MODIFICATION OF GROWTH RATE AND HABIT OF ADIPIC ACID

1730

ALANS. MICHAELS AND FREDERICK W. TAUSCH, JR.

Vol. 65

MODIFICATION OF GROWTH RATE AND HABIT OF ADIPIC ACID CRYSTALS WITH SURFACTANTS BY ALANS. MICHAELS AND FREDERICK W. TAUSCH, JR. Departnmit of Chemical Engineering, Massachusetis Institute of Technology, Cambridge, Massachusetts Received March 1 . 1861

The isothermal (32.7”) growth of crystals of adipic acid from aqueous solution under carefully controlled conditions has betm studied as a function of (a) supersaturation level (1 t o 13%) and (b) concentration of various anionic and cationic surfactants (0 to 360 mg./l.), using a specially designed crystallizing apparatus. Growth rates of the characteristic faces ((0011, (010) and (110)) of the crystals were determined microscopically. Sorption of surfactants on the Crystals was independently determined. While results are in general qualitative agreement with earlier work on this system, a number of very significant and unusual effects have been detected which could not have been observed without control of temperature and supersaturation. The growth-retardation on certain faces is far greater than previously reported, and the effect of additive is strongly dependent on supersaturation level; a t low supersaturation, increasing additive concentration results in drastic reduction or cessation of growth on certain faces, while at high supersaturation levels the additives have relat.ively little effect on growth, regardless of concentration. A particularly interesting result is t h a t anionic additives actually significantly accelerate growth on the (001) face. It is also found that additives increase the supersaturation level at which extensive three-dimensional nucleation occurs, and also result in better-formed crystals. The results are interpreted in terms of two-dimensional nucleation and dislocation theories of crystal growth, and mechanisms for growth and habit modification are developed.

I. Introduction It has long been known that trace concentrations of certain additives can have profound effects on crystal growth rate and habit. These effects are of great importance in many fields of science and technology, but the mechanisms by which additives affect crystal growth are not clear. It is generally agreed that, additives must adsorb to some extent on a crystal surface in order to affect growth on that face. There has also been some evidence that the effectiveness of additives decreases with increasing “tempo” of crystallization.‘,:: Previous studies of the effect of additive on crystal growth from solutioii, however, have generadly involved neither measurements of additive adsorption nor careful control of the fact.ors which determine growth rate. Recmt ~ o r k has ~ , shown ~ that certain surface active agents modify the habit. of adipic acid crystals grown from aqueous solution. Adipic acid crystallizes from distilled water as thin hexagonal plates (see Fig. 1) with prominent hexagonal (001) faces (referred t,o as C faces), (010) side faces (B faces), and (110) end faces (A faces). X-Ray studies5 have shown that the linear, six-carhon, dicarboxylic adipic acid molecules are lined up in this crystal end-to-end so that the C faces represent an end view of the molecule and are entirely carboxyl in nature, while the A atid H faces represent, side views of the adipic acid molecule and are therefore partially carboxyl arid part8ially hydrocarbon i i i naturt:. As little as oiie mg./liter of a cationic surfactant. modifies the habit from t hili hexagonal plates to even thinner hexagcinal plates (see 1;ig. I), while as little as 25 rng./lit:er of at1 anionic surfactant results i i i thick(1r

hexagonal plates or prisms. It has been postulated that the partially-ionized negatively-charged surface carboxyls on all faces result in coulombic adsorption of the cationic surfactant on all faces, but more extensively on the C faces (due to higher carboxyl density) than on the A and B faces, resulting in relatively greater retardation of growth on the C faces and hence thinner plates. The anionic surfactant, on the other hand, is coulombically repelled from all faces by the surface carboxyls, but can adsorb amphipathically (nonionically) on the partially-hydrocarbon A and R faces, thus retarding growth on these faces more than on the C faces and resulting in thicker plates and prisms. In the light of previous work, the present investigation has involved direct measurement of isothermal (32.7’) growth rates normal to each of the three faces of adipic acid crystals grown from seeds in aqueous solution, under carefully controlled constant conditions, as a function of supersaturation level and additive concentration, and correlation of the effects of additives on growth with measurements of additive adsorption. 11. Experimental

