INVESTIGATION OF MICELLESTRUCTURE the general agreement of the experimental points and theoretical curve supports our rate constant of 1.25 M-'sec-'. With ka = 1.25 and k13 = 1.6 X lo7 M-l sec-', the equilibrium constant for the reaction e,i-
+ D20
D
+ OD-
583 is 0.78 X lo-', and AF, the free-energy change is +9.7 kcal/mole. Combining this free energy with those for D 4 '/zDz (-49.4 kcal) and D + OD- -t. D 2 0 (-20.3 kcal), one obtains a AF of -60.0 kcal for edD + -t '/2Dz. The standard potential E" for ed- is then 2.60 V. These values are substantially identical with those for
+
+
Investigation of Micelle Structure by Fluorine Magnetic Resonance. 11. Effects of Temperature Changes, Added Electrolyte, and Counterion Size' by Norbert Muller and Ronald H. Birkhahn Department of Chemistry, Purdue University, Lafayette, Indiana
47907
(Received July 17,1967)
Fluorine chemical shifts have been determined as a function of concentration for aqueous solutions of the two fluorine-labeled soaps CF3(CH2)&OONa and CF3(CH2)&OONa at three temperatures between 18 and 60". For each soap, the critical micelle concentration passes through a minimum in this range, showing that micelle formation is slightly endothermic at lower temperatures and becomes exothermic at higher temperatures. The degree of penetration of water into the micelles appears to increase somewhat upon heating. Addition of electrolyte depresses the critical micelle concentration but does not affect the chemical shifts for the ions within the micelles. Since it is believed that aggregation numbers of micelles formed by ionic detergents generally increase with increasing ionic strength, this observation seems to require that the larger micelles be ellipsoidal rather than spherical. Substitution of lithium, potassium, or tetramethylammonium for sodium as the counterion has very little effect. It is shown that the presence of the trifluoromethyl group does not produce any striking difference in behavior between these soaps and their more widely studied nonfluorinated analogs.
Introduction This paper is the second of a series in which we report results of nuclear magnetic resonance (nmr) studies of detergent solutions containing fluorine-labeled surfactants or solubilized fluoroorganic compounds. The over-all objective is to explore the usefulness of nmr as a source of information about the nature of the micelles formed in these solutions, and thus to attempt to elucidate the molecular processes involved in the formation of hydrophobic bonds. I n the first paper2 we presented data for surface-active salts of the type CFB(CHJ.COONa and used them to calculate the critical micelle concentrations (cmc), the chemical shifts of the monomeric soap ions, S(S), and the shifts for the ions in the micellar form, S(S,). We pointed out that 6(S,) is a new measura,ble property characteristic of the micellar interior, and .we concluded from the values obtained
that there is appreciable penetration of water into the micelles. We have now studied in more detail the effects of temperature changes, addition of electrolytes, and changes in the nature of the counterion upon these solutions. The results, presented below, are discussed in the light of existing views of the nature of micellar solutions. They also yield additional evidence in support of the key assumption that there is a close correspondence between the behavior of these fluorinelabeled detergents and their more extensively studied nonfluorina t ed analogs.
