The Rate of Crystallization

FIGURE 10-22 Graph of the degree of crystallinity versus time [redrawn from the data of E. Ergoz, J. G. Fatou, L. Mandelkem, Macromolecules, 5, 147 (1972)]..  

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By cooling the solution in a freezing mixture (ice and salt, ice and calcium chloride, or solid carbon dioxide and ether). It must be borne in mind that the rate of crystal formation is inversely proportional to the temperature cooling to very low temperatures may render the mass... 

This intricate mode of crystallization requires more time to accomplish than, say, the entry of small ions into growing salt crystals. This, coupled with low chain mobility due to viscous effects, makes the rate of crystallization slow and accounts in part for the fact that with rapid cooling-called quenching-the temperature drops below T without crystallization. 

As noted above, not all techniques which provide information regarding crystallinity are useful to follow the rate of crystallization. In addition to sufficient sensitivity to monitor small changes, the method must be rapid and suitable for isothermal regulation, quite possibly over a range of different temperatures. Specific volume measurements are especially convenient for this purpose. We shall continue our discussion using specific volume as the experimental method. 

From the lengths of the arrows drawn in Fig. 4.8b, estimate the change in time scale which will produce the same effect on the rate of crystallization as changing the temperature from 130 to 128°C. Do the same for a temperature change from 126 to 128°C. 

At HOY speeds, the rate of increase in orientation levels off but the rate of crystallization increases dramatically. Air drag and inertial contributions to the threadline stress become large. Under these conditions, crystallization occurs very rapidly over a small filament length and a phenomenon called neck-draw occurs (68,75,76). The molecular stmcture is stable, fiber tensde strength is adequate for many uses, thermal shrinkage is low, and dye rates are higher than traditional slow speed spun, drawn, and heat-set products (77). 

Because of the capacity to tailor select polymer properties by varying the ratio of two or more components, copolymers have found significant commercial appHcation in several product areas. In fiber-spinning, ie, with copolymers such as nylon-6 in nylon-6,6 or the reverse, where the second component is present in low (<10%) concentration, as well as in other comonomers with nylon-6,6 or nylon-6, the copolymers are often used to control the effect of sphemUtes by decreasing their number and probably their size and the rate of crystallization (190). At higher ratios, the semicrystalline polyamides become optically clear, amorphous polymers which find appHcations in packaging and barrier resins markets (191). 

Crystallization. Raw natural mbber may freeze or crystallize during transit or prolonged storage, particularly at subzero temperatures. The mbber then becomes hard, inelastic, and usually much paler in color. This phenomenon is reversible and must be differentiated from storage hardening. The rate of crystallization is temperature-dependent and is most rapid at —26° C. Once at this temperature, natural mbber attains its maximum crystallinity within hours, and this maximum is no more than 30% of the total mbber. 

Ammonium tetraborate tetrahydrate is prepared by crystallization from an aqueous solution of boric acid and ammonia having a B202 (NH4)20 ratio of 1.8 2.1. Ammonium pentaborate is similarly produced from an aqueous solution of boric acid and ammonia having a B202 (NH4)20 ratio of 5. Supersaturated solutions are easily formed and the rate of crystallization is proportional to the extent of supersaturation (130). A process for the production... 

Second, the molecular orientation of the fiber and the prepolymer matrix is important. The rate of crystal nucleation at the fiber-matrix interface depends on the orientation of matrix molecules just prior to their change of phase from liquid to solid. Thus, surface-nucleated morphologies are likely to dominate the matrix stmcture. 

C The solvation rate must exceed the rate of crystallization. 

Silica glass is formed when molten Si02 is cooled rapidly. It experiences slow crystallization. Will the rate of crystallization be higher at room temperature or at 1000 °C ... 

Crystallization involves formation of a solid product from a homogeneous liquid mixture. Often, crystallization is required as the product is in solid form. The reverse process of crystallization is dispersion of a solid in a solvent, termed dissolution. The dispersed solid that goes into solution is the solute. As dissolution proceeds, the concentration of the solute increases. Given enough time at fixed conditions, the solute will eventually dissolve up to a maximum solubility where the rate of dissolution equals the rate of crystallization. Under these conditions, the solution is saturated with solute and is incapable of dissolving further solute under equilibrium conditions. In fact, the distinction between the solute and solvent is arbitrary as either component can be considered to be the solute or... 

Also, hydrates are more soluble in water-miscible solvents than are the corresponding anhydrous forms. For example, the solubility of caffeine hydrate is lower than that of anhydrous caffeine in water but higher in ethanol. The maximum concentration seen may be due to the solubility of the anhydrous crystalline phase or due to a temporary steady state in which the rate of dissolution of the metastable anhydrous form and the rate of crystallization of the stable hydrate are equal. The decreasing concentration represents crystallization of the stable hydrate from a solution supersaturated with respect to it. If the maximum concentration of the solute in the dissolution experiment corresponds to the solubility, then the initial increase in concentration follows the Noyes-Whitney equation [15]. Van t Hoff plots of log solubility versus the reciprocal of temperature give linear relationships (Fig. 16). 

