1612
J. Phys. Chem. 1981, 85, 1612-1616
of the crystallites. The stresses induced by spreading probably play a role in the rupture and fragmentation of the crystallites and in the pit formation.
Appendix It is well-known that the stress needed to separate two atomic layers is very large and that in the presence of cracks it can be appreciably decreased. Griffith12 has derived the following expression for the critical stress uc needed to initiate crack growth: (12)Griffith, A. A,, Phil. Trans..R. Soc., Ser. A. 1920,221, 163.
where E is the Young elastic modulus, y is the surface tension, and r is a length characterizing the crack. Using E N 1OI2 dyn/cm2, y = lo3 dyn/cm, and r N lo-' cm, one obtains uc N lo1' dyn/cm2. For a crystallite of lo4 cm size the stress generated by wetting cannot be larger than about y/104 z1! lo9 dyn/cm2 which is small compared with uc 10l1dyn/cm2. For this reason we are inclined to believe that the oxidation occurring a t the tip of the crack, a process which is not accounted for in Griffith's derivation, plays an essential role in this case.
High-pressure Study of Micelle Formation in Aqueous Solutions of Sodium Perfluorooctanoate Gohsuke Sugiharaf and Pasupatl Mukerjee" School of Pharmacy, University of Wisconsin, Madison, Wisconsin 53706 (Received: December 1, 1980; In Final Form: February 24, 198 1)
Electrical conductivities of sodium perfluorooctanoate solutions have been measured at different pressures from 1 atm to 2000 kg/cm2 (1936 atm). The critical micellization concentration (crnc) increases with pressure up to -1200 atm and then decreases slightly at higher pressures. The differential conductivity below the cmc decreases nearly linearly with pressure, in qualitative accord with increasing viscosity. The differential conductivity above the cmc increases nearly linearly with pressure. This increase has been ascribed to an increasing degree of dissociation, a,of the micelles. Values of a have been estimated. For calculating the volume changes accompanying micelle formation from cmc data, AVmo,an approach based on the mass-action model has been formulated. The results from this approach differ from the charged phase separation model generally used. AVmofor sodium perfluorooctanoate is considerably higher than that of a comparable hydrocarbon surfactant. This higher value is attributed to more pronounced chain-water interactions for the fluorocarbon surfactant. A literature value for the AVmo of perfluorooctanoic acid has been shown to be consistent with a substantial amount of covalent bonding of the counterions with the head groups of micellized perfluorooctanoicacid.
Introduction In comparison to extensive and numerous investigations at atmospheric pressures, relatively few investigations on physical-chemical properties of surfactant solutions at high pressures have been carried 0 ~ t . l - l ~No high-pressure study has been reported on an important class of surfactants, namely, surfactants containing completely fluorinated chains. One of the major goals of high-pressure studies of equilibria is to estimate volume changes accompanying various processes and to relate these changes to other equilibrium properties. It is known that the volume associated with micelle formation is substantially greater for a perfluoro surfactant than for a corresponding hydrocarbon surfactant. This fact suggests that a highpressure study on micelle formation in solutions of a fluorocarbon surfactant might lead to a better understanding of pressure effects on micellar equilibria, and their theoretical interpretation. An additional interest arises from extensions of such studies to mixtures of hydrocarbon and fluorocarbon surfactants which are known to be highly nonideal in mixed micelles.14 Such studies are in progress. In this paper we present some electrical conductivity data on sodium perfluorooctanoate at several pressures. These t Chemistry Department, Fukuoka University, Fukuoka City 814-01,Japan
0022-3654/81/2085-1612$01.25/0
