Crystallization kinetics plots

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. 

Figure 20.22 Plots of ln[- ln(1 - Xc) as a function of In a at various temperatures for P(HB80-ET20)/PET (weight ratio, 4 3) T, 144°C A, 149 °C , 153 °C , 157 °C [44]. From Park, J. K., Park, Y. H., Kim, D. J. and Kim, S. FI., Crystallization kinetics of TLCP with polyester blends, J. Korean Fiber Soc., 37, 69-76 (2000). Reproduced with permission of The Korean Fiber Society...

When the crystal purity is plotted against the total crystal mass in the slurry calculated from the mass balances, the purity decrease seems to start at some constant value of the crystal mass as shown in Figure 5. As mentioned earlier in the text, there are possibilities of existence of the D-enantiomer as small particles on the surface of the seed crystals. If we assume that the breeding of the D-enantiomer starts only when that enantiomer has grown to a certain size, the amount of the L-enantiomer crystals must have also increased to a certain value, the latter being proportional to the former. The crystallization kinetics of the both enantiomers are believed to be the same, the relative amounts of crystals of the both enantiomers must therefore be constant before nucleation of the D-enantiomer starts. 

Crystallization kinetics. Figure 5 shows the relation between the dominant particle size Im and the residence time 0 for each run. Im decreases linearly with increase of 0 in log-log plot. The slope of lines decreases with the addition of NaCl. 

In figure 6 the resulting Cd-concentration in the crystals is plotted versus the sulfate content of the solution. In 5.5 M phosphate solutions, K(Cd) seems to decrease from 0.02 to 0.5 M sulfate contents, while above 0.1 M sulfate K(Cd) increases. This tendency of higher uptake at higher sulfate concentrations has also been found for DH. The high K values at very low sulfate contents indicates a major influence of kinetics. 

Figure 9. Kinetic plot for 0.01% (w v) B-lactoglobulin and 1.0% (w v) alginic acid adsorption on and desorption from germanium ATR crystal as a function of time of flow. Key D1548 cm 1 band of 13-lactoglobulin 1034 cm 1 band of alginic acid. (All data not shown for clarity.)...

Figure 5 shows the Fisher-Tumbull plot for the crystallization of blends of PS in sesame oil (26, 42, 60, and 80%) (9). This model system is a complex crystallization system. PS is a mixture of TAG obtained through fractional crystallization from refined, bleached, and deodorized palm oil (14). Tripalmitin is the TAG with the highest melting temperature in PS (15), and here its concentration was 16.46% w/w ( 0.17%) (9). Our previous research showed that tripalmitin mostly determines the crystallization kinetics of PS and its blends with vegetable oils (i.e.. 

RIM elastomers without crystallizing components show no deviation from the straight line dependence of the kinetic plots. 

The application of computer calculations to DTA studies of the crystallization kinetics of polymers was described by Gornick (51). Calculations were made of the temperature of a polymeric sample during the cooling process using a Burroughs Mode 5500 computer. Morie et al. (52) used an IBM Model 1130 computer to prepare standard vapor-pressure plots of In P versus 1/T the vapor-pressure data being obtained from DTA or DSC curves. The heat of vaporization was calculated by the Haggenmacher method as modified by Fishtine. 

Figure 3.55 shows the plots of the times to reach maximum crystallization rate and the maximum crystallization rate, d /dr, as a function of the melting temperature. Both plots show that, at higher melting temperatures, the resulting rate of crystallization is diminished, with the implication that crystal nuclei are destroyed. As seen, under none of the conditions utilized did the overall rate of crystallization of the samples under high stress reduce to those observed for the samples under low stress. Jaffe also found that the time spent in the melt had an effect similar to the melt-temperature level. As the melt time increases, crystallization kinetics slow down. 

Isothermal DSC crystallization kinetics are usually converted to the weight fraction crystallized X t) at time t and fitted via double log plots to the Avrami equation [38] ... 

To determine the parameters Go and Kg, one needs to measure the growth rate G(7). For materials with slow crystallization kinetics, one can easily measure the spherulite growth rate as a function of temperature from micrographs (Fig. 4.2). Then Gq and Kg are determined by plotting In G + W/Rg T - T ) against T + T ) jlT AT. 

Temporal pXRD measurements enable monitoring in situ isothermal crystallization kinetics from ASD (Ivanisevic et al. 2010). Relative crystallinity is often estimated using the area ratio method at different time periods. The crystallinity degree at each time point is normalized with that at the point where crystallization reaches a maximum and is stationary. The extents of crystallization can be plotted as a function of time and modeled using diverse models of crystallization. Since the fractals and particulate properties of growing virgin crystals are difficult to predict, only relative crystallinity can be estimated with such experiments and is sufficient for... 

The representative plots in Figs. 4.26 and 4.27 present a serious dilemma that needs to be resolved before any progress in understanding crystallization kinetics can be made. This is a fundamental concern that lies well beyond how best to represent the data. In the temperature range of present interest, attention will be... 

---