Homogeneous Versus Heterogeneous Systems

The concept of homogeneous versus heterogeneous used as basis for systematization refers to the relationship of the extent or size of the solid mass (S phase) to the extent of the reaction phase (L phase). 

With increasing floe diameter (or in the case of biofilm processes increasing film thickness), the system becomes truly heterogeneous. Transport within and between different phases is significant, and differential equations must be formulated for the different situations. These complex cases often can be reduced to pseudohomogeneous ones by introducing an algebraic factor, and this is the concept of reaction rate efficiency (cf. Sect. 4.5). 

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Criticaiity Design for Low-Enriched Ura-nium/Water Systems A Different Perspective of Homogeneous Versus Heterogeneous, E. (Uker, R. I. SMth fBechtel)... 

Fig. 1. Effects of homogeneous versus heterogeneous UOj-HjO system moderation bn the minimum criticality size of the system. Points for heterogeneous system correspond to the moderator/fuel volume ratio and fuel rod diameter for maximum material buckling at various fuel lump densities.

Both batch and continuous reactors are used in industrial vinyl polymerization processes. Agitated kettles, tower reactors, and linear flow reactors are just a few examples of industrially used polymerization reactors. The choice of reactor type depends on the nature of polymerization systems, (homogeneous versus heterogeneous), the quality of product, and the amount of polymer to be produced. Sometimes, multiple reactors are used and operated at different reaction conditions. Whichever reactor system is used, it is always necessary to maximize the process productivity by reducing the reaction time (batch time or residence time) while obtaining desired polymer properties consistently. 

The log G versus log G" plots of the various PHB/PEN/PET blends are presented in Figure 20.16, where and the slopes of the plots are measures of the homogeneity of the system [35], If the slope is zero, then the blend system is heterogeneous, and if it approaches 2, it means that the blend system is tending to a homogeneous system. The slopes of the plots in Figure 20.16 increase with the addition of excess PHB to the blend system. 

Figure 15.5. Buffer intensity versus pH for some heterogeneous systems and for the homogeneous dissolved carbonate system. Buffer intensities 0ct (dissolved carbonate, Cr = 10 M) /Scacoj (carbonate solution in equilibrium with calcite), (carbonate solution in equilibrium with pco2 atm), /3an kaoi (solution in equilibrium with...

The 9,10-anthraquinone system is a classic example of an EE mechanism, which includes a synproportionation process. Absorbance versus distance profiles were measured for this reaction and the homogeneous and heterogeneous rate constants were in agreement with those derived from cychc voltammetry [169]. Protonation of the benzophenone anion radical by benzoic add and o-cresol was studied using this technique [170]. A variety of electrode geometries were explored in determining the heterogeneous... 

PLS nanoeomposites always exhibit significant deviations from the empirical Cox-Merz relation, while all neat polymers obey the empirical relation, which requires that, for 7 = w, the viscoelastic data obeys the relationship 77(7) = r] uj). Two possible reasons may be offered for the deviation from the Cox-Merz relation in the case of nanoeomposites. First, this rule is only applicable for homogeneous systems like homo-polymer melts, but nanoeomposites are heterogeneous systems. Second, the slrueture formation is different when nanoeomposites are subjected to dynamic oscillatory shear versus steady shear measurements. 

In the case of heterogeneous catalysis, a DCKM or microkinetic model must incorporate the added dimension of adsorbed chemical species as well as active versus non-active sites. To obtain the full predictive capability from reactant influent to product effluent, all possible reactions in the system, both heterogeneous and homogeneous, must be accounted for. To properly understand the catalytic reaction sequence, it is possible that seemingly unimportant intermediates on the surface may be what initiate gas phase reactions. To begin this elucidation, the surface chemical species and their properties must be known. 

A clear problem of heterogeneous versus homogeneous systems is the fact that there are often many different active sites on a metal particle. In regions of the particle, which have low densities of chiral modifiers, the racemic reaction over the bare surface can compete strongly with the enantioselective reaction, leading to poor ee values. In the Ni/tartrate-type system, the loss of modifier over the course... 

Figure 4.2-8 shows the effect of the heterogeneity parameter n on the heat curve. The higher the value of n, the more uniform the heat curve. This is in accordance with what was said earlier about the behaviour of the adsorption isotherm curve versus the reduced pressure when n is increased, that is the system is more homogeneous. 

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