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INDUSTRIAL AND ENGINEERING CHEMISTRY
137' C. The third run was made under the same conditions using ' concentrated sulfuric acid as catalyst. The temperature 1% ranged from 135-132" C. during the 3-hour run, and the final percentage of esterification was 92.9. The three final products were very light in color. In all cases there was an initial drop in temperature after the acid and alcohol had reacted. PROCEDURE FOR OCTYL PHTHALATE
For this series the flask was loaded with 92 grams of octyl alcohol and 49 grams of technical-grade phthalic anhydride. Three runs were made similar to the octyl maleate series (Table IC). On the first run, with the column charged with 55 grams of Florite Desiccant, the temperature was maintained between 135' and 224" C.for the first 3 hours and resulted in 90.1% esterification. An additional hour run between 221' and 287" C.increased esterification only 0.3%, while the color darkened considerably. The second run without any desiccant started a t an initial temperature of 196" but dropped to 135" C. The temperature range thereafter was between 110' and 139O C.,with vigorous refluxing, while an equilibrium esterification percentage of about 67 was reached. A 3-hour run using no desiccant and 1% concentrated sulfuric acid as catalyst resulted in a final esterification percentage of 90.5. The initial reaction temperature was 135' and the temperature range was 104-121' C. The reactants charred as soon as the sulfuric acid was added and the final product was very dark. In all cases of esterification under a desiccant, a yield of 85-90% of theoretical or p d e d ester could be obtained by distillation of the final product under reduced pressure. THEORY OF ESTERIFICATION
The theory of the rate of esterification is covered thoroughly by Groggins (6). In general, because of the equilibrium established by the water of the reaction, it is necessary to use a catalyst, a large excess of alcohol, or some means of water removal to ensure a rapid rate of esterification. Previous references (8, 4 ) gave methods for removing the water by sending the condensed vapors of reaction through a separate chamber containing a desiccant material. However, in actual practice the simplest method would be to reflux only the acid and alcohol under a column of desiccant.
Vol. 37, No. 8
The procedure for octyl maleate, as outlined in this paper, has been tested in a factory production unit of 15-gallon capacity with excellent resuIts. The esterification is accomplished in less than 2 hours, and the final product can be used without further treatment in the manufacture of copolymers. To illustrate the factor of corrosion, strips of stainless steel (18-8) were placed in the reaction chambers during the synthesis of octyl maleate, using the desiccant in one case and 1% sulfuric acid catalyst in another. The first strip was completely unaffected, but the strip immersed in the catalized mixture was deeply pitted and discolored the final product. Since present conditions necessitate the careful preservation of equipment, this factor assumes considerable importance. The procedure covered by this investigation offers a simple method for water removal where the only important point of control is the temperature of reaction, provided the reactants are suitable. A number of attempts were made to synthesize butyl phthalate using Florite, alumina, and anhydrous calcium sulfate; but after reaching an esterification of about 50%, the butyl alcohol seemed to be absorbed into the desiccants and the acid number of the reactants rose. It is apparent that the overhead desiccant method will operate only when the desiccant has a selective absorption for the water vapor. To provide another example of a suitable reaction mixture. maleic anhydride was esterified by decyl alcohol. The results and comparison with the sulfuric acid catalyst method are shown in TabIe ID. Where experiments indicate its applicability, this method seems to offer a simple and economical means for esterification, which involves a less serious equipment corrosion problem than in the case of acid catalyst addition. LITERATURE CITED
(1) Carney, S. C., U.S. Patent 2,081,322(May 25, 1937). (2) Gumming, Hopper, and Wheeler, "Systematic Organic Chemistry", p. 255,New York, D. Van Nostrand Co., 1937. (3) Dykstra, U. 8.Patent 1,945,307(Jan. 30, 1934). (4) Gilmsn, Henry, "Organic Syntheses", Collective Vol. 1,pp. 25660,New York, John Wiley & Sons, 1932. (5) Groggins, P. H., "Unit Processes in Organic Synthesis", pp. 53378,2nd ed., New York, McGraw-Hill Bo& Co., 1938. (6) Strumnikov, M.F., Trans. Lcning~ad, Ind.Inst., 7,18-28 (1937).
