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nonionic surfactant that the limit of solubilization was one dye molecule per surfactant micelle. He recently suggested2 that if this limit were general, it could serve as the basis of a new method of determining micellar molecular weights. One would merely have to saturate an aqueous surfactant solution with a “water-insoluble” dye, filter to remove unsolubilized dye, and measure the absorbancy. Combining this information with the molar extinction coefficient of the dye and the critical micelle concentration of the surfactant, one could then calculate the ratio of the moles of aggregated surfactant (total moles of surfactant minus that present at the critical micelle concentration) to moles of solubilized dye. This ratio would represent the average number of surfactant molecules (ions) per micelle, i.e., the aggregation number. Since the calculation would not be charge dependent, the method would have a decided advantage over techniques such as light scattering and ultracentrifugation where this is not the case. Although Schott’s dye solubilization procedure gave aggregation numbers for two nonionic detergents which agreed well with values provided by light scattering, it yielded an aggregation number for sodium decylsulfonate some seven times larger than that rendered by light scattering.s The light-scattering value is undoubtedly low, since no correction for micellar charge was made. However, it is extremely unlikely that a charge correction could reduce the disagreement significantly. Schott2stated that a possible source of error in the dye solubilization procedure is the assumption that the solubilization ratio, Le., the number of micelles per solubilized dye molecule at saturation, is unity. He subsequently dismissed this possibility, at least in the case of sodium decylsulfonate, by pointing out that a solubilization ratio smaller than unity would increase the discrepancy between the dye solubilization and light-scattering aggregation numbers and by remarking that “solubilization ratios greater than one are extremely unlikely for highly purified detergents.” It is my view that the assumption of unit solubilization ratio is the weak point in the dye-solubilization procedure for calculating aggregation numbers. A unit solubilization ratio may be a good approximation for the nonionic detergents used by Schott, but it cannot be valid generally. Kinetic considerations force one to conclude that the micelle is a dynamic entity whose size fluctuates about some equilibrium value. The ability of a surfactant monomer unit to enter into or leave the micelle structure must also be possessed by a dye molecule. The probability that a dye molecule will escape from the micelle in which it is solubilized in a specified time interval is not zero. The lower the barrier to escape, the shorter is the average time of residency of a dye molecule in a micelle, the greater is the fraction of “empty” micelles in solution, and the higher is the solubilization ratio. If the escape barrier is very high and there is room in each micelle The Journal of Physical Chemistry
for only one dye molecule, the solubilization ratio will be only slightly greater than unity. If the barrier is low, the solubilization ratio will be appreciably greater than unity. Presumably, the latter situation pertains in the sodium decylsulfonate solutions which Schott examined. Conditions are conceivable for which the solubilization ratio would be less than unity, Le., for which there would be on the average more than one solubilized dye molecule per micelle. Whereas a spherical micelle might not be able to accommodate more than a single dye molecule, a rod-like micelle would not be so restric ted. Schott2 found aggregation numbers of 128, 124, 131, and 101 by his dye-solubilization procedure for micelles of sodium lauryl sulfate in 0, 0.03, 0.10, and 0.40 m sodium chloride, respectively. The first three values are somewhat larger than those obtained at corresponding sodium chloride concentrations by other investigator~.~ The last value, however, is appreciably lower than all published aggregations for the surfactant in 0.40 m sodium chloride. The drop in aggregation number when the sodium chloride concentration is increased to 0.40 m is contrary to the usual observation4-’ that the addition of simple salts to solutions containing ionic surfactants is accompanied by an increase in the aggregation number. I suggest that Schott’s experiments with sodium lauryl sulfate are best explained by solubilization ratios greater than unity in the dilute sodium chloride solutions and a ratio less than unity in the 0.40 m sodium chloride solution. I n other words, the ratio has some dependence on the supporting electrolyte concentration. (1) H.Schott, J. Phys. Chem., 68,3612 (1964). (2) H.Sohott, ibid., 70, 2966 (1966). (3) H.V. Tartar and A. L. M. Lelong, ibid., 59, 1185 (1955). (4! See Figure 8 in E. W.h a c k e r , R. M. Rush, and J. 8. Johnson, ibad., 68,81 (1964). (5) K.Granath, Acta Chem. Scand., 4, 103 (1950). (6) J. N. Phillips and K. J. Mysels, J. Phys. Chem., 59, 325 (1955). (7) W. Prins and J. J. Hermans, Koninkl. N e d . Akad. Wetenschap. Proc., B59, 298 (1966).
