Thermodynamics of Solution Growth

Industrial mass crystallization is essentially solution growth. It is estimated that about 75% of all solid products of the chemical and pharmaceutical industries are crystals. Also, most natural crystals are the product of solution growth. 

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. 

Crystallization from solution may be associated with a chemical reaction between different constituents in the solution, or it may be a physical process without chemical reaction. 

The two most important aspects for solution growth are a) the absolute solubility of a material to be crystallized, and b) the temperature dependence of the solubility. 

The most basic approach to the thermodynamics of crystal growth from solution can again be easily derived from the fundamental equihbrium condition 

---

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). 

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). 

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. 

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. 

The level of impurity uptake can be considered to depend on the thermodynamics of the system as well as on the kinetics of crystal growth and incorporation of units in the growing crystal. The kinetics are mainly affected by the residence time which determines the supersaturation, by the stoichiometry (calcium over sulfate concentration ratio) and by growth retarding impurities. The thermodynamics are related to activity coefficients in the solution and the solid phase, complexation constants, solubility products and dimensions of the foreign ions compared to those of the ions of the host lattice [2,3,4]. 

The rapid expansion of supercritical solutions (RESS) has been explored recently as a novel route for the production of small and monodispersed particles (1-2.). Particle formation involves nucleation, growth and agglomeration. In RESS, nucleation is induced by a rapid decompression growth and agglomeration occur within the expanding solution. The thermodynamics of the supercritical mixture influences the relative importance of these mechanisms, and thus play a key role in sizes or size distribution of final particles. 

Miscible blends of poly(vinyl methyl ether) and polystyrene exhibit phase separation at temperatures above 100 C as a result of a lower critical solution temperature and have a well defined phase diagram ( ). This system has become a model blend for studying thermodynamics of mixing, and phase separation kinetics and resultant morphologies obtained by nucleation and growth and spinodal decomposition mechanisms. As a result of its accessible lower critical solution temperature, the PVME/PS system was selected to examine the effects of phase separation and morphology on the damping behavior of the blends and IPNs. 

Crystals form in supersaturated solutions in which the solute concentration exceeds its solution solubility. Supersaturation is usually expressed as either of the ratios dc or (c — c )lc, where c is the concentration of solute before crystallization and is the solute equilibrium saturation concentration. Supersaturated solutions are thermodynamically metastable. Equilibrium can be restored by reducing the solute concentration through precipitation or formation of nuclei and subsequent crystal growth. The super saturation requirements for nucleation and... 

---