Monte bond-fluctuating

Since this behavior is universal, it is obvious that the simplest simulation models which contain the essential aspects of polymers are sufficient to study these phenomena. Two typical examples of such models are the bond fluctuation Monte Carlo model and the simple bead-spring model employed in molecular dynamics simulations. Both models are illustrated in Fig. 6. 

FIG. 6 Illustration of the bond fluctuation Monte Carlo model and the standard bead-spring chain (see, e.g. [4]). 

FIG. 11 Plot of squared bond length vs T for five cooling rates, glass-forming bond fluctuation Monte Carlo simulations [47]. 

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... 

Y. Rouault, A. Milchev. Monte Carlo study of living polymers with the bond-fluctuation method. Phys Rev E 57 5905-5910, 1995. 

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. 

I. Gerroff, A. Milchev, W. Paul, K. Binder. A new off-lattice Monte Carlo model for polymers A comparison of static and dynamic properties with the bond fluctuation model and application to random media. J Chem Phys 95 6526-6539, 1993. 

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... 

While thin polymer films may be very smooth and homogeneous, the chain conformation may be largely distorted due to the influence of the interfaces. Since the size of the polymer molecules is comparable to the film thickness those effects may play a significant role with ultra-thin polymer films. Several recent theoretical treatments are available [136-144,127,128] based on Monte Carlo [137-141,127, 128], molecular dynamics [142], variable density [143], cooperative motion [144], and bond fluctuation [136] model calculations. The distortion of the chain conformation near the interface, the segment orientation distribution, end distribution etc. are calculated as a function of film thickness and distance from the surface. In the limit of two-dimensional systems chains segregate and specific power laws are predicted [136, 137]. In 2D-blends of polymers a particular microdomain morphology may be expected [139]. Experiments on polymers in this area are presently, however, not available on a molecular level. Indications of order on an... 

Monte-Carlo Simulation of the Bond-Fluctuation Model. 108... 

Mapping Atomistically Detailed Models of Flexible Polymer Chains in Melts to Coarse-Grained Lattice Descriptions Monte Carlo Simulation of the Bond Fluctuation Model... 

With the Monte Carlo technique, a very large number of membrane problems have been worked on. We have insufficient space to review all the data available. However, the formation of pores is of relevance for permeation. The formation of perforations in a polymeric bilayer has been studied by Muller by using Monte Carlo simulation [67] within the bond fluctuation model. In this particular MC technique, realistic moves are incorporated, such that the number of MC steps can be linked to a simulated time. 

Lattice Monte Carlo Model for Polymers A Comparison of Static and Dynamic Properties with the Bond-Fluctuation Model and Application to Random Media. 

Polymer Melts A 2-D Monte Carlo Study in the Framework of the Bond Fluctuation Method. 

Initially, the protein-like HP sequences were generated in [18] for the lattice chains of N = 512 monomeric units (statistical segments), using for simulations a Monte Carlo method and the lattice bond-fluctuation model [34], When the chain is a random (quasirandom) heteropolymer, an average over many different sequence distributions must be carried out explicitly to produce the final properties. Therefore, the sequence design scheme was repeated many times, and the results were averaged over different initial configurations. 

The coil-to-globule transition was studied for designed HP copolymer chains both by means of lattice Monte Carlo simulations using bond fluctuation algorithms and multiple histogram reweighting [100,101] and by a numer-... 

This idea that the solvent flow field can be approximated by the Brinkman equation has been used in several recent simulations of a polymer brush in simple shear flow. In these simulations, the solvent is not included explicitly but it s effect is modeled using the Brinkman equation. Lai and Binder [65] and Lai and Lai [66], using a bond fluctuation lattice model, and Miao et al. [67], using a continuum model, studied the properties of a dense polymer brush in a flow field by modifying the standard Metropolis Monte Carlo transition probability to take into account the effective force acting upon the brush chains by the moving sol-... 

Gerroff, A. Milchev, K. Binder, and W. Paul, /. Chem. Phys., 98, 6526 (1993). A New Off-Lattice Monte Carlo Model for Polymers A Comparison of Static and Dynamic Properties with the Bond-Fluctuation Model and Application to Random Media. 

H. P. Wittman, K. Kremer, and K. Binder, /. Chem. Phys., 96, 6291 (1992). Glass Transition of Polymer Melts A Two-Dimensional Monte Carlo Study in the Framework of the Bond Fluctuation Method. 

A quantitative comparison between the mean field prediction and the Monte Carlo results is presented in Fig. 15. The main panel plots the inverse scattering intensity vs. xN. At small incompatibility, the simulation data are compatible with a linear prediction (cf. (48)). From the slope, it is possible to estimate the relation between the Flory-Huggins parameter, x, and the depth of the square well potential, e, in the simulations of the bond fluctuation model. As one approaches the critical point of the mixture, deviations between the predictions of the mean field theory and the simulations become apparent the theory cannot capture the strong universal (3D Ising-like) composition fluctuations at the critical point [64,79,80] and it underestimates the incompatibility necessary to bring about phase separation. If we fitted the behavior of composition fluctuations at criticality to the mean field prediction, we would obtain a quite different estimate for the Flory-Huggins parameter. 

Fig. 15. Inverse maximum of the collective structure factor of composition fluctuations, N/S k 0), as a function of the incompatibility, x - Symbols correspond to Monte Carlo simulations of the bond fluctuation model, the dashed curve presents the results of a finite-size scaling analysis of simulation data in the vicinity of the critical point, and the straight, solid line indicates the prediction of the Flory-Huggins theory. The critical incompatibility, XcN = 2 predicted by the Flory-Huggins theory and that obtained from Monte Carlo simulations of the bond fluctuation model M 240, N = 64, p = 1/16 and = 25.12) are indicated by arrows. The left inset compares the phase diagram obtained from simulations with the prediction of the Flory-Huggins theory (c.f. (47)). The right inset depicts the compositions at coexistence such that the mean field theory predicts them to fall onto a straight line. Prom Muller [78]...

Fig. 21. Ratio between the interface tension 7 and the simple expression for the strong segregation limit yssL in (54) as a function of inverse incompatibility. Symbols correspond to Monte Carlo results for the bond fluctuation model, the solid line shows the result of the SCF theory, and the dashed line presents first corrections to (54) calculated by Semenov. Also an estimate of the interface tension from the spectrum of capillary waves is shown to agree well with the results of the reweighting method. Adapted from Schmid and Muller [107]...

I. Carmesin and K. Kremer (1988) The bond fluctuation method - a new effective algorithm for the dynamics of polymers in all spatial dimensions. Macromolecules 21, pp. 2819-2823 H.-P. Deutsch and K. Binder (1991) Interdiffusion and self-diffusion in polymer mixtures - a monte-carlo study. J. Chem. Phys. 94, pp. 2294-2304... 

Coarse-Grained Lattice Simulations for Glassy Polymer Melts Bond-Fluctuation Model and Monte Carlo Approach... 

Monte Carlo and Cooling Procedure. As a result of the competition between energy and packing constraints the structural relaxation time strongly increases during the cooling process if the usual bond-fluctuation dynamics is used. This kind of dynamics consists of the following steps ... 

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