Soft spheres, high concentration

To our knowledge there have been no reported measurements of equilibrium defect concentrations in soft-sphere models. Similarly, relatively few measurements have been reported of defect free energies in models for real systems. Those that exist rely on integration methods to connect the defective solid to the perfect solid. In ab initio studies the computational cost of this procedure can be high, although results have recently started to appear, most notably for vacancies and interstitial defects in silicon. For a review see Ref. 109. 

Soft Spheres at High Concentration At the maximum volume fraction, of the electrostatically stabilized suspension low and high... 

Concentrated emulsions or high internal phase emulsions (HIPE) are systems in which the volume fraction of the dispersed phase is larger than about 0.74, which is the close-packing volume fraction of monodispersed hard spheres. The dispersed soft entities of a concentrated emulsion are no longer spherical. They deform into polyhedra separated by thin films of continuous phase. The structure is thus analogous to a conventional gas-liquid foam with low liquid content. The structure, properties, stability, and applications of highly concentrated emulsions were recently reviewed by Cameron and... 

The concentration dependence of q of hard-sphere suspensions is the same as the concentration dependence of q found in many polymer solutions, namely t](c) is a stretched exponential in c at smaller c and a power law in c for larger c. The frequency dependences of G (a>) and G"(co) for a colloid suspension and for a polymer solution are also very nearly the same, namely a stretched exponential in (o at smaller a>, a power law in co at large a> and various high-frequency small additive components. At the extreme large-concentration limit, the dynamic moduli of a soft-sphere melt composed of polystyrene microgel particles have very nearly... 

In the case of finite star chains with very high functionality, the units are concentrated near and in the star core. Therefore, their theoretical behavior can approximately be described by a rigid sphere [2]. The form factor of a sphere presents a series of oscillations. The experimental data of stars with 128 arms [67] show a smooth function covering the first two oscillations of the sphere, followed by a peak coincident with the third oscillation and the asymptotic behavior for high q previously described for stars of lower functionalities. It seems that the chain resembles a soft spherical core with a peripheral region of considerably smaller density. 

Precrosslinked poly(organosiloxane) particles are composed of crosslinking trifunctional and linear difunctional siloxane units (T and D units, respectively) [5]. The molar ratios of D and T units can be varied without restrictions thus, hard spheres (fillers) as well as soft, elastic silicone particles are accessible. In this study, the siloxane particles were synthesized in emulsion. The particle size was controlled by emulsifier concentration and crosslink density highly crosslinked particles were obtained with particle diameters ranging from 20-50 nm the size of elastic particles could be varied between 70 and 150 nm. The composition of precrosslinked poly(organosiloxane) particles is summarized in Scheme 1 further, organic radicals R which can be incorporated into the partieles are listed [6,7]. 

---