1404
PASUPATI MUKERJEE
by the coulombic interaction of the charges. A further factor favoring attraction of the two ions is the flexibility of the twelve carbon chain of the LSwhich can wrap itself around the surface of the quaternary ion. Molecular models show that this can be done with ease (Fig. 5). Finally, the resulting lowering of the dielectric constant of the medium separating the charges may have an additional effect. Since lauryl sulfate dimers are probably more rigid, because of the repulsion of the charged heads, than the monomers, the above mechanism for the formation of ion-pairs makes unlikely the formation of the charged triplet MLS2- (equation 3) already discounted on quantitative grounds. The change in free energy on ion-pair formation can be calculated from the equilibrium constant Kf for the process. Kf is the reciprocal of K, and has the values 3.3, 12.5, 18.5 and 21 for Ag+, (CH3)4N+, + lauryl sulfates, respec(C2H&N+ and (TZ-C~H,)~N
Vol. 62
tively, at 25". This corresponds to energy changes of 1.2, 2.5, 2.9 and 3.0kT, respectively, per molecule or 0.7, 1.5, 1.7 and 1.8 kcal. per mole. For the quaternary ammonium compounds the order of these energy values is as might be expected for the processes involved. The slight progressive increase in the homologous series from (CH3)4N+ to (nC3H7)4N+ presumably is due to a corresponding increase in the cohesive and interfacial energy contributions balanced by a decrease in the coulombic interaction brought about by increasing separation of charges. The values may also be compared to the estimated2 free energy of dimerization of LS-, namely, 5.5kT. Acknowledgment.-This work was supported by the Office of Naval Research under Project NR 356-254 and was presented as part of the 10th technical report of this project. Reproduction in part or in whole for purposes of the United States Government is permitted.
DILUTE SOLUTIONS OF AMPHIPATHIC IONS. IV. SOME GENERAL EFFECTS OF DIMERIZATION1 BY PASUPATI MUKERJEE~ Department of Chemistry, University of Southern California, Los Angeles 7, California Received September 16, 1967
B
Some of the literature data are reviewed in terms of the finding that amphipathic ions tend to form dimers. uantitative agreement is found with conductivity and osmotic coefficient measurements on dodecylsulfonic acid and wit solubility measurements on dodecylamine thiosulfate. The irreversible dimerization and trimerization previously proposed by Kraus and co-workers on the basis of high dilution conductivity measurements are examined critically and a reinterpretation of the data in terms of reversible dimerization is proposed which leads to structurally reasonable consequences.
In the preceding papers of this series various lines of evidence based on new experimental data for several salts of the lauryl (dodecyl) sulfate ion (LS-) were used to show that in dilute solutions it dimerizes reversibly to form LS2- ions and also that with quaternary ammonium salts it forms, reversibly again, ion pairs such as (n-pr~pyl)~NLS. Both of these reactions were explained in terms of the reduction of interfacial energy as hydrocarbon parts of two ions amalgamate. In the present paper these ideas will be applied to some already known facts from previous measurements by others in order to show that dimerization is a rather general phenomenon in solutions of amphipathic ions and that it helps to correlate a number of previously unexplained observations. Unfortunately the number of measurements which can be used to test the idea of reversible dimerization is not large. This is due in part to the difficulty of obtaining values of the required accuracy and precision, and in part to the earlier emphasis on concentrated and hydrolyzing systems whose interpretation is too difficult, and to the more recent. emphasis on more dilute but still micellar systems. Because of the complications stemming (1) Based in part on the Ph.D. dissertation of P. Mukerjee, University of Southern California, 1957, and presented a t the Kendall award symposium honoring P. J. W. Debye at the Miami meeting of the A.C.S., April, 1957. (2) Department of Chemistry, Brookhaven National Laboratory, Upton, Long Island, New York.
