Soft spheres

Tadros (1986) describes four types of interparticle forces hard sphere, soft (electrostatic), van der Waals, and steric. Hard-sphere interactions, which are repulsive, become significant only when particles approach each other at distances slightly less than twice the hard-sphere radius. They are not commonly encountered. 

This chapter is an in-depth review on rheology of suspensions. The area covered includes steady shear viscosity, apparent yield stress, viscoelastic behavior, and compression yield stress. The suspensions have been classified by groups hard sphere, soft sphere, monodis-perse, poly disperse, flocculated, and stable systems. The particle shape effects are also discussed. The steady shear rheological behaviors discussed include low- and high-shear limit viscosity, shear thinning, shear thickening, and discontinuity. The steady shear rheology of ternary systems (i.e., oil-water-solid) is also discussed. 

Fig. 9. Volumes of the supercooled fluid and vitreous phases of hard spheres, soft spheres, and Lennard-Jones molecules (at p— 0) relative to their respective crystalline phases as a function of temperature reduced according to the equilibrium freezing temperatures.

Fig. 10. Isobaric heat capacities of the amorphous phases of hard spheres,soft spheres, and Leonard-Jones molecules as a function of density.

Turning to the results of dynamic simulation experiments. Fig. 16 compares radial distribution functions for hard-sphere, soft-sphere, and LJ glasses, all in comparable states. The compression rates (p dp/dT) for the preparation of the soft-sphere sample, the LJ sample, and the hard-sphere case were 0.024, 0.010, and 0.003 psec respectively, all on a time scale appropriate for LJ argon. Also the densities are all comparable as judged by the reference scales discussed in Section IV.C. If one uses the... 

We now proceed to more realistic models of adsorption systems. As a preliminary step, comparative simulations of various gases on various model surfaces should be mentioned. These include hard spheres at a soft repulsive wall [73] and hard spheres, soft repulsive spheres, and Lennard-Jones atoms between hard, soft repulsive, and soft attractive walls [741. For coverages greater than one monolayer, these simulations show that the local density n z) is relatively insensitive to the detailed nature of the interactions [74]. It is the repulsive cores of the adsorbed atoms that are the determining factor. This point is illustrated in Fig. 9. 

In his original works, Rosenfeld considered hard spheres, soft spheres, Lennard-Jones system, and one-component plasma [52,53]. Thereafter, the excess entropy scaling was applied to many different systems, including core-softened liquids [17,18,51,54,55], liquid metals [56,57], binary mixtures [58,59], ionic liquids [60,61], network-forming liquids [54,60], water [62], chain fluids [63], and bounded potentials [51,64,65]. 

Royall CP, Poon WCK, Weeks ER (2012) In search of colloideil hard spheres. Soft Matter 9 17-27... 

G. R. Farrell, K. M. Martini, and N. Menon. Loose packings of frictional spheres. Soft Matter, 6 2925, 2010. 

---