A. Xaterials.-Distilled water fret. of surface active impurities was used throughout. Commercial adipic acid was furthrr purified by crystallizing three timrs from distilled water, and was found to contain no significant amount of surface active contaminant. Three pure, well-characterized surface active additives were uwd: (1) sodium dodecyl-( trtrapropy1)-benzene sulfonate, an anionic surfactant referred to as SDBS; (2) sodium nonyl-( tripropy1)-benzene sulfonate, another anionic referred to as SNBS; and (3) trirnethyloctadecylammonium choride, a cationic surfactant referred to as TMODAC The two anionic surfactants were specially prepared and were reported to be free of sodium sulfate and to contaiii less than 0.1% unsulfonated hydrocarbon; the SDRS waq (1) €1. E. Buckley. “Crystal Growth.” John Wiley and Sons, Ine.. the same as that used in previous Although thew 19.51, p. 378. Kew York, N. I-., surfactants were not further purified before use, foam-frac(2) F. C . Frank, “Groxvth and Perfection of Crystals.” Ilorerniis, tionation of a sample of the SDBS revealed no significant Roberts :ind Turnbull, editors, John Wiley and Sons,Inc., New York, amount of highly surface active contaminant. N. Y.. 11158. p. 8. B. Adsorption Measurements.-Calibration plots of (3) D. Fysh, reported in “Surface Activity.” J. L. Moilliet and B. surface tension versus surfactant concentration, in both Collie, editors. Third Ed., I). Van Nostrand and Co., New York. N. Y . . distilled water and saturated adipic acid solution, were prr1951. p. 133-145. pared from measurements on solutions of known conccn( 4 ) A . S. Michaels and A. K. Coli-ille. Jr., J . P h y s . Chem.. 64, 13 tration, using a Cenco-Du Nouy Interfacial Tensiomrter. (19130). All surface tension measurements were carried out in a constant temperature room maintained at 25 i lo, on solutions ( 5 ) R. I:. Morrison and A . R. Robertson, J . Chem. SOC..987 (1949).

Oct., 1961

GROWTHRATEOF ADIPICACIDCRYSTALS WITH SURFACTANTS

which were equilibrated for at least 24 hours in t h a t room. Crystals for the adsorption measurements were grown from solution by cooling, and were always kept in saturated adipic acid solution to avoid contamination. Crystals of various shapes were obtained by controlling cooling rate and by using SDBS to modify crystal habit; when SDBS was used to obtain needles, crystals were washed several times t o remove adsorbed surfactant. Specific surface area of each batch of crystalis was estimated by microscopic examination of a sample of ten crystals chosen a t random. The procedure for determining isotherms for adsorption of surfactant on adipic acid crystals conbisted of: (1) equilibrating at 25" about 25 g. of the specially prepared crystals with a measured volume of saturated adipic acid solution containing a known concentration of surfactant; (2) after 24 hours, removing the supernatant solution for determination of surfactant concentration by surface tension measurement; (3) washing the crystals with two 10-ml. portions of warm distilled water to dissolve the crystals partially and remove the adsorbed surfactant. The concentration of adipic acid in the wash solution generally corresponded almost exactly to saturation at 25", a t which surface tension was measured. Material balances on the surfactant indicated that all of the original surfactant could usually be accounted for in the supernatant and the wash solution, although with very high concentrations of surfactant there was an apparent loss of surfactant due to incomplete washing of the crystals. For this reason, calculatrd values for adsorption, assuming that all surfactant not remaining in solution or mechanically entrained in the crystal cake is adsorbed, are more reliable and hence are reported. C. Crystal Growth Rate Measurements.-A schematic drawing of the apparatus developed for growing crystals is presented in Fig. 2. The crystallizer consisted of a 500-m,. three-neck flask fitted with a thermometer readable to 0.01 . Vigorous agitation was provided in the crystallizer by a speciallydesigned magnetically-driven stirrer, and the crystallizer was immersed in a water-bath maintained at 32.7 i 0.01". Supersaturation was maintained in the crystallizer by circulating the solution (by means of a peristaltictype pump operating on a short length of silicone rubber tubing) through a (crystal separating column (to prevent carryover of crystah in the crystallizer), thence through a bed of adipic acid crystals in the dissolver maintained at a slightly higher temperature than the crystallizer, and finally through a filter (to prevent carryover of crystals from the dissolver) and back t o the crystallizer. The circulating solution dissolved solme of the crystals in the dissolver and became virtually saturated at the temperature of the dissolver; upon returning to the crystallizer, and cooling to the temperature of the crystallizer, the solution became supersaturated. Preliminary work showed that a t steady-state the supersaturation level in the crystallizer remained constant and the temperature of the solution in the crystallizer was constant within 0.01". The absolute temperature level in the crystallizer varied from zero to several tenths of a degree higher than the 32.7" water bath, due to heat from the warmer entering solution. The entire apparatus in contact with the solutioii was constructed of glass, except for the Teflon and stainless steel stirrer and the short length of silicone rubber tubing in the pump. Great care was exercised to avoid contamination of the solution, and periodic surface tension measurements on the solution indicated absence of surface-active impurities. All the seeds used in the SDBS and SNBS runs were thin plates from a single batch, grown from pure adipic acid solution, dried, sieved, and the 30-40 mesh fraction collected for use; these seeds were well formed and, because of the sieving, of quite uniform size (average dimensions, referring to Fig. 1, I; = 0.767 mm,W = 0.50 mm., T = 0.14 mni.). Thick prisms were umied for seeds in the TMODAC runs, since thin seeds would have resulted in extremely thin plates which would have been haird to handle and measure. The prisms for all TMODAC rum were prepared in a single batch by growing the thin plate seeds mentioned above in solution containing SDBS, then drying; these prisms were also well formed and, becamis of the uniformity of the seeds, quite uniform (L= 0.934 mm., W = 0.473 mm., T = 1.58 mm.). The procedure for growing crystals involved: (1) establishing steady-state in the apparatus with the desired supersaturation level and additive concentration in the crystallizer; (2) adding about 100 seeds which were briefly washed in distilled water just prior to addition to the crystallizer in

