Monte Carlo simulations, polymer

Henstenburg, R.B. and Phoenix, S.L. (1989). Interfaeial shear strength studies using the single-filament-compositc test, part II, A probability model and Monte Carlo simulation. Polym. Composites 10, 389-408. 

Esoobedo F A and de Pablo J J 1996 Expanded grand oanonioal and Gibbs ensemble Monte Carlo simulation of polymers J. Chem. Phys. 105 4391-4... 

The parameter /r tunes the stiffness of the potential. It is chosen such that the repulsive part of the Leimard-Jones potential makes a crossing of bonds highly improbable (e.g., k= 30). This off-lattice model has a rather realistic equation of state and reproduces many experimental features of polymer solutions. Due to the attractive interactions the model exhibits a liquid-vapour coexistence, and an isolated chain undergoes a transition from a self-avoiding walk at high temperatures to a collapsed globule at low temperatures. Since all interactions are continuous, the model is tractable by Monte Carlo simulations as well as by molecular dynamics. Generalizations of the Leimard-Jones potential to anisotropic pair interactions are available e.g., the Gay-Beme potential [29]. This latter potential has been employed to study non-spherical particles that possibly fomi liquid crystalline phases. 

Monte Carlo simulations, which include fluctuations, then yields Simulations of a coarse-grained polymer blend by Wemer et al find = 1 [49] in the strong segregation limit, in rather good... 

Deutsoh H-P and Binder K 1993 Mean-field to Ising orossover in the oritioal behavior of polymer mixtures—a finite size sealing analysis of Monte Carlo simulations J. Physique II 3 1049... 

Models Used in Monte Carlo Simulations of Polymers... 

Mesoscale simulations model a material as a collection of units, called beads. Each bead might represent a substructure, molecule, monomer, micelle, micro-crystalline domain, solid particle, or an arbitrary region of a fluid. Multiple beads might be connected, typically by a harmonic potential, in order to model a polymer. A simulation is then conducted in which there is an interaction potential between beads and sometimes dynamical equations of motion. This is very hard to do with extremely large molecular dynamics calculations because they would have to be very accurate to correctly reflect the small free energy differences between microstates. There are algorithms for determining an appropriate bead size from molecular dynamics and Monte Carlo simulations. 

Many simulations attempt to determine what motion of the polymer is possible. This can be done by modeling displacements of sections of the chain, Monte Carlo simulations, or reptation (a snakelike motion of the polymer chain as it threads past other chains). These motion studies ultimately attempt to determine a correlation between the molecular motion possible and the macroscopic flexibility, hardness, and so on. 

The hst which follows gives an outline of the properties of a Monte Carlo simulation used in the context of molecular modeling studies for sampling either multiple conformations of smaller, flexible stmctures or multiple local minima of larger macromolecules or polymers ... 

Fig. 7 gives an example of such a comparison between a number of different polymer simulations and an experiment. The data contain a variety of Monte Carlo simulations employing different models, molecular dynamics simulations, as well as experimental results for polyethylene. Within the error bars this universal analysis of the diffusion constant is independent of the chemical species, be they simple computer models or real chemical materials. Thus, on this level, the simplified models are the most suitable models for investigating polymer materials. (For polymers with side branches or more complicated monomers, the situation is not that clear cut.) It also shows that the so-called entanglement length or entanglement molecular mass Mg is the universal scaling variable which allows one to compare different polymeric melts in order to interpret their viscoelastic behavior. 

The bond fluctuation model (BFM) [51] has proved to be a very efficient computational method for Monte Carlo simulations of linear polymers during the last decade. This is a coarse-grained model of polymer chains, in which an effective monomer consists of an elementary cube whose eight sites on a hypothetical cubic lattice are blocked for further occupation (see... 

A. Milchev, D. P. Landau. Adsorption of living polymers on a solid surface A Monte Carlo simulation. J Chem Phys 204 9161-9168, 1996. 

K. Binder, P. Y. Lai, J. Wittmer. Monte Carlo simulations of chain dynamics in polymer brushes. Faraday Discuss Chem Sci 95 97-109, 1994. 