from hydrolysis and from the precipitation of illdefined hydrolytic products, the work on soaps of carboxylic acids will not be considered although it led to the original ~ u g g e s t i o n of s ~the ~ ~ existence of dimers. Only non-hydrolyzing systems will be discussed. More specifically, we will consider the conductivity and colligative properties of dilute laurylsulfonic acid, the solubility of dodecylamine thiosulfate, and the body of conductivity measurements which led Kraus, et al., t o suggest the irreversible dimerization of cationics.6-' Conductometric Studies.-The work of Wright, et CZZ.,~ on some sodium alkyl sulfonates, although not carried out with any particular attention to very dilute solution, was one of the first to draw attention to the fact that the conductivities of some of these substances do not conform to the DebyeHuckel-Onsager theory. Their plots of the equivalent conductivities A against the square root, of concentration exhibited lower slopes than expected (Le., the A values were higher). This qualitative fact was emphasized later by M. E. L. McBain, et al., who studieds the homologous members of the (3) P.Ekwall, Kolloid Z.,80,77 (1937). (4) J. Stauff, ibid,, 96,244 (1941). (5) E.J. Bair and C. A. Kraus, J . A m . Chem. Soc., 78, 1129 (1951). (6) D. W.Kuhn and C. A. Kraus, ibid., 74, 3676 (1950). (7) M.J. McDowell and C . A. Kraue, ibid., 78, 2173 (1951). (8) K. A. Wright, A. D. Abbott, V. Siverta and H. V. Tartar, ibid., 61, 549 (1939).
Nov., 1958
GENERAL EFFECTS OF DIMERIZATION OF AMPHIPATHIC IONS
alkyl sulfonic acids. These authors report values up to high dilutions (10-4-10-3 M) and although their experimental technique did not give a high accuracylo they established well the qualitative fact of conductivities higher than expected from the Onsager theory. The explanation suggested by M. E. L. McBain, et uL19and by J. W. McBain" involved the formation of small ionic micelles. We have discussed in the first paper how extremely unlikely it is that such ionic micelles exist in dilute solutions of NaLS. The same arguments hold here, and again reversible dimerization can explain the observed behaviors qualitatively since the conductivities are higher than expected, just as for NaLS. Quantitatively, the available data are usually not sufficient to' make calculations meaningful. The data for laurylsulfonic acidg provide, however, a somewhat stringent test of the theory because of the pronounced deviations they exhibit. The data, plotted in Fig. 1, have been converted from the molal scale employed by the authors to t.he molar scale by assuming the density of these dilute solutions to be the same as that of water a t 25.00". The data were extrapolated to infinite dilution by giving equal weight to all the data, even for the most dilute solutions. From the value obtained, 372.9, the value for H+ a t 25" (349.812)was subtracted to give the conductivity of the lauryl sulfonate monomer at infinite dilution. The mean values of the dimerization constant K D (1.0 X lo3) and of the conductivity of the dimer at infinite dilution (31.4) were obtained by the procedure employed for NaLS (Paper I). The continuous line drawn through the experimental points, in Fig. 1, was calculated from these values using the assumptions previously employed. Considering the uncertainty of the experimental data and the approximations of the theory, the agreement can be considered as satisfactory. The absolute values of the constants employed and hence the actual position of the calculated curve are quite uncertain because they depend strongly on the extrapolated value, so that the data in the dilute solutions, which are least reliable, assume the greatest importance. However, the important and curious features of the data-pronounced deviation from the simple theory, the sudden change in slope, and the crossing of the Onsager line-are all reproduced by the calculated curve and explained on the basis of the monomerdimer equilibrium. The change in slope arises from the fact that the K D is high so that about half of the monomers are dimerized at about 0.001 M. Beyond this concentration the rate of increase of the fraction dimerized decreases progressively and cannot balance the effect of the increasing ionic strength on the mobility of the ions (9) M. E. L. McBain, W. B. Dye and S. A. Johnston, i b i d . , 6 1 , 3210
(1939).
(10) The conductivity of the inyristyl acid, for example, had to be changed later by almost 2% (M. E. L. McBain, J . Colloid Sci., 10, 223 (1955)). (11) J. W. McBain, "Colloid Science," D. C. Heath and Co., Boston, Mass., 1950. (12) H. 9. Harned and B. B. Owen, "The Physical Chemistry of Electrolyte Solutions," 2nd Edition, Reinhold Publ. Corp., New York, N. Y . , 1950.