DEPARTMENT OF CHEMISTRY E. W. ANACKER MONTANA STATEUNIVERSITY BOZEMAN, MONTANA59715 RECEIVED SEPTEMBER 5, 1967
Reply to Comments on the Paper “Solubilization of a Water-Insoluble Dye as a Method for Determining Micellar Molecular Weights,” and Remarks on Molecular Weight Determination of Charged Micelles by Light Scattering
The solubilization limit of one molecule of Orange OT per micelle was found for the nonionic detergents
Sir:
COMMUNICATIONS TO THE EDITOR l-dodecanol-28 ethylene oxide units, Clz(EO)zS,' C12and NPh(EO)30,8 where NPh is branched nonylphenol. 'This was shown by the agreement of the micellar molecular weights (mmw) determined by dye solubilization, calculated on the assumption of unit solubilization ratio, with the mrnw determined by light scattering or ultracentrifugation. Micelles of Cls(E0)is were found to contain three dye molecules at saturation, since the mmw determined by light scattering was 2.99 times greater than the mmw calculated from dye solubilization on the assumption of unit solubilization ratio. This is due to the larger hydrocarbon core of micelles of the latter detergent (calculated radoius, 24 d) as compared to radii between 15 and 18 A calculated for the hydrocarbon cores of micelles of the three previous detergents. Disagreement between mmw determinations by dye solubilization and by light scattering is found for charged micelles of anionic2 and cationic3 detergents in water and at low concentrations of supporting electrolyte. Dye solubilization measurements indicate that the mmw values of sodium decanesulfonate (SDS03), sodium dodecyl sulfate (SDS),a dodecyl trimethyl ammonium bromide (DTAB), and cetyl pyridinium chloride (CPyC)3 are essentially constant and independent of the concentration of added electrolyte, up to the point where the micelles show appreciable polydispersity according to equilibrium ultracentrifugation.4 At that point, there is a slight decrease in mmw, probably indicating a rearrangement of the micelles. Light-scattering measurements, on the other hand, indicate an apparent increase in mmw with increasing electrolyte concentration until this concentration becomes high enough to suppress or swamp the effective charge of the micelles. At that point, further increase in electrolyte cowentration produces no further increase in mmw (see references listed in ref 4). The dyesolubilization mrnw of SDS and DTAB at electrolyte concentrations low enough to leave the micelles predominantly r n o n o d i ~ p e r s eare ~ ~in~ good agreement with the light-scattering mmw determined in swamping electrolyte.4 To account for the discrepancy in mmw of ionic detergents at less than swamping electrolyte concentrations, Anacker suggests that the solubilization ratio depends on the concentration of added electrolyte. This seems unlikely in view of the following. The dye has negligible solubility in water and in solutions of NaCl and Na2SOc (less than 2 X lo-* mole/l.), probably because the hydroxyl is internally hydrogen bonded to the azo group, but is moderately soluble in solvents of low or medium polarity. Therefore, the solubilized dye molecules are probably located in the hydrocarbon core of the micelles, out of contact with the aqueous phase. An alternative explanation for the discrepancy is given by Hutchinson's treatment of light s ~ a t t e r i n g . ~Hutch-
38 1 inson concludes that (a) light-scattering measurements of charged micelles in solutions containing little or no supporting electrolyte give information on the charge rather than on the size of the micelles; (b) the correct mmw is obtained by light scattering only in the presence of swamping electrolyte, where the situation is essentially nonionic; and (c) the mmw is unchanged by the addition of electrolyte. This points to the need for much more extensive corrections in interpreting light scattering by multicomponent systems involving charged particles than are presently made, a viewpoint which has received considerable support The concept of a small, constant, and integral number of solubilized molecules per micelle at saturation, independent of the concentration of detergent and of added electrolytes, was established by G. Spencer Hartley thirty years ago.1° For Orange OT, we found this number to be unity for all detergents mentioned here, except for Cls(EO)ls and CPyC, where it is 3. This concept can readily be reconciled with Anacker's kinetic considerations if one considers that the solubilized dye molecules act as nuclei for micelle formation. When a micelle containing