New Development of Monte Carlo Techniques for Studying Bottle-brush Polymers

Due to the complex characteristics of bottle-brush polymers, it became a challenge to develop an efficient algorithm for studying such macromolecules under various solvent conditions or some constraints in the space by using computer simulations. In the limit of a bottle-brush polymer with a rather stiff backbone (straight rigid backbone), we generalize the variant of the biased chain growth algorithm, the pruned-enriched Rosenbluth method, for simulating polymers with complex architecture, from star polymers to bottle-brush polymers, on the simple cubic lattice. With the high statistics of our Monte Carlo results, we check the theoretical predictions of side chain behavior and radial monomer density profile. For the comparison of the experimental data for bottle-brush polymers with a flexible backbone and flexible side chains, based on the bond fluctuation model we propose another fast Monte Carlo algorithm combining the local moves, the pivot move, and an adjustable simulation lattice box. By monitoring the autocorrelation functions of gyration radii for the side chains and for the backbone, we see that for fixed side chain length there is no change in the behavior of these two functions as the backbone length increases. Our extensive results cover the range which is accessible for the comparison to experimental data and for the checking of the theoretically predicted scaling laws.Comment: 9 pages, 10 Figures, Proceedings of the 24nd Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics, Feb 21-25, 2011, Athens, Georgia, US

Lattice Monte Carlo Simulations of Polymer Melts

We use Monte Carlo simulations to study polymer melts consisting of fully flexible and moderately stiff chains in the bond fluctuation model at a volume fraction $0.5$. In order to reduce the local density fluctuations, we test a pre-packing process for the preparation of the initial configurations of the polymer melts, before the excluded volume interaction is switched on completely. This process leads to a significantly faster decrease of the number of overlapping monomers on the lattice. This is useful for simulating very large systems, where the statistical properties of the model with a marginally incomplete elimination of excluded volume violations are the same as those of the model with strictly excluded volume. We find that the internal mean square end-to-end distance for moderately stiff chains in a melt can be very well described by a freely rotating chain model with a precise estimate of the bond-bond orientational correlation between two successive bond vectors in equilibrium. The plot of the probability distributions of the reduced end-to-end distance of chains of different stiffness also shows that the data collapse is excellent and described very well by the Gaussian distribution for ideal chains. However, while our results confirm the systematic deviations between Gaussian statistics for the chain structure factor $S_c(q)$ [minimum in the Kratky-plot] found by Wittmer et al.~\{EPL {\bf 77} 56003 (2007).\} for fully flexible chains in a melt, we show that for the available chain length these deviations are no longer visible, when the chain stiffness is included. The mean square bond length and the compressibility estimated from collective structure factors depend slightly on the stiffness of the chains.Comment: 15 pages, 12 figure

2-Dimensional Polymers Confined in a Strip

Single two dimensional polymers confined to a strip are studied by Monte Carlo simulations. They are described by N-step self-avoiding random walks on a square lattice between two parallel hard walls with distance 1 << D << N^\nu (\nu = 3/4 is the Flory exponent). For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. We measure the densities of monomers and of end points as functions of the distance from the walls, the longitudinal extent of the chain, and the forces exerted on the walls. Their scaling with D and the universal ratio between force and monomer density at the wall are compared to theoretical predictions.Comment: 5 pages RevTex, 7 figures include

Detailed analysis of Rouse mode and dynamic scattering function of highly entangled polymer melts in equilibrium

We present large-scale molecular dynamics simulations for a coarse-grained model of polymer melts in equilibrium. From detailed Rouse mode analysis we show that the time-dependent relaxation of the autocorrelation function (ACF) of modes $p$ can be well described by the effective stretched exponential function due to the crossover from Rouse to reptation regime. The ACF is independent of chain sizes $N$ for $N/p<N_e$ ($N_e$ is the entanglement length), and there exists a minimum of the stretching exponent as $N/p \rightarrow N_e$. As $N/p$ increases, we verify the crossover scaling behavior of the effective relaxation time $\tau_{{\rm eff},p}$ from the Rouse regime to the reptation regime. We have also provided evidence that the incoherent dynamic scattering function follows the same crossover scaling behavior of the mean square displacement of monomers at the corresponding characteristic time scales. The decay of the coherent dynamic scattering function is slowed down and a plateau develops as chain sizes increase at the intermediate time and wave length scales. The tube diameter extracted from the coherent dynamic scattering function is equivalent to the previous estimate from the mean square displacement of monomers.Comment: 8 pages, 7 figures, to be published in EPJST special issue on "Phase transitions and critical phenomena" (2017

Monte Carlo Protein Folding: Simulations of Met-Enkephalin with Solvent-Accessible Area Parameterizations