1405
370
4365
360
1 I
0
I
I
I
5
I
I
I
I
10
d m . Fig. 1.-The ex erimental equivalent conductivities of lauryl sulfonic .aciBaccording to M. E. L. McBain, et ~ l . , ~ as compared m t h the Onsager theory and with calculations based on reversible dimerization.
which finally leads to the crossing of the 1-1 Onsager slope. The mixture effect13was neglected in this calculation although it is much greater in the present case because of the high mobility of the H+ ion. M solution it amounts to 1.6, Thus in 6.1 X ie., to 0.45%. Furthermore, as has been discussed already,14K D probably increases slightly with concentration in this range. Both factors lower the theoretical curve at higher concentrations and thus tend to improve agreement with experimental data. It should be mentioned that a specific attempt was made by Scott and Tartar15to examine whether the deviations from the simple theory are real or not in the case of association colloidal electrolytes. They found that sodium ethyl benzenesulfonate behaved approximately according to the theory for 1-1 electrolytes. As will be pointed out below this is not necessarily incompatible with a reversible dimerization. More important, the ethylbenzene sulfonate does not have a long enough chain to make extensive dimerization likely. Colligative Properties.-The osmotic coefficients of many association colloidal electrolytes have been measured by McBain and ~ o - w o r k e r s . ~ J ~Be-~~ cause of experimental difficulties these investigators seldom have gone below 0.001 M. Most of the measurements have one striking feature in common: below the critical micelle concentration the values of the osmotic coefficients are less than the values predicted by the Debye-Huckel theory. Although this theory does not apply a t such high concentrations, all deviations expected and found for strong 1-1 electrolytes are in the opposite direction. Thus salts of amphipathic ions do not seem to behave as typical simple strong electro(13) L. Onaager and S. K. Kim, THISJOURNAL, 61, 215 (1957). (14) Paper I1 of this series, P. Mukerjee, i b i d . , 62, 1397 (1958). (15) -4.B. Scott and H. V. Tartar, J . A m . Chem. Soc., 65, 692 (1943). (16) S. A. Johnston and J. W. McBain, Proc. Roy. SOC.(London), A181, 119 (1942). (17) M. N. Fineinan and J. W . McBain, J . Phys. Colloid Chen., 62, 881 (1948). (18) J. W. McBain and 0. E. A. Bolduan, THISJOURNAL, 47, 94 (1943).
PASUPATI MUKERJEE
1406
Vol. 62 I
3
.j0.98 8
4 0.96 1 0
0.94
1
',
,
,
;MERlZATON'\\\P,]
4
2
0
6
8
d5sF. Fig. 2.-The experimental osmotic coefficient from freezing point lowering of laurylsulfonic acid solutions according to M. E. L. McBain, et al.: as compared with the DebyeHuckel theory and with calculations based on reversible dimerization. Dotted lines show deviations expected from . theory in real solutions as indicated by NaC1.
6 -
P 0.
2 x4
Q
-
P
1
=
51 ZZi%i
a = 1.122 at 25O, mi is the concentration of the ionic species i, and zi its valence. The solid lines of Fig. 2 have been calculated according to this equation for a simple 1-1 electrolyte and for a dimerizing one using K D = 5 X lo2. Experimental values for NaCl which should conform to the upper line are also shown and give a measure of the deviation from ideal equations to be expected in this region. If both lines are now corrected by the same amount so as to bring the 1-1 line in accord with the NaCl data, it may be seen that the dimerization hypothesis accounts quantitatively for the behavior of the amphipathic ion within the experimental uncertainty. This value of 5 X IO2 for K D is probably not significantly different from 1 X lo3which was obtained above from the conductivity data of this compound at 25". Solubility Measurements.-The solubility of a simple salt in the presence of common ions is determined by its solubility product constant. Neglecting activity coefficients, this is given directly by the concentration product of the two ions in the saturated solution. For salts of amphipathic ions, if dimerization occurs, the product thus obtained, K,, should not be constant since a fraction 2 a of the measured concentration, car is dimerized, and only the monomeric ions participate in the equilibrium. Hence the true solubility product constant is Ksp
ca(l
- 201). X cC = K p ( l - 201)'
where cc is the Concentration of the x valent counterion. In turn CY is related directly to the dimerization constant by KD = a/cs(l
- 201)'
