Soft particle diffuse

Hard-sphere or cylinder models (Avena et al., 1999 Benedetti et al., 1996 Carballeira et al., 1999 De Wit et al., 1993), permeable Donnan gel phases (Ephraim et al., 1986 Marinsky and Ephraim, 1986), and branched (Klein Wolterink et al., 1999) or linear (Gosh and Schnitzer, 1980) polyelectrolyte models were proposed for NOM. Here the various models must be differentiated in detail—that is, impermeable hard spheres, semipermeable spherical colloids (Marinsky and Ephraim, 1986 Kinniburgh et al., 1996), or fully permeable electrolytes. The latest new model applied to NOM (Duval et al., 2005) incorporates an electrokinetic component that allows a soft particle to include a hard (impermeable) core and a permeable diffuse polyelectrolyte layer. This model is the most appropriate for humic substances. 

Throughout this section, we will use the notation X (t),..., X t) to denote a unspecified set of L Markov diffusion processes when discussing mathematical properties that are unrelated to the physics of constrained Brownian motion, or that are not specific to a particular set of variables. The variables refer specifically to soft coordinates, generalized coordinates for a system of N point particles, and Cartesian particle positions, respectively. The generic variables X, ..., X will be indexed by integer variables a, p,... = 1,...,L. 

Figure 2.5. Molecular D)oiainics simulation of self-diffusion in a dense fluid of "soft" spherical particles near a "hard" solid wail. The "wall" exerts no force on the particles but reverses the z-component of the velocity if a molecule attempts to cross it a is the length parameter in the repulsive part of the Lennard-Jones interaction. (Redrawm from J.N. Cape. J. Chem. Soc., Faraday Trans. II 78 (1982) 317.)...

The second key observation is that the intersections between a twin boundary and a crystal surface represent chemically activated sites (and mechanically soft areas) (Novak and Salje 1998a, 1998b). It appears safe to assume that similarly activated sites exist also at the intersection of APBs and dislocations with the surface (e.g. Lee et al. 1998, Hochella and Banfield 1995). Besides the obvious consequences for the leaching behaviour of minerals, these key observations lead to the hypothesis of confined chemical reactions inside mesoscopic patterns. The idea is as follows as the surface energy is changed near mesoscopic interfaces, dopant atoms and molecules can be anchored near such interfaces. Some particles will diffuse into the mineral and react with... 

Fig. 3. Variation with temperature of the diffusion coefficients for various simulated fluids and actual laboratory fluids. Sources of data are, from left to right LJ argon, simulated Refs. 7 (DC) and 12 (C) laboratory. Ref. 41 bard spheres (for which temperature axis corresponds to pV/NkT X.50), Ref. 82 soft spheres. Ref. 20 xenon. Ref. 41 toluene. Ref. 42 methyl cyclohexane. Ref. 43 carbon tetrachloride. Ref. 44 o-terphenyl. Ref. 45 molten KQ, simulated using Tosi-Fumi (TF) potential parameters. Ref. S repellent Gaussian core particles. Ref. 21 (F. H. Stillinger kindly deduced the values his simulation results would infer for argonlike particles in familiar units) Na ions diffusing in molten 6KN03-4Ca(N0j)2 solvent medium. Ref. 46. The dashed extension of lower temperature in the case of xenon is based on the Arrhenius parameters quoted for the data. ...

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