Polymeric systems Monte Carlo simulation

As stated in Sec. 3.1, only ideal systems will be considered in this section. This definition implies that there is no intramolecular reaction, a condition which is satisfied in practice for very low concentrations of Af monomers (f >2), in the A2 + Af chainwise polymerization. To take into account intramolecular reactions it would be necessary to introduce more advanced methods to describe network formation, such as dynamic Monte Carlo simulations. 

S. K. Kumar, I. Szleifer, and A. Z. Panagiotopoulos, Phys. Rev. Lett., 66, 2935 (1991). Determination of the Chemical Potential of Polymeric Systems from Monte Carlo Simulations. 

This chapter discusses the form and parameterization of the potential energy terms that are used for the atomistic simulation of polymers. The sum of potential terms constitutes a molecular force field that can be used in molecular mechanics, molecular dynamics, and Monte Carlo simulations of polymeric systems. Molecular simulation methods can be used to determine such properties as PVT data, selfdiffusion coefficients, modulus, phase equilibrium, x-ray and neutron diffraction spectra, small molecule solubility, and glass transition temperatures with considerable accuracy and reliability using current force fields. Included in the coverage of Chapter 4 is a review of the fundamentals of molecular mechanics and a survey of the most widely used force fields for the simulation of polymer systems. In addition, references to the use of specific force fields in the study of important polymer groups are given. 

Tobita, H., Yanase, F., 2007. Monte Carlo simulation of controlled/living radical polymerization in emulsified systems. Macromol. Theory Simul. 16, 476-488. 

Binder has written an introduction to the theory and methods of Monte Carlo simulation techniques in classical statistical mechanics that are capable of providing measurements of equilibrium properties and of simulating transport and relaxation phenomena. The standard Metropolis algorithm of system sampling has latterly been supplemented by the force bias, Brownian dynamics, and molecular dynamics techniques, and, as noted in the first report, with the aid of these the study has commenced of the behaviour of polymeric systems. 

Wilding, N.B. Muller, M. Accurate measurements of the chemical-potential of polymeric systems by Monte-Carlo simulation. J. Chem. Phys. 1994, 101 (5), 4324-4330. 

To illustrate the use of equation (6), it is useful to consider a specific algorithm for Monte Carlo simulation of polymers. Assuming that the system under investigation consists of a single polymeric chain in solution, an efficient simulation algorithm must explore as many configurations as possible, as... 

The present chapter has centered on experimental efforts performed to study confined polymer crystallization. However, molecular dynamics simulations and dynamic Monte Carlo simulations have also been recently employed to study confined nucleation and crystallization of polymeric systems [99, 147]. These methods and their application to polymer crystallization are discussed in detail in Chapter 6. A recent reference by Hu et al. reviews the efforts performed by these researchers in trying to understand the effects of nanoconfinement on polymer crystallization mainly through dynamic Monte Carlo simulations of lattice polymers [147, 311]. The authors have performed such types of simulations in order to study homopolymers confined in ultrathin films [282], nanorods [312] and nanodroplets [147], and crystallizable block components within diblock copolymers confined in lamellar [313, 314], cylindrical [70,315], and spherical [148] MDs. 

With the development of molecular closures, PRISM theory has shown the ability to predict a x parameter with composition and degree of polymerization dependence that is consistent with simulation results [114]. Smdies of symmetric block copolymer liquids show qualitative agreement with Monte Carlo simulation, but both the R-MMSA and R-MPY closures fail to predict a point of spinodal decomposition for finite degrees of polymerization [73, 74], These results are for the somewhat unrealistic system of a symmetric blend model where each species has the same chain length and site diameter and the interactions between monomers of the same type are purely repulsive while the cross term has an attractive tail. 

The complexity of polymeric systems make tire development of an analytical model to predict tlieir stmctural and dynamical properties difficult. Therefore, numerical computer simulations of polymers are widely used to bridge tire gap between tire tlieoretical concepts and the experimental results. Computer simulations can also help tire prediction of material properties and provide detailed insights into tire behaviour of polymer systems. A simulation is based on two elements a more or less detailed model of tire polymer and a related force field which allows tire calculation of tire energy and tire motion of tire system using molecular mechanisms, molecular dynamics, or Monte Carlo teclmiques 1631. 

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