Crystal Growth Regimes

Crystal growth process involves two fundamental steps the deposition of the first stem on the growth front ( secondary nucleation process ) and the attachment of subsequent stems in the chain on the crystal surface ( surface spreading process ). 

For regime I (rapid substrate completion) each surface nucleation act rapidly leads to new layer of thickness b and length / at the surface growth front before a new nucleation act occurs. This leads to relatively smooth growth surface over the length L and Gj = ibL where i is the nucleation rate. A from equation (2.7) is thus defined as  

Where b is the layer thickness, a is lateral surface free energy, is the fold surface free energy, T[ is the equilibrium temperature, Ah is the enthalpy of fusion and k is Boltzmann s constant. 

For regime II, large numbers of surface nuclei form on the substrate at a rate I and spread slowly at a velocity g. This results in multiple nucleation acts commencing before previous ones have finished. The newly formed surface is rough and uneven on a molecular scale. Gjj = b(2ig), i.e. polymer crystal growth is proportional to the square root of the surface nucleation rate and A is thus defined  

This allows values for k and n to be determined for various crystallization temperatures. These values are then substituted into equation (2.7). Hoffman found that U = 1500 cal/mol and T = - 30K by fitting the 

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Clark and Hoffmann [11], utilizing several data sources [13, 62, 113-117], showed the existence of two crystal growth regimes. According to their studies, the regime III-II transition occurred near 137°C. A transition from regime II to regime I was reported by... 

By definition, this is equal to the substrate, or persistence, length Lp (see Sect. 3.4.2) which by this criterion can easily take values so large that nonlinear growth should be observed for small crystals in regime I. 

Table III. Stationary values of G and for a DTB crystallizer operated with a fines r oval system and a size dependent growth regime. The values are given before and 35000 second after a step in the heat input of the crystallizer from 120 to 170 kW. The simulation has been performed with kOO gridpoints...

Bulk phase formation by current or voltage pulses results in different nucleation and crystal growth conditions compared to dc deposition and depends on the electrolyte and the pulse regime (unipolar, bipolar, pulse reverse, etc.) itself [6.98]. Several effects, which are of significance for the pulse plating process, can be distinguished. 

A primary example is the resolution of optical isomers by continuous crystallization in fluid beds. Control of low supersaturation by control of the temperature difference between the continuous feed and the seed bed is critical to maintaining an essentially all-growth regime in which the individual isomers grow on their respective seeds in separate crystalfi-zers. The seed beds in both crystallizers are massive in relation to the amount of racemic solution passing through in order to present sufficient seed area to maintain low supersaturation. Uncrystallized isomers in the overhead streams are recycled to dissolve additional racemic feed. Crystal size is maintained by sonication. See Examples 7-6 and L1-6 for a discussion of resolution of optical isomers by continuous crystallization. 

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