Thermodynamics solution growth

The analysis of thermodynamic data obeying chemical and electrochemical equilibrium is essential in understanding the reactivity of a system to be used for deposition/synthesis of a desired phase prior to moving to experiment and/or implementing complementary kinetic analysis tools. Theoretical and (quasi-)equilibrium data can be summarized in Pourbaix (potential-pH) diagrams, which may provide a comprehensive picture of the electrochemical solution growth system in terms of variables and reaction possibilities under different conditions of pH, redox potential, and/or concentrations of dissolved and electroactive substances. 

There are two major factors which have to be considered in the process of the electrolytic metal deposition (i) the thermodynamic and growth properties of the crystalline phase which can be treated as largely independent of the presence and character of the ambient phase and (ii) the properties of the ionic solution affecting primarily the structure of the interface boundary and the kinetics of the mass and charge transfer across it. In the first part of this chapter the problems connected with the formation and growth of the crystals of the metal deposit will be discussed more closely, while the problems arising from the ionic solution side will be treated as simply as possible (see also Vol. 1 of this series). 

Melt growth is the formation of a crystalline solid from a liquid phase that has essentially the same composition as the solid. If the composition of the liquid shows a larger deviation from that of the solid one deals with solution growth. Fundamentals of thermodynamics of melt growth can be found, e.g. in (15). 

For a thermodynamic analysis of solution growth precise information about the final products and the starting material is needed. The end product is a pure, stoichiometrically well-defined soHd in its crystalline state, while the initial state is usually a homogeneous solution of the constituent(s) of the crystal to be formed in a solvent. Thus, for a thermodynamic treatment of solution growth, the difference between values of the characteristic thermodynamic data for the crystal on the one hand and for its constituents in the feeding solution on the other hand are required. The difficulties lie in the precise knowledge of the nature of the dissolved particles and an adequate description of the solution. Frequently, one does not know in detail the nature of the growth solution. Particles that eventually form the crystal can be ionized, they are probably solvated and/or associated in solution, they show different kinds of attractive or repulsive interactions with solvent or solute particles. 

Gas AntisolventRecrystallizations. A limitation to the RESS process can be the low solubihty in the supercritical fluid. This is especially evident in polymer—supercritical fluid systems. In a novel process, sometimes termed gas antisolvent (GAS), a compressed fluid such as CO2 can be rapidly added to a solution of a crystalline soHd dissolved in an organic solvent (114). Carbon dioxide and most organic solvents exhibit full miscibility, whereas in this case the soHd solutes had limited solubihty in CO2. Thus, CO2 acts as an antisolvent to precipitate soHd crystals. Using C02 s adjustable solvent strength, the particle size and size distribution of final crystals may be finely controlled. Examples of GAS studies include the formation of monodisperse particles (<1 fiva) of a difficult-to-comminute explosive (114) recrystallization of -carotene and acetaminophen (86) salt nucleation and growth in supercritical water (115) and a study of the molecular thermodynamics of the GAS crystallization process (21). 

Part of the gas can escape from the solution at a specific concentration and a fixed temperature, as the pressure level falls to under P < Pg. This takes place in two phases appearance of nuclei, and growth of bubbles of the free gas phase. Thermodynamic conditions for stable nucleation are formulated in [1], They are analogous to the conditions for starting the boiling of low-molecular liquids. The following changes take... 

Equilibria considerations on solution-grown zinc chalcogenide compounds have been put forward by Chaparro [28] who examined the chemical and electrochemical reactivity of solutions appropriate for deposition of ZnS, ZnSe, ZnTe (and the oxide ZnO) in order to explain the results of recipes normally used for the growth of such thin films. The author compared different reaction possibilities and analyzed the composition of solutions containing zinc cations, ammonia, hydrazine, chalcogen anions, and dissolved oxygen, at 25 °C, by means of thermodynamic diagrams, applicable for concentrations usually employed in most studies. 

Here Jta(x) denotes the a-th component of the stationary vector x of the Markov chain with transition matrix Q whose elements depend on the monomer mixture composition in microreactor x according to formula (8). To have the set of Eq. (24) closed it is necessary to determine the dependence of x on X in the thermodynamic equilibrium, i.e. to solve the problem of equilibrium partitioning of monomers between microreactors and their environment. This thermodynamic problem has been solved within the framework of the mean-field Flory approximation [48] for copolymerization of any number of monomers and solvents. The dependencies xa=Fa(X)(a=l,...,m) found there in combination with Eqs. (24) constitute a closed set of dynamic equations whose solution permits the determination of the evolution of the composition of macroradical X(Z) with the growth of its length Z, as well as the corresponding change in the monomer mixture composition in the microreactor. 

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