Spheres, soft, theoretical models

For nanoaerosol, e 1 because of the great rigidity. Several theoretical models of adhesion energy can be found in the literature. Two of the most well-known ones are JKR model and DMT model. These two models contradict each other because they represent two extremes in the Tabor parameter spectrum. JKR model is applied for soft material, large radius, compliant spheres, and large adhesion energy, and DMT model is for hard material, small radius, and low adhesion energy. Therefore, DMT model should be considered first for nanoaerosol thermal rebound analysis. 

Fig. 39. Measurement of the apparent diffusion coefficient Dapp = 17q2 for two concentrations of a PVAc microgel in methanol 88 189. The full lines are theoretical curves for a soft sphere model with 7 branching shells93 ...

Electrokinetic equations describing the electrical conductivity of a suspension of colloidal particles are the same as those for the electrophoretic mobility of colloidal particles and thus conductivity measurements can provide us with essentially the same information as that from electrophoretic mobihty measurements. Several theoretical studies have been made on dilute suspensions of hard particles [1-3], mercury drops [4], and spherical polyelectrolytes (charged porous spheres) [5], and on concentrated suspensions of hard spherical particles [6] and mercury drops [7] on the basis of Kuwabara s cell model [8], which was originally applied to electrophoresis problem [9,10]. In this chapter, we develop a theory of conductivity of a concentrated suspension of soft particles [11]. The results cover those for the dilute case in the limit of very low particle volume fractions. We confine ourselves to the case where the overlapping of the electrical double layers of adjacent particles is negligible. 

Corresponding theoretical analysis of concentration dependence of Dt in solutions of flexible coil macromolecules have been carried out exclusively using the classical theory embodied in Equation 37 and have also turned out to be very sensitive to details of the particular model. The original treatment of Pyun and Fixman (75) based on a model of soft interpenetrable spheres of uniform segment density has been most commonly applied to these data. Their result is ... 

Ultrasoft repulsive interactions (without the long-range Coulomb part) have been extensively studied, both for its theoretical aspects and as a description of a soft matter system. Studies reveal two distinct behaviors. Some ultrasoft potentials supports stacked configurations, where two or more particles collapse, even though no true attractive interactions come into play [51, 52]. This behavior leads to a peak in a correlation function around r = 0. To this class of potentials belongs the penetrable sphere model [53]. The Gaussian core model [54], on the other hand, represents the class of soft particles unable to support stacked configurations. 

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