W a r r e n L. McCabe, of the Carnegie lnstitute of Technology, Pittsburgh, was born in Bay City, Mich., 7899. H e obtained his B.S., M.S., and Ph.B. degrees from the University of Michigan in 1922, 7923, and 7928, respectively. H e was an assistant and instructor in chemical engineering a t the Massachusetts Institute of Technology from 1923 to 7925 and then became instructor, assistant professor, and associate professor in chemical engineering a t the University o f Michigan from 7 9 2 5 to 7937. Since that date he has been professor and head o f the Chemical Engineering Department o f the Carnegie lnstitute o f Technology. M c C a b e is a member of the American Chemical Society and the American Institute o f Chemical Engineers. His publications include the book “Elements o f Chemical Engineering”, with W . 6 . Badger, and research papers on unit operations and thermodynamics.
Warren
A
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LTHOUGH progress during the last few years in the unit
operation of crystallization has not been spectacular, some new methods and novel applications of old procedures have appeared. Interesting scient,& treatments of the processes of nucleation and growth have also been presented. The purpose of this article is t o review briefly some of the advances in the art and scioncc of industrial crystallization. Specifically the nuclctztion theories of Volmer, Stranski, Becker, and others, and the rvorlc of Van Hook on sucrose crystallization will be surnmarizcd, and rccent developments in ammonium nitrate crystallization nnd i n general crystallization practice will be described. SCIENTIFIC. ~ D V A N C E S . As usual, the. literature of crystallization duriiig the past few years has been extensive and scattcrcd. Considerable work has been reported on various phases of sugar boiling and crystallization, theory of drop formation, effect of added substances on crystallization, various theories of growth and nucleation, and specialized problems of crystallizing speqific materials. Much of the currcnt theoretical work is based on t h e work of Volmer ( 8 ) ,Stranski and collaborators (4), Beckcr ( I ) , and ntlicrs. The ideas and approach of these investigators have bccn applied effectively by Mehl and collaborators (3) to metallurgical problems, and analogous results car1 be expected i i i the study of crystallization from solutions with the aid of the samc basic concepts. Some of thc ideas brought forward i i i t,hcse treatments are described in t,hc folloning paragraphs. All competent tlicorics of stallization divide the over-all process into two parts-nucleation and growth-and assign a rate to each. Ttic iiucleation rate is defined as the number of nuclei formed per unit time per unit volume of reaction phase, aqd the rate of growth is expressed as the rate of linear translat,ion of a growing crystal facc. A process of crystallization would be complctcly described if the rates of growth and of nucleation were entirely known, and the objective ol work in crystallization kinetics is to obtain quantitative kno\\.lcdgc of such ratcs. Neither nucleation nor growth can occur unless the precipitated substance has a lower thermodynamic potential after precipitation than before. I n a solution this means t h a t nucleation and growth occur only in a supersaturated solution. The over-all driving force is the negative value of the free energy difference : AF, = F - ii 18
McCabe where F = molal free energy of crystallized material based on zero specific surface fi = molal chemical potential of the same component in the solution The well-known Gibbs-Thomsen law shows that P increases n i t h decreasing particle size and is very large for very small particles. It is convenient to divide the A F between a smnll particle and its mother phase into two parts: 3F = AFI
+ Ai's
(1)
ivlicre AF, = over-all free enrrgy change, not including surfam, effects 3P2 = difference between free energy of a very largch particle and the small particle under consideration
If the solution is supersaturat’cd, is negative, decreases with supersaturation, and is proportional to the bulk number oi‘ atoms in the crystal. It is, therefore, proportional t o the cube of the linear size, but AP2 is positive and is proportional t o thc number of molecules in the surface of the crystal. I t is, therefore, proportional to t’hesquare of thc lincar size. As the crystal size increases, the free energy change AF increases t o a maximum and then decreases for a definite crystal size, called the “critical size”. The higher the supersaturat,ion,the smaller is the critical size. A crystal smaller than the critical size will tend to dissolve, and one larger than the critical size can grow. The value of Al‘ corresponding t o the critical size represents an energy barrier that must be surmounted by a nucleus before it is stable. The cnergy required can come only from momentary and local fluctuatioils of both concentration and energy. The energy fluetuations are statistical in nature and arc of thc usual kinetic type that give use t’o homogeneous reactions of all kinds. The concentration fluctuation requires transport by molecular diffusion of the requisite number of molecules close enough to one another to form a nucleus large enough to exceed the critical sizo. I3ccker ( I ) proposes the following equation for nucleation r:itr: AT = c e - Q / k T e - A ( T ) / k T
(2)
where A‘ = nucleation rate, number per unit volume per unit time Q = activation energy for diffusion
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
Vol. 38, No. 1
A ( T ) = work required to form surface of nucleus T = absolute temperature c = a constant k = Boltzman constant
'
Several important qualitative deductions can be made from Equation 2. The work term A ( T ) increases markedly with decrease in supersaturation and is infinite a t the saturation curve. The term is, therefore, zero at saturation, and increases with increase in supersaturation. The term e - Q I k T decreases with decreasing temperature, since for a diffusion process Q is not independent of temperature; therefore, e - Q I k T docreages with increase in supersaturation. The N us. T curve has a pronouncedi maximum t h a t corresponds to a definite supersaturation. Also, the shape of the N us. T curve is such that the value of N is very low for an appreciable supersaturation but increases rapidly when a definite supersaturation is rea known metastable region and the Miers s are explained by .the N us. T relation. saturation curve represents a zone where N increases rapidly with T , rather than a sharp boundary, allowed, nucleation will eventually occur The state of a crystal a t the boundary is abnormal because of the unbalanced forces acting on the surface atoms. The surface molecules can possess a lower activation energy for diffusion. Also, the presence of the solid interface can affect the molecules in the mother liquor in such a manner as t o affect the terms of Equation 2 and increase the nucleation rate N . Such interface behavior may account for the inoculating effect obtained by seed crystals, or in some cases by foreign particles, in supersaturated solutions. The growth process is also amenable to much the same kind of treatment as that for nucleation on the assumption that crystal growth is essentially a two-dimensional nucleation process. Papers by Van Hook ('7) on sucrose crystallization are of interest because his fundamental results are probably of general applicability in crystallization from solution Van Hook shows that the rate of growth of sucrose crystals is proportional to the difference between the thermodynamic activity .of the sucrose in the solution and the equilibrium activity a t the temperature of the process. H e shows that the rate may be increased, but is usually decreased, by the presence of electrolytes and other added substances. H e also confirms previous beliefs that the rate-controlling step in the growth of sucrose crystals is a surface reaction and not diffusion of solute from the bulk of thc solution t o thc surface.
