Heterogeneous crystal growth

It has been reported that the overall rate of crystallization of pure PHB is relatively low compared to that of common synthetic polymers, showing a maximum in the temperature range of 55-60°C [23]. The spherulite growth rate kinetics have been evaluated [59] in terms of the theory by Hoffmann et al. [63], At about 90 °C, the spherulite growth rate displayed a maximum, which is not excessively low compared to that of common synthetic polymers. Therefore it was stated that the low overall crystallization rate of PHB centers on the nuclea-tion process rather than the subsequent crystal growth. Indeed, it has been shown that PHB has an exceptionally low level of heterogeneous nuclei [18]. 

Heterogeneous nucleation of CaC03 on 5-AI2O3. Example for the sequence of nucleation and subsequent crystal growth. The latter is plotted as a 2nd order reaction (as is typical for screw dislocation catalysis). 

As we have seen in Chapter 6, the crystal growth has to be preceded by nucleation (Fig. 6.7). In fresh waters this nucleation occurs heterogeneously on particle surfaces. In seawater nucleation occurs primarily upon the templates of calcareous organisms. 

The geochemical fate of most reactive substances (trace metals, pollutants) is controlled by the reaction of solutes with solid surfaces. Simple chemical models for the residence time of reactive elements in oceans, lakes, sediment, and soil systems are based on the partitioning of chemical species between the aqueous solution and the particle surface. The rates of processes involved in precipitation (heterogeneous nucleation, crystal growth) and dissolution of mineral phases, of importance in the weathering of rocks, in the formation of soils, and sediment diagenesis, are critically dependent on surface species and their structural identity. 

Condensation is generally a transient operation in which, as discussed by Ueda and Takashima(106), simultaneous heat and mass transfer are further complicated by the effects of spontaneous condensation in the bulk gaseous phase. After the creation of supersaturation in the vapour phase, nucleation normally occurs which may be homogeneous in special circumstances, but more usually heterogeneous. This process is followed by both crystal growth and agglomeration which lead to the formation of the final crystal product. As a rate process, the condensation of solids from vapours is less well understood than vaporisation(98). Strickland-Constable(107) has described a simple laboratory technique... 

Vatamanu, J. Kusalik, P.G. (2006). Molecular insights into the heterogeneous crystal growth of si methane hydrate. J. Phys. Chem. P>, 110 (32), 15896-15904. 

The scope of kinetics includes (i) the rates and mechanisms of homogeneous chemical reactions (reactions that occur in one single phase, such as ionic and molecular reactions in aqueous solutions, radioactive decay, many reactions in silicate melts, and cation distribution reactions in minerals), (ii) diffusion (owing to random motion of particles) and convection (both are parts of mass transport diffusion is often referred to as kinetics and convection and other motions are often referred to as dynamics), and (iii) the kinetics of phase transformations and heterogeneous reactions (including nucleation, crystal growth, crystal dissolution, and bubble growth). 

Mass transfer during crystal growth or dissolution (heterogeneous reactions)... 

In this section, we focus on diffusive mass transfer. The mathematical description of mass transfer is similar to that of heat transfer. Furthermore, heat transfer may also play a role in heterogeneous reactions such as crystal growth and melting. Heat transfer, therefore, will be discussed together with mass transfer and examples may be taken from either mass transfer or heat transfer. 

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