data are analyzed with special emphasis on the effect of pressure on conductances, on degrees of ionization of micelles, and on the critical micellization concentration (cmc). Methods of interpretation of cmc data for evaluating volume changes accompanying micelle formation (1)S. D. Hamann, J.Phys. Chem., 66, 1359 (1962). (2) R. F.Tuddenham and A. E. Alexander, J.Phys. Chem., 66,1839 (1962). (3)J. Osugi, M. Sato, and N. Ifuku, Nippon Kagaku Zasshi, 87,329 (1966);Reu. Phys. Chem. Jpn., 35, 32 (1965). (4)M. Tanaka, S.Kaneshina, T. Tomida, K. Noda, and K. Aoki, J. Colloid Interface Sci., 44, 525 (1973). (5)M. Tanaka, S.Kaneshina, A. Shinno, K. Okajima, and T. Tomida, J. Colloid Interface Sci., 46, 132 (1974). (6)S.Kaneshina, M. Tanake, T. Tomida, and R. Matuura, J. Colloid Interface Sa., 48, 450 (1974). (7) G. Sugihara, T. Ueda, S. Kaneshina, and M. Tanaka, Bull. Chem. SOC.Jpn., 50, 604 (1977). (8)S.Rodriquez and H. Offen, J. Phys. Chem., 81,47 (1977). (9)S. Kaneshina, M.Yoshimoto, H. Kobayashi, N. Nishikido, G. Sugihara, and M. Tanaka, J. Colloid Interface Sci., 73, 124 (1980). (10)N. Nishikido, M. Shinozaki, G. Sugihara, M. Tanaka, and S. Kaneshina, J. Colloid Interface Sci., 74, 474 (1980). (11)N. Nishikido, N. Yoshimura, and M. Tanaka, J.Phys. Chem., 84, 558 (1980). (12)N. Nishikido, N. Yoshimura, M. Tanaka, and S. Kaneshina, J. Colloid Interface Sci., in press. (13)N. Nishikido and M. Tanaka, Hyomen, 17,215 (1979). (14)P.Mukerjee and A. Y. S. Yang, J.Phys. Chem., 80,1388 (1976).
0 1981 American Chemical Society
The Journal of Physical Chemistry, Vol. 85, No. 11, 198 1
High-pressure Study of Micelle Formation
I
Molarity ( m o l / I ) x IO3
T
P X
IO
20
30
t
C
40
t'
50
60
D
1613
m0 401
im:
x
D
0
1000
Pressure ( k g / c m 2 1
2000
Flgure 2. Effect of pressure on the cmc of NaPFO at 30 OC, using molality and molarity scales.
u IO 20 30 40 50 M o l a l i t y ( r n o l / k g ) x IO3
72
i47
66t
i
t\
Flgure 1. Plots of specific conductivity of NaPFO against molar and molal concentrations. Molal scale: (A) 1 atm; (B) 2000 kg/cm2. Molar scale: (C) 1 atm; (D) 2000 kg/cm2. Cmc's are represented by arrows. Temperature, 30 OC.
using different theoretical models are also examined.
Experimental Section Perfluoro-n-octanoic acid (HPFO) was purchased from PCR Research Chemicals, Inc., Lot no. 8999. Solutions of the sodium salt (NaPFO) were prepared by neutralization with sodium hydroxide. Such fluorocarbon acids are known to be strong acids. The purity of NaPFO was assessed by surface-tension measurements above and below the cmc. No minimum was observed. Electrical conductivity measurements were made with a Beckman ac conductivity bridge, Model RC-MA, as reported earlier.14 Capacitance balance sometimes required the use of an additional external capacitor (General Radio Co.). Measurements at l and 3 k Hz gave indistinguishable resistance values. The high-pressure apparatus was nearly identical with one described earlier.' Kerosene was used as the pressure fluid, and a light-weight transformer oil was used as the fluid for the thermostat which was kept at 30.00 "C. Results and Discussion The specific conductivity ( K ) of NaPFO solution at all concentrations, below and above the cmc, was found to increase with pressure up to -1300 atm and then decrease with further increase in pressure. The conductivity above the cmc is in part affected by the change in the cmc with pressure. The conductivity of the micelles at different pressures is discussed later in this paper. From the intersection of the conductivity-concentration curves above and below the cmc at a constant pressure, the cmc can be determined in the usual manner. Figure 1 shows typical data at 1atm and at 2000 kg/cm2 (1atm = 1.033 kg/cm2) of the conductivity of NaPFO using both the molality and molarity concentration scales. The molarities were calculated from the experimental molality values by using density values of pure water at different pressures at 30 OC estimated from the extensive data of Bridgman.15 For the dilute solutions used here, this procedure was considered to be satisfactory. K was found to vary linearly with concentration both above and below ~
~~
(15) P. W. Bridgman, Proc. Am. Acad. Arts Sei., 48, 307 (1913).
