Aggregation instantaneous

The ionic atmosphere is not a static structure, so its composition is best treated statistically. An aggregation of ionic charges, if static, would allow for crystallization if the solution was at ail concentrated. In dilute solutions, while the charges might instantaneously have a three-dimensional structure similar to that in an ionic repeat lattice, thermal vibrations soon cause such momentary interactions to break down (i.e. shake free) and reform. 

The solid is in equilibrium with the instantaneous melt, or, the last drop of the extracted (aggregated) melt by the following relationship... 

Next we analyze the sorption kinetics of a sorbate with constant aqueous concentration, C°, sorbing into a porous spherical aggregate with radius rQ. More precisely, the macroparticle is a homogeneous aggregate of microparticles which are separated by micropores filled with water (Fig. 19.17). The sorbate diffuses in these pores and sorbs to the microparticles. It is not relevant whether sorption occurs at the surface or in the interior of the microparticles as long as we can assume that sorption equilibrium between the solute concentration and the microparticles at each position within the aggregate is attained instantaneously. 

Figure 19.17 Spherical macroparticle with radius ra consisting of an aggregate of microparticles separated by micropores filled with water. A chemical with constant concentration C° diffuses into the pore volume of the macroparticle. The local dissolved pore concentration Cw is at instantaneous equilibrium with the local sorbed phase C ( K d is microscopic equilibrium coefficient). Note that the macroscopic distribution coefficient Kd is time dependent (see Eq. 19-78.)...

Transport control of flocculation is realized in an especially direct way in the process known as diffusion-limited cluster-cluster aggregation5 (aggregation as used in this term means flocculation in the present chapter). In this process, which is straightforward to simulate and visualize on a computer, particles undergo Brownian motion (i.e., diffusion) until they come together in close proximity, after which they coalesce instantaneously and irreversibly to form floccules (or clusters ). The clusters then diffuse until they contact one another and combine to form larger clusters, and so on, until gravitational... 

Because of the EPR effect quantum systems that have interacted before remain correlated even when the interaction no longer persists. The experiments have shown that, even when all interaction comes to an end, information about the second of a pair of particles can be obtained by performing a measurement on the first. The conclusion is that the physical world cannot be correctly described by a realistic local theory. It is necessary either to abandon the criterion of reality or to accept the possibility of action at a distance. The latter occurs because each particle is described by a wave function which is, in general, a non-local entity that collapses when a measurement is made. This collapse is instantaneous and complete. It occurs everywhere, also at the position of a particle not involved in the measurement and therefore predicts the correlation of distant events. Most particles or aggregates of particles, usually regarded as separate objects, have interacted in the past with other objects and must hence remain correlated and to constitute an indivisible entangled whole. This observation represents the scientific rediscovery [45] of holism [46]. 

The reactant species impinging from the vapor phase is attracted to the surface of the substrate mainly due to the instantaneous dipole moment of the substrate surface atoms. Adsorption of the condensed species is accompanied by lateral diffusion, i.e., the species moves along the surface of the substrate for a particular distance before it resides on the surface. An aggregate of condensed reactant species that reside on the surface of the substrate is termed a "nucleus". This could vary from a single atom or molecule to a cluster of species, and the process is referred to as nucleation. Nuclei are usually three dimensional island type structures formed on the surface of the substrate and nucleation is usually the initial stage of the film formation. It is worthwhile to note that, while simple condensation is usually exothermic, CVD adsorption and subsequent film formation is usually an endothermic reaction with few exceptions. 

Seebach, Dunitz and cowoikers fust described the THF-solvated tetrameric aggregates obtained from THF solutions of 3,3-dimethyl-2-butanone (pinacolone) and cyclopentanone lithium enolates. These are represented as (137). The pinacolone enolate also crystallizes as the unsolvated hexamer (138) from hydrocarbon solution, but this hexamer rearranges instantaneously to the tetramer (137) in the presence of THF. Williard and Carpenter completed the characterization of both the Na+ and the K+ pinacolone enolates.Quite unexpectedly the Na pinacolone enolate is obtained from hydrocarbon/THF solutions as the tetramer (139) with solvation of the Na atoms by unenolized ketone instead of by THF. Hie potassium pinacolone enolate is a hexameric THF solvate depicted as (140) and described as a hexagonal prism. A molecular model of (140) reveals slight chair-like distortions of the hexagonal faces in (140) so that the solvating THF molecules nicely fit into the holes between the pinacolone residues. 

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