1731

,TOIOI

No

Cotionic

Fig. 1.-Effect

additive

Anionic

of additives on adipic acid crystal habit.

Fig. 2.-Schematic

cross-section of Crystallizer (approximately to scale).

/r , , , , , I 10 100 1000 SDBS concn. in soln., mg./l. Fig. 3.-Adsorption of SDBS on adipic acid crystals of various shapes.

0.1 1 1.0

, ,I

,

order to remove surface impurities; (3) permitting growth to occur on the freely-suspended seeds for periods of onehalf hour to several days until about one to five millimeters growth had occurred on the fastest growing faces; (4) after growth had occurred for the desired period of time, pipetting a 10-ml. sample of solution from the crystallizer for determination of adipic acid concentration by titration and surfactant concentration by surface tension messurement ; and (5) simultaneously sucking the crystals out of the crystallizer, drying them, and microscopically measuring the crystal dimensions of ten crystals chosen a t random. Since the seeds were very uniform and no nucleation occurred, the entire sample was of uniform size within about 10%. From the ditrerence in average dimensions of the seeds and the grown crystals, along with the duration of growth and the crystal geometry, growth rates normal to the A, B and C faces were calculated. The supersaturation level was calculated from the solubility of adipic acid at the temperature of the crystallizer ( CO,about 33 g. per liter a t 32.7') and the actual concentration of adipic acid in the crystallizer (C), i.e., S = (C/C,) = supersaturation ratio, and ( C - CO/CO) = ( S - 1) = supersaturation.

1732

ALANS. MICFIAELS AND FREDEXICK W. TAUSCH, JR.

Vol. 65

surface area than indicated by microscopic measurements of crystal size and shape, although a “rugosity factor” of 50 for a solution-grown crystal face seems improbably high. An isotherm for adsorption of TMODAC on adipic acid crystal plates is presented in Fig. 4. ?g 0.2 A monolayer of TMODAC also corresponds to ,$0.1 about 1.3 mg. per lo4 cm.*, and Fig. 4 shows that 2 o-*T=z--r-, , , , I no more than a monolayer adsorbed at even very 0.1 1.0 10 100 TMODAC concn. in soln., mg./l. high concentrations, thus supporting the validity Fig. 4 --Adsorption of TMODAC on adipic acid crystals of the procedure and, in turn, supporting the hypo(plates). thesis of multilayer adsorption of SDBS. B. Crystal Growth Rate Studies.-Using the i I 1 apparatus developed in this investigation, growth I c Ii Face rates normal to each of the three faces of adipic 1 X B Fa:e acid crystals grown at 32.7’ were directly measured as a function of supersaturation level (from less than 1% rip to the point where extensive threedimensional nucleation occurred) and additive concentratiov and character. The latter included : no additive; SDBS at concentrations of 10, 2Fi. 45, 80 and 360 mg./l., SNBS a t a concentration of 100 mg./l.; and TMODAC at concentrations of 30 and 100 mg./l. The growth rate results, for each crystal face and additive concentration, are presented in Fig. 5 to 10. The maximum supersaturation level at which i’ v i crystals could be grown from seeds without ex, , , , tensive secondary nucleation increased with addi0.01 -L tive concentration from about 5% in the absence 0.I 1.0 10.0 of additive to over 20% at very high additive con% supersaturation, (S - 1) x 100. centration. Although high supersaturation levels Fig 5.---No additive, In (growth rate) uerms In (super- could not be maintained after extensive nucleation saturation) for all three faces. occurred, measurements on the nucleated crystals showed that the relative growth rates on the 111. Results various faces were the same as, and the absolute A. Adsorption Isot.herms.-Figure 3 shows thaL SDBS :&orbed about ten times more extensively, growth rates approximately the same as, crystals per unit total surface area, on plate- and needle- grown simultaneously from seeds. In the absence of additive, and at low supershaped crystals than on laths. Referring to the specific surface areas for the various crystal shapes saturation levels, growth on the A faces was more (see Fig. 3), however, the surface of the lath- rapid than on the B and C faces, resulting in thin shaped crystals consisted almost entirely of C faces, elongated-hexagonal plates (laths). At higher with only 8.5% A and B faces, while 52% of the supersaturation levels growth rate on the B faces area of the plates and 94% of the area of the needles approached growth rate on the A faces, resulting consisted of A and B faces. In fact, adsorption in more regular, hexagonal, thin plates. Figure 5 values based on mg. SDBS adsorbed per unit A- shows that growth rate on the A faces increased and B-face area correlate reasonably well on a with the first power of supersaturation, growth rate single curve for all three crystal shapes, indicating on the C faces increased with approximately the that adsorption of SDBS is far stronger on the A 3/2 power of supersaturation, and growth rate on the B faces increased with the second power of and B faces than on the C faces. The amount of SDBS adsorbed increased rapidly supersaturation a t low levels and the first power of with SDBS concentration in solution. An ad- supersaturation a t high supersaturation levels. Low Concentrations of SDBS (25 mg./l. and less) sorbed monolayer of SDBS, based on 50 A.* per molecule, corresponds to about 1.3 mg. SDBS had little effect on growth rate on any face, as per lo4 cm.2; according to Fig. 3, this level of shown in Fig. 6 to 8, but higher concentrations adsorption is reached with as little as 15-25 mg./l. caused drastic retardation of growth on the A SDBS m solution, and perhaps iifty monolayers and B faces. The retardation was strongly deform at higher concentrations. While adsorption pendent on SDBS concentration and supersaturaof this magnitude is not common, it is also not im- tion level (or growth rate), resulting in complete probable ; the critical micelle concentration of stoppage of growth at high additive concentration SDBS was lowered from over 1000 mg./l. in distilled and low supersaturation levels, but having very wster to about 300 mg./l. in saturated adipic acid little effect a t high supersaturation levels regardsolution, and adipic acid crystals may induce a less of additive concentration. Because of this, sort of micellar or pseudo-crystalline adsorption of growth rate on the A and B faces increased with as SDBS. It is, however, possible that the crystal much as the iifth power of supersaturation. faces are highiy stepped, resulting in higher specific At the same time that growth on the A and B ,