41
0
1000
Pressure
2000
( kg / c m 2 )
Figure 3. Effect of pressure on dddc (A) above cmc and (B) below crnc.
the cmc on both concentration scales (Figure 1). Figure 2 shows the cmc data on the molality scale as also the molarity scale. These two scales differ significantly at high pressures, As seen in Figure 2, each curve exhibits a maximum at a certain pressure. Such maxima have been observed for several ionic surfactants including sodium dodecyl sulfate (SDS).14 Rodriguez and Offens have recently reported some cmc measurements on SDS using a naphthalene solubilization method which do not show such a maximum. This anomalous result may in part be due to the perturbation of the system by the additive naphthalene present in significant amounts. It is interesting to note that NaPFO and sodium decyl sulfate (SDeS) have similar cmc values at 1atm.15 The effect of pressure on the cmc of NaPFO, however, as determined here, is more than twice as high on a fractional basis as compared to published data on SDeSa6 Analysis of Conductivity Data. The differential conductivity, drldc, above the cmc, where c is the molar concentration scale, can provide some information about the degree of dissociation of micelles.la The influence of pressure on dK/dc is of considerable interest. Figure 3 shows that drc/dc above the cmc increases nearly linearly with pressure. The value at 2000 kg/cm2 is higher than that at 1 atm by nearly 7.2%. In contrast, dx/dc below the cmc decreases nearly linearly with pressure (Figure 3)) its value being reduced by -9.2% at 2000 kg/cm2 as (16) P. Mukerjee, K. J. Mysels, and P. Kapauan, J. Phys. Chem., 71, 4166 (1967).
1614
The Journal of Physical Chemistty, Vol. 85, No. 11, 1981
compared to the value of 1atm. This latter effect can be attributed only in part to the increase in the viscosity, q, of the medium. The viscosity of water at 30 "C, as estimated from published data,l'J* changes in a complex fashion with pressure. The effect on the viscosity of low pressures, up to -400 kg/cm2, is very small. At higher pressures, the viscosity increases nonlinearly, the value at 2000 kg/cm2 being higher than that at 1 atm by -8.9%. Thus, although the total change in dK/dc value below the cmc from 1atm to 2000 kg/cm2 is roughly consistent with the increase in Viscosity, the linear variation of dK/dc below the cmc with pressure indicates that other complex factors must be involved. In view of the increase in viscosity with pressure, and the overall decrease in the mobility of the single ions with pressure as reflected in the dn/dc values below the cmc, the increase in the value of dK/dc above the cmc with pressure indicates very strongly that the degree of dissociation of micelles16 increases with pressure. This result, of inherent interest, is also of significance in estimating free energy changes on micelle formation at different pressures, as discussed later. The increase in the degree of dissociation is consistent with the observed increase in the dielectric constant of water with pressure.lg The dielectric constant increases nearly linearly with pressure, the value at 2000 kg/cm2 being -8.2% higher than the value at 1 atm. At higher dielectric constants Coulombic interactions causing counterion association are expected to be weaker. I t has been found previously that dissociation constants of ion pairs also increase with pressure.20 In order to obtain a somewhat more quantitative estimate of the change in the degree of dissociation of micellar counterions ( a )with pressure, we have used an approach developed some years ago and applied to dodecyl sulfate micelles at 1 atm.16 Based on the usual assumption that dK/dc above the cmc measures the contribution of the micellar component alone to the conductance, i.e., the monomer concentration is constant above the cmc, the relation obtained is eq 1,where A+ is the equivalent condK/dC = &[A+ + F p ] (1) ductance of the counterion, Na+ in the present case, at the cmc, p is the electrophoretic mobility of the micelles, and F is the Faraday constant. Previous investigations have shown that, for some anionic and cationic micelles, the mobility is nearly independent of the nature of the surfactant, its value being primarily determined by the total ionic strength of the 1-1 electrolytes employed at the cmc.21 When this approach is