Phase transformations, overall transformation rate

Nucleation and Growth (Round 1). Phase transformations, such as the solidification of a solid from a liquid phase, or the transformation of one solid crystal form to another (remember allotropy ), are important for many industrial processes. We have investigated the thermodynamics that lead to phase stability and the establishment of equilibrium between phases in Chapter 2, but we now turn our attention toward determining what factors influence the rate at which transformations occur. In this section, we will simply look at the phase transformation kinetics from an overall rate standpoint. In Section 3.2.1, we will look at the fundamental principles involved in creating ordered, solid particles from a disordered, solid phase, termed crystallization or devitrification. 

An overall conversion rate may depend on rates of mass transfer between phases as well as chemical rates. In the simplest case, mass transfer and chemical transformation occur in series advantage is taken of the equality of these two rates at steady state conditions to eliminate interfacial concentrations from the rate equations and thus to permit integration. Item 8 of Table 17.2 is an example. 

A discontinuous transformation generally occurs by the concurrent nucleation and growth of the new phase (i.e., by the nucleation of new particles and the growth of previously nucleated ones). In this chapter we present an analysis of the resulting overall rate of transformation. Time-temperature-transformation diagrams, which display the degree of overall transformation as a function of time and temperature, are introduced and interpreted in terms of a nucleation and growth model. 

When SAS are present in solution, pesticide compounds partition between the bulk aqueous solution and the (sub)micellar phase (Figure 17). This partitioning may affect the overall rates and products of transformation of these compounds if their rates of reaction in the (sub)micellar phase are significantly different from those in the aqueous phase (Barbash, 1987 Macalady and Wolfe, 1987 Barbash and Resek, 1996). In some cases, relatively minor variations in SAS stmcture can have substantial impacts on pesticide transformation rates (Kamiya et ai, 1994). Even if reaction rates are not substantially different in the (sub)mi-cellar phase, however, the presence of SAS may modify reaction rates in solution for sparingly soluble pesticide compounds by simply increasing their dissolved concentrations, as may occur in the presence of polar solvents (e.g., Barbash and Reinhard, 1989a Schwarzenbach et al. 

Under actual conditions of reforming, several species are chemisorbed on the Pt/Al203 surface and they influence the overall dynamics(l-6). Significant adsorbate-adsorbate interactions can be present and they affect the sorption and reaction rates and equilibrium (6-11) markedly, especially for bi-molecular reactions. These also can have pronounced consequences in surface dynamics(7-16). While their roles in surface phase transformations have been demonstrated, using ideal single crystal surfaces(12,13), their consequences in surface dynamics are much less understood.(l,12-14)... 

The sphemlitic growth rate, the overall crystallization rate, and the melting temperature of PB-1 are depressed by the presence of HOCP. The verified HOCP interferences on the kinetics of PB-1 crystal transformation from form II to form I indicate that in the crystallized mixtures the HOC molecules are rejected in inter-lamellar and/or interfibriUar regions of PB-1 spherulites where, dependening on the blend composition, they can form a homogeneous mixture with uncrystaUized PB-1 molecules or a conjugated amorphous phase, one rich in PB-1 component and the other rich in HOCP component. 

With prolonged exposure, the concentration of ion pairs in the aqueous phase gradually increases. If supersaturation is reached, the ion pairs precipitate into a solid phase. This transformation is complex and the ion pairs may pass through the colloidal state before they reach the solid state. Nucleation of precipitated species is facilitated by the heterogeneous nature of the substrate surface and the overall formation rate of the precipitate seems more often to be limited by its growth rate rather than by its nucleation rate. Evidence of this lies in the frequent observation of many small precipitated nuclei rather than a few larger ones, see Fig. 5 [11]. 

In the case of slow reactions, the transformation rate is limited by intrinsic kinetics. A drastic increase of the temperature allows exponential acceleration of the reaction rate in agreement with the Arrhenius Law. Moreover, the pressure can be advantageous to accelerate reactions, to shift equilibrium, to increase gas solubility, to enhance conversion and selectivity, to avoid solvent evaporation, and to obtain single-phase processes [8, 13]. The overall transformation rate of such reactions could be significantly increased in these wove/ operating windows. 

FIGURE 6.22 For a phase transformation that occurs on cooling a system below Tg, the overall nucleation rate is a result of two factors the concentration of critical nuclei n, which obtains a peak at intermediate temperatures below Fg, and the diffusion term v = which increases exponentially with increasing temperature. As a result, the peak for N is skewed toward higher temperatures than the peak for n. However, as T approaches Fg, both n and N fall to zero. Similarly, at very low temperature, both n and N approach zero. Thus, there is an intermediate cooling temperature that results in the greatest rate of nucleation. 

FIGURE 6.25 For a phase transformation that occurs on cooling a system helow Tg, the overall transformation rate F is a nonlinear product of the nucleation rate N and the growth rate G. Because both N and G obtain a peak at intermediate temperatures, so does F. 

Phenols have been phosphorylated under phase transfer conditions in the presence of a nucleophilic catalyst [31, 32]. The reaction of 4-nitrophenol with dimeth-oxythiophosphoryl chloride is ordinarily slow and leads to a mixture of the desired methyl parathion and hydrolysis products. Addition of N-methylimidazole enhanced the rate but the best results were obtained when both the imidazole and a quaternary ammonium salt (TBAB) were used at the same time. The co-catalysis was accounted for in terms of nucleophilic activation of the acylating agent by imidazole and solubilization of the phenoxide by ion pairing with the quaternary ion. The overall transformation is formulated in equation 6.13. 

---