Treating realistically the ambient water is one of the main difficulties in applying Monte Carlo methods to protein folding. The solvent-accessible area method, a popular method for treating water implicitly, is investigated by means of Metropolis simulations of the brain peptide Met-Enkephalin. For the phenomenological energy function ECEPP/2 nine atomic solvation parameter (ASP) sets are studied that had been proposed by previous authors. The simulations are compared with each other, with simulations with a distance dependent electrostatic permittivity $\epsilon (r)$, and with vacuum simulations ($\epsilon =2$). Parallel tempering and a recently proposed biased Metropolis technique are employed and their performances are evaluated. The measured observables include energy and dihedral probability densities (pds), integrated autocorrelation times, and acceptance rates. Two of the ASP sets turn out to be unsuitable for these simulations. For all other sets, selected configurations are minimized in search of the global energy minima. Unique minima are found for the vacuum and the $\epsilon(r)$ system, but for none of the ASP models. Other observables show a remarkable dependence on the ASPs. In particular, autocorrelation times vary dramatically with the ASP parameters. Three ASP sets have much smaller autocorrelations at 300 K than the vacuum simulations, opening the possibility that simulations can be speeded up vastly by judiciously chosing details of the forceComment: 10 pages; published in "NIC Symposium 2004", eds. D. Wolf at el. (NIC, Juelich, 2004

Polymers Confined between Two Parallel Plane Walls

Single three dimensional polymers confined to a slab, i.e. to the region between two parallel plane walls, are studied by Monte Carlo simulations. They are described by $N$-step walks on a simple cubic lattice confined to the region $1 \le z \le D$. The simulations cover both regions $D > R_F$ (where $R_F \sim N^\nu$ is the Flory radius, with $\nu \approx 0.587$), as well as the cross-over region in between. Chain lengths are up to $N=80,000$, slab widths up to D=120. In order to test the analysis program and to check for finite size corrections, we actually studied three different models: (a) Ordinary random walks (mimicking $\Theta$-polymers); (b) Self-avoiding walks (SAW); and (c) Domb-Joyce walks with the self-repulsion tuned to the point where finite size corrections for free (unrestricted) chains are minimal. For the simulations we employ the pruned-enriched-Rosenbluth method (PERM) with Markovian anticipation. In addition to the partition sum (which gives us a direct estimate of the forces exerted onto the walls), we measure the density profiles of monomers and of end points transverse to the slab, and the radial extent of the chain parallel to the walls. All scaling laws and some of the universal amplitude ratios are compared to theoretical predictions.Comment: 8 pages, 14 figures include

Growth Algorithms for Lattice Heteropolymers at Low Temperatures

Two improved versions of the pruned-enriched-Rosenbluth method (PERM) are proposed and tested on simple models of lattice heteropolymers. Both are found to outperform not only the previous version of PERM, but also all other stochastic algorithms which have been employed on this problem, except for the core directed chain growth method (CG) of Beutler & Dill. In nearly all test cases they are faster in finding low-energy states, and in many cases they found new lowest energy states missed in previous papers. The CG method is superior to our method in some cases, but less efficient in others. On the other hand, the CG method uses heavily heuristics based on presumptions about the hydrophobic core and does not give thermodynamic properties, while the present method is a fully blind general purpose algorithm giving correct Boltzmann-Gibbs weights, and can be applied in principle to any stochastic sampling problem.Comment: 9 pages, 9 figures. J. Chem. Phys., in pres

A coarse-grained polymer model for studying the glass transition

To study the cooling behavior and the glass transition of polymer melts in bulk and with free surfaces a coarse-grained weakly semi-flexible polymer model is developed. Based on a standard bead spring model with purely repulsive interactions an attractive potential between non-bonded monomers is added, such that the pressure of polymer melts is tuned to zero. Additionally, the commonly used bond bending potential [Everaers et al., Science 303, 823 (2004)] controlling the chain stiffness is replaced by a new bond bending potential. For this model, we show that the Kuhn length and the internal distances along the chains in the melt only very weakly depend on temperature, just as for typical experimental systems. The glass transition is observed by the temperature dependency of the melt density and the characteristic non-Arrhenius slowing down of the chain mobility. The model is set to allow for a fast switch between models, for which a wealth of data already exists.Comment: 6 pages, 5 figures; published version (including erratum

Chain retraction in highly entangled stretched polymer melts

We use computer simulations to study the relaxation of strongly deformed highly entangled polymer melts in the non-linear viscoelastic regime, focusing on anisotropic chain conformations after isochoric elongation. The Doi-Edwards tube model and its GLaMM extension, incorporating contour length fluctuation and convective constraint release, predict a retraction of the polymer chain extension in all directions, setting in immediately after deformation. This prediction has been challenged by experiment, simulation, and other theoretical studies, questioning the general validity of the tube concept. For very long chains we observe the initial contraction of the chain extension parallel and perpendicular to the stretching direction. However, the effect is significantly weaker than predicted by the GLaMM model. We also show that the first anisotropic term of an expansion of the 2D scattering function qualitatively agrees to predictions of the GLaMM model, providing an option for direct experimental tests.Comment: 6 pages, 3 figures, 7 references adde