I

I

1

,k

,,I

Qct., 1961

GROWTH RATEOF ADIPICACIDCRYSTALS WITH SURFAIXANTS

1733

faces was retarded by SDBS, growth rate on the C faces increased with increasing additive concentration (see Fig. 8 and 10). With 80 mg./l. SDBS and low supersaturation, growth rate on the C faces was about five times higher than in the absence of addit,ive; still higher concentrations of SDBS resulted$ in slightly decreased growth rate, although still significantly higher than in the absence of additive. The only concentration of SNBS studied was 100 mg./l., and the growth results were virtually the same, for all three faces, as with 80 mg./l. SDBS, indicat,ing that the effects of these two anionic additives are almost identical. Concentrations of both 30 and 100 mg./l. TMODAC resulted in complete stoppage of growth on the C faceis at all supersaturation levels, and Significantly retarded growth on the A and B faces, with the ret:irdation most marked a t lower supersaturation levels, as shown in Fig. 9. As a result, growth rate 011 both the A and B faces, in the presence of both 30 and 100 mg./l. TMODAC, increased witchthe second power of supersaturation level.

IV. Discussion A. Effect of Additives on Three-dimensional Nucieation.-The ooserved effect of additives on three-dimensional nucleation is consistent with numerous reports that additives inhibit nucleation.6 Since there appears to be no mechanism by which additives that reduce the crystal-solution interfacial free eneirgy can thermodynamically inhibit homogeneous tiucleatior-i. it is believed that the inhibition of iiucleation is due to poisoning of either heterogeneous nuc!ei or homogeneouslyformed embryos. The chain lengths of the surfactants used in this investigation are of the order of 50-100 8., which is of the same order as the estimated edge length of a witical-sized threedimensional nucleus. It might therefore be expected that the surfactants would preferentially admrb on (and poison) the larger (and more adive) embryos, thereby resulting in progressively increased critical supersaturation levels as additive concentration is increased and smaller potential nuclei are poisoned. B. Effect of Additives on Crystal QualityNeedle-like Formations.-It was found that, for a given supersaturation level, crystals grown in the presence of additives were better formed and had smoother faces than crystals grown in the absence of additives. Needle-like projections did not generally occur on either the A or the B faces a t growth rates below about 0.2 mg./cm.a min., corresponding to about 30 molecular layers per second, and additives which reduced growth rate below this levcl were found to improve crystal quality by preventing needle-like formations. The C faces were generally quite smooth except a t the very high C-face growth rates occurring at the very high supersaturation levels ( e . g . , 10%) which could be maintained in Lhe presence of high concentrations of SDBS; needle-like projections then occurred profusely on the C faces at growth rates above (6) P. M.