used, the mobility of NaPFO micelles at 1 atm is estimated to be 3.85 X lo4 cm2 V-l s-l at 25 "C. If one assumes that the mobility varies inversely with viscosity over the small temperature range of 25-30 "C, the calculated mobility of NaPFO micelles at 30 "C is 4.30 X cm2 V-' s-l. When this figure for the mobility is used, a for NaPFO micelles is estimated to be 0.452 at 30 "C at 1 atm. This value is substantially higher than the value for SDS at 25 "C, which is -0.28. The effect of small variation in temperature on a is estimated to be small from similar analysis of some published data on temperature effects on dK/dc of SDSZ2 From this analysis, therefore, it appears that NaPFO micelles have a significantly higher degree of dissociation ~
(17) K. E. Bett and J. B. Cappi, Nature (London),207, 620 (1965). (18)R. A. Horne and D. S. Johnson, J.Phys. Chem., 70,2182 (1966). (19) K. R. Srinivasan and R. L. Kay, J. Chem. Phys., 60,3645 (1974). (20) S. D. Hamann, P. J. Pearce, and W. Strauss, J.Phys. Chem., 68, 375 (1964). (21) H. W. Hoyer and A. Greenfield,J.Phys. Chem., 61, 735 (1957). (22) E. D. Goddard and G. C. Benson, Can. J Chem., 36,986 (1957).
Suglhara and Mukerjee
w
0.58
0.56
B 0.54 0.52
I
I
0
1000 Pressure ( k g /cm2
2000
I
Flgure 4. Effect of pressure on a and p: (curve A) estimates based on eq 2; (curve B) estimates based on data from ref 26.
when compared to SDS micelles at low pressures. In the calculation of free energy changes on micelle formation using the mass-action m o d e P or ~ ~the ~ charged phase separation a quantity @ is frequently used. @ is obtianed from the variation of the cmc of an ionic surfactant with an added 1-1 neutral electrolyte containing a common counterion. When In (crnc) is plotted against In 2, where 2 is the total counterion concentration at the cmc, the curve is usually linear and p is the absolute value of the slope. @ is often interpreted as the degree of binding of counterions in a thermodynamic sense. For SDS, it was found previously16that, if a, determined from electrical conductivity data, is assumed to be the degree of dissociation, the value of 1- a, 0.72, is fairly close to the ex0.69. In the case of NaPFO, some perimental estimate of @, unpublished data on the effect of added NaCl on the cmc of NaPF026lead to a value of 0.56 for @. This figure is also close to the value of 0.55 calculated from the previously determined a. Since the values of @ at higher pressures are required for a thermodynamic analysis of the effect of pressure on the cmc of NaPFO, and since d@/dP,as discussed later, is of some importance, we have modified the analysis of the dxldc data above the cmc at high pressures slightly. We now assume that at 1 atm a equals 1 - @, namely, 0.44, rather than 0.45, obtained from the previous estimate of p. This slightly revised value of a leads to an estimate of 4.56 X 10" cm2 V-' s-l for the mobility of NaPFO micelles at 30 "C and 1 atm. This procedure is unlikely to affect the estimates of relative changes in a with pressure very much and allows the calculation of /3 at different pressure from the estimates of a. To determine the effect of pressure on a from dKc/dc data, one needs the effects of pressure on A+ and p in eq 1. The former has been determined in two ways. From some unpublished data on the effect of pressure on A+ of Na+ at infinite dilution, A+O, at 10 and 25 0C,26values of A+O at 30 "C were obtained by extrapolation using h+*v as the quantity which has a small temperature dependence. Changes in A+ at the crnc were assumed to be proportional to changes in A+O. In the second method, A+ at a pressure P was estimated from eq 2, where A is the equivalent A+(P) = A+(l)(AP/Al) (2) conductivity at the cmc of NaPFO and the subscripts 1 and P refer to 1 atm and higher pressures, respectively. Following the arguments presented earlier,16the variation in 1.1 with presure has been estimated by assuming p to be proportional to a and inversely proportional to q over the restricted ranges involved. We thus obtain eq 3. Figure (23) P. Mukerjee, A d a Colloid Interface Sci., 1, 241 (1967). (24) K. Shinoda and E. Hutchinson, J. Phys. Chem., 66,577 (1962). (25) P. Mukerjee and A. Y. S. Yang, to be published. (26) K. Pribadi and R. L. Kay, unpublished data; K. Pribadi, PhD. Thesis, Carnegie-Mellon University, Pittsburgh, PA, 1971.
