Thermodynamic properties supersaturation

It has been established experimentally that all thermodynamic properties of supersaturated phases (a supersaturated vapor, a liquid heated beyond the boiling point, or a liquid cooled down below the melting point) are in no way remarkable and fail to show any substantial deviations that would point to strong heterophase fluctuations. All the more, d, fortiori, it may hence be concluded that before the transition point and at the point itself the quantity J is negligibly small. 

Hygroscopic behavior has been well characterized in laboratory studies for a variety of materials, for example, ammonium sulfate (Figure 14), an important atmospheric material. When an initially dry particle is exposed to increasing RH it rapidly accretes water at the deliquescence point. If the RH increases further the particle continues to accrete water, consistent with the vapor pressure of water in equilibrium with the solution. The behavior of the solution at RH above the deliquescence point is consistent with the bulk thermodynamic properties of the solution. However, when the RH is lowered below the deliquescence point, rather than crystallize as would a bulk solution, the material in the particle remains as a supersaturated solution to RH well below the deliquescence point. The particle may or may not undergo a phase transition (efflorescence) to give up some or all of the water that has been taken up. For instance, crystalline ammonium sulfate deliquesces at 79.5% RH at 298 K, but it effloresces at a much lower RH, 35% (Tang and Munkelwitz, 1977). This behavior is termed a hysteresis effect, and it can be repeated over many cycles. 

Similar to solubility, the metastable zone width and induction time of a supersaturated solution are affected by various factors, including temperature, solvent composition, chemical structure, salt form, impurities in the solution, etc. Therefore, although the spinodal point is a thermodynamic property, it is very difficult to measure the absolute value of the metastable zone width experimentally. Regardless, understanding the qualitative behavior of the metastable zone width and the induction time can be helpful for the design of crystallization processes. 

To calculate gas solubility in natural geochemical systems, basic thermodynamic properties such as the Henry s law constant and, in the case of weak electrolytes the dissociation constant, must be combined with a thermodynamic model of aqueous solution behavior. An analogous approach has been used to predict mineral solubilities in concentrated brines (1). Such systems are also relevant to the atmosphere where very concentrated solutions occur as micrometer sized aerosol particles and droplets, which contain very small amounts of water relative to the surrounding gas phase. The ambient relative humidity (RH) controls solute concentrations in the droplets, which will be very dilute near 1(X)% RH, but become supersaturated with respect to soluble constituents (such as NaCl) below about 75% RH. The chemistry of the aerosol is complicated by the non-ideality inherent in concentrated electrolyte solutions. 

It has been experimentally confirmed that hydroxyapatite cannot be precipitated directly from a supersaturated calcium phosphate solution (for example, Nancollas and Wu, 2000). Instead, it is thought that precursor compounds such as octacalcium phosphate (OCP) (Brown, 1966) and/or ACP (for example Eanes, Gillessen and Posner, 1965 Termine and Posner, 1966) are required as intermediates, the thermodynamic properties of which act towards lowering the Gibbs energy of formation of hydroxyapatite. OCP shows some structural similarity to hydroxyapatite and forms with HAp epitaxially controlled interlayered single... 

Loftsson T, Fririksddttir H, Gumundsdottir TK (1996) The effect of water-soluble polymers on aqueous solubility of drugs. Int J Pharm 127 293-296 Matteucci ME, Miller MA, Williams RO, Johnston KP (2008) Highly supersaturated solutions of amorphous drugs approaching predictions from configurational thermodynamic properties. J Phys Chem B 112 16675-16681. 

In an alternative to counting the number of condensed particles, one can try to monitor the concentration of remaining solute [44], or some other thermodynamic property that evolves with cluster formation for example, microcalorimetry can measure the heat absorbed as crystallization occurs, and thus can draw a de-supersaturation curve [45]. Needless to say, none of the above directly or indirectly touches upon the question of the internal structure of the generated clusters. 

As shown in Fig. 2 [37], and also in the work of Barraclough and Hall [34], moisture uptake onto sodium chloride as a function of relative humidity is reversible as long as RH0 is not attained. This is evidence that actual dissolution of water-soluble crystalline substances does not occur below RH0. This is consistent with thermodynamic rationale that dissolution below RHo would require a supersaturated solution (i.e., an increased number of species in solution would be necessary to induce dissolution at a relative humidity below that of the saturated solution, RH0). In this regard, one should only need to consider the solid state properties of a purely crystalline material below RH0. As will be described, other considerations are warranted for a substance that contains amorphous material. 

However, the thermodynamic supersaturation condition does not suffice to predict or control various properties of a precipitate, because the solid-phase formation proceeds through several stages, each of which can affect the composition, size, and shape of the final particles. 

The rates of nucleation as expressed by the classical expression of Volmer are related to various thermodynamic and physical properties of the system such as surface free energy (y), temperature (T), degree of supersaturation (a), solubility (hidden in the... 

In an example from the pharmaceutical industry Sudo et a/. (1991) studied the relative nucleation properties of forms A and B of cimetidine, which is reported to have four polymorphic non-solvated forms and three polymorphic monohydrates. Modification A is preferred for pharmaceutical formulations. The waiting time method was used to study the primary nucleation process (Harano and Oota 1978), mainly for competitive crystallization of the A and B modifications. A is a thermodynamically metastable form and is more soluble than B in any solvent. At high supersaturation... 

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