NUCLEATION AND GROWTH IN SUCROSE SOLUTIONS BY ANDREW VAN HOOK AND ARTHUR J. BRUNO Received 3rd February, 1949 Schweizer has pointed out the difficulty of preparing, by ordinary procedures, supersaturated solutions of highly soluble materials which do not exhibit a tendency to nucleate spontaneously. He was able to prepare stable, supersaturated solutions of sucrose and other substances, which were 1.8-fold supersaturated on a sugar to water basis, and which did not crystallize over periods of several months. On the other hand, Waterman and Gentil found that all oversaturated solutions of sucrose crystallized, given sufficient time. Both behaviours find support in the voluminous literature on the nucleation of solutions and melts, e.g., Cassel and Landt,3 K~charenko,~ Meyer and Pfaff,5 Dorsey,6 Volmer,’ Stranski,8 etc., on the basis of the heterogeneous or thermodynamic theories ; Richards, Tammann,lO Van Ginnekin and Smit,ll Fouquet,12 etc., on the basis of the homogeneous theory.It is the purpose of this paper to review this situation for sucrose solutions, from the theoretical and practical viewpoints. Such matter has been considered previously by Cassel and Landt,3 Naveau l3 and Ca~e1le.l~ Preparation of Stable Supersaturated Sucrose Solutions.-Both Schweizer’s and Waterman and Gentil’s experiences were confirmed, using their respective techniques. However, in the latter procedure, which involves dissolution in sealed tubes, it was observed to be possible to prepare slightly oversaturated syrups which have not crystallized over several months, if fine, alcohol-precipitated material was used and/or complete solution was assured by prolonged rotation at temperatures at least zoo above the saturation point.If these precautions are not observed, or if the supersaturation is too high (> 144, crystallization inevitably occurs. It was likewise found possible to duplicate Schweizer’s experience with solutions prepared by means of quick, active boiling, followed by curing (after sealing, or covering with a thick layer of Nujol oil) for at least 20 min. and zoo above the saturation point of the final solution. Presumably the potential nuclei, otherwise preserved, are deactivated by this treatment. One is limited to prepare, at most, approximately 80 yo solutions by either technique ; since beyond this concentration either degradation is unavoid- 1 Schweizer, Rec.trav. cham., 1933, 52, 678 ; I n t . Sugar J . , 1933, 35, 385. 2 Waterman and Gentil, Chem. Weekblad, 1926, 23, 345. 3 Cassel and Landt, 2. dtsh. Zuzker-Ind., 1927, 77, 483. 4 Kucharenko, Planter Sugar Mfg., 1928, 75. Meyer and Pfaff, 2. anorg. Chem., 217, 257 ; 222, 382 : 224, 305. 6Dorsey, Trans. Amer. Phil. Soc., 1948, 38, 248. Volmer, Kinetih der Phasenbildung (Steinkopff, Dresden, 1939). * Stranslri, Physik. Z., 36, 393 ; Ann. Physik, 23, 330. Richards, J . Amer. Chem. SOC., 1936, 38, 2243. 10 Tammann, Kristallisieren und Schelmzen (Barth, Leipzig, 1903) ; States of Aggrega- tion (Van Nostrand. N.Y.. 1925). 11 Van Ginnekin and Smit, Chem. Weekblad, 1919, 16, 1210. 12 Fouquet, Compt.rend., 1910, 150, 280. 13 Naveau, Sucre Belge, 1943, 62, 310, 336. l4 Capelle, Sucre Belge, 1943, 62, 335. I I2ANDREW VAN HOOK AND ARTHUR J. BRUNO 113 able l5 or crystallization sets in.16 This limit is equivalent to a super- saturation of 2.0 at the usual observation temperature of zs0 C, but may be increased slightly to about 2.4 by cooling to - I o O C . This temperature is a lower limit set by the ice-sucrose eutectic point. Sugar/ Water Sugar/ Water at Saturation Supersaturation, 0 = ___ FIG. ti time of appearance of crystals in sucrose syrups prepared by vacuum evapora- tion or active boiling, and curing at 20° C above saturation. Points are individual samples at 25' C unless designated as the average of several samples, or other temperatures. I signifies partly degraded solutions. The times at which the beginning of crystallization was observed in solu- tions prepared in this way are presented in Fig.I. The usual observation temperature was 25' C, others being properly designated on the Figure. The tubes were rotated slowly and the usual sample was about 10 g. solution. Inversion, by test, and/or degradation, by colour, was apparent in solutions above 0 = 2.0. None the less, observations were made in this higher range, and while some results suggest a monotonous extension of lS Montgomery and Wiggins, J . SOC. Chenz. Ind., 1947, 66, 31. l6 Stare, Chern. Zlb., 1940, 2, 2826 ; A.C.S. Abstr., 36, 6033.114 NUCLEATION AND GROWTH IN SUCROSE SOLUTIONS the curve, others indicate a radical change in its nature.It is considered, however, that this change is caused by the impurities present ; for addition of invert sugar, caramel or degraded syrups to pure syrups at lower con- centrations, greatly prolongs the time required for crystallization. The data suggest the stability of solutions less than about 1.6 super- saturated,17 and the very rapid onset of nucleation above this concentration. The beginning of crystallization in syrups, prepared in the ordinary manner may be represented empirically by equations of the form : (0 - a) t = const., where 0 is the supersaturation, t the time and a a constant: a was evaluated as 1-0, 1.2 and 1.05 in three cases surveyed, and 1-37 from some of Waterman and Gentil's2 data. These are tantamount, of course, to Ostwald's metastable limit.Effect of Stirring.