The Journal of Physical Chemistry. Vol. 85, No.
High-pressure Study of Micelle Formation (dK/dc)p = ~ X + ( P + ) F 1 1 i ~ ~ ~ i / ( ~ i t l(3) ~)l 4 shows how the estimated cup varies with P. The two curves determined by using the two different estimates of show the range of uncertainty in cup. The increase in cup with pressure appears to be significant. As mentioned before, this increase is qualitatively consistent with the increase in the dielectric constant of the medium with pressure. It is also consistent with some previous considerations which indicate that the binding of counterions to micelles, resulting in high local concentrations, is likely to cause an increase in volume.z7 The electrostriction of the solvent caused by individual ions is reduced when the concentrations of ions increase^.^^-^^ Figure 4 also shows the variation in P with pressure estimated from the lower values of cup. Volume Changes on Micelle Formation. The calculation of the change in partial molal volume, AT,, accompanying formation of micelles from monomers from cmc-pressure data has usually been done by using the charged phase separation model.6 According to this model AT, = RT(1 + P ) [ d In (cmc)/dP]~ (4) R here is the molar gas constant and T is the absolute temperature. Many arguments suggest that a two-phase model for micellar solutions is inappropriatez3even for nonionic systems. For ionic surfactants, the meaning of a charged phase in conventional thermodynamic terms is not clear.23 We, therefore, propose an alternative approach using the mass-action model of micelle formation in ionic surfactants which has been analyzed in detail.16s23According to this model, the equilibrium between monomers and micelles can be represented by eq 5, nS- + PnNa+ + M-(l-B)n (5) where S- represents the anionic surfactnt, M represents the micelle, and n is the aggregation number of the micelle. The standard free energy of micelle formation per monomer unit, AGO,, according to this model is given by eq 6, AGo,/(R7') = In [S-] + P In [Na+] - ( l / n ) In [M-(l-fl)n] (6)
where the concentrations are expressed in mole fraction units, and the usual approximation of a constant n is made. If it is further assumed that the small fraction of the monomers micellized at the experimentally determined cmc is 2% and, therefore, the monomer concentration is 0.98 cmc, AGO, can be evaluated by using the cmc (eq 7). AG",/(RT) = (1 + P) In [0.98(cmc)] - ( l / n ) In [0.02(cmc)/n] (7) The corresponding volume change, ATDO, is then given by eq 8. Since, for the large values of n usually encountered AT,' = (dAGo,/dP), = RT(1 + P - l/n)[d In (cmc)/dPIT + RT(dP/aP), In [0,98(cmc)] (8) in micelle formation, l / n is small with respect to 1 + p, the first term on the right-hand side is nearly identical with the expression derived from the charged phase separation model, eq 4. The mass-action model requires a second term involving (dP/dP),. Figure 5 shows the estimates of AVm using the charged phase separation model (eq 4) and AVDo using the mass(27) P. Mukerjee, J.Phys.Chem., 66,943 (1962). (28) P. Mukerjee, J. Phys. Chem., 66, 1733 (1962). (29) P. Mukerjee, J. Phys. Chem., 65, 740, 744 (1961).