(1) Presented a t the 154th National Meeting of the American Chemical Society, Chicago, Ill., Sept 1967. (2) N. Muller and R. H. Birkhahn, J . Phys. Chem., 71, 967 (1967). Volume 78, Number 8 February 1968
584
NORBERT MULLER AND RONALD H. BIRKHAHN
Experimental Procedures and Results The fluorinated carboxylic acids, CF3(CH2)&OOH and CF3(CHz)&OOH, which will be designated below by the abbreviations HFClo and HFC12, respectively, were prepared and purified as described previou~ly.~~3 To prepare stock solutions of the soaps (NaFClo or T\'aFC12),equivalent amounts of the acid and of NaOH were weighed into volumetric flasks, and either water or a standard electrolyte solution was added until the volume reached the desired value. Volumetric dilution of these solutions with water or the appropriate electrolyte solution yields sets of samples in which the molar concentration of soap is immediately obtainable. The molar concentration of electrolyte in each set of samples is not constant and differs by as much as 10% from I 5 IO 15 the molarity of the standard solution employed, but 1/S, (Liters/Mole) the molality is very nearly invariant. (It would be Figure 1. Fluorine chemical shifts for CFa(CH&COONa exactlyvso, except for the effect of the small amount of solutions plotted us. the reciprocal of the total soap water formed in the reaction of the acid and base.) concentration at three temperatures. All shifts are in ppm, upfield from external benzotrifluoride. For example, a stock solution made with standard 0.400 M NaCl and containing 0.50 mole of NaFClo/l. has a specific gravity of 1.06. The molarity of NaCl in this solution is 0.366, while the molality is 0.404 in the standard solution and 0.400 in the stock solution. Solutions of the lithium, potassium, and tetramethylammonium (TMA) soaps were prepared by substituting the appropriate base for the NaOH. Nmr determinations were carried out as described earlier,2 except for the use of a Varian V-4331 THR dewar probe insert in place of the high-sensitivity insert and of the associated V-4340 variable-temperature accessories. Although this resulted in some loss of sensitivity, the fluorine signals could readily be found a t concentrations down to 0.02 M , without the use of signal averaging techniques. Past experience with this apparatus4 indicated that the sample temperatures, measured with a thermocouple junction, may be con10 20 30 40 l/S, (Liters/Moiei sidered accurate to within *lo. The chemical shifts of solutions of NaFClo and Figure 2. Fluorine chemical shifts for CFa( CH&COONa solutions plotted vs. the reciprocal of the total NaFClz were determined as a function of concentration soap concentration at three temperatures. a t three temperatures between 18 and 60". The results are presented in Figures 1 and 2 as plots of 6 against l/So, the reciprocal of the total soap concentration. Table I shows the temperature dependence of the chemical shifts for dilute solutions of NaFClo and several related compounds in water or organic solvents. Table I : Temperature Dependence of the Fluorine Chemical Chemical shifts of NaFClo as a function of concentraShifts (ppm from External Benzotrifluoride) for Dilute in the presence of added NaCl are shown in Figure tion Solutions of Trifluoromethyl Derivatives in Various Solvents 3. These measurements were made a t the ambient temperature of the nmr probe, about 35". Attempts ----Fluorine shiftsSolute Solvent 220 40° 60' to obtain similar data for NaFClz were only partially successful (Table 11) because the soap tends to precipiCFs(CHz)sCFs Hexane 3.94 3.99 4.05 CFaCeH6 AcOH -0.24 -0.29 -0.34 tate when the ratio of electrolyte concentration to soap 3.70 3.82 3.57 CFa(CH2)sCFs Ethanol concentration becomes large. Analogous data for CFa(CHz)sCOONa CFs(CH2)sCOONa CF~(CHZ)&OON~ CFaCHzOH
Ethanol
Ha0 HzO H20
The Journal of Physical Chernistrg
3.56 1.62 1.67 12.47
3.68 1.30 1.31 12.14
3.80 1.00 1.02 11.89
(3) R. H. Birkhahn, Ph.D. Thesis, Purdue University, Lafayette , Ind., 1967. (4) N. Muller and 0. R. Hughes, J. Phys. Chem., 70, 3975 (1966).
INVESTIGATION OF MICELLESTRUCTURE
585 I
Table 11: Fluorine Chemical Shifts (ppm from External Benzotrifluoride) for Aqueous Solutions of CFs( CHz)loCOONa in the Presence of Excess Electrolyte Soap concn, M
--------Fluorine
0.50 0.40 0.35 0.30 0.25 0.225 0.200 0.175 0.150 j0.125 0.100 0.075 0.050
shift------
M
0.4 M
0.6
NaCl
NaCl
NaCl
2.61 2.60 2.58 2.56 2.54 2.54 2.52 2.52 2.50 2.45 2.42 2.35 2.19
2.65 2.61 2.61 2.59 2.57 2.57 2.55 2.54 2.54 2.51 2.49 2.43
2.70 2.70 2.69 2.67 2.66 2.65 2.64 2.61 2.61 2.59 2.57 2.54
0.2
'
...
M
V S , (Liters/Mole)
Figure 3. Fluorine chemical shifts for CFs( CH2)BCOONa solutions in the presence of excess sodium chloride: open circles, 0.2 M NaC1; filled circles, 0.4 M NaC1; and half-filled circles, 0.6 M NaC1.
*..
