Parameters of molecular transport

Figure 4 Parameters of molecular transport in granulated zeolite KaCaA in dependence on the time on stream in a petroleum refinery (Reproduced with permission from Ref. 6. Copyright i987 Butterworth)...

Figure 2 summarizes the three main parameters of molecular transport accessible by PEG NMR and illustrates the conditions under which they may be obtained. Sections 3 and 4 provide examples of the message provided by the study of long-range diffusion (Dh ) and intercrystalHne exchange rates (Tjjjtra )- Since the scientific interest in molecular propagation is primarily focussed on intracrystalline diffusion, the main part of this contribution (Sect. 5) will be devoted to the measurement of Dintra. 

Fig. 2 Parameters of molecular transport in beds of zeolite crystallites as accessible by PPG NMR measurements...

Section 4 is entitled Ideas (for mechanisms and models). It deals with how we can interpret/calculate the behavior of molecular transport junctions utilizing particular model approaches and chemical mechanisms. It also discusses time parameters, and coherence/decoherence as well as pathways and structure/function relationships. 

Many other time parameters actually enter - if the molecule is conducting through a polaron type mechanism (that is, if the gap has become small enough that polarization changes in geometry actually occur as the electron is transmitted), then one worries about the time associated with polaron formation and polaron transport. Other times that could enter would include frequencies of excitation, if photo processes are being thought of, and various times associated with polaron theory. This is a poorly developed part of the area of molecular transport, but one that is conceptually important. 

All the work just mentioned is rather empirical and there is no general theory of chemical reactions under plasma conditions. The reason for this is, quite obviously, that the ordinary theoretical tools of the chemist, — chemical thermodynamics and Arrhenius-type kinetics - are only applicable to systems near thermodynamic and thermal equilibrium respectively. However, the plasma is far away from thermodynamic equilibrium, and the energy distribution is quite different from the Boltzmann distribution. As a consequence, the chemical reactions can be theoretically considered only as a multichannel transport process between various energy levels of educts and products with a nonequilibrium population20,21. Such a treatment is extremely complicated and - because of the lack of data on the rate constants of elementary processes — is only very rarely feasible at all. Recent calculations of discharge parameters of molecular gas lasers may be recalled as an illustration of the theoretical and the experimental labor required in such a treatment22,23. ... 

Although we shall not directly use these four postulates of irreversible thermodynamics as a foundation to our study of molecular transport in separations, a number of important principles are illuminated here. For instance, postulate 2 permits us to use—and this is in no way obvious— equilibrium parameters such as entropy and temperature in descriptions of systems where no equilibrium exists. The importance of this is evident when we ask ourselves how we would describe a system if these parameters were not available. Postulate 3 demonstrates that in the range of our typical experiences, the fluxes of matter or of heat are proportional to the gradients or forces that drive them. However, there are exceptions nonlinear terms enter if the forces become intense enough. 

One of the advantages of PPG NMR is its ability to provide direct information about the entirety of molecular transport phenomena in pelletized adsorbents and catalysts (316). As an example, Table I presents the transport parameters for methane in granulated zeolite NaCaA (16,53). 

Table til. Parameters NaOaA alter of Molecular Transport in oranuiate Deterioration by contact with Hydro Different Boiling Ranges d Zeolite carDons oi... 

In Chapter 11, we indicated that deviations from plug flow behavior could be quantified in terms of a dispersion parameter that lumped together the effects of molecular diffusion and eddy dif-fusivity. A similar dispersion parameter is usefl to characterize transport in the radial direction, and these two parameters can be used to describe radial and axial transport of matter in packed bed reactors. In packed beds, the dispersion results not only from ordinary molecular diffusion and the turbulence that exists in the absence of packing, but also from lateral deflections and mixing arising from the presence of the catalyst pellets. These effects are the dominant contributors to radial transport at the Reynolds numbers normally employed in commercial reactors. 

Let us assume that the molecular transport is governed only by the differences in the chemical potential (diffusion) and neglect a possible order parameter transport by the hydrodynamic flow [1,144,157]. Then, one can postulate a linear relationship between the local current and the gradient of the local chemical potential difference p(r) [146,147] as... 

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