E& and S. Z e r f w , D~scuesionrForadou SOC.,6, 6 1 (1940).

!

0.001 i--, .,-I._-_-_-0.1 1.0 10.0 100.0 yo supersaturation, (S - I) x 100. Fig. 7.-Effect of SDBS on B-face growth rate.

lor---

0.1

1

'

"

4 1

"

1.0

10.0

% supereaturation, (S - 1) X 100.

Fig. 8.-Effect

of SDBS on Cface growth rate.

ALAN8.hIICHAELS

1734

.4ND F R E D E R I C K

i

0.0.

L

,

1

'

1

1'1

1 '

0.1

J

1.0 10.0 yo supersaturation, ( S - I) X 100. Fig. R.-I:ffect of TMODAC on A- and B-face growth rate.

about 1.0 mg./cm.* min., which also corresponds to about 30 layers per second. These results indicate that there is a critical rate of initiation of new layers, a t about 30 layers per second, above which needle-like projections form. In the light of the mechanism of dendritic and whisker growth (e.g., ref. 7, 8) the following interpretation is proposed. The rate of initiation of new layers increases, in most cases, with supersaturation to a power greater than unity, while the rate of advance of a layer across the crystal surface increases more or less directly with supersaturati~n.~,'OWith increasing supersaturation (7) F. R. h. Nabarro and P. J. Jackaon, in ref. 2. (8) D. D. faratovkin, "Dendritic Crystallization," translated from Rusrian, Conaultant Bureau, Inc., New York, N o Y..1959,

MT. T A U S C H , JR.

Vol. 65

level, therefore, a point will eventually be reached at which the rate of initiation of new layers is much faster than the rate of advance of these layers away from the point of initiation, so that a small surface protrusion forms (ie,, the layers pile up); because of the more favorable diffusion environment of this protrusion, it will become unstable and grow into the solution faster than, and at the expense of, the adjacent surface. Since additives were found to improve crystal quality, it appears that additives retard initiation of new layers more than advance of layers across the crystal surface. C. Relation between Additive Adsorption and Effect on Growth.-The observation that SDBS adsorbs far more extensively on the A and B faces than on the C faces is consistent with the postulated pattern of adsorption (Le., amphipathic adsorption on the A and B faces despite coulombic repulsion from all faces) and with the observed effects of SDBS on growth (ie.,retardation on A and B faces, but accelerated growth on C faces). The fact that concentrations of SDBS below about 25 mg./l. had little effect on growth, despite the indicated monolayer adsorption, indicates that very extensive adsorption (involving a complete monolayer and perhaps multilayers) is necessary for SDBS to retard A- and B-face growth. Since both additive adsorption and growth retardation increased with increasing SDBS concentration, it appears that the degree of retardation is related to the amount of adsorption, although increased rate of adsorption from more concentrated additive solution may also be a factor. Although adsorption of TMODAC on the various crystal faces could not be resolved because only one crystal shape was used, the distinct step in the adsorption isotherm (Fig. 4) presumably corresponds to completion of a monolayer on the C faces, since the cationic ThIODAC would be expected (from the postulated pattern of adsorption) to adsorb most strongly on the high-carboxyldensity C faces; the fact that TMODAC retarded growth on the C faces more than on the 4 and B faces supports this. Furthermore, the fact that both 30 and 100 mg./l. TMODAC retarded grou-th on the h faces to the same extent indicates that the maximum retardation had been reached; the adsorption isotherm indicates that little additional adsorption occurs above 30 mg.11. TMODAC in solution, and presumably even very high concentrations of TMODAC would not further retard growth. This suggests that additive diffusion is not the limiting step for growth retardation, at least for TMODAC a t 30 and 100 mg./l., and that with increasing additive concentration additional adsorption either does not occur or does not further retard growth. Comparison of the anionic and cationic additives with regard to adsorption and effect on growth indicates that less-than-monolayer adsorption of TMODAC ( e . g . , a t 30 mg./l. in solution) retards growth on the A and B faces more than multilayer adsorption of SDBS (e.y., a t 360 mg./l.). Since (9) U'. K. Burton. N. Cabrera and F. C . Frank, P h d . Trans. R o y , SOC.(London), A248, 299 (1951). (10) & R. Verma, "Crystal Growth and Dislocations " Academia

Press, Inc., S e w York, N. Y.,1953.

