Crystallization kinetic considerations

The thickness depends on the supercooling, which, in turn, is the result of kinetic considerations. Accordingly, crystal thickness is related to T, but neither have much to do with T . 

The fundamental equilibrium relationships we have discussed in the last sections are undoubtedly satisfied to the extent possible in polymer crystallization, but this possibility is limited by kinetic considerations. To make sense of the latter, both the mechanisms for crystallization and experimental rates of crystallization need to be examined. 

The following section deals with the crystallization and interconversion of polymorphic forms of polymers, presenting some thermodynamic and kinetic considerations together with a description of some experimental conditions for the occurrence of solid-solid phase transitions. 

Crystallizations and Interconversions of Polymorphic F orms 3.1 Thermodynamic and Kinetic Considerations... 

Whether a task can be performed concurrently with other tasks depends on two factors. One is whether the input information for the activity under consideration depends on the output from other activities. The other is the availability of manpower and equipment. Consider a team that has only one chemical engineer to design both the reactor and the crystallizer. Even though reaction kinetics, solid-liquid equilibrium data and crystallization kinetics can be measured in parallel, the total time for these activities is determined by what the single individual can achieve. 

The so-called glass transition temperature, Tg, must be considered below this temperature the liquid configuration is frozen in a structure corresponding to equilibrium at Tg. Around Tg a rather abrupt change is observed of several properties as a function of temperature (viscosity, diffusion, molar volume). Above 7 , for instance, viscosity shows a strong temperature dependence below Tg only a rather weak temperature dependence is observed, approximately similar to that of crystal. Notice that 7 is not a thermodynamically defined temperature its value is determined by kinetic considerations it also depends on the quenching rate. 

Questions on the transferability of crystallization microtechniques to larger scale processes that are reproducible require careful consideration and study of crystallization kinetics. While operationally useful variables that describe crystallization methods are often related to crystallization outcomes, this approach lacks meaningful information for developing a process that yields reliable outcomes because the factors that determine the crystallization kinetics and outcomes are not explicitly considered. For instance, compare the following two approaches to describe the processes for the selective crystallization of polymorphs ... 

Kinetic considerations were suspected to be overriding factors in the case of crystallization of hydrous aluminum phosphates (McConnell, 1976b), and an attempt was made to relate the crystalline vs. the amorphous condition to the atomic products (A1 P )/H per 8 oxygens contained in the unit cell. The boundary between vashegyite, wavellite, kingite, etc. [crystalline] and bolivarite and evansite [amorphous] was approximately 0.01 = A1 P /H. ... 

Size-dependent structure and properties of Earth materials impact the geological processes they participate in. This topic has not been fully explored to date. Chapters in this volume contain descriptions of the inorganic and biological processes by which nanoparticles form, information about the distribution of nanoparticles in the atmosphere, aqueous environments, and soils, discussion of the impact of size on nanoparticle structure, thermodynamics, and reaction kinetics, consideration of the nature of the smallest nanoparticles and molecular clusters, pathways for crystal growth and colloid formation, analysis of the size-dependence of phase stability and magnetic properties, and descriptions of methods for the study of nanoparticles. These questions are explored through both theoretical and experimental approaches. 

Like varying the solvent, varying the salt form also affects other crystal properties including morphology, polymorphs, crystallization kinetics, formulation, drug stability, etc. Therefore, selection of the salt form always involves other considerations in addition to solubility. 

Although crystallization by antisolvent addition shares many characteristics with that caused by chemical reaction, the processes often differ in the rate of creation of supersaturation (e.g., a rapid reaction leading to a compound of very low solubihty). Reactive crystallization is also subject to other kinetic considerations which are sometimes less predictable than the known solubility effects caused by addition of an antisolvent. 

All SFC processes operate at above the critical temperature (Tc) of supercritical fluids. Temperature is a critical controlling variable of the SFC process based on both thermodynamic and kinetic considerations. First, solubility is a function of temperature, and this will determine the supersaturation ratio or the driving force for the crystallization of individual polymorphs. Second, the kinetics of polymorphic transformation is governed by the Arrhenius law and is also temperature dependent. The rate constant of the conversion is related to the activation energy and the mass transfer process involved (i.e., diffusion, evaporation, or mixing in supercritical fluids). 

