Solvated particles

The frictional coefficient of an asymmetric particle depends on its orientation. At low velocities such particles are in a state of random orientation through accidental disturbances, and the resistance of the liquid to their motion can be expressed in terms of a frictional coefficient averaged over all possible orientations. For particles of equal volume the frictional coefficient increases with increasing asymmetry. This is because, although the resistance of the liquid is reduced when the asymmetric particle is end-on to the direction of flow, it is increased to a greater extent with side-on orientations, so that on average there is an increase in resistance. The frictional coefficient is also increased by particle solvation. 

Due to the lesser mobility of the solvated e s and e+s, as compared to that of the quasi-free particles, solvation sets a time limit to Ps formation in polar solvents. The absence of solvation in nonpolar solvents therefore usually results in a much higher Ps yield. Furthermore, the Onsager radius, the distance at which the attractive potential between charged particles (here, e+... 

Figure 3.4 Schematic representation of a quantum particle solvated in a bath of classical molecules. The cyclic path represents the quantum particle in the field created by the classical solvent molecules.

At a given temperature, the rate of dissolution of a solid increases if large crystals are ground to a powder. Grinding increases the surface area, which in turn increases the number of solute ions or molecules in contact with the solvent. When a solid is placed in water, some of its particles solvate and dissolve. The rate of this process slows as time passes because the surface area of the crystals gets smaller and smaller. At the same time, the number of solute particles in solution increases, so they collide with the solid more... 

Different expressions relating the reaction probability 7 to other parameters of the system have been proposed in the case of liquid particles (see e.g., Schwartz, 1986 Hanson and Ravishankara, 1994 Hu et al, 1995 Hanson, 1997a, b Seinfeld and Pandis, 1998). Adopting the scheme shown in Figure 2.4 to account for the transfer of molecules from the gas phase to the surface (adsorption with a corresponding transfer coefficient noted ka(js), from the surface to the gas phase (desorption noted kdes), from the surface into the bulk of the particle (solvation noted ksoi), and from the bulk to the surface (kgs), Hanson (1997b) has... 

Figure 16. Plot of the mean-squared displacement for a quantum particle solvated in a classical Lennard-Jones fluid. The solid line is the CMD/PIMC algorithm described in Section III.C.l, while the dashed line is for classical MD.

The A/Zjoiv n, and AH components of the solution cycle are difficult to measure individually. Combined, they equal the enthalpy change for solvation, the process of surrounding a solute particle with solvent particles. Solvation in water is called... 

A particular case is that of the particle solvation. For consistency in the definition, the following reaction is indeed warranted ... 

Cheatham T E III, J L Miller, T Fox, T A Darden and P A Kollman 1995. Molecular Dynamics Simulations on Solvated Biomolecular Systems The Particle Mesh Ewald Method Leads to Stable Trajectories of DNA, RNA and Proteins. Journal of the American Chemical Society 117 4193-4194. 

The second term allows for solvation, which effectively increases the volume fraction of the particles to a larger value than that calculated on the basis of dry solute. Equation (9.18) shows how this can be quantified. 

Rigid particles other than unsolvated spheres. It is easy to conclude qualitatively that either solvation or ellipticity (or both) produces a friction factor which is larger than that obtained for a nonsolvated sphere of the same mass. This conclusion is illustrated in Fig. 9.10, which shows the swelling of a sphere due to solvation and also the spherical excluded volume that an ellipsoidal particle requires to rotate through all possible orientations. 

Figure 9.10 Schematic relationship between the radius Rq of an unsolvated sphere and the effective radius R of a solvated sphere or of a spherical volume excluded by an ellipsoidal particle rotating through all directions.

Since f is a measurable quantity for, say, a protein, and since the latter can be considered to fail into category (3) in general, the friction factor provides some information regarding the eilipticity and/or solvation of the molecule. In the following discussion we attach the subscript 0 to both the friction factor and the associated radius of a nonsolvated spherical particle and use f and R without subscripts to signify these quantities in the general case. Because of Stokes law, we write... 

R/Ro)soiv(f/fo)ellip = n + (mib/m2)(P2/Pi)] (f/fo)eiiip-Briefly justify this expansion of the (f/fo oiv factor. Assuming these particles were solvated to the extent of 0.26 g water (g protein)", calculate (f/fo)eiHp-For prolate ellipsoids of revolution (b/a < 1), Perrin has derived the following expression ... 

Monomer compositional drifts may also occur due to preferential solution of the styrene in the mbber phase or solution of the acrylonitrile in the aqueous phase (72). In emulsion systems, mbber particle size may also influence graft stmcture so that the number of graft chains per unit of mbber particle surface area tends to remain constant (73). Factors affecting the distribution (eg, core-sheU vs "wart-like" morphologies) of the grafted copolymer on the mbber particle surface have been studied in emulsion systems (74). Effects due to preferential solvation of the initiator by the polybutadiene have been described (75,76). 

Dental abrasives range in fineness from those that do not damage tooth stmcture to those that cut tooth enamel. Abrasive particles should be irregular and jagged so that they always present a sharp edge, and should be harder than the material abraded. Another property of an abrasive is its impact strength, ie, if the particle shatters on impact it is ineffective if it never fractures, the edge becomes dull. Other desirable characteristics include the abiUty to resist wear and solvation. 

This equation is a reasonable model of electrokinetic behavior, although for theoretical studies many possible corrections must be considered. Correction must always be made for electrokinetic effects at the wall of the cell, since this wall also carries a double layer. There are corrections for the motion of solvated ions through the medium, surface and bulk conductivity of the particles, nonspherical shape of the particles, etc. The parameter zeta, determined by measuring the particle velocity and substituting in the above equation, is a measure of the potential at the so-called surface of shear, ie, the surface dividing the moving particle and its adherent layer of solution from the stationary bulk of the solution. This surface of shear ties at an indeterrninate distance from the tme particle surface. Thus, the measured zeta potential can be related only semiquantitatively to the curves of Figure 3. 

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