Hence if K8, and K D are constant, the simple product K , should increase as the concentration of am0 phipathic ion increases in the saturated solution, 0 0.004 0.008 0.012 and vice versa. Concn. of dodecylammonium bromide. The only available pertinent measurements are Fig. 3.-The solubility product of dodecylamine thio- those of Kolthoff and Johnson20who measured the sulfate calculated from data of ref. 20, assuming: 0,no solubility of dodecylammonium thiosulfate in the dimerization; 0 , dimerization with KD = 120. presence of the corresponding bromide. Results lytes. Since the formation of dimers always lower * below the c.m.c. of the latter are suitable for our the osmotic coefficient, it is again in qualitative purposes. As shown in Fig. 3 the product K , calagreement with the facts. On the other hand, as culated directly from the measured solubility20inwas mentioned already in the first paper, the devia- creases by much more than the scatter of the data tions from the theory do not increase sufficiently and than the analytical uncertainty estimated by the authors. The increase is also much more than with concentration to permit higher aggregate. The uncertainties of the osmotic coefficient data could be accounted for by a change in activity make quantit,ative calculations meaningless in coefficients of simple ions, which could give an inmost cases. The freezing point data of dode- crease of at most 20% over the range of concentracylsulfonic acid? however, are precise enough t o tions involved. On the other hand if a dimerizapermit a quantitative test. These osmotic coef- tion constant K D = 120 is assumed and the soluficients are plotted in Fig. 2. The uncertainties are bility product K,, recalculated in terms of monocomputed from the uncertainties of the measure- meric ions, the values show no trend although they ments as reported by the authors. still scatter more than the analytical error. The generalized Debye-Huckel equation for the Irreversible Dimerization.-Since dimerization is presumably favored by the reduction of interfacial osmotic coefficient g of a mixed electrolytelgis energy and opposed by the repulsion of the charged where (19) E. A. Guggenheim, "Thermodynamics." North Holland Publiehing Co.,Amsterdam, 1949.
(20) I. M. Kolthoff and W. F. Johnson, J . Am. Cham. Soc., 74, 20 (1952); also W. F. Johnson, Ph.D. dissertation, Univ. of Minnesota 1949. The values of solubility product there reported do not agree exactly with the one8 we obtain from their solubility data but they show the same trend.
Nov., 1958
GENERALEFFECTS OF DIMERIZAT~ON OF AMPHIPATHICIONS
heads, it is obvious that increasing chain length should favor dimerization. Kraus and co-workers, in a series of papers on conductivities of alkyltrimethyl quaternary salts,~-’ advanced the idea that there is no dimerization a t all until the chain length reaches 14 and that there is complete dimerization for 16 and 18 carbons in the chain and trimerization for one 16 carbon chain compound with a particularly bulky polar group. The evidence came from the slopes of the equivalent conductivity lines. Even if “no” dimerization is interpreted as “less than 10%’) dimerization and “complete” dimerization as “over 90%” dimerization, and if these are to hold only over a tenfold range in concentration, the above hypothesis implies a more than thousand-fold change in the dimerization constant for a two carbon atom change in chain length. This implies a change in standard free energy of 7kT per dimer or over 4 kcal. per mole of dimer. It is difficult to see how such a small change in structure could give such a large change in energy. The complete removal of a methylene group from water has been estimated at about l.lkT,21and the total repulsive energy in water of two charges separated by 7 A. (the length of only 6 carbon atoms) is about 1kT. Furthermore, as already discussed in the first paper, a trimer is unlikely on structural ground and, again, the sudden complete change from dimer to trimer or upon making the polar head bulkier seems unlikely. On the other hand, while reversible dimerization leads to a low slope of equivalent conductivity in NaLS solutions, it seems plausible that it may lead to high slopes in solutions of quaternaries. We may recall that the low slope of equivalent conductivity in NaLS was the result of the gradually increasing proportion of the dimer which itself had a higher conductivity and higher slope than the monomer. This case is shown schematically in Fig. 4A. The higher slope of the dimer is required by its higher charge according to the Onsager theory (unless its conductivity is very much lower) but the conductivity depends on structural considerations and could, for,other ions, be equal or lower than that of the monomer. This would lead to the resultant conductivities indicated in Figs. 4B and C. In all cases of Fig. 4 the conductivity of the equilibrium mixture is an S shaped curve. Its middle portion closely approaches a straight line having a slope which may be lower or higher than the Onsager slope for a 1-1 or a 1-2 electrolyte. Frequently it is only this middle portion that is available for observation and interpretation. The first curvature may be in the too dilute region and the second may be either above the c.m.c. or above the solubility limit or at concentrations too high for the Onsager theory to apply. On the basis of reversible dimerization it is thus possible, by assuming proper constants, to calculate curves which closely approach straight lines of high slope over considerable ranges of concentration, Now the relative conductivity of the monomer and of the dimer depends on the relative compactness and symmetry of the shapes assumed by them (21) J. Th. G. Overbeek and D. Stigter. Rsc. bau. chim., 76, 1204 (1956); K. Shinoda, Bull. Chem. Soc. Japan, 46, 101 (1953).