Discussion Temperature Efects. A graph of 6 against l/So for a
characterize such a plot are the intercept, S(S,); the cmc; the dilute-solution shift, S(S); and the approximate radius of curvature in the cmc region. Table I11 and Figures 1 and 2 show that all four parameters vary as the temperature is changed, so that the marked temperature dependence of the observed chemical shifts results from a combination of several factors. The cmc is not drastically altered when the temperature is changed, but for each soap it appears to pass through a minimum between 20 and 60". This implies that the process of micelle formation is slightly endothermic in the lower part of the temperature range and becomes exothermic a t higher temperatures. Similar behavior has previously been reported and discussed for several ordinary soaps and ionic detergents with 10- or 12-carbon alkyl chains.6 We conclude that the thermodynamic parameters for the process of micelle formation are only slightly affected by the presence or absence of the CF3 label, and that for the fluorinated soaps, as for ordinary soaps, most of the free energy of micelle formation results from a favorable entropy changeeB The rapid shift of S(S) to smaller values as the temperature rises is remarkable, in view of the fact that the fluorine shift of monomeric NaFClo in ethanol increases on heating (Table I). Since the fluorine shift of CFaCHzOH in water (Table I) acts very similarly, it seems that the unusual temperature dependence reflects changes in the structure of water and is not connected with the surface activity of the soap ions. It should be emphasized that the reference compound, benzotrifluoride, itself has a temperature-dependent chemical shift. Taking gaseous carbon tetrafluoride as the nearest available approximation to a temperature invariant standard, Evans' found a temperature
given soap consists of a linear portion with negative slope a t high concentrations, a line of zero slope at low concentrations, and a curved region in the neighborhood of the cmc.2 Four parameters which may be used to
J. Colloid Sci., 16, 484 (1961). (6) E. D. Goddard, C. A. J. Hoeve, and G. C. Benson, J. Phys. Chem., 61, 593 (1957). (7) D. F. Evans, J . Chem. Soc., 877 (1960).
NaFClo with added NaOH and for solutions of the lithium, potassium, and TMA salts of HFClo have been omitted in the interest of brevity, and may be found in ref 3. Parameters derived from these data are among those presented in Table 111, which summarizes the
Table I11 : Cmc Values and Nmr Parameters for Salts of HFClo and HFCxt under Various Conditions Compound
NaFClo NaFClo NaFClo NaFCla NaFClz NaFClz NaFClo NaFClo NaFClo NaFClo NaFCto NaFClo LiFClo KFCio TMAFCio a
Temp
18" 40' 60' 22 O 40 O 60 '
a a a
a a a
a a a
Added electrolyte
... ... ...
... ... ...
... 0.2 M 0.4 M 0.6 M 0.6 M 1.O M
NaCl NaCl NaCl NaOH NaOH
...
...
...
Cmc
6(Sm)
6(S)
0.176 0.157 0.162 0.045 0.043 0.046 0.163 0.111 0.087 0.072 0.060 0.040 0.153 0.156 0.155
2.74 2.55 2.43 2.79 2.60 2.43 2.65 2.57 2.58 2.58 2.54 2.58 2.67 2.63 2.48
1.69 1.30 1.00 1.67 1.31 1.02 1.40 1.41 1.38 1.34 1.34 1.27 1.41 1.37 1.52
Ambient temperature of the nmr probe, about 35"
cmc values, the monomer shifts, 6(S), and the micelle shifts, 6(S,), derived from the various dilution-shift plots.
