Soft sphere liquid

The effect of the magnitude of dx on the efficiency of transition path sampling can be systematically analyzed by calculating correlation functions of various quantities as a function of the number of simulations cycles. Ideally, such correlation functions decay quickly, indicating that path space is sampled with high efficiency. In [11], we carried out such an efficiency analysis for transition path sampling of isomerizations of a model dimer immersed in a soft sphere liquid. In that study, we calculated correlation functions... 

Fig. 9.10. Plot of g obtained to first order in t using equation (9.56) for the soft sphere liquid at p = 0.7 and y = 1.0. The curve is predicted from the relaxation time theory using equation (9.60) with TD = 0.24. The points are from the NEMD simulation of Hanley et al. (1987).

As an example we reproduce, without elaboration, some of the results reported in the paper of Hanley et al. (1988). The properties of a soft sphere liquid - a liquid whose particles interact with a 1/r potential in this case - undergoing Couette flow at a density equal to 7/8 of the freezing density were simulated. The radial distribution function was calculated by the procedure of Rogers Young (1984), and the relaxation time TO = 0.24 was estimated from the Einstein frequency. Figures 9.10-9.12 display how the theory agrees with the NEMD. Since the curves are entirely predictive, the agreement is excellent for these reduced variables. 

The noble gases are mostly unreactive. In some instances, they act mostly as a place holder to fill a cavity. For dynamical studies of the bulk gas phase or liquid-phase noble gases, hard-sphere or soft-sphere models work rather well. 

The structure formation in an ER fluid was simulated [99]. The characteristic parameter is the ratio of the Brownian force to the dipolar force. Over a wide range of this ratio there is rapid chain formation followed by aggregation of chains into thick columns with a body-centered tetragonal structure observed. Above a threshold of the intensity of an external ahgn-ing field, condensation of the particles happens [100]. This effect has also been studied for MR fluids [101]. The rheological behavior of ER fluids [102] depends on the structure formed chainlike, shear-string, or liquid. Coexistence in dipolar fluids in a field [103], for a Stockmayer fluid in an applied field [104], and the structure of soft-sphere dipolar fluids were investigated [105], and ferroelectric phases were found [106]. An island of vapor-liquid coexistence was found for dipolar hard spherocylinders [107]. It exists between a phase where the particles form chains of dipoles in a nose-to-tail... 

B. Laird, D. Kroll. Freezing of soft spheres a critical test for weighted density functional techniques. Phys Rev A 42 4810, 1990 D. Kroll, B. Laird. Comparison of weighted density functional theories for inhomogeneous liquids. Phys Rev A 42 4806, 1990. 

Fig. 3.58. Pair correlation functions from Monte Carlo simulation for Charged soft sphere model for LiCI liquid at 883 Kand 28.3 cm mol" .

We have carried out MD simulations for the 3-d binary soft-sphere model with N=500 atoms in a cubic cell. First, we have simulated a liquid equilibrium at Feff = 0.8 then with using the configuration at the final step of this run, the system was quenched down to Teff = 1.50 (quenching process) followed by annealing MD simulation at this Fefr over ten million time steps. This Feg- is still lower than Fj (=1.58, the glass transition), but slightly higher than F (=1.45, kinetic transition) in the supercooled fluid phase. 

The first attempt to evaluate the viscosities of a liquid crystal model system by computer simulation was made by Baalss and Hess [31]. They mapped a perfectly ordered liquid crystal onto a soft sphere fluid in order to simplify the interaction potential and thereby make the simulations faster. The three Mies-owicz were evaluated by using the SLLOD equations of motion. Even though the model system was very idealised, the relative magnitudes of the various viscosities were fairly similar to experimental measurements of real systems. 

Tanemura et al. examined crystallization in a liquid of soft spheres and found both fee and bcc structures. They used the method of Voronoi polyhedra to characterize the evolving solid clusters. Hsu and Rahman extended the use of Voronoi polyhedra in a systematic study of the effect of potential on the structure observed. They found that a model rubidium potential always crystallized to a bcc structure, while a truncated rubidium, Lennard-Jones,... 

Time resolved studies on dye molecules can help to elucidate the solvation dynamics and can give information on the time constants of diffusion of the ionic components of an RTIL [69-75], Time resolved fluorescence studies show the diffusional motion of the dissolved solutes [76], Luminescence quenching of fluorescent transition metal dyes by oxygen has been used in case of so-called core-shell soft-sphere ionic liquids [77] to monitor the oxygen permeability of these ILs [78],... 

Fig. 16. Calculated phase diagram of the soft-sphere plus mean-field model, showing the vapor-liquid (VLB), solid-liquid (SI.E ), and solid-vapor (SVE) coexistence loci, the superheated liquid spinodal (s), and the Kauzmann locus (K) in the pressure-temperature plane (P = Pa /e-,T =k T/ ). The Kauzmann locus gives the pressure-dependent temperature at which the entropies of the supercooled lit]uid and the stable crystal are equal. Note the convergence of the Kauzmann and spinodal loci at T = 0. See Debenedetti et al. (1999) for details of this calculation.

Hansen and Verlet [156] observed an invariance of the intermediate-range (at and beyond two molecular diameters) form of the radial distribution function at freezing, and from this postulated that the first peak in the structure factor of the liquid is a constant on the freezing curve, and approximately equal to the hard-sphere value of 2.85. They demonstrated the rule by application to the Lennard-Jones system. Hansen and Schiff [157] subsequently examined g r) of soft spheres in some detail. They found that, although the location and magnitude of first peak of g r) at crystallization is quite sensitive to the intermolecular potential, beyond the first peak the form of g(r) is nearly invariant with softness. This observation is consistent with the Hansen-Verlet rule, and indeed Hansen and Schiff find that the first peak in the structure factor S k) at melting varies only between 2.85 n = 8) to 2.57 (at n= ), with a maximum of 3.05 at n = 12. 

The n= 12 soft sphere model is the high-temperature limit of the 12-6 Lennard-Jones (LJ) potential. Agrawal and Kofke [182] used this limit as the starting point for another Gibbs-Duhem integration, which proceeded to lower temperatures until reaching the solid-liquid-vapor triple point. The complete solid-fluid coexistence line, from infinite temperature to the triple point, can be conveniently represented by the empirical formula [182]... 

Mixture of hard and soft spheres can undergo a phase separation if the size ratio is large enough (Biben and Hansen 1991). However, the most recent results suggest that this phase separation occurs when the larger spheres crystallize (Coussaert and Bans 1997). Crystallization is an entirely different phenomenon and we are concerned only with liquids here. So we will not venture further into considering morphology of such repulsive interactions. 

Oligschleger and Schober also investigated the intermittent diffusion processes in supercooled liquids. They generated a glass using a modified soft-sphere potential. 

Increasing the dipole coupling shifts the transition densities to lower densities. For instance, in dipolar soft spheres (256 particles) magnetic ordering sets in at a density p pa 0.85 for 7, 4 [103], p pa 0.65 for X 6.25 [102,103] and p pa 0.55 - 0.60 at A, 9 [102,103]. Transition densities are similar in DHS [113,135], but are much higher in Stockmayer fluids where a ferroelectric transition exists only for A, > 4 [127,136] at densities generally larger than the liquid densities at 1-g coexistence. MC simulations by Gao and... 

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