A. Milchev, W. Paul, K. Binder. Polymer chains confined into tubes with attractive walls A Monte Carlo simulation. Macromol Theory Simul 5 305-323, 1994. 

R. B. Pandey, A. Milchev, K. Binder. Semidilute and concentrated polymer solutions near attractive walls Dynamic Monte Carlo simulation of density and pressure profiles of a coarse-grained model. Macromolecules 50 1194-1204, 1997. 

V. Yamakov, A. Milchev. Polymer chain in a flow through a porous medium A Monte Carlo simulation. Phys Rev E 5(5 7043-7052, 1997. 

A. Milchev, K. Binder. Dewetting of thin polymer films adsorbed on solid substrates A Monte Carlo simulation of the early stages. J Chem Phys 705 1978-1989, 1997. 

P. Y. Lai. Statics and dynamics of a polymer chain adsorbed on a surface Monte Carlo simulation using the bond fluctuation model. Phys Rev E 49 5420-5430, 1994. 

K. Kremer, K. Binder. Dynamics of polymer chains confined into tubes Scaling theory and Monte Carlo simulations. J Chem Phys 7 6381-6394, 1984. 

S. K. Kumar, M. Vacatello, D. Y. Yoon. Off-lattice Monte Carlo simulations of polymer melts confined between two plates. J Chem Phys 59 5206-5215, 1988. 

A. Yethiraj, C. K. Hall. Monte Carlo simulation of polymers confined between flat plates. Macromolecules 25 1865-1872, 1990. 

A. Yethiraj. Monte Carlo simulation of confined semiflexible polymer melts. J Chem Phys 707 2489-2497, 1994. 

A. Milchev, K. Binder. Osmotic pressure, atomic pressure and the virial equation of state of polymer solutions Monte Carlo simulations of a bead-spring model. Macromol Theory Simul 5 915-929, 1994. 

In fact, the variable x /Gi controls the "crossover" from one "universality class" " to the other. I.e., there exists a crossover scaling description where data for various Gi (i.e., various N) can be collapsed on a master curve Evidence for this crossover scaling has been seen both in experiments and in Monte Carlo simulations for the bond fluctuation model of symmetric polymer mixtures, e.g Fig. 1. One expects a scaling of the form... 

As for polymer mixtures in the Monte Carlo simulation of simple... 

Miller J.A., Speckhard T.A., Homan J.G., and Cooper S.L. Monte Carlo simulation study of the pol3mier-ization of polyurethane block co-polymers. 4. ModeUng of experimental data. Polymer, 28, 758, 1987. Speckhard T.A., Miller J.A., and Cooper S.L., Monte Carlo simulation study of polymerization of polyurethane block co-pol3miers. 1. Natural compositional heterogeneity under ideal polymerization condition, Macromolecules, 19, 1550, 1986. 

A general method has been developed for the estimation of model parameters from experimental observations when the model relating the parameters and input variables to the output responses is a Monte Carlo simulation. The method provides point estimates as well as joint probability regions of the parameters. In comparison to methods based on analytical models, this approach can prove to be more flexible and gives the investigator a more quantitative insight into the effects of parameter values on the model. The parameter estimation technique has been applied to three examples in polymer science, all of which concern sequence distributions in polymer chains. The first is the estimation of binary reactivity ratios for the terminal or Mayo-Lewis copolymerization model from both composition and sequence distribution data. Next a procedure for discriminating between the penultimate and the terminal copolymerization models on the basis of sequence distribution data is described. Finally, the estimation of a parameter required to model the epimerization of isotactic polystyrene is discussed. 

Special considerations are required in estimating paraimeters from experimental measurements when the relationship between output responses, input variables and paraimeters is given by a Monte Carlo simulation. These considerations, discussed in our first paper 1), relate to the stochastic nature of the solution and to the fact that the Monte Carlo solution is numerical rather than functional. The motivation for using Monte Carlo methods to model polymer systems stems from the fact that often the solution... 

We have presented applications of a parameter estimation technique based on Monte Carlo simulation to problems in polymer science involving sequence distribution data. In comparison to approaches involving analytic functions, Monte Carlo simulation often leads to a simpler solution of a model particularly when the process being modelled involves a prominent stochastic coit onent. 

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