(5) B. D. Flockhart,
Volume 78, Number I February 1968
NORBERT MULLER AND RONALD H. BIRKHAHN
586 coefficient A6/AT = 1.06 X ppm/deg for benzotrifluoride. Making allowance for this, we calculated corrected values of A6/AT ranging from 0.8 to 1.8 X ppm/deg for several trifluoromethyl derivatives in various organic solvents, including the hydrogen-bonding solvents ethanol and acetic acid, whereas in water A6/AT is about -0.6 X ppm/deg. A positive temperature coefficient is far easier to rationalize, since the gas-phase chemical shift for an organofluorine compound is expected to lie at higher fields than the shift in liquid solvents, and thermal expansion should cause the liquid-phase shift to approach the gas-phase value a t higher temperatures.' The temperature variation of S(S), is intermediate between those found for S(S) and for the shift of monomeric NaFClo in ethanol. This suggests again that CF3 groups inside the micelle are exposed to water to an appreciable degree. It was proposed in the first paper that the chemical shift of a CF3 group could be used to define a parameter which approximately represents the degree of nonaqueous character of the surrounding medium
on p. Therefore the observed trend could reflect a change of either or both of these coefficients, and no unambiguous interpretation can be offered. We could not find any light-scattering data on the variation of micelle size with temperature for ionic detergents.9 The nonionic surfactant hexaoxyethylene glycol monon-dodecyl ether reportedlylO forms micelles which increase in weight by almost two orders of magnitude as the temperature is raised from 15 to 45", in sharp contrast to the apparent behavior of our materials. Added Electrolyte. Plots of 6 vs. 1 / 8 0 in the presence of a simple salt, such as those in Figure 3, show a t a glance that the cmc is strongly dependent on the electrolyte concentration. Such behavior has often been noted for unfluorinated ionic detergents,11J2illustrating again that the properties of the surfactant ions are not drastically changed by incorporation of the CF3 group into the alkyl chain. Figure 4 is a graph of the logarithm of the cmc for NaFClo from Table I11 os. the logarithm of the total counterion concentration (the molality of the added electrolyte plus the cmc). The points fall very near the straight line
- S(S)aql/[S(s)organio
log crnc = -1.24 - 0.58 log (Naf)
2 =
[S(Sm)
-
S(S)aql
(1)
On the basis of data in ref 1, it seems reasonable to adopt the shift of NaFClo in ethanol a t any given temperature as the value for 6(S)organia.Then 2 may be evaluated as a function of temperature with results as follows, temperature, 2 values (NaFClo), and 2 values (NaFCI2), respectively: 18", 0.56, no value; 22", no value, 0.59; 40", 0.53, 0.55; and 60°, 0.51, 0.51. As noted before,2the 2 values change only very slightly with increasing chain length, but there is a significant trend toward lower 2 ' s with rising temperature, suggesting a loosening of the micellar structure and increasing penetration of water into the micelles. Finally, close inspection of Figures 1 and 2 shows that the curvature of the plots of 6 vs. 1/80in the neighborhood of the cmc is temperature dependent. If the process of micelle formation is represented by the oversimplified (but often useful2) equation
mS-
zS,-"
(2)
it is readily shown that the plot has a sharp break at So = cmc if the aggregation number, m, is infinite, while for finite m values the break is replaced by a smooth bend with a radius of curvature which increases as m decreases.8 On this basis, one is tempted to conclude that the aggregation numbers of NaFClo and NaFCl2 diminish with rising temperatures. However, the data are not precise enough to allow quantitative evaluation of m or its temtIerature dependence. Moreover, if micelle formation is described by the somewhat more realistic equation mS-
+ pNa+ zNa,S,-("-p)
(3)
the curvature in the crnc region depends both on m and The Journal of Physical Chemistry
(4)
when the added electrolyte is NaCl at concentrations up to 0.6 M . It has been shown11J3that such a linear relationship can be simply rationalized by applying the law of mass action to the formation of a single micellar species which includes bound counterions. The slope of the straight line obtained should be equal13 to -p/m, where p and m are the coefficients in eq 3 which define the micelle composition. Our data yield p / m = 0.58, in good agreement with results for a variety of detergents cited by C0rrin.1~ It should be noted that other methods of measuring p / m often yield substantially larger ~ a 1 u e s . l ~ ~ ' ~ We attempted to find the crnc of NaFCto in 1.0 M h'aC1 but failed because of solubility problems. I n the belief that the effect of added electrolyte would be independent of the nature of the anion,ll we studied samples made with 1.0 M NaOH, in which the soap was soluble, but the resulting point fell rather far from the line through the NaCl data (Figure 4). A set of (8) J. Grindley and C. R. Bury, J. Chem. Soc., 679 (1929). (9) We are indebted to an anonymous referee for the information that in a paper by A. L. M. Lelong and I. M. Natale, Anales Asoc. Quim. Arg., 53, 11 (1965), which we have not had an opportunity to read, it is reported that the micellar molecular weights of decyl and dodecyl sodium sulfates drop by about 20% as the temperature goes from 25 to 45O. (10) R. R. Balmbra, J. 5. Clunie, J. M. Corkill, and J. F. Goodman, Trans. Faraday Soc., 58, 1661 (1962). (11) M. L. Corrin and w. D. Harkins, J. Am. Chem. SOC..69, 683 (l94')* (12) M.J. Schick, J . Phys. Chem., 68,3585 (1964). (13) M.L. Corrin, J. Colloid Sci., 3, 333 (1948). (14) P. H.Elworthy and K. J. Mysels, J. Colloid Interface Sci., 21, 331 (1966). (15) M. J. void, J. Colloid sci., 5 , 506 (1950).