1407
Fig, 4.-Schematic presentation of the effect of the relative conductivity of the dimer upon the observed slopes: 1, equivalent conductivity of monomers; 2, of dimers; 3, of the equilibrium mixture; A, dimer much more conducting; B, slightly more conducting; C, less conducting.
in solution. The shape of the dimer will necessarily be quite elongated to permit the two charged heads to be as far apart as possible. The monomer will have a coiled chain which will result in an elongated structure if the polar head is to be exposed to water but may be highly symmetrical if the head can act as a center for this coil. The sulfate head is clearly hydrophilic and should remain exposed. On the other hand, the weakness of (CH&NLS indicates strongly, as was shown in the preceding paper and will be again discussed elsewhere, that there is considerable tendency for the long chains to coil around the methylene surface of the quaternary head. Hence, while the LS- monomer should be elongated, the quaternary one should be very compact and symmetrical. In the former case the formation of dimer should (and does) lead to higher conductivity, while in the latter it may well lead to a lesser equivalent conductivity, as would be required to give the higher slopes of Fig. 4B and C and as found by Kraus, et al. This line of reasoning is supported by the fact that Kraus, et al.,6,22found, as expected, that small symmetrical quaternary ions offer a lower hydrodynamic resistance than the unsymmetrical ones having the same number of carbon atoms. They also found, however, that when the number of carbon atoms increases and the chain length exceeds 7 the situation is reversed, the long chain ions offering less resistance than the symmetrical ones of same total number of carbon atoms. This points strongly to a very tight coiling of the long chain around the polar head. Incidentally, the simple fact that a lower friction factor is possible for the same.volume, shows that the shape of the symmetrical quaternaries differs significantly from spherical. Consideration of models suggests that it is a “spiky” tetrahedron. On the other hand, the C12 sulfate ion offers a hydrodynamic resistance closer to the Cld-trimethy1 than to the Cl2-trimethyl quaternary ion (Ao = 21.6, 21.13 and 22.48, respectively6). The contribution of the two polar heads can only be estimated at present from their dry volume, which gives a definitely Iafger radius of 3.5 A. for the trimethyl group than the 2.9 A. for the sulfate. Since for anions of this ~ ~ ~ ~ ~ ~small, the size hydration is g e n e r a l l considered polar head of the sulfate should offer less resistance. To give a larger over-all resistance, the C12 chain must be less symmetrically arranged in the (22) M. J. McDowell and C. A. Kraus, J. Am Chem. Soc., 73,2170 (1961). (23) E. Glueckauf, Trans. Faraday SOC.,61, 1235 (1955). (24) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” Academic Press, Inc., New York, N. Y., 1955.
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A. C. CHATTERJI AND R. N. SINGH
VOl. 62
sulfate as required by our interpretation. of long-chain trimethyl quaternaries at the same In our view, the observed slope depends prima- point between C14 and CIS where the slopes became rily on the relative conductivities of the monomer abnormally large. These limiting values were oband dimer and should increase as the bulkiness of tained by direct extrapolation using the large exthe polar heads makes the dimer less compact and perimental slope. In our view, on the other hand, symmetrical. This is confirmed by the facts since the extrapolation should be conducted along the the abnormal slopes found by Kraus seem to in- S-shaped curve which tends to the lower, 1-1 Oncrease with the bulkiness of the heads, being 137, sager slope. This leads necessarily to lower limiting 139 and 150 for the CIStri-methyl, -ethyl and -pro- conductances and would a t least reduce the repyl, respectively. The 2-1 Onsager slopes, on the ported discontinuity. other hand, decrease slightly in this series. In the Acknowledgment.-The author acknowledges CISseries the slope increases even more markedly gratefully the help and encouragement of Profesfrom 142 for the trimethyl to 210 for the tributyl sor Karol J. Mysels throughout the work and durhead. The comparison of the two series is not ing the preparation of the manuscript. simple because the additional factor of different This work was supported by the Office of Naval chain length and therefore different dimerization Research under Project NR 356-254 and was preconstant comes in, so that a different portion of the sented as part of the 10th technical report of this S-shaped curve probably is observed. project. Reproduction in part or in whole for purFinally, it may be noted that Kraus, et al., found poses of the United States Government is pera discontinuity in tAe limiting conductance values mitted.