I
I
0
11, 1981 1815
1000
2000
Pressure ( kg /crn2)
Estimated volume changes on micelle formation: A Pm0, using the charged phase separation model, eq 4; AVm, using the mass-action model, eq 8. Figure 5.
action model (eq 8). The /3 values of Figure 4 have been used in these equations and for calculating (dP/aP),. A value of 20 has been used for n;the results are not very sensitive to _the choice of n or some variation in n with pressure. AV, and AV,O are similar at low pressures but diverge significantly at higher pressures, showing the influence of (dp/dP),. The decrease of both AV, and ATmo with pressure is consistent with the compressibility of the micelles. Unlike AT,, ATmodoes not become negative at high pressures. Although the exact values of (d/3/dP), may be unreliable because of the various assumptions made, the trend should remain. Direct experimental determination of at high pressures from cmc measurements are difficult. If such data become available, the estimates from conductance data can be checked. The interpretation of ATmoin terms of molecular interactions is difficult. A number of qualitiative factors can be identified as contributors to the net volume change on micelle formation of ionic surfactants. A hydrocarbon or fluorocarbon chain, on transfer from an aqueous to a nonaqueous medium, is expected to cause an increase in volume, at least at low pressures. As discussed a few years ago, interactions of counterions with micelles can produce different volume changes, depending upon whether the interactions are purely electrostatic or whether specific interactions such as covalent bonding or charge-transfer or desolvation effects are present.27 It is also likely that the ionic head groups of the surfactants might cause significant volume changes on micellization because of an increase in the ~ e l f - p o t e n t i awhen l ~ ~ the head group is transferred from an aqueous medium to the micellar interface. The micellar interface region has been characterized as having a significantly lower effective dielectric constant than that of water.30 Upon micellization, therefore, the head group is expected to produce a reduction in volume because of higher electrostriction effects. Although the absolute values of ATmoare difficult to interpret, some relative comparisons are of some interest. As discussed before, NaPFO and SDeS have nearly identical cmc values in water. The value of AGO, for NaPFO derived from eq 7 is -6.60 kcal/mol. The corresponding value for SDeS at 30 "C is estimated to be close to the calculated value at 23 0C,31-7.01 kcal/mol, because of the known small variation of AGO, with temperature in this region. Thus, the net interactions in micelle formation for NaPFO as compared to SDeS are somewhat weaker. (30) P. Mukerjee, J. R. Cardinal, and N. R. Desai, Micellization, Solubilization, Microemulsions,[Proc. Int. Symp.],1976,1, 241 (1977). (31) P. Mukerjee, Kolloid. Z. Z. Polym., 236, 76 (1970).