Kinetics of Sucrose Crys llization MECHANISM OF REACTION' ANDREW V A N HOOK2 Lafayette Collage, Eastan, Pa.
A
PHYSICAL (diffusional) process is most frequently implied in describing the course of crystallization of sucrose from necessarily viscous solutions; however, it has been frequently suggested (7,16, 11, $1,$7) that such previous transport of sucrose across the crystal-solution boundary may not necessarily control the rate of total growth under ordinary operating conditions. I n this situation i t may be, rather, the proper fitting and orienting of the individual molecules into the crystal lattice which is the slower and, therefore, rate-controlling step in the crystallization process. The present paper reports an analysis and some experiments favoring the latter interpretation.
The mechanism of heterogeneous reaction in general and crystallization in particular is discussed by many authors (10,19,19, 13, $6, 16). The consensus of conclusions is that the NoyesWhitney-NernstrBrunner hypothesis of a diffusion-controlling step is not adequate for all cryshllization, not solution ( U ) , processes. The usual considerations leading to this decision are: rates of solution and deposition of different crystalline faces; rates of diffusion and viscosity LJS. reaction velocity; effects of stirring; and effects of added colloids. These i t e m are discussed beIow in connection with the crystallization of sucrose from pure aqueous solution. RATES OF DEPOSITION OF CRYSTALLINE FACES
The 5ret two papers in this aeries appeared in November, 1944, mgea 1042 and 1048. I Present address, University of Wyoming, Laramie, Wyo. 1
Any simple diffusion theory of heterogeneous reaction rates. would demand that the rates of the reciprocal processes of eolu-
August, 1945
tion and crystallization be the same at equal displacements from saturation and also identical over all the surfaces of individual growing crystals. The former specificationhas been shown to be untenable in the case of sucrose crystals (19) even after allowing liberally for any change in available surface by etching. In the latter connection i t is well known that sucrose crystals are frequently elongated and otherwise distorted (9, 16, 90,91,SO), an indication of unequal rate of growth, and solution (9), of different faces. Such forms appear upon growth from pure solutions and are exaggerated upon growth from impure sirups. Although this inequality of rate of growth (and solution) of different faces seems to be the normal situation, there is a practical working rule (due to Kuoharenko, 16) that “under equal conditions of crystallization, there settle on a unit$ of surface (average surface, 13) of a crystal, equal quantities of substance”.
Frequently it is assumed that a physical process (diffusion or viscosity) is the rate-determining step in the crystallization of sucrose from ordinary sirups. Several workers have indicated that this is not necessarily so, but that a homogeneous and interfacial (chemical) reaction may be the primary kinetic step. These works are reviewed, and are supplemented with stirring and colloid addition experiments. The conclusion is confirmed that a homogeneous surface reaction is the rate-determining one.
molalities or sucrose-water ratios are appropriate, and even ordinary degrees of supersaturations,
s
DIFFUSION AND VISCOSITY u8. REACTION VELOCITY
In the formal Noyes-Whitney-Nernst-Brunner theory the unimolecular velocity constant, in the rate expression -(dc/dt)
= k (C
- C,U.)