AMMONIUM NITRATE CRYSTALLIZATION. Considerable activity has centered around the commercial crystallization of ammonium nitrate in a form suitable for fertilizer use. The large ammonia capacity remaining from the war program has given considerable impetus t o such efforts. The main problem IS to prepare ammonium nitrate in a form that can be stored without caking and 'can be fed easily by drills. The problem is complicated by the fact that ammonium nitrate undergoes a transition at about 32" C., and crystals must be prepared either above or below this temperature. Also, if stored crystals pass through 32" C. during storage, caking difficulties tend t o occur w e n in single, well-sized crystals. For this and other reasons, the crystal is coated with inert materials to prevent caking. Two ncw methods have becn used t o prepare ammonium nitrate. This first process, known as prilling, consists in spraying ammonium nitrate solution into the top of a large spray tower, in the bottom of which is blown a stream of air. The spray flows in countercurrent contact with the air, and the ammonium nitrate crystallizes into spherical agglomerates which are screened and coated. The second mcthod, which yields single true crystals of uniform January, 1946
size, is to crystallize the material in the Krystal type of equipment ( 5 ) in which a mass of crystals is maintained in an upward flow of supersaturated solution. It is essential t h a t the entire crystallization be conducted either definitely above, or definitely below, the transition temperature of 32" C. GENERALCRYSTALLIZATION PRACTICE. The trend of recent years to moderately large, uniform-size crystalline products has continued, and much of the effort in improving crystallizer design and crystallization technique has been directed t o the manufacture of crystals of the desired size. Two general methods are used, based largely on the practices of the two main companies that engineer crystallization equipment. I n one method the solution is supersaturated in the absence of the crystalline crop and is passed upward through a bed of crystals that is agitated by the flow of supersaturated solution. Only a fraction of the leased per pass. The second method is to the presence of the solution when the superped by vacuum cooling. I n both cams vacuum cooling and evaporation can be used. I n both casea large crystals are prepared by allowing sufficient time for growth and by limiting the supersaturation to a range in which the nucleation rate is low. I n the vacuum type crystallizer, in which supersaturation is developed in the presence of crystals, effective agitation is important and improved techniques have been found that achieve more uniform suspension. Large crystals of copper sulfate have been readily obtained in this manner ( 2 ) . Although most crystallization equipment operates under vacuum and does not require the transfer of heat through a metal cooling surface, cooling crystallizers are used where the type of solubility curve or the boiling point elevation of the solution require such equipment. A large, seven-stage cooling crystallizer is in operation in*Chileon sodium nitrate (6). The effect of small concentrations of impurities on crystallization is found t o be important in practice. Usually the presence of impurities inhibits crystallization, either by reducing nucleation rate or growth rate or both. Occasionally, however, increased rates ?re obtained when foreign materials are added. Thus, the crystallization of potassium chloridc wa.s accelerated when a small quantity of a sulforated oil was accidentally added to the crystallizing solution ( 2 ) .
FUTURE POSSIBILITIES. Improved control over crystallization processes and increases in the capacity of crystallizers can be expected in the future. The most promising approaches are t o continue fundamental studies of crystallization and t o conduct carsful experimental determinations of the rates of nucleation and growth, so as t o obtain quantitative data on the effects of solution composition, supersaturation, temperature, stirring rate, and other variables on these rates. Knowledge of this kind can eventually lead to rational solutions of crystallization problems. LITERATURE CITED
(1) Beaker, R., Am. J Phys., 32,128 (1938). (2) Caldwell, H. C., private communication. (3) Mehl, R. F., and Jetters, L. X., Age Hardening Symposium, Am. Soc. for Metals, 1939; Mehl, R. F., Trans. Am. SOC. Metals, 29, 813 (1941) : Hull, E. C., and Mehl, R. F.,Ibid., 30, 381 (1942). (4) Stranski, I. N., and collaborators, 2. p h y s i k . Chem., B17, 132 (1932); A163, 399 (1933); A170, 295 (1934); B26, 100, 114, 312, 317 (1934); Physik Z.,36, 393 (1935); Sitzber. Akad. Wise. Wien, Math.-naturw. Klasse, Abt. IIb, 145, 840 (1936); Monatsh., 69, 234 (1936). (5) Svanoe, Hans, IND.ENG.CHEM.,32, 636 (1940).
(6) Svanoe, Hans, private communication. (7) Van Hook, Andrew, IND.ENG. CHEM.,36, 1042, 1048 (1944); 37, 782 (1945). ( 8 ) Volmer, Max, "Kinetik der Phasenbildung", Dresden and Leip~ig,T. Steinkopff, 1939 (photolithographic ed. available from Edwards Brothers, Ann Arbor, Mich.).
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