From thermodynamic principles, under specified conditions only one polymorph is the stable form (except at a transition point) [5], In practice, however, due to kinetic considerations, metastable forms can exist or coexist in the presence of more stable forms. Such is the case for diamond, which is metastable with regard to graphite, the thermodynamically stable form of carbon under ambient conditions. In practice, the relative stability of the various crystal forms and the possibility of interconversion between crystal forms, between crystals with a different degree of solvation and between an amorphous phase and a crystalline phase, can have very serious consequences on the life and effectiveness of a polymorphic product and the persistence over time of the desired properties (therapeutic effectiveness in the case of a drug, chromatic properties in the case of pigment, etc). 

CaS04 deposition can be controlled by keeping the concentration below the saturation value at any point in the system. This means control of the degree of concentration of the sea water in relation to the temperature. The situation is complicated by the fact that CaS04 exists in three different crystal forms that are stable in contact with solutions and by the fact that the crystal form actually deposited is more likely to be determined by kinetic considerations than by equilibrium. Thus anhydrite is the stable solid phase in all cases encountered in sea water distillation, but the actual phases found are either gypsum or hemihydrate. 

For the design and optimization of melt crystallization processes it is vital to have a complete understanding of the process. To this, a detailed knowledge about the crystallization kinetics is essential. Nevertheless, there is only little theory available to describe melt crystallization processes mathematically or to predict their separation efficiency. This is mainly a consequence of the complex heat and mass transfer processes prevailing in the crystallizers which lead to a non-linerar system of differential equations for the transfer processes. These equations can only be solved numerically and even then require a considerable number of simplifying assumptions and boundary conditions. 

The analysis of batch crystallizers normally requires the consideration of the time-dependent, batch conservation equations (e.g., population, mass, and energy balances), together with appropriate nucleation and growth kinetic equations. The solution of these nonlinear partial differential equations is relatively difficult. Under certain conditions, these batch conservation equations can be solved numerically by a moment technique. Several simple and useful techniques to study crystallization kinetics and CSDs are discussed. These include the thermal response technique, the desupersaturation curve technique, the cumulative CSD method, and the characterization of CSD maximum. 

Kinetic considerations. Studies of phosphate solubility reveal kinetic limitations to dissolution rates. Harrison and Watson (1984) and Rapp and Watson (1986) measured the dissolution rates of apatite and monazite, respectively, and found that the dissolution rate is limited by diffusion of P or LREEs away from the dissolving apatite or monazite. Furthermore, the diffusivity, and hence dissolution rate, is strongly dependent on the H2O content of the melt. In dry melts, dissolution is so slow that complete dissolution of even small crystals of apatite or monazite is unlikely. In melts produced by dehydration melting of muscovite or biotite, where the H2O content is in the range of 4-8 wt % H2O, apatite crystals on the order of 500 pm diameter will dissolve in 100-1000 years. 

This section describes a means to enhance the crystallization kinetics of absorbable polymers via polymer chemistry. It will show how this can be achieved by using an appropriate combination of mono- and difunctional alcohol initiators for ring-opening polymerization (ROP). Diols have been used commercially in ring-opening "prepolymerizations" to produce a,p-dihydroxy macroinitiators that are then used in a subsequent copolymerization to produce materials with special sequence distributions. This sequential addition ROP, in which a monomer feed portion is added in a subsequent step, is one method to make block copolyesters. An example is a glycolide/e-caprolactone copolymer that has enjoyed considerable commercial success. ... 

This short introduction to possible paths and mechanisms of melting and crystallization indicates how difficult it is to develop a detailed kinetics that links the molecular mechanism to the observed, macroscopic kinetics. Considerable molecular scale information is needed for the interpretation of the macroscopic thermal analysis data. Few data on melting rates are available for polymers, due to the tendency of large crystals to superheat [31], and small crystals to melt very fast. 

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