Polymeric systems dynamic Monte Carlo

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. 

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. 

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. 

Science is in incessant evolution it grows with more precise theories and better instrumentation. The thermodynamic theories of polymers and polymeric systems move toward atomistic considerations for isomeric species modeled mathematically by molecular dynamics or Monte Carlo methods. At the same time good mean-field theories remain valid and useful—they must be remembered not only for the historical evolution of human knowledge, but also for the very practical reason of applicability, usefulness, and as tools for the understanding of material behavior. 

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. 

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. 

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