Pure kinetic case hypothesis

The pure kinetic case hypothesis consists of supposing that there is, among the different steps, a step that can be considered much slower than the other ones. To go further, we will also suppose that all of the other steps are fast enough to be considered at equilibrium. 

Suppose the pure kinetic case is controlled by step j all kinetic constants — 

In the pure kinetic case controlled by step j, the process can be described by a sequence of steps at eqirihbrium prior to step j and by a second sequence of steps at equilibrium following j. 

The equilibrium condition for the upstream sequence is here expressed by the following relations  

Similariy, starting from the last step n of the downstieam sequence, we have  

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The solutions are necessarily different from those we have obtained using the hypothesis of pure kinetic cases because they only involve kinetic constants ki, unlike the pure cases which bring into play the kinetic constants k, as well as the equilibrium constants Ki. 

This model is treated as the Itypothesis for a pure kinetic case or limiting step. This choice, which necessarily implies the hypothesis of a stationaiy state, allows us to deal with a simpler mathematical system. 

This observation constitutes the basic idea of the local equilibrium model of Prigogine, Nicolis, and Misguich (hereafter referred to as PNM). One considers the case of a spatially nonuniform system and deduces from (3) an integral equation for the pair correlation function that is linear in the gradients. This equation is then approximated in a simple way that enables one to derive explicit expressions for all thermal transport coefficients (viscosities, thermal conductivity), both in simple liquids and in binary mixtures, excluding of course the diffusion coefficient. The latter is a purely kinetic quantity, which cannot be obtained from a local equilibrium hypothesis. 

We can also try to deduce the radiation formula, not as above from the pure wave standpoint by quantisation of the cavity radiation, but from the standpoint of the theory of light quanta, that is to say, of a corpuscular theory. For this we must therefore develop the statistics of the light-quantum gas, and the obvious suggestion is to apply the methods of the classical Boltzmann statistics, as in the kinetic theory of gases the quantum hypothesis, introduced by Planck in his treatment of cavity radiation by the wave method, is of course taken care of from the first in the present case, in virtue of the fact that we are dealing with light quanta, that is, with particles (photons) with energy hv and momentum Av/c. It turns out, however, that the attempt to deduce Planck s radiation law on these lines also fails, as we proceed to explain. 

The whole discussion of polymer adsorption so far makes the fundamental assumption that the layer is at thermodynamic equilibrium. The relaxation times measured experimentally for polymer adsorption are very long and this equilibrium hypothesis is in many cases not satisfied [29]. The most striking example is the study of desorption if an adsorbed polymer layer is placed in contact with pure solvent, even after very long times (days) only a small fraction of the chains desorb (roughly 10%) polymer adsorption is thus mostly irreversible. A kinetic theory of polymer adsorption would thus be necessary. A few attempts have been made in this direction but the existing models remain rather rough [30,31]. 

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