2996
J . Phys. Chem. 1985, 89, 2996-3000
the maximum as the limit is approached from below, and the induction time then falls again once the system goes above the limit. l 6 Concluding Remarks We have made a thorough reinvestigation of the use of methyl isocyanide for the testing of thermal explosion theory and have performed a large number of consistency tests, none of which shows any signs that would invalidate this system for testing purposes. We have reported sets of experiments, measured independently by three workers at 2-yr intervals, which demonstrate the remarkable reproducibility of this reaction for the determination of explosion limits. Because of the improved temperature monitoring procedures in the latest measurements (C84), they are the ones in which we can place the most confidence. Since Table I1 shows that dp,/dTll,,, -0.1 torr OC-' for a 2-L sphere, the principal uncertainty for the larger vessels in the determination of pcrarises from the pressure calibration; however, dp,,/dTl, varies inversely as 9so that for the 0.3-L vessel, it is -0.35-0.4 torr OC-' at 350 OC, and here the error in the temperature control is dominant. Given the difference in the quality of the temperature control between the two series P82 and C84, all the results in Table I are within acceptable agreement of each other, even including the 0.3 L result. Here, the older result is clearly the less reliable: the longest induction time (0.36 s) was much too short; also, repetition of this experiment with a different sample of methyl isocyanide from that used in the C84 experiment gave 8.17 and 8.18 torr, respectively, for the highest subcritical and lowest supercritical pressures, confirming the correctness of the newer measurements in this case. Thus, we conclude that the recommended values for the critical explosion pressures of methyl isocyanide at 350 OC may be taken to be the mean of the two C84 values given for each case in Table I, with a total uncertainty of about *0.05 torr which allows for small excursions of the temperature from the desired set point, errors in the pressure calibration, and the bracketing range of the limit in those cases where coincidence was not obtained: similar (16) Gray, B. F.; Griffiths, J. F.; Hasko, S.M. J . Chem. Technol. Biotechnol. 1984, 34A, 453.
remarks apply to the data in Table 11. Because of the complication that this reaction is a unimolecular reaction in its falloff region, so that both the reaction order and activation energy are pressure dependent, it is not a simple matter to make the standard tests. Qualitatively, there, appears to be reasonable agreement between theory and experiment insofar as the variation of pcrwith variation in To for fixed r is concerned, but not for the variation at fixed To for different r; also, the square-root relationship for the ignition delay vs. pressure in excess of pm holds quite well once p > l.O5p,, but fails at pressures only slightly in excess of pcr. We hope to be able to resolve these difficulties in numerical simulations of these experiments in a separate publication. Acknowledgment. This work was supported by the Natural Sciences and Engineering Research Council of Canada. We would also like to acknowledge help from John Collister, who performed all of the alkylmercury experiments reported here. Appendix
An Accidental Explosion with Liquid Methyl Isocyanide at Room Temperature. Ever since methyl isocyanide was first prepared by Gautier, it has been known that it explodes when distilled; however, we are not aware of any report that the room temperature liquid itself may explode (except when sensitized by the presence of certain azides17). We had been in the habit of purifying 0.2-mL samples of the liquid by preparative gas-phase chromatography and, over a period of some years, had purified several hundred milliliters in this manner. The desired volume of liquid was injected on to the chromatographic column (inlet port and column at 42 "C) by using a Hamilton CR-700 spring-loaded hypodermic syringe. We presume that the explosion of this 0.2 mL sample of liquid methyl isocyanide occurred as a result of the sudden compression of the liquid by the spring-loaded plunger: the glass barrel (1.2-in. long, 0.3-in. o.d., 0.175-in. id.) was reduced to granules, and the 0.02-in. wall steel sheath surrounding the barrel was expanded from about 3/8 in. to nearly in. diameter at the middle of the viewing slit. Registry No. Methyl isocyanide, 593-75-9. (17) Wohler, L.; Roth, J. F. Chem.-Zrg. 1926, 50, 761.
The Structure of Sodium Dodecyl Sulfate Micelles In Solutions of H20 and D20 N. James Chang and Eric W. Kaler* Department of Chemical Engineering, BF- 10, University of Washington, Seattle, Washington 981 95 (Received: October 9, 1984; In Final Form: April 2, 1985)
The sizes of sodium dodecyl sulfate (SDS) micelles in mixtures of H 2 0 and D 2 0 have been measured at several different ionic strengths and temperatures. The changes in micelle size due to H20/D20substitution are greatest at high ionic strength. Electrical conductivity and light scattering measurements indicate that head group repulsions between surfactant molecules, as well as intermicellar interactions, are the same in H 2 0 and D 2 0 solutions. The conclusion is that a small difference in the strength of hydrophobic bonds between H 2 0 and D20 is responsible for the dramatic changes in micelle size. In addition, the critical micelle concentrations of a homologous series of sodium alkyl sulfates in H20and D 2 0and for SDS in solutions containing various ratios of H 2 0 / D 2 0are reported.