-Increased rate of rotation of the tukes had no appreciable effect on the observed nucleation times. Neither did glass propeller stirring, under oil, up to 300 rev./min. and below 0 = 1.4. Above this concentration, however, the nucleation times were greatly reduced the higher the concentration and faster the stirring. For instance, at Q = 1-4, stirring at 300 rev./min. for two days did not especially encourage crystallization. At IOO rev./min. a 1.5 supersaturated syrup crystallized in 4$ hr., whereas without stirring or with gentle rotation it is normally stable for weeks. At 0 = 2.0, where unstirred solutions take about a day to develop a visible crystal, a cloud shows up within a few hours at IOO rev./min. and in about an hour at 300 rev./min.Any accidental contact of the stirrer with the sides of the container, or with added glass beads, induces crystallization very promptly, even at low supersaturations. The foreign, suspended material of ordinary refined sugar seems to have no appreciable effect upon the nucleation time, provided the curing treatment is sufficient. These irregular results with stirring suggest the influence of viscosity ; which factor, therefore, was investigated by means of the temperature coefficient of reaction. Three tubes in a set, at a constant supersaturation of 2.0 with respect to oo, 2-5' and 40' C, were rotated slowly. The times of nucleation noted were remarkably uniform. If the rate of nucleation is taken to be inversely proportional to the time, and the energy of activation assumed constant between each pair of temperatures, the following activation energies are computed.TABLE I TIME OF NUCLEATION AND ENERGY OF ACTIVATION, AT 0 = 2.0 Time I EAct. 1 EAct. for growth l* (kcal./mole) Temp. O C 1 (kcal./mole) I _- l- I --I 0 25 40 5'3 10.6 24'4 I 1.7 Effects of Surface- active Agents .-The addition of surface-ac tive materials in minute amounts had no significant effect, contrary to expectations from discussion in the literat~re.~ l3 l4 The action of Aerosol OT (octyl sodium 17 This is equivalent to a supercooling of about 50°, which is somewhat larger than those reported for many melts and solutions ; Van Hook, A n n u a l Tables of Physical Constants (Princeton, N. J.) (in progress). 18 Van Hook, I n d . Eng. Ckem., 1945, 37, 782.ANDREW VAN HOOK AND ARTHUR J.BRUNO 11.5 sulphosuccinate), which is summarized in Table 11, is typical of the many different types which were studied. The absence of any marked effect confirms our earlier experience l9 that these agents alter neither the nucleation nor growth kinetics of sucrose solutions. However, when nucleation does occur in their presence it is much more prolific than otherwise.20 TABLE I1 EFFECT OF *AEROSOL OT ON THE TIME O F NUCLEATION O F SUCROSE SOLUTIONS Supersat. ' 1 - p Appear- (2j") ' I . , ance Discussion The times reported represent the sum of the time required to establish at least one stable nucleus, and the time for this embryo to grow to visible size. There is likewise the disturbance involved in the transfer from the curing temperature to that of the bath.The growth time is undoubtedly short at all but very small supersaturations ; while the transfer factor is common to all observations and will only alter the position of the curve and not its nature.2122 This shift cannot be appreciable in the present instance, since essentially the same results are obtained under various treatments. The performance reported here is definitely contrary to the homogeneous theory of nucleation as espoused by Tammann and his school.l* Any straightforward heterogeneous theoryJ6 in the sense of foreign n ~ c l e i , ~ 5 likewise seems inapplicable ; since variable curing (provided this is at least zoo above the saturation point, yet not so severe as to hydrolyze or degrade the sugar) has no effect upon the observations.It seems quite clear that those concentration fluctuations which form at least critical-size nuclei are the origin of the crystallization observed in these experiments. The Volmer theory' for condensed systems is adequate to explain the results. and extended by the absolute reaction rate theory,24 suggests that the rate of nucleation is This theory, as modified by the influence of where AF* is the free energy of activation involved in forming the nucleus, l9 Bruno, M.S. Thesis (Holy Cross College, 1947). 2o Van Hook, Ring Surface Tensions (in preparation). Highly concentrated sucrose solutions apparently salt out even traces of most of the surface-active materials investigated. 21 Othmer, 2. aizorg. Chem., 91, 209. 