OCL, 1961

GROWTH KATE

OF

ADIPICACIDCRYSTALS WITH

TMODAC is al;t.racted to the A and B faces both coulombically and amphipathically, while SDBS is adsorbed amphiphatically despite coulombic repulsion, it appears that adsorptive-bond-strength (which probably influences sorbate mobility) is a more inportant factor than sorbate surface concentration. D. Mechanism of Growth. 1. Comparison with Theory..--The experimentally observed dependence of growth rate on supersaturat’ionlevel to powers greater than unity, and the fact, that crystals generally grew as well-formed polyhedra, indicate t’hat t.he diffusional resistance is not, the rat8e-controllingmechanism. Correlation in terms of two-dimensional nucleat i ~ n ~ , ’ was ~ - ’ found ~ to be unsatisfactory because of t’he non-linearity of plots of In R oersus l/ln S; in most cases the curves exhibited two rather linear regions, with E, i0-W slope a t low supersaturation levels and a high slope a t high supersaturation levels, and with a distinct break between them (e.g., see Fig. 1 0 ) ~ Furthermore, even the highest values of crys t,ai--soiut>ioninterfacial free energy deduced from. tlnis 1:orrelation were only one to three ergsicrn .z* which seems unreasonably low even for tile crystal--soliit,icininterface. With this correlation, however, slopes were found to increase with addit.ire concentmtioii. which js consistent with a mechanism inr,olvinr increased activation energy for nucleus fimnatio:i c;ue to contamination of the crystal surface on n.hic.h i~ucleationoccurs. The dislocation mwiiaiiism of growthg,l o ,1 2 , l4 - I 6 was found to be an attruciive possibility for growth in the absence of additive, because of the observed dependence of growt,h rate on the second power of supersaturation levci a t ioiv growth rat’esand on the first power a t high growth rates. In the presence of SDBS, however, the observed dependence of growth rate on powers of supersaturation as high as five is difficult t’o explain iii terms of growth from dislocations alone. 2. Proposed Mechanisms of Growth Retardation.-The two-dimensional nucleation mechaniym would be attractive if the very low activation energies for nucleus formation could be just,ified. The dislocation mechanism would also be attractive if the strong dependence of growth rate on supersaturation level (in the presence of SDBS) could be accounted for. It was found that the effects of both supersaturation level and additive concentration on growth retardation could be accounted for in terms of the following analysis. Although the solubility of a part,icle (either threeor two-dimensional) increases wit’h decreasing size, and in general the critical radius of curvature of a particle in equilibrium with supersaturated solution is given by the well-known relation T -l/ln S , it is neverthellsss possible for a stable two-dimensional sub-critical embryo to exist on a crystal surface, e . g . , the st,ep created by the intersection (11) W. Becker and R. Doring, Ann. Physik. 24, 719 (1935:. (12) W. K.Burton and N. Cabrera, Disc. Faraday SOC.,6 , 33 (1949). i13) hl. Volmr?r and H. Flood, 2. p h y s i k . Chem., 8170,273 (1934). (14) N. Cabrera rind D . 9. Vermilyea, in ref. 2. (15) F . C. Frank, Discussions Faraday SOC.,6. 49 (1849). (16) W. T. Head. Jr., “Dielooations in Crystals,” McGtaw-Hill Book Co., New ’Ilork, N, Y.,Chapter 10, 19.53,

SURFACTASTS

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of two closely spaced screw dislocations of opposite sign.9 The supersaturation level necessary to activate such an embryo to initiate a growth layer is far less than the supersaturation level necessary for initiation of a layer on a perfect crystal surface, ie., two-dimensional nucleation. Furthermore, the probability of activation of such an embryo at a given supersaturation level increases exponentially with increasing embryo size. It is proposed that the effect of these stable two-dimensional subcritical embryos on crystal growth (initiation of new layers) is analogous to the well-known effect of heterogeneous nuclei on three-dimensional nucleation (initiation of a new phase). According to this proposed mechanism of growth, the rate of growth can be expressed as

where i represents a class of embryos characterized by a specific value of B, C, is the surface concn. of embryos of size 1 B1corresponds t o an energy of activation t o permit groa th of an embryo of size i expj -p,/ln S) can be considered as t h e probahlit> of activation of an embryo of size i

Actually, it was found that all of the growth rate results could be fitted by only two terms of such an expression, i .e. IZ = CI exp( -bl/ln 9) + Ca exp( -pJn 8 ) (2; with the constants C1, C2,p1 and B2 functions of additive concentration. The use of only two terms of the expansion can be justified by assuming a distribution of embryo sizes which favors small embryos, which is rather likely; this leads to the conclusion that only the very large embryos (which are present in low concentration but have a very high probability of activation) and the small embryos (which are present in very high concentration but have a low probability of activation) may contribute significantly to the summation. Values of the constants determined from the experimental growth rate results are consistent with this model: the first term is characterized by very low values of the constants C1and p1and this term predominates a t low supersaturation levels and therefore apparently represents the contribution of the group of large embryos, while the second term is characterized by high values of the constants Cz and p2 and therefore predominates a t high supersaturation levels and apparently represents the contribution of the small embryos. The effect of additive on the values of the constants nas also found to be consistent with the propovd mechanism. Valucs of p1 and & were found to increase n.ith increasing additive concentration (reflecting increasing slopes on plots of In R uersus 1, hi S),indicating that additives inhibit activation of embryo5 of all sizes. Additive also decreased values of C,, indicating poisoning of larger embryos (as might be expected and in agreement with the postulated effect of additives on three-dimensional nucleation), but additive actually increased values of Cz; the latter observation is interpreted to indicate that, as larger embryos are preferentially

