Lennard-Jones temperature

Van Amerongen measured the heat effects of various gases in several elastomers. He found that AH of elastomers also mainly depends on the boiling points (or the Lennard-Jones temperatures) of the gas and is hardly dependent on the nature of the polymer. A representative expression is ... 

Our conclusion is, that the three parameters of the solution (sorption) process of simple gases can be estimated from three hall-marks of the polymer-gas combination the Lennard-Jones temperature of the gas (s/k), the glass transition temperature (Tg) and the degree of crystallinity (xc) of the polymer. 

Freeman [40] demonstrates that solution-diffusion transport theory predicts the existence of an upper bound if diffusion is an activated process, the activation energy depends linearly on the square of the molecular diameter, and solubility depends exponentially on the Lennard-Jones temperature. Although one adjustable parameter is introduced to specify the dependence of activation energy on molecular size, a single value gives excellent predictions of the location of the upper bound for all gas pairs examined. 

The diffusivity was described as a function of the glass transition temperature, Tg, and degree of crystallinity, < c, of the polymer and the Lennard-Jones temperature, sA, of the gas. Similarly, the solubility can be estimated with good accuracy from the same variables. The pertinent expressions are (Van Krevelen, 1990), for elastomers (and for polymers in the rubbery state) ... 

Truncation at the first-order temi is justified when the higher-order tenns can be neglected. Wlien pe higher-order tenns small. One choice exploits the fact that a, which is the mean value of the perturbation over the reference system, provides a strict upper bound for the free energy. This is the basis of a variational approach [78, 79] in which the reference system is approximated as hard spheres, whose diameters are chosen to minimize the upper bound for the free energy. The diameter depends on the temperature as well as the density. The method was applied successfiilly to Lennard-Jones fluids, and a small correction for the softness of the repulsive part of the interaction, which differs from hard spheres, was added to improve the results. 

Here Tq are coordinates in a reference volume Vq and r = potential energy of Ar crystals has been computed [288] as well as lattice constants, thermal expansion coefficients, and isotope effects in other Lennard-Jones solids. In Fig. 4 we show the kinetic and potential energy of an Ar crystal in the canonical ensemble versus temperature for different values of P we note that in the classical hmit (P = 1) the low temperature specific heat does not decrease to zero however, with increasing P values the quantum limit is approached. In Fig. 5 the isotope effect on the lattice constant (at / = 0) in a Lennard-Jones system with parameters suitable for Ne atoms is presented, and a comparison with experimental data is made. Please note that in a classical system no isotope effect can be observed, x "" and the deviations between simulations and experiments are mainly caused by non-optimized potential parameters. 

A dimerizing Lennard-Jones fluid has been studied for the bulk density p = 0.75, and at temperature T — 1.35, for different values of the assoeia-tion energy, namely = 2, 6, 10, and 11.5 [118]. The results for... 

Recently, many experiments have been performed on the structure and dynamics of liquids in porous glasses [175-190]. These studies are difficult to interpret because of the inhomogeneity of the sample. Simulations of water in a cylindrical cavity inside a block of hydrophilic Vycor glass have recently been performed [24,191,192] to facilitate the analysis of experimental results. Water molecules interact with Vycor atoms, using an empirical potential model which consists of (12-6) Lennard-Jones and Coulomb interactions. All atoms in the Vycor block are immobile. For details see Ref. 191. We have simulated samples at room temperature, which are filled with water to between 19 and 96 percent of the maximum possible amount. Because of the hydrophilicity of the glass, water molecules cover the surface already in nearly empty pores no molecules are found in the pore center in this case, although the density distribution is rather wide. When the amount of water increases, the center of the pore fills. Only in the case of 96 percent filling, a continuous aqueous phase without a cavity in the center of the pore is observed. 

In a review of the subject, Ubbelohde [3] points out that there is only a relatively small amount of data available concerning the properties of solids and also of the (product) liquids in the immediate vicinity of the melting point. In an early theory of melting, Lindemann [4] considered that when the amplitude of the vibrational displacements of the atoms of a particular solid increased with temperature to the point of attainment of a particular fraction (possibly 10%) of the lattice spacing, their mutual influences resulted in a loss of stability. The Lennard-Jones—Devonshire [5] theory considers the energy requirement for interchange of lattice constituents between occupation of site and interstitial positions. Subsequent developments of both these models, and, indeed, the numerous contributions in the field, are discussed in Ubbelohde s book [3]. 

We now describe a relatively simple MD model of a low-index crystal surface, which was conceived for the purpose of studying the rate of mass transport (8). The effect of temperature on surface transport involves several competing processes. A rough surface structure complicates the trajectories somewhat, and the diffusion of clusters of atoms must be considered. In order to simplify the model as much as possible, but retain the essential dynamics of the mobile atoms, we will consider a model in which the atoms move on a "substrate" represented by an analytic potential energy function that is adjusted to match that of a surface of a (100) face-centered cubic crystal composed of atoms interacting with a Lennard-Jones... 

Figure 5. Velocity and temperature profiles for the cut-off Lennard-Jones potential. The system consists of 1152 atoms enclosed in a box of side length equal to 32 6 6.

FIG. 1 The calculated surface tension of an argon fluid represented as a Lennard-Jones fluid is shown as a function of temperature. The GvdW(HS-B2)-functional is used in all cases. The filled squares correspond to step function profile and local entropy, the filled circles to tanh profile with local entropy, and the open circles to tanh profile with nonlocal entropy. The latter data are in good agreement with experiment. 

Figure 5. Molecular dynamics simulation of the decay forward and backward in time of the fluctuation of the first energy moment of a Lennard-Jones fluid (the central curve is the average moment, the enveloping curves are estimated standard error, and the lines are best fits). The starting positions of the adiabatic trajectories are obtained from Monte Carlo sampling of the static probability distribution, Eq. (246). The density is 0.80, the temperature is Tq — 2, and the initial imposed thermal gradient is pj — 0.02. (From Ref. 2.)...

Figure 8 shows the r-dependent thermal conductivity for a Lennard-Jones fluid (p = 0.8, 7o = 2) [6]. The nonequilibrium Monte Carlo algorithm was used with a sufficiently small imposed temperature gradient to ensure that the simulations were in the linear regime, so that the steady-state averages were equivalent to fluctuation averages of an isolated system. 

Figure 9. Simulated thermal conductivity X/(t) for a Lennard-Jones fluid. The density in the center of the system is p = 0.8 and the zeroth temperature is To = 2. (a) A fluid confined between walls, with the numbers referring to the width of the fluid phase. (From Ref. 6.) (b) The case I, — 11.2 compared to the Markov (dashed) and the Onsager-Machlup (dotted) prediction.

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