Inter-particle

Assuming that additive pair potentials are sufficient to describe the inter-particle interactions in solution, the local equilibrium solvent shell structure can be described using the pair correlation fiinction g r, r2). If the potential only depends on inter-particle distance, reduces to the radial distribution fiinction g(r) = g... 

Another immediate application of r-RESPA is to the case when the force can be subdivided into a short range part and a long range part. One way for effectuating this break up is to introduce a switching function, s x) that is unity at short inter-particle separations and 0 at large inter-particle separations. We introduced this strategy in our earlier non-reversible RESPA paper [15] where we expressed the total force as. 

For linear molecules, the coulombic potential is unchanged (because the set of all inter-particle distances are unchanged) by rotations about the molecular axis (the z axis) ... 

The most important conclusions of their work were that the inter-particle effects are reasonably small for the particular recycle reactor design, and that kinetic constants determined in the recycle reactor were trustworthy. 

All commercial carbons have been made for uses other than natural gas storage. They are for the most part granular materials and pack into vessels with a substantial inter-particle void volume which results in low bulk densities. Some... 

Fluidised beds have been used previously for the industrial-scale recovery of the antibiotics streptomycin and novobiocin.30 However, more recently, considerable interest has been shown in the use of fluidised beds for the direct extraction of proteins from whole fermentation broths.31 In a packed bed, the adsorbent particles are packed within the contactor. The voidage, that is, the inter-particle space, is minimal and thus feedstock clarification is mandatory to avoid clogging of the bed. In a fluidised/expanded bed, the adsorbent bed is allowed to expand by irrigation with feedstock. Bed voidage is increased, allowing the passage of particulates in the feed. The diameters of the adsorbent beads are exaggerated for illustrative clarity. 

Maillard F, Savinova E, Simonov PA, Zaikovskii VI, Stimming U. 2004b. Infrared spectroscopic study of CO adsorption and electrooxidation on carbon-supported Pt nanoparticles Inter-particle versus intra-particle heterogeneity. J Phys Chem B 108 17893-17904. 

Fig. 5.5.3 ]H NMR spectrum obtained from a sample containing catalyst and reaction mixture (i.e., methanol, acetic acid, methyl acetate and water). Peaks A and B are the intra- and inter-particle ]H resonances, respectively, associated with the OH group. Peak C is the ]H resonance of the CH30 group associated with...

Fig. 5.5.7 A 2D slice through a H 3D MR image of the fixed-bed of catalyst particles. The catalyst particles appear as black fluid within the inter-particle space is indicated by lighter shades. Chemical conversion within ten selected volumes within each of the three transverse sections indicated is investigated in Figures 5.5.9-5.5.11. The direction of superficial flow (z) is also shown. Reproduced with permission from Ref. [24], copyright Elsevier (2002).

Any fundamental study of the rheology of concentrated suspensions necessitates the use of simple systems of well-defined geometry and where the surface characteristics of the particles are well established. For that purpose well-characterized polymer particles of narrow size distribution are used in aqueous or non-aqueous systems. For interpretation of the rheological results, the inter-particle pair-potential must be well-defined and theories must be available for its calculation. The simplest system to consider is that where the pair potential may be represented by a hard sphere model. This, for example, is the case for polystyrene latex dispersions in organic solvents such as benzyl alcohol or cresol, whereby electrostatic interactions are well screened (1). Concentrated dispersions in non-polar media in which the particles are stabilized by a "built-in" stabilizer layer, may also be used, since the pair-potential can be represented by a hard-sphere interaction, where the hard sphere radius is given by the particles radius plus the adsorbed layer thickness. Systems of this type have been recently studied by Croucher and coworkers. (10,11) and Strivens (12). 

We look first at deviations from the ideal-gas equation, caused by inter-particle interactions. Having described induced dipoles (and hydrogen bonds) the interaction strengths are quantified in terms of the van der Waals and virial equations of state. 

In these studies, chemical conversion was determined in situ by measuring the lH resonance associated with OH groups present. In practice two such resonances exist associated with chemical species inside and outside the catalyst particles, respectively. The difference in chemical shift between these intra- and inter-particle species arises because of the different electronic environment of the molecules inside the catalyst particles compared to their environment in the bulk fluid in the inter-particle space. In this work, chemical conversion was determined from the MR signal acquired from species in the inter-particle space of the bed because the signal from inside the catalyst particles is also going to be influenced, to an unknown extent, by relaxation time contrast. In addition to possible relaxation contrast effects, there will also be modifications to the chemical shifts of individual species resulting from adsorption onto the catalyst this may cause peak broadening and reduces the accuracy with which we can determine the chemical shift of the species of interest. As follows from eqn (11) which describes the esterification reaction of methanol and acetic acid to form methyl acetate and water ... 

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