1616
Additions and Corrections
The Journal of Physical Chemistty, Vol. 85, No. 11, 1987
Nevertheless, the AV, for NaPFO is higher than that estimated for SDeS5by a factor of 2.3. This difference can be ascribed to a more pronounced chain-water interaction for the fluorocarbon chain. I t has been argued that attractive chain-chain interactions in the micelle make a very important contribution to AGom.23932 These interactions are known to be considerably weaker in fluorocarbon liquids as compared to hydrocarbon Thus AGO, for NaPFO is likely to have a much larger contribution from the hydrophobic interactions of the monomers than is the case for SDeS. Thus a more pronounced volume change caused by structural perturbations of water is expected for NaPFO and is responsible for the higher value of AV,,,, This finding is consistent with the surface tensions of dilute solutions of NaPFO and SDeS measured re~ e n t l y .The ~ ~ former is more than 6 times as effective as the latter in reducing the surface tension of water. It is also consistent with the temperature dependence of the cmc of NaPF0.35 The cmc decreases continuously over the range of 25-40 “C, whereas SDeS exhibits a shallow minimum in its cmc around 25 “C, the cmc increasing at higher temperature^.^^ Another interesting comparison is that between the AVmo of NaPFO of 19.4 mL/mol and the value of 21.5 mL/mol estimated for perfluorooctanoic acid, HPF0.37 Some years ago, it was suggested that the change in partial molal volumes of micelles and other charged colloidal systems on substituting counterions provides a useful approach in examining whether the interactions of the counterions are purely electrostatic or whether more specific interactions are involved.27In the case of the strong acid, dodecyl sulfonic acid, the micellar partial molal volume, V,, was estimated to be -2 mL/mol less than (32)P. Mukerjee, Micellization, Solubilization, Microemulsions, [Proc. Znt. Symp.], 1976, 1, 171 (1977). (33)J. H Hildebrand, J. M. Prausnitz, and R. L. Scott, “Regular and Related Solutions”, Van Nostrand-Reinhold, New York, 1970. (34)P. Mukeriee and T. Handa, unwblished work. (35)P.MukeGee and G. Sugihara, Gnpublished work. (36)P. Mukerjee and K. J. Mysels, Natl. Stand. Ref. Data Ser. (U.S., Natl. Bur. Stand.), 36 (1971). (37)K.Shinoda and T. Soda, J. Phys. Chem., 67,2072(1963).
that of the corresponding sodium salt, and the difference was shown to be consistent with nonspecific electrostatic interactions. Fluorocarbon acids are known to be moderately strong, with dissociation constants of 1L/mol.% Below the cmc, therefore, the acid is completely dissociated and the partial molal volume of HPFO in the monomeric form is expected to be -1.2 mL/mol greater than that of NaPFO, arising from the difference in volume of H+ and Na+ in dilute solution^.^^,^^ When this value is used, 77, for HPFO is calculated from the AT’, values to be larger than that of NaPFO by 3.3 mL. When compared to the dodecyl sulfonate system, V , for HPFO is thus -5 mL/mol higher than that expected for purely Coulombic interactions of H+ ions at the micelle surface. This discrepancy indicates that there is a substantial amount of covalent bonding between PFO- ions and H+ at the surface of HPFO micelles. It is well-known that such association reactions lead to marked increases in ~olurne.~’Two factors are likely to contribute to significant covalent association of PFO- groups and H+ ions at the micelle surface as compared to monomeric solutions. The dissociation constant of HPFO is expected to decrease on micelle formation on the basis of some studies on the effect of solubilization in micelles on the dissociation constants of anionic indicator dyes.30 It is also expected that local concentrations of counterions at the micelle surface are high even for slightly charged micelles.39 Covalent association of HPFO in micelles has also been proposed by Hoffmann et al.,40who reported that above the cmc the conductivity of HPFO increases very little with concentration.
-
Acknowledgment. This material is based on work supported by the National Science Foundation, under Grant No. ENG-78-16860, and by funds from Fukuoka University, Japan. The authors are grateful to Professor M. Tanaka and Dr. S. Kaneshina for encouragement and help. (38)A. L.Henne and C . J. Fox, J. Am. Chem. SOC., 73,2323 (1951). (39)P.Mukerjee and K Banerjee, J. Phys. Chem., 68,3567 (1964). (40)H. Hoffmann and W. Ulbricht, 2.Phys. Chem. (Frankfurt am Main), 106,167 (1977).
ADDITIONS AND CORRECTIONS ~~
1980, Volume 84
Huguette Fabre, Nicole Kamenka, Ali Khan, Goran Lindblom, Bjorn Lindman,* and Gordon J. T. Tiddy: Self-Diffusion and NMR Studies of Chloride and Bromide Ion Binding in Aqueous Hexadecyltrimethylammonium Salt Solutions. Page 3428. The 13th line in column 2 should read 21 instead of 21 + 1. Page 3432. The third line of the caption to Figure 2 should read mole fraction of CI6TAB in the surfactant instead of molar ratio of C1- t o Br-.