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ALANS. MICHAEUAND FREDERICK W. TAUSCH, JR.

poisoned, the contribution of smaller embryos becomes more important and is reflected in higher values of C,. The foregoing analysis does not, however, take into consideration the inescapable reality that the surface-concentration of an adsorbed additive on a growing crystal face must be different from (and probably less than) the equilibrium concentration on a nort-growing face. In the case of TMODAC, at least at the concentrations studied, the kinetics of additive adsorption are apparently not important since the same degree of retardation was obtained with 30 and 100 mg./l. With SDBS, however, the degree of retardation increased with additive concentration and the kinetics of additive adsorption may be important. If it is postulated that a propagating lattice layer on a growing face sweeps the surface clean of adsorbed additive, then clearly, the steady-state average surfacr-concentration of additive during growth will he directly related to (a) the rate of diffusion of additive to the surface, and (h) the rate of advance of a lattice layer and the time-interval between successive layer-depositions. These postulates lead to the prediction that the growth-inhibitory action of a surfactant must increase with the surfachnt concentration in solution, and &crease with increasing growth rate (or level of supersaturation), in complete agreement with the experimental ohservations. The authors have had fair suceess in deveiopirig kinetic expressions incorporating these concepts, which are qualitatively consistent with the observed growth-rate data; proper test and refinement of these relations will, however, reqL''ire more extensive experimental information than is presently available. 3. Mechanism of Growth Acceleration.-While additives have generally been found to retard growth, it has often been suggested that incorporation of additives into a growing crystal could increase growth rate by creating dislocations (e.g., ref. 14), and there is evidence that additives can increase the rate of two-dimensional nucleation by reducing edge free energy (e.g., ref. 17). The increasing C-face growth rate with SDBS concentration (see Fig. 10) may well be due to additive incorporation; with 360 mg./l. SDBS, perhaps the retarding effect of SDBS adsorption begins to overshadow the accelerating effect. Increased rate of two-dimensional nucleation dow not seem likely, however, since the results of this investigation indicate that growth does not involve twodimensional nucleus formation as such, and it also seems unlikely that sufficient additive could adsorb on a nucleus edge during its formation to significantly influence its free energy of formation. It might be mentioned that the results suggest that the accelerated C-face growth may be directly related to retarded A- and B-face growth; Gface growth increased with SDBS concentration at the same timt? that A- and B-face growth decreased, but with 360 mg./l. SDBS (when A- and B-face growth had been virtually stopped) C-face growth rate did not further increase. While there is evidence that surface diffusion is an important factor (17) G. W. Seam, in ref. 2.

Vol. 65

in growth from the vapor phase (e.g., ref. 8, IS), however, rapid surface flow of solute on crystals growing from concentrated solutions seems more difscult to justify.

V. Conclusions The major conclusions drawn from this investigation are the following. (1) Surfactants increase the supersaturation level a t which adipic acid crystals can be grown from seeds without occurrence of secondary nucleation, apparently by poisoning sub-critical embryos or heterogeneous nuclei. (2) All of the additives studied greatly modify adipic acid crystal habit and relative growth rates on different crystal faces by adsorbing in a specific manner. The anionic surfactants adsorb far more extensively on the A and B faces than on the C faces. The cationic surfactant adsorbs only to the extent of one monolayer, and apparently adsorbs more strongly on the C faces than on the A and R faces. (3) The effects of additives on growth rate are strongly dependent on additive concentration and on supersaturation level (or growth rate itself), resulting in drastic effects a t low supersaturation levels and high additive concentration, but having very little effect at high supersaturation levels, regardless of additive Concentration. (4) Both anionic surfactants studied produce similar effects. Concentrations less than 25 mg./l. (corresponding to monolayer adsorption) have little effect on growth rate, but higher concentrations (at which very extensive multilayer adsorption on the A and B faces occurs) result in greatly reduced growth rate on the A and B faces, while a t the same time growth rate on the C faces increases by as much as fivefold over the rate without additive. Two possible explanations for the accelerated growth on the C faces due to anionic surfactants are: (1) creation of dislocations by additive incorporation; and (2) surface flow of solute from faces retarded by additive. ( 5 ) The cationic surfactant, with less than monolayer adsorption on all faces, virtually stops growth on the C faces a t all supersaturation levels and significantly decreases growth rate on the A and B faces. (6) Combination of the concepts of two-dimensional nucleation and growth from dislocations permits satisfactory correlation of the growth rate results. This proposed mechanism explains both the effect of supersaturation level and the effect of additive concentration on growth rate. The kinetics of additive adsorption also appear to be of importance, however, at least with anionic additivea. Acknowledgment.-The authors gratefully acknowledge the financial support of the Solar Energy Research Fund (in the form of Fellowship aid to the junior author), and of the Esso Education Foundation (in the form of a Research Award to the (18) M. Voimer and L EsterrP.nn. 2. PBvdk,7 , 13 (1921).

