Crystallization kinetic

Samples can be concentrated beyond tire glass transition. If tliis is done quickly enough to prevent crystallization, tliis ultimately leads to a random close-packed stmcture, witli a volume fraction (j) 0.64. Close-packed stmctures, such as fee, have a maximum packing density of (]) p = 0.74. The crystallization kinetics are strongly concentration dependent. The nucleation rate is fastest near tire melting concentration. On increasing concentration, tire nucleation process is arrested. This has been found to occur at tire glass transition [82]. 

While there are several instances of redundancy among the Avrami exponents arising from different pictures of the crystallization process, there is also enough variety to make the experimental value of this exponent a valuable way of characterizing the crystallization process. In the next section we shall examine the experimental side of crystallization kinetics. 

Crystallization Kinetics. Crystallization of HDPE proceeds in two separate stages. During the first stage, HDPE crystaUizes rapidly. 

Population balances and crystallization kinetics may be used to relate process variables to the crystal size distribution produced by the crystallizer. Such balances are coupled to the more familiar balances on mass and energy. It is assumed that the population distribution is a continuous function and that crystal size, surface area, and volume can be described by a characteristic dimension T. Area and volume shape factors are assumed to be constant, which is to say that the morphology of the crystal does not change with size. 

Determination of Crystallization Kinetics. Under steady-state conditions, the total number production rate of crystals in a perfectly mixed crystallizer is identical to the nucleation rate, B. Accordingly,... 

Crystallization kinetics have been studied by differential thermal analysis (92,94,95). The heat of fusion of the crystalline phase is approximately 96 kj/kg (23 kcal/mol), and the activation energy for crystallization is 104 kj/mol (25 kcal/mol). The extent of crystallinity may be calculated from the density of amorphous polymer (d = 1.23), and the crystalline density (d = 1.35). Using this method, polymer prepared at —40° C melts at 73°C and is 38% crystalline. Polymer made at +40° C melts at 45°C and is about 12% crystalline. 

The crystallization kinetics defines the open time of the bond. For automated industrial processes, a fast crystallizing backbone, such as hexamethylene adipate, is often highly desirable. Once the bond line cools, crystallization can occur in less than 2 min. Thus, minimal time is needed to hold or clamp the substrates until fixturing strength is achieved. For specialty or non-automated processes, the PUD backbone might be based on a polyester polyol with slow crystallization kinetics. This gives the adhesive end user additional open time, after the adhesive has been activated, in which to make the bond. The crystallization kinetics for various waterborne dispersions were determined by Dormish and Witowski by following the Shore hardness. Open times of up to 40 min were measured [60]. 

Rielly and Marquis (2001) present a review of crystallizer fluid mechanics and draw attention to the inconsistency between the dependence of crystallization kinetic rates on local mean and turbulent velocity fields and the averaging assumptions of conventional well-mixed crystallizer models. 

The CSD from the continuous MSMPR may thus be predicted by a combination of crystallization kinetics and crystallizer residence time (see Figure 3.5). This fact has been widely used in reverse as a means to determine crystallization kinetics - by analysis of the CSD from a well-mixed vessel of known mean residence time. Whether used for performance prediction or kinetics determination, these three quantities, (CSD, kinetics and residence time), are linked by the population balance. 

Given expressions for the crystallization kinetics and solubility of the system, the population balance (equation 2.4) can, in principle, be solved to predict the performance of both batch and of continuous crystallizers, at either steady- or unsteady-state... 

In addition to induction time measurements, several other methods have been proposed for determination of bulk crystallization kinetics since they are often considered appropriate for design purposes, either growth and nucleation separately or simultaneously, from both batch and continuous crystallization. Additionally, Mullin (2001) also describes methods for single crystal growth rate determination. 

Evidence for secondary nucleation has came from the early continuous MSMPR studies. MSMPR crystallization kinetics are usually correlated with supersaturation using empirical expressions of the form... 

Plots of log population density versus crystal size of the type shown in Figure 5.14 enable the crystallization kinetics to be determined. Some early literature data reporting such analyses are summarized in Table 5.2. 

Crystallization kinetics erystal nueleation, growth, aggregation and disruption kineties (Chapters 5 and 6). 

Garside, J. and Shah, M.B., 1980. Crystallization kinetics from MSMPR crystallizers. Industrial and Engineering Chemistry Process Design and Development, 19, 509-514. 

Gutwald, T. and Mersmann, A., 1990. Determination of crystallization kinetics from batch experiments. In Industrial crystallization 90. Gamiiscli-Partenkirclien, September 1990. Ed. A. Mersmann, Dtisseldorf GVC-VDI, p. 331. 

Hostomsky, J. and Jones, A.G., 1991. Calcium carbonate crystallization kinetics, agglomeration and fomi during continuous precipitation from solution. Journal of Physics D Applied Physics, 24, 165-170. 

Hurley, M.A., Jones, A.G. and Drummond, J.N., 1995. Crystallization kinetics of cyanazine precipitated from aqueous ethanol solutions. Chemical Engineering Research and Design, 73B, 52-57. 

Jones, A.G. and Mullin, J.W., 1973. Crystallization kinetics of potassium sulphate in a draft-tube agitated vessel. Transactions of the Institution of Chemical Engineers, 51, 362-368. 

Nyvlt, J., 1989. Calculation of crystallization kinetics based on a single batch experiment. Collection of Czechoslovakian Chemical Communications, 54, 3187-3197. 

Qian, R., Chen, Z., Ni, H., Fan, Z. and Cai, F., 1987. Crystallization kinetics of potassium chloride from brine and scale-up criterion. American Institution of Chemical Engineers Journal, 33, 1690-1697. 

Qui, Yangeng and Rasmuson, A.C., 1994. Estimation of crystallization kinetics from batch cooling experiments. American Institute of Chemical Engineers Journal, 40, 799-812. 

Swinney, L.D., Stevens, J.D. and Peters, R.W., 1982. Calcium Carbonate Crystallization Kinetics. Industrial and Engineering Chemistry Fundamentals, 21, 31. 

Tavare, N.S., 1986. Crystallization kinetics from transients of an MSMPR crystallizer. The Canadian Journal of Chemical Engineering, 64, 752-758. 

Most of the high-pressure crystallization kinetics studies have shown that ECC grows one dimensionally at high pressures [113-116]. 

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