Cluster-void approach

The initial porous texture of a catalyst pellet and the change in texture caused by metal deposition in it can be described using the percolation theory. In the percolation approach the pellet is constructed as a binary interdispersion of void space and (deposited) solid material. In this binary interdispersion, the void space can exist as (1) isolated clusters surrounded by solid material or (2) sample overspanning void space that allows mass transport from one side to the other. The total void space c can be split into the sum of the volume fraction of isolated clusters t1 and the volume fraction of accessible void space tA, If is below a critical value, called the percolation threshold all the void space is distributed as isolated clusters and transport is impossible through the pellet. 

Basically, the process of tablet compression starts with the rearrangement of particles within the die cavity and initial elimination of voids. As tablet formulation is a multicomponent system, its ability to form a good compact is dictated by the compressibility and compactibility characteristics of each component. Compressibility of a powder is defined as its ability to decrease in volume under pressure, and compactibility is the ability of the powdered material to be compressed into a tablet of specific tensile strength [1,2], One emerging approach to understand the mechanism of powder consolidation and compression is known as percolation theory. In a simple way, the process of compaction can be considered a combination of site and bond percolation phenomena [5]. Percolation theory is based on the formation of clusters and the existence of a site or bond percolation phenomenon. It is possible to apply percolation theory if a system can be sufficiently well described by a lattice in which the spaces are occupied at random or all sites are already occupied and bonds between neighboring sites are formed at random. 

Another possible approach to indirectly characterize the membrane morphology is based on the investigation of the free volume within the matrix. Density measurements [119,120] and positron annihilation lifetime spectroscopy evaluation [47] are common methods. Typically, the comparison between the theoretical density or free volume (calculated by simple additivity rules) and the experimental one can reveal the presence of a good interfacial morphology or the presence of interface voids or clustering formation. Fig. 7.13 shows the influence of filler content on the morphology of poly(trimethylsilyl propyne) (PTMSP)/Ti02 NCMs in terms of the volumetric fraction of interface voids as calculated from a comparison of the expected and measured membrane density [119],... 

Easier diffusion of B produces features such as a smoother dissolution front, internal vacancy clusters (polyatomic voids), and islands of A-type atoms hindered from dissolution. Qualitatively similar conclusions are drawn on 3D lattices except for the specific generation of pores with easier diffusion of B atoms as predicted [201 ] by a nonstochastic approach. This tendency to generate a tunneling attack at the cost of only surface diffusion could be considered as a likely explanation of pit nucleation at the atomic level, with no need for the concept of passive film breakdown. 

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