is comprised of several components as follows:
k where
703
INDUSTRIAL AND ENGINEERING CHEMISTRY
c, Cut&
=
OD/VS
= Concentration of sucrose in actual and satu-
rated sirups respectively D = diffusion coehcient 0 = area cf reaction 7 = viscosity V = volume of solution 6 = thickness of adhering saturated fluid film
The dimensions of C are most accurately defined as activities ($7). However, over not too great a spread in concentration,
are approximately valid a t low concentrations. The facts expressing the behavior of pure sucrose solutions are that values of k (16, 97) increase and values of D decrease ($0) with increasing concentration under conditions equivalent to constant 0 and V . Decreasing diffusivities are also expressed by the transposition (99)
D
-
f (l/d
According to the preceding expression. this combination of behaviors demands a diminishing fluid-film thickness as concentration is increased. Since this behavior is exactly contrary to the accepted expectation, i t throws considerable question on the validity of the original expression and its physical interpretation, as applied to the particular case of growing sucrose crystals. .\bsolute values of 6 have been computed (6) for some reactions for which complete data are available, with the general conclusion that unreasonably large values are realized. ks suggested above, the discrepancy would undoubtedly be further exaggerated in the case of sucrose solutions. Since incompletely known hydrodynamic factors seriously affect the significance of such computations of absolute values, it is preferred to compare the possibility of a truly heterogeneous or homogeneously controlled reaction on the basis of their temperature coefficients; by this means the uncertain fluid-film thickness is eliminated from con-
\ GrowtA ’8
Figure 1. Aetivation Energies of Crystallization Diffusion, and V h a i t y of Sucrose Solutions at Conatant Supersaturationof 1.05
% sucrose in sirup* % sucrose in satd. sirup
t
Fi w e 2. Rate of Crystallization of Sucrose (4% purity, 40’ C., 1.05 Supersaturation)ws. Stirrer Speed for a Piston-Type Stirrer (IS)
0 shag 5700
0 stup 5702
INDUSTRIAL AND ENGINEERING CHEMISTRY
784
Vol. 37, No. 8
would seem to indicate that diffusion (or viscosity) is not the rate-controlling step in the crystal-growing process. Similar computations a t other constant supersaturations give the same relative results. EFFECTS O F STIRRING
I t is generally recognized (18) that the reaction rate constant is a power function of the rate of stirring:
K
= or(N)b
where K = velocity constant N = rate of stirring a, ~9 = constants When the reaction is diffusion-controlled, Bassumes the value of 1 or nearly 1; its value approaches zero for reactions controlled by Figure 3. Effect of Stirring on Velocity of Growth of Sucrose Crystals an interfacial reaction. When both actions ( S 1.02, 30’ C.) are significant, it is usually found that p will 0 Different e ede on opindle run through the complete range of values if 0 Spindled ofiifferent diameter#, rotated at mame sped a sufliciently wide range of stirrer speeds is observed. sideration. This comparison has already been performed in a In some growth experiments in which an abundance of sucrose preliminary way ( 2 7 ) ; but with data which have since become crystals were suspended in the growing medium, it was observed available (89), it is possible to improve, extend, and confirm the (87) that the measured velocity constant was erratic a t low rates former presentation which indicated the predominance of a homoof stirring (below about 100 revolutions per minute in the apgeneous reaction. paratus used), but became linear a t speeds between 100 and 300 The temperature dependence of the rates of the factors inr.p.m. and then slackened off to a constant value beyond 350volved in such a comparison-diffusion (or the reciprocally re400 r.p.m. This linear section is also reported by Amagasa (I), lated viscosity) and crystallization velocity-is best expressed but only for three different stirring rates; the same leveling off is in the usual exponential form, observed by others (8,231)a t speeds depending on the dimensions of the apparatus used. If the curves are appraised according to k = koe-E/RT the above logarithmic suggestion, exponents of less than 0.4 are where k = diffusivity, viscosity, or specific reaction rate constant realized in all cases; this suggests that diffusion is not the conE = a constant designated as activation energy of cortrolling step in this reaction, although the writer (27) believes responding process that the effects of false graining obscure the issue in this type of R = gas constant experiment. I n fact, it has been suggested (27) that the linear T = absolute temperature portion of the curve may be largely the result of attrition of the E is determined from the slope of a plot of log K us. 1/T plot; larger size crystals for, with an equal weight of very finely i t is obviously definitive of the temperature-velocity relation and powdered seeds, there is no appreciable difference in the rate of may be considered as an energy barrier to be surmounted for the ensuing action. In any sequence of reactions, the larger activation energy will dictate the controlling course of the reaction. Table I and Figure 1 represent schematically the activation energies of the proceases of crystallization, diffusion, and vis1.6 cosity of sucrose solutions. The values are computed from the data of Kucharenko (9,16), Van Hook ( 2 7 , 1 8 , 9 9 ) ,S.2gham and Jackson (d), and h n d t (2, 17). (Taimni’s viscosity data and equations seem to be somewhat irregular at higher concentrations, 2.4.) The values realized for diffusion and Viscosity are within the range usually allotted to “physical” processes ( 9 ) , LS while the consistently higher values for the growth process are of the order usually assigned to purely “chemical” reactions. This
-
??