a dye molecule dissociates, most likely a few detergent molecules remain attached to this dye molecule. This aggregate then acts as the nucleus around which another micelle forms. The reason why light-scattering determinations of the mmw of charged micelles at less than swamping concentrations of supporting electrolyte are low is probably connected with the downward curvature occurring in the light-scattering plots of polymeric polyelectrolytes at low concentrations. Plots of the kind shown in Figure 1, where H is an optical constant, T the turbidity, and c the polymer concentration, have been reported for a variety of polyelectrolytes such as sodium polymethacrylate," bovine serum albumin,12 phosphotungstic,13 and silicotungstic a ~ i d s . ~ J Going ~ J ~ from swamping concentration of added salt to 0.1 M and to water results in progressively steeper decreases in H C / T with decreasing polyelectrolyte concentration, (1)H.Schott, J. Phys. Chem., 68, 3612 (1964). (2) H.Schott, ibid., 70, 2966 (1966). (3) H.Schott, ibid., 71,3611 (1967). (4) E. W. Anacker, R. M. Rush, and J. S. Johnson, ibid., 68, 81 (1964). (5) E.Hutchinson, J . Colloid Sci.,9, 191 (1954). (6) A. Vrij and J. Th. G . Overbeek, ibid., 17,570 (1962). (7) R.K. Bullough, Proc. Roy. Soc. (London), A275, 271 (1963). (8) E. F. Casassa and H. Eisenberg, Advan. Protein Chem., 19, 287 (1964). (9) J. P. Kratohvil, L. E. Oppenheimer, and M. Kerker, J . Phye. Chem., 70, 2834 (1966). (10) G.S. Hartley, J. Chem. Soc., 1968 (1938). (11) A. 0 t h and P. Doty, J. Phys. Chem., 56,43 (1952). (12) P.Doty and R. F. Steiner, J . Chem. Phys.,20,85 (1952). (13) M.Kerker, J. P. Kratohvil, R. H. Ottewill, and E. Matijevic, J. Phys. Chem., 67, 1097 (1963). (14) M.J. Kronman and 8. N. Timasheff, ibid., 63, 629 (1959). Volume 76,Number 1
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gregates of detergent molecules. However, such small aggregates may be able to exert repulsive forces far greater in proportion to the repulsive forces exerted by micelles than their contribution to turbidity is in proportion to the turbidity caused by micelles, owing to binding of counterions in the latter.l5J8 Thus, the downturn in the Hc/r vs. c curve for detergents in water with decreasing detergent concentration would not be expected to occur at a very low concentration of micelles, ie., just above the cmc, but at a still lower over-all detergent concentration, where there is a very low concentration of submicellar aggregates as well. This latter concentration can only be reached below the cmc, Le., after disappearance of the micelles. This hypothesis explains (a) why Hc/r vs. c plots for ionic I I I 0 l0 20 30 association colloids in water do not show the downturn e, g./L at low concentration of micelles which is observed for Figure 1. Light-scattering plot for polyelectrolytes. low concentrations of nonassociated polyelectrolytes, and (b) why the light-scattering mmw of ionic micelles owing to strong repulsive forces between the p~lyions.'~ determined in water is from two to seven times smaller than the correct mmw, found by dye solubilization in Only the curve in swamping concentration of added salt water and at low electrolyte concentrations, and by light is linear over the whole range of polyelectrolyte concenscattering in swamping electrolyte. tration. Extrapolating the linear portions of the plots Since swamping electrolyte concentrations are of the in water to zero concentration results in intercepts with order of 0.1-0.3 M439and the cmc values of the common the ordinate which are from 3 to 6 times greater than the ionic detergents in water are about ten times smaller, the actual intercepts. Therefore, molecular weights calcuconcentration of nonmicellar detergent is far too small to lated from the extrapolated intercepts would be from swamp the effective charge of the micelles. three to six times too small. For light-scattering plots of detergents, one uses the concentration of micelles, Le., the over-all detergent (15) A.P.Brady and D. J. Salley, J . Am. Chem. SOC.,70,914 (1948). concentration minus the critical micelle concentration (16) K.J. Mysels and C. I. Dulin, J. Colloid Sci., 10,461 (1955). (cmc) , Since turbidity is proportional to the square of HANSSCHOTT U. S. FOREST PRODUCTS LABORATORY the mass of the scattering particle, the light-scattering MADISON, WISCONSIN53705 contribution of micelles will be far greater than that of RECEIVED OCTOBER30, 1967 monomers, dimers, trimers, and other submicellar ag-
The Journal of Physical Chemistry
