Lennard-Jones glasses

Bhattacharya, K.K. Sethna, J.P., Multicanonical methods, molecular dynamics, and Monte Carlo methods comparison for Lennard-Jones glasses, Phys. Rev. E 1998, 57, 2553-2562... 

Faller, R. de Pablo, J. J., Density of states of a binary Lennard-Jones glass, J. Chem. Phys. 2003,119, 4405 1408... 

Fig. 10. The densities obtained at different cooling rates at T = 0 and p = 1 for the Lennard-Jones glass. The cooling rate is the value of the stochastic collision frequency per particle, v. The number of runs employed to obtain the reported average is shown inside each point. (From Fox and Andersen (67).)...

Induced scattering from rock salt [641, 650] and CS2 [629] has been studied. Disordered solids were reviewed by Signorelli et al. [648,651] studies of partially disordered molecular solids have been reported in ice [642,646], a-AgI [628, 643, 644, 647], and other solids [627, 639, 645, 664]. Lennard-Jones glasses [649] and various plastics [632, 637] have also been studied. 

Kob, W. and Barrat, J.-L. 1997. Aging effects in a Lennard-Jones glass. Phys. Rev. Lett. 78 4581. 

Berthier L. and Kob W. 2007. The Monte Carlo dynamics of a binary Lennard-Jones glass-forming mixture. J. Phys. Condens. Matter 19 205130. 

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. 

As we discussed in the section on the structural properties of amorphous polymers, the relative size of the bond length and the Lennard-Jones scale is very different when comparing coarse-grained models with real polymers or chemically realistic models, which leads to observable differences in the packing. Furthermore, the dynamics in real polymer melts is, to a large extent, determined by the presence of dihedral angle barriers that inhibit free rotation. We will examine the consequences of these differences for the glass transition in the next section. 

Liquid-Glass Transition in a Lennard-Jones Binary Mixture. 

The polydihalophosphazenes are examined by conformational analysis using nonbonding intramolecular interactions based on a 6-12 Lennard-Jones potential and a Coulombic term. The results provide an insight into the reasons for the low glass transition temperatures, the high chain flexibilities, and the conformational preferences of these molecules. Minimum energy conformations are discussed. 

It has been discussed in the previous section that the long-time part in the memory function gives rise to the slow long-time tail in the dynamic structure factor. In the case of a hard-sphere system the short-time part is considered to be delta-correlated in time. In a Lennard-Jones system a Gaussian approximation is assumed for the short-time part. Near the glass transition the short-time part in a Lennard-Jones system can also be approximated by a delta correlation, since the time scale of decay of Tn(q, t) is very large compared to the Gaussian time scale. Thus the binary term can be written as... 

Lennard-Jones binary mixture of particles is a prototypical model that describes glass-forming liquids [52,53,158,162-165]. The temperature and the density dependence of diffusivity D(T, p) have been obtained by computer simulations for the Lennard-Jones binary mixture in the supercooled state. To relate fragility of binary Lennard-Jones mixture to thermodynamic properties necessitates determination of the configurational entropy SC(T, p) as well as the vibration entropy Sv,h(T, p) at a given temperature and density. 

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. 

Figure 1.38. Molecular dynamics simulation of the density profiles for spherical molecules in a cylinder, mimicking SFg in controlled pore glass (CPG-10). Fluid-fluid and fluid-wall interaction modelled by Lennard-Jones interactions. Reference A. de Keizer. T. Michalski and G.H. Findenegg, Pure Appl. Chem. 63(1991) 1495.

The interaction between water molecules and silica substrate is described in the framework of the PN-TrAZ model [15] which has proven to model successfiilly the adsorption of simple adsorbates on various zeolites [20]. In this model, the pair potential decomposes in two parts a repulsion term Ae" due to electronic clouds and the attractive dispersion terms. The repulsive parameters (A,b) for silica atoms (Si, O, H) are those obtained from studies of adsorption of simple gazes on various zeolites [20] and mesoporous glass [21]. Those for water oxygen are chosen to fit the repulsive part of Lennard-Jones from SPC model in the range around equilibriiun distance, and those for water hydrogen are taken equal to the parameters for surface hydrogen of vycor. The cross repulsive parameters A and b are obtained by Bohm and Ahlrichs [22] combination mles. The dispersion terms are calculated from polarizabilities and effective niunber of electron Neff according to the PN-TrAZ model up to order r °. Values are listed in table 1. 

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