NUCLEATION FROM QUIET SUPERSATURATED SOLUTIONS OF ALKALI HALIDES. PART I. POTASSIUM AND AMMONIUM CHLORIDES, BROMIDES AND IODIDES BY A. C. CHATTERJI AND RAMNARESH SINGH" Department of chemistry, University of ,heknow, India Received January 6 , 1968
The kinetics of precipitation of KC1, KBr, KI, "&I, NH4Br and NHJ from their quiet supersaturated aqueous solutions has been investigated using electrical conductivity measurements at 35.00 f 0.002'. The maximum time 0 required where for the first indication that precipitation has occurred is in fair agreement with the relation log e 0: l!log* (XIX,), X and XOare the mole fractions of solute in supersaturated and saturated salt solutions a t 35", respectively.
Introduction The purpose of our work has been to study nucleation in relatively unstable supersaturated solutions of crystalline substances, in which even if all nuclei are removed the solid phase separates after a limited time. As used in this paper the term "nucleation" includes the deposition of crystalline solids (phase 2) on dusts, metallic surfaces, other surfaces or their spontaneous formation in the bulk of the solution but excludes the deposition on the surfaces of the same material. The start has been made from the aqueous solutions of cubic crystals of alkali halides. The experiments on nucleation of KC1, when none of the foreign nucleating crystals were added, have also been repeated because of the experimental uncertainties in the previous work done by Preckshot and Brown. The waiting time e taken by a nucleus to formin the bulk of solutions is assumed to be a measure of the frequency of nucleus formation. For the case of spontaneous, Le., homogeneous nucleation Preckshot and Brown1 have used the relation log e a 1/ log2 ( X / X o ) ,which applies strictly to isothermal measurements. To obviate this difficulty, ex* Radiochemistry Division, Atomic Energy Establishment, Trombay, India. (1) G. W . Preckshot and G. G. Brown, I n d . Ene. Ckem.. 44, 1314 (1951).
periments have been carried out at a fixed temperature and solutions of different supersaturations have been produced by dissolving calculated quantities of salt in water and bringing the solution to 35" for observations. Apparatus.-The conductivity bridge set was similar to that of Callendar and GrBith's bridge arrangement. Its sensitivity was 0.0004% when total resistance of the conductivity cell filled with saturated solution ranged in the vicinity of 2000 ohms. All resistances used were calibrated by Callendar and Griffith's Bridge (Type Cambridge L318022 with certificate of test) with respect to Croydon Precision Resistance Box (Type RBA4 No. 1627 with certificate of test) using direct current. The total length of bridge wire was kept 100 cm., the resistance of the wire at 35" being 0.13875 ohm/cm. The minimum could be determined with an accuracy of 0.5 mm. within a few seconds using 1000 c./sec. audio-oscillator (G.E. Cat. 7472242) as a source of current. Conductivity Cells.-The cell I (cell constant a t 35" = 645.21) used for studying nucleation was similar to that of Preckshot and Brown' except a few alterations. The electrodes were made of platinum foil and were fused completely with the walls (Pyrex) of the cel1.z Another simple cell I1 (cell constant at 35' = 91.957) was used for verification of specific conductivities determined by cell I. Before each experiment the cells were cleaned with warm chromic acid, steamed and dried by passing filtered air through them. Temperature Control.-Two thermostats were used. During conductivity measurements cells were housed in thermostat I, in which a bath of transformer oil was main(2) W.B. Campbell, J . Am. Chem. Soc., 61, 2419 (1929).