587
INVESTIGATION OF MICELLESTRUCTURE
-Log [No*]
Figure 4. Log-log plot of the cmc of CFs( CH2)&OONa, in the presence of eircess electrolyte, us. the total concentration of sodium ion a t the cmc. Open circles obtained using NaC1; filled circles obtained using NaOH.
solutions was made with 0.6 M NaOH in order to get results (Table I11 and Figure 4)which would be directly comparable with those obtained using 0.6 M NaC1. They show that a t higher electrolyte concentrations the nature of the similion does have a measurable effect on the cmc. A second effect of electrolyte addition for NaFClo is a slight downfield shift of the signal from the monomeric ions (Table 111). This shift is in the same direction as that which results from heating the solutions, suggesting that it reflects a net structure-breaking effect of NaCl on water. Such an effect was invoked previously to account for the observed dependence of the proton magnetic resonance shift of water upon the concentration of added NaCI.16 A more surprising finding, foreshadowed by the is preliminary results reported in ref 2, is that 6(S,) essentially unchanged when electrolyte is added, at least for NaFClo. It has often been reported that ionic micelles increase considerably in size with increasing salt eoncentration,17f1sbut there is some disagreement as to the shape of the larger micelles. Emerson and Holtzer believe that the available facts support the opinion that the micelles are spherical and, for a given detergent, have a nearly constant radius.18 One objection to this view is that some of the reported aggregation n ~ m b e r s ~are ~ v so ~ ~high as to imply an unreasonably high density for the micellar core, unless the radius exceeds the length of the alkyl chain. The nmr results also seem incompatible with the assumption of spherical micelles at high ionic strength. Packing a variable number of long-chain ions into a region of essentially constant volume, the remaining space being presumably olccupied by intramicellar water, should produce a micelle within which the effective degree of nonaqueous character, which determines S(S,), depends strongly on the aggregation number and therefore on the electrolyte concentration. The alternative view
preferred by Stigterlg and others is that the larger micelles are prolate spheroids. The nmr data can readily be rationalized on this basis, since additional monomers can be accommodated in a spheroidal micelle by progressive elongation with little or no change in the composition of the micellar core. Two further possibilities should perhaps be mentioned since, though they seem highly unlikely, they cannot be absolutely excluded. First, the. reported dependence of micelle number on ionic strength could conceivably be an artifact resulting from some error in the use of the light-scattering method.20 Secondly, in spite of the many similarities between NaFClo and other ionic detergents, NaFClo might differ from the others in forming micelles which do not increase appreciably in size when electrolyte is added. The limited results for NaFClz agree for the most part with those for NaFClo. Again the crnc apparently obeys an equation similar to eq 4, but the coefficients could not be accurately evaluated because, in the presence of salt, solubility considerations and spectrometer sensitivity made it impossibleto measure chemical shifts, except a t concentrations far above the cmc. The points obtained in the region 0.175 2 SO2 0.05 give good straight lines on a 6 us. 1 / 8 0 plot, which again yield by extrapolation 6(S,) values nearly independent of the sodium ion concentration. A new phenomenon, which requires further study, is that at higher values of Sothere is an indication of an abrupt change in slope of the 6 us. l/Soplot, which becomes more pronounced a t higher salt concentrations.3 Nature of the Counterion. It has been reported12*'7 that there are significant differences between the cmc's of the Li, Na, and TMA salts of laurylsulfuric acid, and we undertook to look for similar differences in the salts of HFClo. As shown in Table 111,the nmr parameters of the four salts including also the potassium salt are nearly the same, except that TMAFClo gives a slightly lower S(S,) and slightly higher S(S) than the others. The differences are too small to serve as support for any tentative interpretation. Mass-Action Calculations. In ref 2, it was shown that the chemical shift a t concentrations above the cmc obeys 6 = 6(Sm)
+ (cmc/So) [@)
- S(Sm) 1
(5)
provided that the concentration of monomeric ions remains constant and equal to the cmc, as required by eq 2 if m is very large. As noted in footnote 16 of that paper and in other place^,'^ this assumption is not (16) J. N. Shoolery and B. Alder, J. Chem. Phys., 23, 805 (1956). (17) K. J. Mysels and L. H. Princen, J . Phgs. Chem., 63, 1696 (1959). (18) M. F. Emerson and A. Holtzer, ibid., 69, 3718 (1965); 71, 1898 (1967). (19) D.Stigter, ibid., 68, 3603 (1964). (20) H.Schott, ibid., 70, 2966 (1966).