22 Hammer, Ann. Physik, 33.445. 23 Becker, Ann. Physik, 1938, 32, 128. 2 4 Turnbull, J . Chenz. Physics, 1949, 17, 71.116 NUCLEATION AND GROWTH I N SUCROSE SOLUTIONS AF%=. the free energy of activation of viscosity, and x the niol fraction of solute. The net free energy required to form the nucleus is also A F = AFS - AF,, where AFs is the free energy required to form the surface, and AF, that gained in forming the mass of the crystal without any surface. Gibbs has shown that AFS = (3/2)AF?J ; whence A F = iAF,. If these reversible values are identified with the energies of activation of the respective processes, we have The energy of activation of viscosity is approximately 1/3 that of growth,ls so that as a crude approximation This relative order of magnitude has been pointed out before in an empirical waV.I8 AEnuc~eatiou = j@Ev.AEnucleation = (5/6)AEgowth. The Thomsen equation, 2cM ln(c/cco ) = c d ’ with A F = (1/3)AF, = (1/3) cr A = (43) n c y2 (as spheres), suggests at constant supersaturation. In these expressions c and c, are the solu- bilities at particle radii Y and CL) respectively, c the interfacial tension, A the surface, and M/d the molar volume. Since the activation energy is observed to increase with rising temperature at fixed interfacial conditions, it seems likely that some factor other than the work of forming the nucleus is involved in the nucleation process. Nothing definite is yet known about the entropy changes concerned in the above approximation, but the marked influence of stirring upon the rate of nucleation at higher concentrations is very suggestive of the viscosity as this factor.Surface Tension.-The interfacial tension, which is so prominent in most crystallization theories, has received special attention in the case of sucrose solution^.^ l3 l4 Since this interfacial tension between a solid and a liquid is difficult to evaluate, it has frequently been correlated with the ordinary surface tension of the liquid, although it seems questionable to specify it in this way. where s, I and g indicate solid, liquid and gas phases respectively, and 0 is the contact angle of wetting of the solid. If the wetting is complete, and the surface tension of the solid is constant, we have AF e 3 / ~ 2 Duprh’s rule for this type of interface is Osz = csg - OLg cos 8, Osl = cssg - czg, and dcsl = - dole The former is Antonoff’s rule for this case, and the latter indicates that ordinary surface-active materials, which usually decrease the liquid surface tension, may actually increase the interfacial tension at the solid surface. It was found impossible to increase the surface tension of crystallizable sucrose solutions to any extent by additives ; but ordinary wetting agents diminish it considerably.Even so, no great influence on the crystallizationANDREW VAN HOOK AND ARTHUR J. BRUNO 117 time was observed, which is contrary to several reports in the literature under similar circumstances.3 l 3 18 25 A twofold oversaturated solution of sucrose in 68 yo alcohol, whose surface tension was 26 dyneslcm., did not display crystals for 8 days, compared to about I day for an aqueous solution of the same supersaturation.Whether this prolongation is the result of lowered surface tension (and therefore possibly increased interfacial tension) or change in environment is not yet evident. These matters are being investigated further in this laboratory. Practical Implications .-The extreme difficulty of preparing and preserving supersaturated sucrose solutions would augur well for the applica- bility of the heterogeneous theory, in spite of the greater significance of the thermodynamic theory. Under conditions which prevail in the sugar house, as well as in ordinary laboratory work, nucleation undoubtedly occurs by chance inoculation. Under these circumstances, it is merely the rate of growth to visible size which determines the observed nucleation time. Since this process has been shown to be unimolecular,26 the observed equilateral hyperbola relation is an obvious one. However, as the concentration increases, a very strong and abrupt influence of true nucleation sets i n ; thus accounting for the metastable limits usually reported.27 Nucleation in condensed systems has all the attributes of a chain reaction,6 28 which feature explains the autocatalytic " false grain " region 27 of the sugar boiler. Conclusions .-The prominent features of the Volmer-Becker theory of nucleation are shown to be qualitatively applicable to supersaturated sucrose solutions. The continuing support of the Sugar Research Foundation, Inc., is gratefully acknowledged. Quantitative aspects will be investigated. Chemistry Department, CoUege of the Holy Cross, Worcester, Mass., U.S.A. z 5 Von Weimarn, 2. Chem. I n d . Koll., 1907, 2, 76 ; A.C.S. Absty., 3, 393. 26 Van Hook, I n d . Eng. Chem., 1944, 36, 1042. 27 Webre, PYOC. 11th Conf. Assoc. tec. azwcare'e7os Cuba, 197, p . 9. 28 Langmuir, PYOG. Amer. Phil. SOC., 1948, 92, 167.