Monte Carlo simulation integration, calculating properties

The equilibrium properties of several approximations (HNC, PYA, MS) for the RPM have been compared with Monte Carlo simulations by Rasaiah et al. (1972) and Hafskjold and Stell (1982). The HNC approximation is found to be the most accurate of the integral equations for electrolytes. The MSA distribution functions, especially at contact, are poor and in some instances even negative However, the MSA predicts the thermodynamic properties of RPM electrolytes in aqueous solution quite accurately when they are calculated from the energy equation. Blum and coworkers (Grigera and Blum, 1976 Triolo et al., 1976, 1977 Triolo and Floriono, 1980) have compared their results with experiment for simple... 

The preparation of a series of 6FDA based Pl-clay nanocomposites and their film properties were reported in ref [154], Studies on the effect of transformer oil on these films [155] and their theoretically calculated glass transition temperature based on Monte-Carlo simulation [156] were documented. These nanocomposites has the potential to prevent the degradation of ultra-large-scale integration (ULSl) and giga-scale integration (GSl) devices due to the ability of silicate layer in these nanocomposites to retard the diffusion of copper at the interfaee [157],... 

Experimental determination of excess molar quantities such as excess molar enthalpy and excess molar volume is very important for the discussion of solution properties of binary liquids. Recently, calculation of these thermodynamic quantities becomes possible by computer simulation of molecular dynamics (MD) and Monte Carlo (MC) methods. On the other hand, the integral equation theory has played an essential role in the statistical thermodynamics of solution. The simulation and the integral equation theory may be complementary but the integral equation theory has the great advantage over simulation that it is computationally easier to handle and it permits us to estimate the differential thermodynamic quantities. 

Except for extremely simple potential models (essentially hard spheres), liquid properties cannot be calculated by theoretical methods and one has to resort on computer simulation methods as Monte Carlo (MC) and molecular dynamics (MD) [55] or to integral equation methods [56]. In principle, simulation techniques are able to provide essentially exact results for the model, i.e. for a given potential function, so they are an ideal tool to test the ability of the potential to reproduce experimental data. As far as the nature of... 

In Chapter 2, we saw that the configuration integral is the key quantity to be calculated if one seeks to compute thermal properties of classical (confined) fluids. However, it is immediately apparent that this is a formidable task because it reejuires a calculation of Z, which turns out to involve a 3N-dimensional integration of a horrendously complex integrand, namely the Boltzmann factor exp [-C7 (r ) /k T] [ see Eq. (2.112)]. To evaluate Z we either need additional simplifjfing assumptions (such as, for example, mean-field approximations to be introduced in Chapter 4) or numerical approaches [such as, for instance, Monte Carlo computer simulations (see Chapters 5 and 6), or integral-equation techniques (see Chapter 7)]. 

This has been tested by using Gibbs Ensemble Monte Carlo (GEMC) simulations to calculate the equilibrium distribution of guest molecules between hydrate and vapour phases as a function of pressure pressures have then been converted to fugacities /using standard thermodynamic integration [43] over the properties of the simulated vapour. 

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