Mean separation work

Kaischev and Lubomir Krastanov within the period 1931-1933 [13-15]. In 1934 I. Stranski and R. Kaischev developed also the so-called theory of mean separation works [11, 16-18], thus shedding, for the first time, light on the interrelation... 

To my knowledge, Ivan Stranski never contributed directly to the field of electrochemical science. However, his definitions of the fundamental concepts half-crystal position and separation work (py2 of single atom therefrom [8, 9], as well as the definition of the concept of mean separation work of the atoms from a crystal face in contact with a vapor phase [16-18], were used by R. Kaischev [19], who in 1946 proposed definitions of these quantities applicable also to the more complex case of crystals in contact with an ionic electrolyte solution (see also [12]). 

In 1933 Kaischev became an assistant of Stranski at the Chemistry Faculty of Sofia University, and they both developed the theory of mean separation works [16-18]. In 1934 Kaischev was invited to visit the Ukrainian Physical-Technical Institute, in Kharkiv, Ukraine, and worked for 3 months in the laboratory for physics of low temperatures. In the autumn of 1937 he joined the Munich University for 1 year, again as a fellow of the Alexander von Humboldt Foundation. Two of his papers from this period related to the physics at low temperatures were published in Zeitschrift fiir Physikalische Chemie [27, 28]. 

In 1934 Stranski and Kaischew made another important step in the development of the nucleation theory. In three papers [1.21-1.23] they proposed the theory of mean separation works, revealing for the first time... 

As expected, for infinitely large crystals oo and the mean separation work tends to the separation work /2,u = from the half-crystal... 

A crucial point in the Stranski - Kaischew theory is the condition for the equality of the mean separation works of the atoms from all crystallographic faces of an equilibrium finite crystal. In the case under consideration the equality leads to ... 

The theory of mean separation works allows us to draw some important conclusions on the equilibrium properties of the two-dimensional crystals formed on the top of three-dimensional ones having the same chemical composition (Figure 1.25). 

Let us now comment upon the crystal-solution equilibrium in terms of the kinetic theory of the mean separation works. Since this theoiy considers the elementary processes of material exchange across the phase boundary it is first necessary to define the frequencies of attachment, and detachment, W-i, of single particles to and from the rth site of the crystal surface. In the case of electrocrystalHzation on a like surface the quantities and W.i are expressed as [1.95-1.98] ... 

An important achievement of the theory of the mean separation works is the detailed kinetic description of the equilibrium between a small crystal and the ambient phase. In that case the equilibrium state is attained only at a supersaturation Ap > Q and is expressed through the equality of the probabilities of attachment P+ t/ and detachment of atoms to and Irom the different crystallographic faces. 

The Stranski - Kaischew theory ofthe mean separation works [1.21-1.23] provides the first consistent atomistic description of the elementary processes taking place on the crystal surface. Considering the nucleation... 

The charge transfer Scheme V is akin to the adiabatic electron transfer cycle in Scheme IV. In this case the work term Wp required to bring the products D+ and A together to the mean separation rp in the CT excited state is given by ... 

We associate such variations in the work term wp with changes in the mean separation r in the EDA complexes. Qualitatively, such changes may be viewed as steric effects which hinder the close approach of the acceptor and the donor. For example, the constancy of wp for the substituted-anthracene donors accords with the minor steric perturbation a substituent is expected to exert... 

It should be noted that application of the Marcus theory to these reactions is much more straightforward than application to reactions in solution. Since we are dealing with a single unimolecular step, namely, rearrangement of the reactant complex to the product complex, we need not be concerned with the work terms (2) which must be included in treatments of solution-phase reactions. These terms represent the work required to bring reactants or products to their mean separations in the activated complex, and include Coulombic and desolvation effects. 

The work required to bring the reactants (assumed to be rigid spheres of radius a and a ) to their mean separation distance in the activated complex (r = a, + aj) then remove the products to infinity. These work terms are w and — respectively, and incorporate electrostatic and nonpolar contributions. 

In this context, direct means separation of the substrate, except solvent extraction, is not a part of the analytical work Only CD has the necessary... 

Usually only differences of chemical potentials A//,- y - m- fjj of atoms in various crystal positions i, j are theoretically considered and because the mean vibrational volumes ti,-, vyare roughly equal, A//, y can be given, according to eq. (2.1), by the respective separation works (j> ... 

Fig. 12.12 DNA molecule in a gel in electric field is stretched if the field is strong (a), but remains an insignificantly deformed coil if the field is weak (b). The inset c shows the dependence of the electrophoretic speed v on the chain length A/ the dependence flattens off for long chains, which means separation in a constant field only works for chains of moderate length.

Recent years have seen vast experimentation with many different process designs for the liquefaction of coals. The degree of coal conversion and composition of the product oil vary with both the coal rank, maceral composition, mineral matter content, and conversion process. Whereas much attention has been focused on the separation and characterization of the product oil by chromatographic and spectroscopic means, less work has been done on the unconverted or process altered residues from liquefaction processes. Although many of the processes do incorporate some sort of bottoms processing , other possible uses of these residues include road materials, carbon electrodes, coal gasification feedstocks, and as direct combustion fuels. Recently, coal conversion by-products have been used as raw materials in the synthesis of thermosetting polyesters. ... 

The actual work supplied to separate the mixture is usually higher than the minimum separation work, as given by Eq. (1-148). Additional energy is required to create additional phases if necessary, to divide phases using mechanical means, to mix or to disperse. The energy losses of the separation units, and the pump work necessary to transport the liquid are not considered in... 

The enrichment of uranium has to be accomplished by some physical process which depends on differential behavior of the two isotopes of uranium. The great majority of separative work has to date been carried out by the gaseous diffusion process, where the distinguishing feature between the isotopes is the rate at which the molecules of different mass diffuse through a porous barrier under an applied pressure differential. In a sample of uranium hexafluoride gas, the mean kinetic energy of the lighter molecules is equal to that of the heavier, i.e.,... 

Triglycerides in seed oils are readily soluble in SC-CO2 at 40 C and at pressures higher than 280 bars. The main parameters important for efficient oil extraction in this method are particle size, pressure and residence time. Small particles of about 1mm mean diameter or less and high pressures (300-500 bar) can strongly reduce the extraction time. After extraction, the SC-CO2 tryglicerides solution is sent to a separator working at subcritical conditions. This operation reduces the solvent power of CO2 and allows the recovery of oil. The complete elimination of gaseous CO2 from oil is also accomplished in this step. The SC-CO2 extraction of seed oils has been tested up to pilot seale for several seed oils. 

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