Volume 78, Number 8 February 1068
NORBERT MULLER AND RONALD H. BIRKHAHN
588
8 (S3
+Defined 2’
O‘\
‘a
.-
E- zi v
‘5 2
I’
5
10
VS,, (Liters / Mole)
Figure 5. Chemical shift as a function of l/Sofor the model system discussed in the text.
compatible with attempts to allow for counterion adsorption using a mass-action model based on eq 3. On the other hand, the linearity of the experimental plots of 6 against 1 / 8 0 seems to support the validity of eq 5, and the graphical method for the evaluation of 6(S,) depends on this equation. I n an effort to elucidate this situation, we computed chemical shift values as a function of concentration for an idealized model system with the following defined properties. (1) Monodisperse micelles form according to the equation 25Na+
+ 50s- J_ Na26Sso-25
(6)
(2) The chemical shift parameters are S(S) = 1.40 and 6(S,) = 2.66 ppm. (3) In order to make the cmc approximately equal to 0.1 M , the equilibrium constant for eq 6 is chosen to be 8.0 X Straightforward computations then show how [S-1, [Na+], and 6 depend on So. The calculated values of 6 are plotted against 1 / 8 0 in Figure 5. I n the region 0.12 < So < 0.5 the calculated points, like the experimental data, fall very close to a straight line. When this line is extrapolated to obtain a value of S(S,), the result is 2.79, which is 0.13 ppm above the true value, and the graphical cmc is 0.110 M . Since this model system should correspond more nearly to reality than one based on eq 2, the values of 6(S,) re-
The Journal o j Physical Chemistry
ported here must be regarded with some caution. Regrettably, the present state of our knowledge does not even allow us to define with confidence the limits of uncertainty for these parameters. Not only are the true values of m and p unknown, but in addition there is every reason to expect that they will vary as the surfactant concentration changes. Moreover, the actual micelles are almost certainly not monodisperse. l7 Hence, even an equation of the type of eq 3 and 6 is too simple to represent the real situation adequately. In this connection, it is noteworthy that the model system yields a 6 vs. 1 / 8 0 curve with a sharper break in the cmc region than the experimental curves of Figures 1 and 2, very possibly reflecting a gradual increase of average micellar weight with increasing concentration in the real system. Difficulties of this sort are encountered in every attempt to calculate from any simple model the concentration dependence of some property of micellar sol~tions.~*J In spite of this, we judge from the above calculations that the uncertainties in our values of 6(S,) are too small to put our major conclusions in danger of being invalidated. If appropriate corrections could be applied, the 2 parameters reported would probably be reduced by a few per cent, but their temperature dependence and approximate independence of chain length and salt concentration would be preserved, as would the inference that water penetrates to some degree into the micelles.21 The finding that the crnc passes through a minimum between 20 and 60” would certainly survive, as would the various other points of similarity between the fluorinated soaps and their unfluorinated analogs. Though the nrnr technique thus has its limitations, there is good reason to expect that further exploitation of the method will result in an improved understanding of the physical nature of surfactant solutions. Acknowledgment. The authors wish to thank the Purdue Research Foundation for providing financial support of this work through a David Ross grant. (21) It should perhaps be emphasised that the idea that there is appreciable paraffin-water contact inside a micelle is not being proposed for the first time in this series of papers. See, for example, ref 2 in paper I a?! also P. A. Winsor, “Solvent Properties of Amphiphilic Compounds, Butterworth and Co., Ltd., London, 1954,p 15.