Oct., 1961

GROWTHRATEOF ADIPICACIDCRYSTALS WITH SWRFACZANTS

senior author), which made this study possible. The assistance of Mr. R. W. Swisher of the Monsarito Chemical Company in providing surfactant samples is appreciated.

DISCUSSJON A. C. ZEITLEMOYER (Lehigh University) .-We have reported that SDBS on graphite surfaces does not form more than one adsorbed layer. Hence, on a hydrocarbon surface, such as your A- and B-faces, similar adsorption characteristics would be expected. Fifty adsorbed layers seem very unlikely especially since the hydrocarbon portions of the SDBS would adsorb next to the A- and B-faces of the adipic acid crystals with the polar anion group outward surrounded diffusely by counterions. It seems unlikely that micelles (hydrocarbon tails turned in) could be adsorbed. A. S. MIcHAELs.--The apparent (and anomalous) high level of sorption of SDBS on the A- and B-faces would, we think, hardly be expected if these faces closely resembled the apolar surfaces of graphite or other hydrocarbow. We are prompted to wonder whether specific interactions between SDBS and the carboxyl groups of the adipic acid molecules located on the crystal surface, or in the adsorbed, hydrated layer adjacent to the crystal surface, may be contributory to sorption of the surfactant. The otmervation that the CMC of SDBS in saturated adipic acid solution is about onethird of the value in distilled water suggests that adipic acid-SDBS complexes, or “mixed micelles,” may form in the solution; perhaps a rather thick, hydrous, poorly ordered “mixed inicellar” layer is deposited on the A- and B-faces whose SDBS content is sufficient to account for such high level of surfactant sorption. LEO SHEDLOVSKY ( Colgate-Palmolive Company) .-To what extent is the surface tension method of estimating ndsorption suitable? Unless foam fractionation was estimated over the concentration range shown in the adsorption isotherms, the possibility of selective adsorption on adipic acid crystals may not be ruled out. Would this influenre the surface tension especially in the steep portion of the curve a t low concentrations and lead to uncertainty for such a method of calibration? A. s. MIcHAELs.-The use of surface tension measurements to estimate surfactant sorption on solid surfaces is

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unquestionably open to serious criticism when applied to commercial surfactants, which usually are mixtures of conipounds of differing interfacial activity. Since the surfactants used in this study were specially prepared, highly purified compounds, the surface tension technique appeared to be much less objectionable, although not completely defensible for this reason alone. The experimental facts that (a) foam-fractionation of quite dilute solutions (100 p.p.m.) of SDBS caused no significant change in solution surface tension, and (b) surface-tension analysis of adipic acid crystals containing sorbed SUBS yielded essentially the same surfactant content as estimated from the surface tension change of the contacting solution, lend confidence to our belief that the surfacetension technique for estimating s o r p tion is of reasonable accuracy for the system studied.

W. A. ZISMAN(Naval Research Laboratory).-At what pH were these experiments run? Also, might there have been inorganic impurities in the distilled water used. I n dealing with carboxylic acids there is aln ays the possibility that any multivalent metallic ion present will form a film of insoluhle soap. The formation of insolut)le carhoxylates uould be promoted above a pll of 2 or 3. In these experimerits such soaps could form on the single crystals of adipic acid and inhibit or restrict crystal g r w t h . However, any water soluble surface active agents present, such as an alkyl sulfate or sulfonate, might serve 119 a dispersing or solubilizing agent to remove the insoluble carboxylate from the crystal face and so let it resume growing. A. S.hfrcHA~~s.-In all cases, crystals were grown from pure, aqueous adipic acid solutions in the absence of added strong acid or alkali. Since the ionization constant of adipic acid is approximately 4 X 10-5, and since saturated solutions are roughly 0.2 molar, the p H of the solutions wm approximately 5.3. Because of the large ratio r?f un-ionized to ionized acid in these solutions, they are quite highly buffered, and the pH is virtually invariant over the range of conditions studied. No specific attempts were made to avoid multivalent cation contamination beyond use of low-conductivity distilled water. However, the process of moltistep recrystallization of the adipic acid used for crystal growth measurements should have allowed removal of anv insolulilr carboxjlate salts formed hy the presenw of t r a m of such cations