Formation of nuclei

In what is considered heterogeneous nudeation, the concentration erf nudeating centers varies, according to the crystallizing material by several orders of magnitude. In poly(ethylene), for example, nudeation center concentrations of 10 nuclei/cm were found, whereas concentrations of 1 nuclei/cm were observed in polj((ethylenc oxide). 

Homogeneous formation of nuclei has not yet beoi established with certainty in macromolecular solutions. If it does in fact exist, then h is more probable that folded-chain nuclei will be formed in this way than micellar nuclei. In contrast to folded chain nuclei in micellar nuclei several molecules must come together in order to form a stable nucleus. Micellar nuclei thus lead to a greater entropy loss. A homogeneous nudeation is more probable in melts than in solutions, since the concentration of centers is potentially greater in the former. Even in melts, however, it is uncertain 

Heterogeneous nudeation can only occur when the growii crystal can wet the surfiice of the foreign material. Thus, a specific interaction between nucleus and melt is necessary. If this interaction is very strong, thai all the crystallization nuclei become effective immediately. Hie number of nuclei remains constant If, on the other hand, the interaction is weak, crystallization is induced by a number of nuclei which initially increases with time and then remains constant. 

In the case of heterogeneous nudeation with strong interactions, on the other hand, the number of spherulites remains constant with time. In addition, all the spherulites are of equal size. In purely homogeneous nudeation, the number of nuclei is constantly increasing, and a spherulite size distribution is observed. 

Only two of the four possible side surfaces need to be considered, since, in the direction, no new surface is created. Differentiating equation (10-14) with respect to and equating to zero, we obtain 

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The growdr of deposits on a subsU ate requhes the initial formation of nuclei and their subsequent growth and agglomeration into a fllm, most probably a... 

Using the Stokes-Einstein equation for the viscosity, which is unexpectedly useful for a range of liquids as an approximate relation between diffusion and viscosity, explains a resulting empirical expression for the rate of formation of nuclei of the critical size for metals... 

Figure 3 Effect of seeding and inhibitors on aggregation reaction. The lag phase (curve c) is characteristic of reactions in which formation of nuclei for polymerization is an unfavorable process. Addition of preformed nuclei or seeds" (curve a) abolishes the lag phase. Inhibitors may affect the formation of nuclei and influence eitherthe lag phase, the extension of the nuclei changing the growth phase, or both (curve d). The inhibitor example (curve d) acts more strongly at nuclei formation than on the slope or plateau level of the growth phase.

In Fig 1.10, Riehle shows log J (J = nuclei per time and volume) as a function of the temperature of the phase transition water - ice different pressures of 1 and 2100 bar. At 2100 bar, J is comparable with J at an approximately 35 °C higher temperature. Under pressure, water can be subcooled further, with a delayed formation of nuclei. 

As would be expected, it is even more difficult to asses the importance of 7S for heterogeneous nucleation (i.e., formation of nuclei on other solids). Only one relevant reference is quoted here157). 

Under conditions leading to a porous shell of magnetite, the kinetic curve displayed an induction period corresponding to formation of nuclei and the subsequent reaction followed the cube root law. Diffusion of the reducing gas to the reactant/ product interface took place readily with a porous product. Whether chemical or diffusion control predominated depended on reaction conditions. With small crystals... 

The atmospheric situation is complicated by varying conditions of temperature, relative humidity, and concentrations of other gases such as NH3 which can enhance nucleation rates over those expected for a well-mixed air mass at a fixed temperature and RH (e.g., see Nilsson and Kulmala, 1998). However, there is a general consensus that the observed rates of nucleation of H2S04 often, indeed usually, exceed those expected from classical binary homogeneous nucleation theory. (Note that this is not always the case. For example, Pirjola et al. (1998) reported that the measured formation of nuclei in the Arctic boundary layer... 

In practice, container walls are usually present, and the liquid is rarely free from dust particles, adsorbed gas, absorbed gas, and foreign ions. Heterogeneous nucleation refers to the formation of nuclei on a foreign object. 

Fig. 25. Effect of superheat on the rate of formation of nuclei. Equation (47) gives this form.

A lay period in the uptake of calcium and phosphate was previously seen in the mineralization in vitro of human aortic tissue338. The lay period found with the elastin samples appears in the result of the early stages of the mineralization process, and involves the formation of nuclei for HA crystal growth. Once a microcrystal of HA is present, the rate of calcium and phosphate uptake will increase markedly,... 

The activation energies of the nucleation and crystal growth can be determined from the crystallization curves at various temperatures with the same batch composition. Assuming that the formation of nuclei of a size stable enough not to redissolve but to grow into a crystal is an energetically activated process, and since the nucleation process is rate-deter-... 

The overall recrystallization process, consisting of the initial nucleation and the subsequent growth of nuclei, can be modelled by the basic equations describing these respective processes. The rate of formation of nuclei as developed is ... 

In dairy products, crystallization is more complex. The impurities (e.g., other milk components), as far as lactose is concerned, may interfere with the crystalline habit. As a result, the crystals tend to be irregularly shaped and clumped, instead of yielding the characteristic crystals obtained from simple lactose solutions. In some instances, the impurities may inhibit the formation of nuclei and thus retard or prevent lactose crystallization (Nickerson 1962). 

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