Spacial density distribution

The amplitude of the ith process (N.) represents the fraction of water molecules in a domain of equivalent solute density or equivalent pore size. A plot of versus l/T. is then an approximation to a spacial density distribution function for the heterogeneous sample. 

The spacial distribution of electron density in an atom is described by means of atomic orbitals Vr(r, 6, (p) such that for a given orbital xp the function xj/ dv gives the probability of finding the electron in an element of volume dv at a point having the polar coordinates r, 6, 0. Each orbital can be expressed as a product of two functions, i e. 0, [Pg.1285]

Brindley and Sempels (1), Vaughan et al. (2) and Shabtai (3) have shown that the experimental conditions of Al intercalation influences the physicochemical properties of the clay. The nature, amount and spacial distribution of the pillars change the thermal stability, texture and acidity of the pillared clays. For example, Rausch and Bale (4) have reported that the OH/Al ratio modifies the structure of the Al complex and that monomeric [Al(0H)x(H20)6-x] " or polymeric [A1i304(0H)24(H20)i2] species can be obtained. Clearfield (5) demonstrated that the polymerisation state of Zr species depends on the temperature, concentration and pH of the solutions. In any case, the height of pillars is largely controlled by the polymerisation state of the intercalated complexes. However, in order to maintain the accessibility of the inner surface, the density or spacial distribution of the pillars has to be controlled. This parameter has been studied by Flee et al (5), and Shabtai et al (7) for Al pillared clays and Farfan-Torres et al (8) for zirconium. 

Here, pe is the local electric charge density in C/m3. With the Poisson equation, the potential distribution can be calculated once the exact charge distribution is known. The complication in our case is that the ions in solution are free to move. Before we can apply the Poisson equation we need to know more about their spacial distribution. This information is provided by Boltzmann5 statistics. According to the Boltzmann equation the local ion density is given by... 

With respect to the hydrochemical structure, one can distinguish the southwestern part, which finds itself under the influence of the Bosphorus and represents an area of intensive redox processes in a multilayered transition zone. Here, the chemical conditions are extremely instable due to the temporal and spacial variations in the supply of the Bosphorus waters. In other regions of the Black Sea, the hydrochemical structure is mainly formed and maintained by a combination of biogeochemical and hydrophysical processes such as advection, turbulence, sedimentation, etc. and can be explained with ID-model approach. This leads to the formation of a chemotropic structure, where all features of the chemical parameters distribution are closely correlated with the water density. 

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