Supersaturation thermodynamic

Nucleation is the growth of clusters of molecules that become a thermodynamically stable nucleus. This process is dependent on the vapor pressure of the condensable species. The molecular clusters undergo growth when the saturation ratio, S, is greater than 1, where saturation ratio is defined as the actual pressure of the gas divided by its equilibrium vapor pressure. S > 1 is referred to as a supersaturated condition (14). 

The manner in which a film is formed on a surface by CVD is still a matter of controversy and several theories have been advanced to describe the phenomena. ] A thermodynamic theory proposes that a solid nucleus is formed from supersaturated vapor as a result of the difference between the surface free energy and the bulk free energy of the nucleus. Another and newer theory is based on atomistic nucle-ation and combines chemical bonding of solid surfaces and statistical mechanics. These theories are certainly valuable in themselves but considered outside the scope of this book. 

Transfomation from a meta-stable phase, such as supersaturated solution, to a thermodynamically more favorable phase requires first the crystal nucleation of a germ of the new phase. According to the classical nucleation theory, the volume nucleation rate J (cm" sec ), describing the number of nuclei(i.e., a critical germ) formed per volume per time, is given by ... 

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. 

Once we have calculated the distribution of species in the fluid, we can determine the degree to which it is undersaturated or supersaturated with respect to the many minerals in the thermodynamic database. Only a few of the minerals can exist in equilibrium with the fluid, which is therefore undersaturated or supersaturated with respect to each of the rest. For any mineral A , we can write a reaction,... 

The dissolution rate, according to the theory, does not depend on the mineral s saturation state. The precipitation rate, on the other hand, varies strongly with saturation, exceeding the dissolution rate only when the mineral is supersaturated. At the point of equilibrium, the dissolution rate matches the rate of precipitation so that the net rate of reaction is zero. There is, therefore, a strong conceptual link between the kinetic and thermodynamic interpretations equilibrium is the state in which the forward and reverse rates of a reaction balance. 

As in the previous example (Fig. 26.1), silica concentration in the calculations asymptotically approaches a single value, regardless of the initial concentration. The final silica concentration, however, does not represent a thermodynamic equilibrium, since (as we can see in Fig. 26.2) it is supersaturated with respect to quartz and undersaturated with respect to cristobalite. 

Slade, L. and Levine, H. 1985. Intermediate moisture systems concentrated and supersaturated solutions pastes and dispersions water as plasticizer the mystique of bound water thermodynamics versus kinetics (Number 24). Presented at Faraday Division, Royal Society of Chemistry Discussion Conference - Water Activity A Credible Measure of Technological Performance and Physiological Viability Cambridge, July 1-3. 

Precipitation can occur if a water is supersaturated with respect to a solid phase however, if the growth of a thermodynamically stable phase is slow, a metastable phase may form. Disordered, amorphous phases such as ferric hydroxide, aluminum hydroxide, and allophane are thermodynamically unstable with respect to crystalline phases nonetheless, these disordered phases are frequently found in nature. The rates of crystallization of these phases are strongly controlled by the presence of adsorbed ions on the surfaces of precipitates (99). Zawacki et al. (Chapter 32) present evidence that adsorption of alkaline earth ions greatly influences the formation and growth of calcium phosphates. While hydroxyapatite was the thermodynamically stable phase under the conditions studied by these authors, it is shown that several different metastable phases may form, depending upon the degree of supersaturation and the initiating surface phase. 

Reaction kinetics. The time-development of sorption processes often has been studied in connection with models of adsorption despite the well-known injunction that kinetics data, like thermodynamic data, cannot be used to infer molecular mechanisms (19). Experience with both cationic and anionic adsorptives has shown that sorption reactions typically are rapid initially, operating on time scales of minutes or hours, then diminish in rate gradually, on time scales of days or weeks (16,20-25). This decline in rate usually is not interpreted to be homogeneous The rapid stage of sorption kinetics is described by one rate law (e.g., the Elovich equation), whereas the slow stage is described by another (e.g., an expression of first order in the adsorptive concentration). There is, however, no profound significance to be attached to this observation, since a consensus does not exist as to which rate laws should be used to model either fast or slow sorption processes (16,21,22,24). If a sorption process is initiated from a state of supersaturation with respect to one or more possible solid phases involving an adsorptive, or if the... 

Despite the importance of the precipitation of calcium phosphates, there is still considerable uncertainty as to the nature of the phases formed in the early stages of the precipitation reactions under differing conditions of supersaturation, pH, and temperature. Although thermodynamic considerations yield the driving force for the precipitation, the course of the reaction is frequently mediated by kinetic factors. Whether dicalcium phosphate dihydrate (CaHPO HoO, DCPD), octacalcium phosphate (Ca HfPO, 2.5 H20, OCP), hydroxyapatite (Cag (PO fOH), HAP), amorphous calcium phosphate (ACP), or a defect apatite form from aqueous solution depends both upon the driving force for the precipitation and upon the initiating surface phase. Thermodynamically, the relative supersaturation, o, is given by... 

The Important conclusion is that complex controlling processes can occur in solubility phenomena in mixed electrolyte solutions. This is especially true of surface coatings formed kinetically or by multistate thermodynamics and which prevent the aqueous solution from interaction with internal bulk phases. One should remember of course that, when the degree of supersaturation is large enough for bulk precipitation to occur, the kinetic and multiphase thermodynamic processes studied above will apply to the actual bulk phases. 

A solution that is in thermodynamic equilibrium with the solid phase of its solute at a given temperature is a saturated solution, and a solution containing more dissolved solute than that given by the equilibrium saturation value is said to be supersaturated. The degree of supersaturation may be expressed by ... 

Whilst the fundamental driving force for crystallisation, the true thermodynamic supersaturation, is the difference in chemical potential, in practice supersaturation is generally expressed in terms of solution concentrations as given in equations 15.1-15.3. Mullin and Sohnel(19) has presented a method of determining the relationship between concentration-based and activity-based supersaturation by using concentration-dependent activity-coefficients. 

In c-Hxn solutions the nucleation behavior is similar to that in EtOH solutions. It is presumed that the concentrations of conformer regarding to the A and B form are competitive and the nucleation process of the polymorph is determined by the supersaturation and the kinetic process. On the other hand in MeCN solutiorrs orrly the stable form nucleates. In MeCN solution it is considered that the thermodynamic stability of the meta-stable form is extremely low due to the large solvent-solute... 

The saturation state of seawater can be used to predict whether detrital calcite and aragonite are thermodynamically favored to survive the trip to the seafloor and accumulate in surfece sediments. Any PIC or sedimentary calcium carbonate exposed to undersaturated waters should spontaneously dissolve. Conversely, PIC and sedimentary calcium carbonate in contact with saturated or supersaturated waters will not spontaneously dissolve. Typical vertical trends in the degree of saturation of seawater with respect to calcite and aragonite are shown in Figure 15.11 for two sites, one... 

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