Soft sphere systems

This is reliable and fairly accurate, if tedious. It was used, for example, by Hoover [92] to locate the melting parameters for soft-sphere systems. The only point to watch out for is that one should not cross any phase transitions in taking the path from 1 to 2 it must be reversible. 

Whittle, M. and Dickinson, E. Brownian dynamics simulation of gelation in soft spheres systems with irreversible bond formation. Mol. Phys., 90, 739, 1997. 

Since the soft-sphere system represents the high-pressure, high-temperature limit of the LJ system, it is predicted from the data above that the thermal manifestation of the laboratory glass transition will weaken with increasing pressure as it is displaced to higher temperatures. Indeed, increasing difficulties in 7 detection have been noted in high-pressure studies. ... 

It is possible but not easy to imagine conditions in which two phases of the same laboratory substance could have identical entropies and also maintain the identity over a range of temperatures it is not possible, however, in the case of classical hard and soft sphere systems since, at constant pressure, equal entropy in these cases implies equal volume, hence the same phase. Since, at constant pressure, there is only one point in temperature— the fusion point—where the free energies of the fluid and ciystal phases of the same substance can be equal, a cannot exist for hard spheres. This raises the question of whether there are other occurrences that might terminate the supercooled fluid state above 7 . Two have been suggested. 

With these possibilities in mind, we plot the courses in temperature of the fluid- and solid-phase entropies for hard- and soft-sphere systems, and compare them with the MD results in Figs. 21 and 22. It should be noted that in classical mechanical models the entropy is usually defined relative... 

Colloidal suspensions can be classified as soft sphere systems because the repulsive intoactions occur at some characteristic distance from the particle surface. For electrostatic and stoic stabilization, this distance is the Debye length (1/ K) and the thickness of the adsorbed polymer layer, respectively. For stoically stabilized suspensions, the adsorbed polymer layer leads to an increase in the hydrodynamic radius of the particle. When the adsorbed layer is densely packed, the principles described above for hard sphere systems are applicable, provided that the volume fraction of particles/is replaced by an effective volume fraction /gy given by... 

For electrostatically and sterically stabilized suspensions (soft sphere systems), the presence of an electrical double layer or an adsorbed polymer layer, as discussed earlier, leads to an increase in the hydrodynamic radius of the particle and a consequent reduction in / with decreasing particle size [Eq. (4.87)]. 

In reference [73], a comparison similar to that in Figure 1.5 was also performed for a soft-sphere system, namely, a dispersion of microgel particles studied by Bartsch et al. [32], who indicate a value of the soft-sphere diameter of 1.0 [im, and report the glass transition to occur at a volume fraction = 0.644. In reference [73], this system was modeled with the soft potential in Equation 1.29. Unfortunately, the experimental report does not define or quantify the degree of softness of the particles, in a manner that serves to determine the parameter t of the model. In reference [73], however, the glass transition volume fraction was calculated for each v using Equation 1.39. 

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