$
Q \ TABLEI. ACTIVATION ENERGIES OF CRYSTALLIZATION, DIFFUSION, AND VISCOSITYOF SUCROSE SOLUTIONS AT A 1.4 CONSTANT SUPERSATURATION OF 1.05 Growth (13-16, 87,$8, 80) Diffusion (#e) Viscosity (8, 4, 17) Tyg.. 10
20
k/k., -.
E , kg.cal./mole
0.028 0.36
1.90 6.0 60 80 12.6 “Extrapolated. b At 30’ C 40
24.4 20.0 11.7 10.0 7.4
day
E kg.dal./ mole
0.065 0.060
8.0 4.7
D eq.
&I./
0.050 2 . 0 -0.007’ 0 . 5 ( ? ) -0.013“ 4.7(?)
-
E , kg.cal./mole 940
ibis 222 214
8.0 7.0
4.6 3.0 2.0
0
1.3
86
/oy RPA
a
Figure 4. Effect of Stirring on Velocity of Growth of Sucrose Crystals, Based on Data of Figure 3
INDUSTRIAL A N D ENGINEERING CHEMISTRY
August, 1945
growth from very low stirring speeds up to 640 r.p.m. in the particular equipment used (i-e., (3 + 0). The difficulties of measuring growth in bulk-seeded solutions may be avoided by measuring the single growing crystal when it is suspended in a medium of constant concentration. This i s accomplished by the technique of Kucharenko (16),especially as developed in the Great Western Sugar Company’s laboratories (IS, 14, 20). Hungerford (13)gives data on the effect of stirring speed, in a reciprocating-type stirrer, which are reproduced in Figure 2; unfortunately these data eover only a small range of stirring speed. ~
~~~~~
~
TABLE 11. EFFECTOF STIRRING ON RAW
OF
GROWTHOF
SUCROSECRYSTALS AT 70” C. (So = 1.01 APPROXIMAWLY) S eedon6-Mm. &aft, R.P.M. n
106 500 1000 2000
Velocity, Grama./ Sq. Meter/Hr. RQ “ I
...... ....
C$h 0.08 0.26
3000
These preliminary results have been extended in two series of experiments. In the first, with speeds greater than 200 r.p.m., individual sucrose crystals 2-3 mm. in major dimension were mounted on a 6-mm. spindle by embedding the truncated prism end in a spot of de Khotinsky wax and rotating a t various speeds in a large volume of supersaturated sirup (usually S = 1.02). Considering the severe restrjction at the embedded end, the crystals grow remarkably well and in a normal manner. The velocity of the growth was computed from microscopic measurements of the lateral a and c axes (9,16). I n the second series, with speeds below 200 r.p.m., crystals were mounted in the same way on a common horizontal bar and rotated. The variow linear speeds were computed back to the equivalent r.p.m. of a &mm. shaft for comparison. The results are presented graphically in Figures 3 and 4. At the higher speeds false grain formation was pronounced; the fact that the observed velocity was higher, the shorter the observation period and the larger the amount of solution used, suggests that the deviation from linearity displayed in Figure 4 may be due to this behavior. Empirically the line represented in Figure 4 corresponds to 0.25 for the exponent in the equation K = a(N)@. A series of similar stirring experiments was performed on a single crystal a t 70’ C. The results are presented in Table I1 together with a pointcto-point computation of exponent 8. The supersaturation of the mother liquor was reduced to 1.01, and periods of observation were short in order to minimize the effects of false graining. During the sequence of exposures,a few nodules developed and grew on the parent crystal, but not to the extent of interfering with the measurements of the size of the major crystal. The corresponding decrease in sirup concentration during the time of measurement could not be detected refractometrically The low values of @ confirm the previous conclusion that a diffusion mechanism is not probable even a t the more significant higher temperatures.
.
