Near hard sphere fluids

Near-hard Sphere Fluids - a Step Towards Stabilised Colloids... 

I. K. Snook, D. Henderson. Monte Carlo study of a hard-sphere fluid near a hard wall. J Chem Phys (55 2134-2139, 1978. 

D. Henderson, S. Sokolowski, D. Wasan. Structure of a hard-sphere fluid near a rough surface a density-functional approach. Phys Rev E 57 5539-5543, 1998. 

The density profiles are shown in Fig. 7(a). Fig. 7(b), however, illustrates the dependenee of the degree of dimerization, x( ) = P i )lon the distance from the wall. It ean be seen that, at a suffieiently low degree of dimerization (s /ksT = 6), the profile exhibits oseillations quite similar to those for a Lennard-Jones fluid and for a hard sphere fluid near a hard wall. For a high degree of dimerization, i.e., for e /ksT = 10 and 11.5, we observe a substantial deerease of the eontaet value of the profile in a wide layer adjacent to a hard wall. In the ease of the highest assoeiation energy,... 

The temperature independence of the CH frequency shifts is also reflected in the nearly constant attractive force parameters (see Table I). In fact, the frequency shifts predicted using the average attractive force parameter, Ca = 0.973, reproduce the experimental results to within 3% throughout the experimental density and temperature range. It thus appears that the attractive force parameter may reasonably be treated as a temperature and density independent constant. This behavior is reminiscent of that found for attractive force parameters derived from high pressure liquid equation of state studies using a perturbed hard sphere fluid model (37). 

HLC have suggested that the solvent dipoles near the colloidal particles are preferentially aligned. This effect is well known in theories of the electrical double layer. One simple way of accounting for this effect is through the use of a Stern layer of low dielectric constant near the colloidal particles. It is difficult to calculate this correction for spherical particles. As a result, HLC considered a hard sphere fluid between two hard walls and with a region of low dielectric constant near the walls. They found that Eq. (62) should be generalized to... 

Figure 7.8 For the unit-diameter hard sphere fluid at p = 0.277, comparison of the Poisson distribution (solid curve) with primitive quasi-chemical distribution Eq. (7.27) (dashed curve). This is the dense gas thermodynamic suggested in Fig. 4.2, p. 74, and the dots are the results of Monte Carlo simulation (Gomez et al, 1999). The primitive quasi-chemical default model depletes the probability of high- and low- constellations and enhances the probability near the mode.

The use of (4.67) in (4.64) appears to yield accurate S2 up to densities of around pa s j at typical liquid temperatures. As p increases beyond this, S2 rapidly begins to be overestimated by the use of (4.67), as shown in Fig. 24 for a hard-sphere fluid. (As seen in the figure, however, for realistic values of a/a, S2 is extremely small in the first place.) An approximation that is far better at typical liquid densities (and nearly as good at lower densities) is one introduced by Stell and Hoye" in their study of the critical behavior of 82-... 

Clarke has examined the thermodynamic equation of state and the specific heat for a Lennard-Jones liquid cooled through 7 at zero pressure. He found that drops with decreasing temperature near where the selfdiffusion becomes very small. Wendt and Abraham have found that the ratio of the values of the radial distribution function at the first peak and first valley shows behavior on cooling much like that observed for the volume of real glasses (Fig. 6), with a clearly defined 7. Stillinger and Weber have studied a Gaussian core model and find a self-diffusion constant that drops essentially to zero at a finite temperature. They also find that the ratio of the first peak to the first valley in the radial distribution function showed behavior similar to that found by Wendt and Abraham" for Lennard-Jones liquids. However, the first such evidence for a nonequilibrium (i.e. kinetic) nature of the transition in a numerical simulation was obtained by Gordon et al., who observed breakaways in the equation of state and the entropy of a hard-sphere fluid similar to those in real materials. 

Real molecules have impenetrable cores (two molecules cannot occupy the same space at the same time), so the high-temperature limit of B(T) is a finite value characteristic of the size and shape of the core for nearly spherical molecules, the value will be that for an equivalent hard-sphere fluid. In practice, experimental data rarely... 

Heni M and Lowen H. 1999. Interfacial free energy of hard-sphere fluids and solids near a hard wall. Physical Review E 60 7057-7065. 

Recently, the HAB approach plus the MV closure has been applied both to hard spheres near a single hard wall [24,25] and in a slit formed by two hard walls. Some results [99] for the latter system are compared with simulation results in Fig. 7. The results obtained from the HAB equation with the HNC and PY closures are not very satisfactory. However, if the MV closure is used, the results are quite good. There have been a few apphcations of the HAB equation to inhomogeneous fluids with attractive interactions. The results have not been very good. The fault hes with the closure used and not Eq. (78). A better closure is needed. Perhaps the DHH closure [27,28] would yield good results, but it has never been tried. 

To be more precise, let us assume, as Boltzman first did in 1872 [boltz72], that we have N perfectly elastic billiard balls, or hard-spheres, inside a volume V, and that a complete statistical description of our system (be it a gas or fluid) at, or near, its equilibrium state is contained in the one-particle phase-space distribution function f x,v,t) ... 

The high population of ion pairs near criticality motivated Shelley and Patey [250] to compare the RPM coexistence curve with that of a dipolar fluid. It is now known that a critical point does not develop in a system of dipolar hard spheres [251]. However, ion pairs resemble dumbbell molecules comprising two hard spheres at contact with opposite charges at their centers. Shelley and Patey found that the coexistence curves of these charged dumbbells are indeed very similar in shape and location to the RPM coexistence curve, but very different from the coexistence curve of dipolar dumbbells with a point dipole at the tangency of the hard-sphere contact. 

Accordingly, Gomez etal. (1999) computed p(n) for the fluid of hard spheres of diameter d = 2.61 K at a density pd = 0.633, and adopted those results as p n). Predictions obtained with this default model are shown in Fig. 8.3. Direct convergence is only seen if four or more moments are included. Though the convergence is more nearly monotonic from the beginning, the prediction obtained from a two-moment model is worse than from the flat and the Poisson default cases. 

The density functional(DF) method is one of the most promising tools for the calculation of structure and orientation in heterogeneous fluids near phase boundaries. Among many proposals for the application of DF method, that by Tarazona has been frequently used in the studies of interfaces and phase transitions in hard sphere systems. 

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