Size distributions of crystals

Fig. 2. Particle size distribution of crystallized Rhovanil Extra Pure vanillin.

Nucleation corresponds to the formation of the new centers from which spontaneous growth can occur. The nucleation process determines the size and the size distribution of crystals produced. 

Figure 2. Size distribution of crystals grown under operational conditions of 15 K initial supercooling and 300 r.p.m.

Depending on conditions during processing and storage, a crystalline microstructure develops in many foods that can significantly impact food propaties. Some important characteristics of the crystalline dispersion include the crystalline phase volume, mean size and size distribution of crystals, shape and surface characteristics of the particles, polymorphic characteristics, and any network structure that forms between... 

Nyvlt, J., H. Kocova, andM. Cerny (1973). Size distribution of crystals from a batch crystaUizer. Coll. Czech. Comm. 38,3199-3209. 

The initial population density n L, 0) for a batch crystallizer is not well defined. For a crystallizer seeded externally, n(L, 0) may be denoted by an initial seed distribution function hs L). However, in an unseeded system, initial nucleation can occur by several mechanisms, and one cannot realistically use a zero initial condition for the size distribution. To overcome this difficulty, Baliga (1970) suggested the use of the size distribution of crystals in suspension at the time of the first appearance of crystals as the initial population density. 

These facts suggests that for letter separation seed crystals should be prepared quickly. The size distribution of crystals kept in a crystallizer for long time showed increased numbers of smaller particles, hence larger surface areas. 

In summary, then, it is necessary to measure the fiaction of crystals, the crystalline orientation factor the amorphous orientation factor and possibly the size and size distribution of crystals in order to relate polymer structure to polymer properties. Although the extent of crystallinity is generally measured using density or heat-of-fusion methods, orientation is determined with the help of optical birefringence, dichroism, sonic modulus, or x-ray diffraction [60]. The size of crystals is observed with an optical or electron microscope. 

Gas AntisolventRecrystallizations. A limitation to the RESS process can be the low solubihty in the supercritical fluid. This is especially evident in polymer—supercritical fluid systems. In a novel process, sometimes termed gas antisolvent (GAS), a compressed fluid such as CO2 can be rapidly added to a solution of a crystalline soHd dissolved in an organic solvent (114). Carbon dioxide and most organic solvents exhibit full miscibility, whereas in this case the soHd solutes had limited solubihty in CO2. Thus, CO2 acts as an antisolvent to precipitate soHd crystals. Using C02 s adjustable solvent strength, the particle size and size distribution of final crystals may be finely controlled. Examples of GAS studies include the formation of monodisperse particles (<1 fiva) of a difficult-to-comminute explosive (114) recrystallization of -carotene and acetaminophen (86) salt nucleation and growth in supercritical water (115) and a study of the molecular thermodynamics of the GAS crystallization process (21). 

Control of supersaturation is an important factor in obtaining crystal size distributions of desired characteristics, and it would be useful to have a model relating rate of cooling or evaporation or addition of diluent required to maintain a specified supersaturation in the crystallizer. Contrast this to the uncontrolled situation of natural cooling in which the heat transfer rate is given by... 

Coefficient of Variation One of the problems confronting any user or designer of crystallization equipment is the expected particle-size distribution of the solids leaving the system and how this distribution may be adequately described. Most crystalline-product distributions plotted on arithmetic-probability paper will exhibit a straight line for a considerable portion of the plotted distribution. In this type of plot the particle diameter should be plotted as the ordinate and the cumulative percent on the log-probability scale as the abscissa. 

Crystallizers with Fines Removal In Example 3, the product was from a forced-circulation crystallizer of the MSMPR type. In many cases, the product produced by such machines is too small for commercial use therefore, a separation baffle is added within the crystallizer to permit the removal of unwanted fine crystalline material from the magma, thereby controlling the population density in the machine so as to produce a coarser ciystal product. When this is done, the product sample plots on a graph of In n versus L as shown in hne P, Fig. 18-62. The line of steepest ope, line F, represents the particle-size distribution of the fine material, and samples which show this distribution can be taken from the liquid leaving the fines-separation baffle. The product crystals have a slope of lower value, and typically there should be little or no material present smaller than Lj, the size which the baffle is designed to separate. The effective nucleation rate for the product material is the intersection of the extension of line P to zero size. 

Chianese, A., Mazzarotta, B., Huber, S. and Jones, A.G., 1993. On the Effect of Secondary Nucleation on the Size Distribution of Potassium Sulphate Fine Crystals from Seeded Batch Ci-ystallization. Chemical Engineering Science, 48, 551-560. 

Hostomsky, J., 1987. Particle size distribution of agglomerated crystal product from a continuous crystallizer. Collection of Czechoslovakian Chemical Communications, 52, 1186-1197. 

Manuo, L., Manna, L., Chiampo, F., Sicardi, S. and Bersano, G., 1996. Influence of mixing on the particle size distribution of an organic precipitate. Journal of Crystal Growth, 166, 1027-1034. 

Another area of TEM application to energetic materials is the work of S.M. Kaye at PicArsn on expls and propints. He used TEM. to establish a procedure for detg the particle size distribution of LA batches of different crystal habits from various manufacturers (Ref 25. ... 

J.W. Lavitt, A Microscopic Method for the Determination of the Particle (Crystal) Size Distribution of 2 Micron RDX , PATR 1909 (1953) 20) J.W. Lavitt, An Improved Micro-... 

Situation There are two vendors for a particular bulk chemical who meet all written specifications. The products are equally useful for the intended reaction as far as the chemical parameters are concerned both comply in terms of one physical parameter, the size distribution of the crystals, but on the shop floor the feeling prevails that there is a difference. Because the speed of dissolution might become critical under certain combinations of process variables, the chemical engineers would favor a more finely divided raw material. On the other hand, too many fine particles could also cause problems (dust, static charging). 

Crystallization, filtration, drying Almost always Pilot studies are usually done using vendor equipment. Caution batch crystallization may not be reproducible with respect to contamination and size distribution of the solid. Filtration and crystallization problems. should often be studied simultaneously. 

Modified amino acids such as N-acyl-dehydroalanine polymers and copolymers with N-vinyl-N-methyl acetamide seem to be particularly effective [396]. The crystallization kinetics in the presence of polyvinylpyrrolidone and tyrosine have been tested by time-resolved experiments [981]. An influence is evident on the particle size distribution of the hydrate [1433]. 

Figure 3 Pt crystal size distributions of cat I.S iuin" F214 (a) and E 4759 (b).

Cavitation bubbles work as nucleation sites of particles. For example, in a supercooled sucrose solution, nucleation of ice crystals induced by cavitation bubbles has been experimentally observed [72], This phenomenon has been called sonocrys-tallization [73]. Although there are some papers on the mechanism of sonocrystal-lization, it has not yet been fully understood [74, 75]. It has been reported that the distribution of crystal size in sonocrystallization is narrower than that without ultrasound [73]. It may be related to the narrower size distribution of sonochemi-cally synthesized particles compared to that without ultrasound [76, 77]. Further studies are required for the mechanism of particle nucleation by ultrasound. 

There are obviously two steps involved in the preparation of crystal matter from a solution, the crystals must first form and then grow. The formation of a new solid phase either on an inert particle in the solution or in the solution itself is called nucleation. The increase in size of this nucleus with a layer-by-layer addition of solute is called crystal growth. Both nucleation and crystal growth have supersaturation as a common driving force. Unless a solution is supersaturated, crystals can neither form nor grow. The particle-size distribution of this weight, however, will depend on the relationship between the two processes of nucleation and growth. 

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