Isobaric expansivity simulation

As molecular packing calculations involve just simple lattice energy minimizations another set of tests have focused on the finite temperature effects. For this purpose, Sorescu et al. [112] have performed isothermal-isobaric Monte Carlo and molecular dynamics simulations in the temperature range 4.2-325 K, at ambient pressure. It was found that the calculated crystal structures at 300 K were in outstanding agreement with experiment within 2% for lattice dimensions and almost no rotational and translational disorder of the molecules in the unit cell. Moreover, the space group symmetry was maintained throughout the simulations. Finally, the calculated expansion coefficients were determined to be in reasonable accord with experiment. 

In 2002, Morrow and Maginn presented an all-atom force field for [C4mim][PF6] using a combination of DFT calculations (B3LYP/6-311+G ) and CHARMM 22 parameter values [13]. MD simulations were carried out in the isothermal-isobaric ensemble at three different temperatures. The calculated properties contained infrared frequencies, molar volumes, volume expansivities, isothermal compressibilities, self-diffusivities, cation-anion exchange rates, rotational dynamics, and radial distribution functions. These thermodynamic properties were found to be in good agreement with available experimental values [13]. 

Shah et al. carried out a Monte-Carlo simulation in the isothermal-isobaric (NPT) ensemble of [C4mim][PF6] [12]. The authors calculated the molar volume, cohesive energy density, isothermal compressibility, cubic expansion coefficient, and liquid structure as a function of temperature and pressure. A united atom force field was developed using a combination of ab initio calculations and literature parameter values were also developed. Calculated molar volumes were within 5% of experimental values, and a reasonable agreement was obtained between calculated and experimental values of the isothermal compressibility and cubic expansion coefficient. [PF6] anions were found to cluster preferentially in two favorable regions near the cation, namely around the C2 carbon atom, both below and above the plane of the imidazole ring [12],... 

The simple physical picture presented above has two consequences. In the first place it suggests a very simple way to include a temperature dependence in t/. Since the radius of the cavity, R, is one of the standard parameters used in implementing the cell theory, one simply needs to replace R with (T), where R(T) could be identified with the inner extremity of lattice vibrations at a given temperature. The second consequence is that the magnitude of this effect is likely to be exaggerated by the isochoral conditions used in the simulations. Under the more common isobaric conditions, the entire lattice will also expand as temperature increases. Consequently the effective size of a cavity will depend on a competition between expansion of the lattice and larger amplitude vibrations within the lattice. 

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