the degree of polymerization is not excessively large.

Physical review. E, Statistical, nonlinear, and soft matter physics, 2003

The breakdown of dynamical scaling for a dilute polymer solution in two dimensions has been suggested by Shannon and Choy [Phys. Rev. Lett. 79, 1455 (1997)]. However, we show here through extensive computer simulations that dynamical scaling holds when the relevant dynamical quantities are properly extracted from finite systems. To verify dynamical scaling, we present results based on mesoscopic simulations in two dimensions for a polymer chain in a good solvent with full hydrodynamic interactions. We also present analytical arguments for the size dependence of the diffusion coefficient and find excellent agreement with the present large-scale simulations.

Macromolecular Theory and Simulations, 1997

We investigate the changes in the average chain length of a solution of semi-flexible living polymers between two hard repulsive walls as the width of the slit, D, is varied. Two different Monte Carlo models, that of the 'slithering snake' and of the 'independent monomer states' are employed in order to simulate a polydisperse system of chain molecules confined in a gap which is either closed (with fixed total density), or open and in contact with an external reservoir. It appears that the mean chain length L in a state of equilibrium polymerization depends essentially on the geometry constraints for sufficiently small D. We find that in the case of an open slit the mean length L(D) decreases with D + 0 for flexible chains whereas it grows if the chains are sufficiently stiff. As the width of a closed gap D is decreased, in a three-dimensional gap L(D) gradually decreases for absolutely flexible chains whereas for semi-rigid chains it goes through a minimum at D = 2 and then grows again for D = 1. In two dimensions, in a closed strip the average chain length L(D) for both flexible and rigid macromolecules goes through a sharp minimum and then grows steeply in compliance with a predicted divergence for semi-rigid polymers as D + 0. We attribute the observed discrepancies of our numeric experiments with some recent analytic predictions to the ordering effect of container walls on the polymer solution when chain stiffness and excluded volume interactions are taken into account.

Journal de Physique Lettres, 1982