Lennard-Jones fluid models

The second generalization is the reinterpretation of the excluded volume per particle V(). Realizing that only binary collisions are likely in a low-density gas, van der Waals suggested the value Ina /I for hard spheres of diameter a and for particles which were modeled as hard spheres with attractive tails. Thus, for the Lennard-Jones fluid where the pair potential actually is... 

Yan, Q.L. de Pablo, J.J., Hyper-parallel tempering Monte Carlo Application to the Lennard-Jones fluid and the restricted primitive model, J. Chem. Phys. 1999, 111, 9509-9516... 

Carlo Application to the Lennard-Jones Fluid and the Restricted Primitive Model. 

An example drawn from Deitrick s work (Fig. 2) shows the chemical potential and the pressure of a Lennard-Jones fluid computed from molecular dynamics. The variance about the computed mean values is indicated in the figure by the small dots in the circles, which serve only to locate the dots. A test of the thermodynamic goodness of the molecular dynamics result is to compute the chemical potential from the simulated pressure by integrating the Gibbs-Duhem equation. The results of the test are also shown in Fig. 2. The point of the example is that accurate and affordable molecular simulations of thermodynamic, dynamic, and transport behavior of dense fluids can now be done. Currently, one can simulate realistic water, electrolytic solutions, and small polyatomic molecular fluids. Even some of the properties of micellar solutions and liquid crystals can be captured by idealized models [4, 5]. 

Liu, Silva, and Macedo [Chem. Eng. Sci. 53, 2403 (1998)] present a theoretical approach incorporating hard-sphere, square-well, and Lennard-Jones models. They compared their resulting estimates to estimates generated via the Lee-Thodos equation. For 2047 data points with nonpolar species, the Lee-Thodos equation was slightly superior to the Lennard-Jones fluid-based model, that is, 5.2 percent average deviation versus 5.5 percent, and much better than the square-well fluid-based model (10.6 percent deviation). For over 467 data points with polar species, the Lee-Thodos equation yielded 36 percent average deviation, compared with 25 percent for the Lennard-Jones fluid-based model, and 19 percent for the square-well fluid-based model. 

A commonly used model system in liquid crystal simulation is the Gay-Beme fluid. It can be regarded as a Lennard-Jones fluid generalised to ellipsoidal molecular cores. 

The model isotherm for each pore size class was calculated by methods described previously [9], modified to account for cylindrical pore geometry. These calculations model the fluid behavior in the presence of a uniform wall potential. Since the silica surface of real materials is energetically heterogeneous, one must choose an effective wall potential for each pore size that will duplicate the critical pore condensation pressure, p, observed for that size. This relationship is shown in Figure 2. The Lennard-Jones fluid-fluid interaction parameters and Cn/kg were equal to 0.35746 nm and 93.7465 K, respectively. 

Wongkoblap et al.307 study Lennard-Jones fluids in finite pores, and compare their results with Grand canonical ensemble simulations of infinite pores. Slit pores of 3 finite layers of hexagonally arranged carbon atoms were constructed. They compare the efficiency of Gibbs ensemble simulations (where only the pore is modelled) with Canonical ensemble simulations where the pore is situated in a cubic cell with the bulk fluid, and find that while the results are mostly the same, the Gibbs ensemble method is more efficient. However, the meniscus is only able to be modelled in the canonical ensemble. 

A comparison of mesoscopic simulation methods with MD simulations has been performed by Denniston and Robbins.423 They study a binary mixture of simple Lennard-Jones fluids and map out the required parameters of the mesoscopic model from their MD simulation data. Their mapping scheme is more complete than those of previous workers because in addition to accounting for the interfacial order parameter and density profiles, they also consider the stress. Their mapping consists of using MD simulations to parameterise the popular mesoscale Lattice Boltzmann simulation technique and find that a... 

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