Phase boundary growth

In this section we discuss the basic mechanisms of pattern formation in growth processes under the influence of a diffusion field. For simphcity we consider the sohdification of a pure material from the undercooled melt, where the latent heat L is emitted from the solidification front. Since heat diffusion is a slow and rate-limiting process, we may assume that the interface kinetics is fast enough to achieve local equihbrium at the phase boundary. Strictly speaking, we assume an infinitely fast kinetic coefficient. 

The characteristic feature of solid—solid reactions which controls, to some extent, the methods which can be applied to the investigation of their kinetics, is that the continuation of product formation requires the transportation of one or both reactants to a zone of interaction, perhaps through a coherent barrier layer of the product phase or as a monomolec-ular layer across surfaces. Since diffusion at phase boundaries may occur at temperatures appreciably below those required for bulk diffusion, the initial step in product formation may be rapidly completed on the attainment of reaction temperature. In such systems, there is no initial delay during nucleation and the initial processes, perhaps involving monomolec-ular films, are not readily identified. The subsequent growth of the product phase, the main reaction, is thereafter controlled by the diffusion of one or more species through the barrier layer. Microscopic observation is of little value where the phases present cannot be unambiguously identified and X-ray diffraction techniques are more fruitful. More recently, the considerable potential of electron microprobe analyses has been developed and exploited. 

An unusual variation in kinetics and mechanisms of decomposition with temperature of the compound dioxygencarbonyl chloro-bis(triphenyl-phosphine) iridium(I) has been reported by Ball [1287]. In the lowest temperature range, 379—397 K, a nucleation and growth process was described by the Avrami—Erofe ev equation [eqn. (6), n = 2]. Between 405 and 425 K, data fitted the contracting area expression [eqn. (7), n = 2], indicative of phase boundary control. At higher temperatures, 426— 443 K, diffusion control was indicated by obedience to eqn. (13). The... 

It has been shown by FM that the phase state of the lipid exerted a marked influence on S-layer protein crystallization [138]. When the l,2-dimyristoyl-OT-glycero-3-phospho-ethanolamine (DMPE) surface monolayer was in the phase-separated state between hquid-expanded and ordered, liquid-condensed phase, the S-layer protein of B. coagulans E38/vl was preferentially adsorbed at the boundary line between the two coexisting phases. The adsorption was dominated by hydrophobic and van der Waals interactions. The two-dimensional crystallization proceeded predominately underneath the liquid-condensed phase. Crystal growth was much slower under the liquid-expanded monolayer, and the entire interface was overgrown only after prolonged protein incubation. 

Growth and transformation of nuclei into the final product of the solid state reaetion by formation of phase boundaries. 

Phase-boundary Controlled Random Growth Diffusion Controlled... 

We have already dealt with two of these. Section 2 dealt with formation of a phase boundary while we have just completed Section 4 concerning nuclei growth as related to a phase boundary. We will consider diffusion mechanisms in nuclei and diffusion-controlled solid state reactions at a later part of this chapter. 

Let us now reconsider our nucleation models of 4.4.1., specifically Models B, D and E. These are examples of phase-boundary controlled growth involving random nucleation. We now assume an exponential embryo formation law (see 4.4.7), with isotopic growth of nuclei in three dimensions and k2 as the rate constant. By suitable manipulation of 4.4.6.,... 

Although the above is complicated, it does aptly illustrate the various mechanisms involved when atoms (ions) migrate by diffusion and start to form a new structure by formation of incipient embryos, then nuclei and finally the growth of phase boundaries. 

We note that the growth of nuclei is associated with the motion of a phase boundary. 

When the reactants involved in a step growth polymerization process are mutually immiscible, we can employ an interfacial polymerization method. Two solutions, each containing one of the monomers, are layered one on top of the other. This creates a phase boundary that forms wth the least dense liquid on top. The different monomers can then meet and polymerize at the interface. A commonly demonstrated example of this is the manufacture of nylon 610 by the interfacial reaction between an aqueous solution of hexamethylenediamine with sebacoyl chloride dissolved in carbon tetrachloride. Because the reaction only occurs at the interface, it is possible to pull the products from this interface to isolate the final product. 

Reid et al. [ 1.12] described the effect of 1 % addition certain polymers on the heterogeneous nucleation rate at-18 °C the rate was 30 times greater than in distilled, microfiltered water and at -15 °C, the factor was still 10 fold hogher. All added polymers (1 %) influenced the nucleation rate in a more or less temperature-dependent manner. However, the authors could not identify a connection between the polymer structure and nucleation rate. None the less it became clear that the growth of dendritic ice crystals depended on to factors (i) the concentration of the solution (5 % to 30 % sucrose) and (ii) the rate at which the phase boundary water - ice crystals moved. However, the growth was found to be independent of the freezing rate. (Note of the author the freezing rate influences the boundary rate). 

All reactions involved in polymer chain growth are equilibrium reactions and consequently, their reverse reactions lead to chain degradation. The equilibrium constants are rather small and thus, the low-molecular-weight by-products have to be removed efficiently to shift the reaction to the product side. In industrial reactors, the overall esterification, as well as the polycondensation rate, is controlled by mass transport. Limitations of the latter arise mainly from the low solubility of TPA in EG, the diffusion of EG and water in the molten polymer and the mass transfer at the phase boundary between molten polymer and the gas phase. The importance of diffusion for the overall reaction rate has been demonstrated in experiments with thin polymer films [10]. 

Mochizuki, T. Mori, Y.H. (2006). Clathrate-hydrate film growth along water/hydrate-former phase boundaries - numerical heat-transfer study. J. Crystal Growth, 290 (2), 642-652. 

The top panel of Fig. 17.2 (Ts = 800 K) reveals that there is very little decomposition of the silane in the gas phase, which is a result of the relatively low temperature. As a result the net growth rates should be expected to be quite low, since the silane sticking coefficient is so low. At a surface temperature of Ts = 1300 K, however, the decomposition of silane to silylene in the gas-phase boundary layer is nearly complete. The relatively high silylene concentrations should lead to high growth-rates. The peak in the silylene profile at about 1.5 mm above the surface results from the competition between production by the homogeneous decomposition reaction and consumption at the surface by heterogeneous reaction. 

Diffusion control, one dimension Diffusion control, two dimensions Diffusion control, three dimensions Phase boundary control, two dimensions Phase boundary control, three dimensions First order (random nucleation) Nucleation and growth, two dimensions Nucleation and growth, three dimensions... 

In Chapter 11, growth morphologies are dealt with and the question is raised as to which conditions make the moving phase boundaries morphologically stable or unstable during solid state reactions. One criterion for instability is met if the interface moves against the flux direction of the rate determining (slow) reaction partner. 

The situation is different for c = 0.9, where the PDMS-enriched central part is stabilized and shifted away from the binodal. But now, the regions outside the central area, where PEMS accumulates, cross the phase boundary into the metastable range. The demixing by nucleation and growth is visible in the lower two micrographs in Fig. 16 in the form of a halo of dark droplets around the written structures. 

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