Why would a manufacturer of polymeric items be interested in the rate of crystallization within a semicrystalline polymer ... 

In the last experiment, the rate of crystallization of NiS04, NiCl2 and Ni(SCN)2 was compared for solutions under normal condition and those agitated by ultrasound for 1 hr. As could be seen in Table 9.10 the ultrasound could reduced the... 

J.D. Hoffman, G.T. Davis and J.I. Lauritzen, The rate of crystallization of linear polymers with chain folding. In N.B. Hannay (Ed.), Treatise on Solid State Chemistry, Plenum Press, New York, 1976. 

As can be seen from Fig. 6, liquid-liquid demixing clearly precedes crystallization in case Cl. Moreover, crystallization in this case occurs at a higher temperature than in cases C2 and C3. Apparently, the crystallization takes place in the dense disordered phase (which has a higher melting temperature than the more dilute solution Fig. 5). In case C2, the crystallization temperature is close to the expected critical point of liquid-liquid demixing, but higher than in case C3. This suggests that even pre-critical density fluctuations enhance the rate of crystal nucleation. 

On the basis of the concept described above, we propose a model for the homogeneous crystallization mechanism of one component polymers, which is schematically shown in Fig. 31. When the crystallization temperature is in the coexistence region above the binodal temperature Tb, crystal nucleation occurs directly from the melt, which is the well-known mechanism of polymer crystal nucleation. However, the rate of crystallization from the coexistence region is considered to be extremely slow, resulting in single crystals in the melt matrix. Crystallization at a greater rate always involves phase separation the quench below Tb causes phase separations. The most popular case... 

The rate of crystallization of polybutadiene depends mainly on the cis content and therefore on the catalyst system. As far as commercial catalysts are concerned it increases in the order Li < Ti < Co < Ni. High-cis SE-BR, like U-BR, crystallizes more rapidly than all the other types (Table III). However, SE-BR with 93 % cis-1,4 content, and even one with only 90 % cis-1,4 content, crystallizes more rapidly than Ti-BR (93 % cis-1,4 content). In our opinion the reason for this anomaly is a structural disorder in molecules with different chain length. 

In fact, by fractional precipitation we found that the fractions with the highest molecular weights are sterically very uniform and contain more than 97 % of cis-1,4 double bonds (Table IV). Lower molecular weight fractions, on the other hand, have relatively high trans-1,4 contents. We therefore take the view that the rate of crystallization is determined mainly by the high molecular weight fractions. 

In observing the time dependent changes in birefringence and stress-optical coefficient, for elongated samples at 25 C, it was found that the rate of crystallization of high trans SBR s was very much faster, some 10 times more rapid, than that for NR (8). This is consistent with the reported rates of isothermal crystallization for NR (2.5 hours at -26°C) and for 807. trans-1,4 polybutadiene (0.3 hours at -3°C) in the relaxed state (12). 

The main conclusions of the strain induced crystallization behavior of high trans polybutadiene based rubber and natural rubber are (1) the rate of crystallization is extremely rapid compared to that of NR (2) the amount of strain induced crystallization is small compared to that of NR, especially at room temperature and (3) for the high trans SBR s relative to NR, crystallization is more sensitive to temperature at low extension ratios, and crystallization is less sensitive to strain. 

According to Hoffman s crystallization theory, a drop in the heat of fusion corresponds to an exponential decrease in nucleation and crystal growth rates [63]. Implicitly, the rate of crystallization is severely retarded by the presence of 3HV comonomer [64, 69, 72]. These low crystallization rates can hamper the melt processing of these copolymers since they necessitate longer processing cycle times. 

The stretching of amorphous but crystallizable materials can greatly increase the rate of crystallization in some cases. Natural rubber and polyethylene terephthalate are examples. The stretching of the polymer initially causes the crystallites to grow so that the chains in the crystallites are oriented parallel to the applied stress. Thus the growth of the crystallites... 

Plastic deformation, unlike elastic deformation, is not accurately predicted from atomic or molecular properties. Rather, plastic deformation is determined by the presence of crystal defects such as dislocations and grain boundaries. While it is not the purpose of this chapter to discuss this in detail, it is important to realize that dislocations and grain boundaries are influenced by things such as the rate of crystallization, particle size, the presence of impurities, and the type of recrystallization solvent used. Processes that influence these can be expected to influence the plastic deformation properties of materials, and hence the processing properties. 

OH ratio on the rate of crystallization and crystallite size investigated Prehydrolysis method. Synthesis using binary mixtures of tetrabutylphosphonium hydroxide and tetraethylphosphonium hydroxide instead of TPAOH as base and template TEOS and TBOT are sources of Si and Ti, respectively. Molar gel composition, SiO2 xTiO2 0.4 ( TEPOH + (1 — jd)TBPOH) 30H2O (x = 0-0.02) temperature = 443 K and synthesis time = 4 days Influence of nature of silicon and titanium alkoxides on the incorporation of Ti Wetness impregnation method... 

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