EFFECT O F ADDED COLLOIDS
If a physical process is the rate-controlling step in sucrose crystallization, one would expect that any agent increasing the viscosity of a given sirup would cause a decrease in the rate of crystallization, and vice versa. This correlation is not observed in the case of electrolytes (1)or with added invert sugar. The addition of the latter to a sirup decreases both the rate of crystallization (97) and the viscosity (6). Likewise, the addition of gum acacia or starch t o sirups increases the viscosity tremendously, yet has little effect on the crystallization velocity. As specific examples, different amounts of gum acacia were dis-
785
persed by steeping in hot sirup equivalent t o a supersaturation of 1.08 at 30’ C. Two clear filtered sirups displayed rising bubble viscosities four and twenty-five times as great as the pure sirup, yet the velocities of crystallization from such sirups were only 98 and 99% of the original velocity, respectively. The total reduction in refractive indices in all three cases was approximately the same, suggesting (1) that the solubility of sucrose was not changed by the presence of these colloids. IMPURE SIRUPS
The only evidence indicating that an interfacial rather than a transport action controls in the crystallization of sucrose from actual sirups is the fact that a high-temperature index of reaction velocity (at least 2 per 10” C. rise or an activation energy of the order of 15 kg.-cal. per mole) prevails while the purity drops aa low as 65% (9U). At lower purities (6OY0is about the practical working limit) the temperature effect diminishes markedly (18,90); but it is also possible that the standard of comparison (1.5 per 10’ C. or about 8 kg.-cal. per mole) may also decrease significantly (8),as suggested by the behavior of pure solutions in Figure 1. CONCLUSION
Several lines of evidence indicate that the rate of growth of sucrose from pure, and probably from impure, solutions is d e termined primarily by some interfacial (homogeneous) reaction rather than an interboundary (heterogeneous) reaction. ACKNOWLEDGMENT
The author acknowledges the support given this work as a grant from the Sugar Research Foundation, Inc., and by helpful discussions with the research staff of the Great Western Sugar Company. LITERATURE CITED
Amagasa, J . Chem. SOC.Japan, 39,Suppl. Binding 263 (1936). Bates, F.J., et d oNatl. , Bur. of Standards, Circ. C440 (1942). Bennett and Nees, IND.ENQ.CHEM.,22,91 (1930). Bingham and Jackson, Bur. Standards, Bull. 14,59 (1917). Browne, C. A., and Zerban, F. W., Handbook of Sugar Analysis. 3rd ed., 1941. Brunner, 2. physik. Chem., 47,56 (1904). Claassen, H., “Die Zuckerfabrikation”, 5th ed., 1922. Daviea and Yearwood, Intern. Sugar J . , 46, 238 (1944); Trop. Agr. (Trinidad),21,43(1944). Glasstone, S., Laidler, K., and Eyring, H., “Rate Processess”, 1941.
Hinshelwood, C. N., “Kinetics of Chemical Change”, 4th ed., 1940.
Hixon, A. W., IND. ENQ.CHEM..23,923,1002,1160(1931). Ibid., 36,488(1944).
Hungerford, E. H., Great Western Sugar Co.. Rept. 35-015 (1935). Ibid., 39-004 (1939).
Hungerford, E. H., Proc. Am. SOC.Sugar Beet T&., 3, 499 (1942).
Kucharenko, Planter Sugar M f r . , 75, May-July, 1928. Landt, Centr. Zucksrincl., 44,102 (1936). MoGinnis, Moore, and Alston, IND.ENO.CHEM.,34,171 (1942). Moelwyn-Hughes, “Kinetics of Reactions in Solutions”, 1933. Nees, A. R., and Hungerford, E. H., IND. ENQ.CHBM.,26,462 (1934). I W . , 28,893 (1936). Orth, P.,Bull. assoc. d i m . , 55,105 (1938). Roller, P.S.,J . Phvs. C h a . , 36,1231 (1932); 39,221(1935). Taimni, Ibid., 33,52(1929). Taylor, H. S.,C h m . Rev.,9,1 (1931). Taylor. H. S.. “Treatise on Phvsioal Chemistry”, 1932. (27) Van Hook, Andrew, IND. ENQ.CHIO]L~., 36,1042(1944). (28) Van Hook, Andrew, unpublished data. (29) Van Hook, Andrew, and Russell, H . , J . Am. Chem. SOC.,67,370 (1945). (30) Ware, L. S., “Beet Sugar Manufacture and Refining”, New York. John Wiley L Sons, 1907. (31) Whittier and Gould, IND.ENQ.CHEM.,23,670(1931)
