Generalized particles-holes separating

This generalized particles-holes separating approach generates an algorithm (GP-H) that emphasizes the role of the 2-RDM— the variable of the 2-CSE— and it is computationally more economical [54]. 

In a rubbery polymer with flexible macromolecular chains (PDMS for example) the cavities forming the free-volume are clearly separated from each other. The detailed evaluation of the movement of a penetrant particle from cavity (1) to the neighboring (2), did not show any immediate back jumps (2) — (1). This is mainly do to the fact that the channel between (1) and (2) closes quiet quickly. In a polymer with stiff chains (glassy polyimide (PI) for example) the individual cavities are closer to each other and a rather large number of immediate back jumps ocurred during the time interval simulated (120). This indicates that once a channel between two adjacent cavities in a stiff chain polymer is formed it will stay open for some 100 ps. This makes the back jump (2) - (1) of the penetrant more probable than a jump to any other adjacent hole (3). This process seems to be one cause for the general tendency that the diffusion coefficient of small penetrants in stiff chain glassy polymers is smaller than in flexible chain rubbery polymers. 

In the approximation (2), A indicates that the two quantities on the right-hand side are obtained by computing separately the initial and the final (hole) states. I note that in the 1970s and early 1980s, the problem of determining the BE of the Is electron in the Be metal (in general, of inner electrons in metals), which is measured via photoelectron spectroscopy, was mostly tackled via models of the independent particle type, with... 

As mentioned above, both electrons and holes must be efficiently separated and both must reach the particle surface. Even when both reach the surface, recombination may still predominate if both are not consumed in appropriate fast reactions. It is worth reiterating that the requirements for fast reactions are twofold. The first is favorable energetics. The redox couples must be included within the band gap as shown in FIGURE 2. But, it is also necessary to maximize the rate of interfacial electron transfer.- This is essentially a standard problem of electrochemical kinetics and, as such, one for which there are extensive precedents. Above, we mentioned the general theoretical rules. Here, we will give more attention to specific examples. In most cases, experimental results can provide precedents. 

Filtration. The general problem of the separation of solid particles from liquids can be solved by using a wide variety of methods, depending on the type of solids, the proportion of solid to liquid in the mixture, viscosity of the solution, and other factors. In filtration a pressure difference is set up and causes the fluid to flow through small holes of a screen or cloth which block the passage of the large solid particles, which, in turn, build up on the cloth as a porous cake. 

Filters may be grouped into two main types Hurd and Spencer, 1991). The pore sizes of depth filters are not well defined, and the separation reUes on physical trapping and surface contact. Generally, the thicker the filter, the smaUer the effective size of particle which passes through. The filter materials include cellulose, metal oxides or glass fibres (see Table 2-1 and Fig. 2-1.). The pore sizes of sieve filters are much better defined. They are made principally from plastic films e.g., polycarbonate (see Table 2-1 and Fig. 2-1). Some types (e.g., Nuclepore filters) have very well defined holes, but the amount of material which can be collected on these filters is normally lower than that recovered on the depth filters . It is also important to note that the effective pore size will change too as more and more particles accumulate on the filter. 

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