Number of crystal nuclei

There will be some differences and it is a quantitative question, whether or not they can be tolerated or not. For a final decision, test runs in a pilot plant should be carried out with freshly frozen product and such which has been resting for 5 h before drying. These tests are recommended because the methods mentioned above use different sized samples in different configuration than are used in the production. The amount of product and its geometrical dimension will also influence the structure as well as the number of crystallization nuclei in the product, which can be very different in a normal laboratory and in a clean production area. 

This method requires the addition of a mixed M(II)/M(III) salt solution to an alkaline solution containing the desired interlayer anion. Preparations under conditions of high supersaturation generally give rise to less crystalline materials, because of the high number of crystallization nuclei. Because this method leads to a continuous change in solution pH, the formation of impurity M(0H)2 and/or M(OH)3 phases, and consequently an LDH product with an undesired M(II)/M(III) ratio, often results. Thermal treatment performed following coprecipitation may help increase the crystallinity of amorphous or badly crystallized materials. 

Hydrate nucleation and growth may have direct analogies in crystallization processes such as the precipitation of salt from solution. Metastability in salt crystallization was hypothesized to occur through supersaturation by Ostwald (1900). (A supersaturated solution is one in which the liquid [solvent] contains more dissolved solute than can be ordinarily accommodated at that temperature the greater the degree of supersaturation, the greater number of crystal nuclei that will form in solution.) Miers and Isaac (1907) experimentally proved metastability and postulated that for each solute-solvent pair, a concentration-temperature relationship exists that defines the metastable limit, formally called the thermodynamic spinodal. 

In spite of the many possible pathways to polymer crystallization, there are two distinct structural characteristics (I) the formation of a single nucleus and (II) the spatial distribution of nuclei originating processes that lead to an increase in the number of crystal nuclei. X-ray scattering can be used to monitor structural changes during (II) [27,28] (Fig. 7.1). 

Fig. 7.1. Evolution of orientation fluctuations that occur when an amorphous polymer evolves to a lamellar crystal. This process can be divided into two distinct processes (I) formation of the anisotropic crystal habit (lamellar crystal) from an amorphous polymer and (II) processes which increase the number of crystal nuclei. Ic and Ld are the crystal thickness and lateral dimension, respectively...

Obviously, t/-induced phase. separation of gels with microcrystallilcs as the crosslinks must occur during their storage due to the increasing number of crystallization nuclei. 

A Constant, E Activation energy of crystal growth, N = Nr+ No/a, Nr is the number of crystal nuclei at the unit volume formed during heat treatment at nucleation temperature, and No/a is the number of crystal nuclei at the unit volume formed during the rise in temperature at speed a. 

The probability to form a crystal nucleus of size n can be approximated by P(n) = N /N, where N is the number of crystal nuclei of size n in a system containing N particles [8, 9, 10], see also Appendix A. The approximation becomes better as N /N becomes smaller, i.e. when the spontaneous formation of clusters is rare. Knowledge of the ratio N /N allows us to define the Gibbs free energy AG(n) for the formation of a nucleus of size n ... 

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