Many of the physical properties of H,O and ~~0are nearly For example, the surface tensions and dielectric constants of the materials are the same to within 0.5%, and other
properties such as refractive index, polarizability, and boiling point are all closely matched. The similarity of the two materials has led to the c0"On substitution of D2O for H20 in many experiments, most notably in neutron scatteringe6 and NMR7-9studies.
(1) G. Nemethy and H. A. Scheraga, J . Chem. Phys., 41, 680 (1964). (2) G. A. Vidulich, D. F. Evans, and R. L. Kay, J . Phys. Chem., 71,656 (1 967). (3) M. K. Phibbs and P. A. Gigriere, Can. J . Chem., 29, 173 (1951).
(4) R. Triolo, L. J. Magid, J. S. Johnson, Jr., and H. R. Child, J . Phys. Chem., 86, 3689 (1982). ( 5 ) R. Zana, C. Picot, and R. Duplessix, J . Colloid Interface Sci., 93, 43 (1983).
Introduction
0022-3654/85/2089-2996$01 SO/O
0 1985 American Chemical Society
SDS Micelles in Solutions of H20 and D2O There are, however, definite differences between the two liquids in several physical properties that are sensitive to the fluid structure. The higher viscosity of DzO (23% higher than H 2 0 at 25 "C), the higher heat capacity (12% higher), and the higher temperature of maximum density (1 1.23 OC compared to 3.98 O C for HzO)strongly suggest that D20 is a more structured solvent than HzO.'O "More structured" means that the strength of hydrogen bonds formed in D 2 0 is greater than in H20. This observation is in accord with the model p r o p e d by N6methy and Scheraga,' in which the concept of stronger hydrogen bonding in D 2 0 leads to good agreement with a variety of experimentally measured thermodynamic properties. Isotopic substitution has been widely used to study hydrophobic interactions (HI) in surfactant solutions with the hope that D 2 0 might prove to be a discriminating probe for the solvent structure aspects of hydrophobic bonding."-14 Although there is not direct evidence available for the relative strength of HI in H20and D20, some have concluded that such interactions are stronger in D 2 0 than in H20.13J4This conclusion is in accord with the idea that D 2 0 is a more structured solvent than H 2 0and is supported by measurements of consistently higher critical micelle temperatures (ant's) and lower critical micelle concentrations (cmc's) for a given surfactant in D 2 0 compared to those in H20.13Nonetheless, the measured solubilities of methane and ethane in H20and D20 have been interpreted as evidence of larger HI in H20than in D20.l5 The opposite effect (stronger HI in D20) is observed for the solubilization of larger hydrocarbons like benzene,15however, and this behavior is more likely to resemble the HI for larger surfactant molecules. To date, there have been few experimental studies probing the effect of different strengths of hydrogen bonding of solvents on surfactant structures. Quasi-electric light scattering (QLS) is a convenient and powerful tool, when used properly,I6 for the study of micellar solution s t r u ~ Y u r e . ' ~ - ~Here ~ are reported QLS measurements of micellar solutions formed with sodium dodecyl sulfate (SDS) and H 2 0 or D20 at various surTactant concentrations, ionic strengths, and temperatures. The major conclusions are that SDS micelles are significantly larger under all conditions in D20than in H 2 0 , but the intermicellar interactions and head group repulsions (as evaluated from electrical conductivity and light scattering measurements) are very similar in the two media. The difference in the free energy change of micellization in H 2 0 and D 2 0 is primarily dbe to the different strengths of the hydrophobic bonds in these two media, and this small difference manifests itself by dramatically changing the micelle sizes under certain conditions.
Experimental Section A . Materials. The SDS used in this study was a specially purified grade obtained from BDH (Poole, U.K.). The material (6) B. Cabane, R. Duplessix, and T. Zemb in "Surfactants in Solution", K. L. Mittal, Ed., Plenum Press, New York, 1984. (7) L. &berg, B. Svens, and I. Danielsson, J . Colloid Interface Sci., 41, 298 (1972). (8) U. Henricksson and L. &berg, J . Colloid Interface Sci., 46, 212 (1974). ' (9jG. Lindblom, B. Lindman, and L. Mandell, J. Colloid Interface Sci., 42, 400 (1973). (10) P. Mukerjee, P. Kapauan, and H. G. Meyer, J . Phys. Chem., 70,783 (1966). (11) S. Chou and D. Shah, J . Colloid Interface Sci., 80, 49 (1981). (12) Zs. Bedd and E. Berecz, Acta Chim. Acad. Sci. Hung., 103, 217 (1980). (13) M. F. Emerson and A. Holtzer, J. Phys. Chem., 71, 3320 (1967). (14) D. Oakenfull and D. E. Fenwick, Aust. J . Chem., 28, 715 (1975). (15) A. Ben-Naim, J. Wilf, and M. Yaacobi, J. Phys. Chem., 77, 95 (1973). (16) D. F. Evans, S. Mukherjee, D. J. Mitchell, and B. W. Ninham, J . Colloid Interface Sci., 93, 184 (1983). (17) G. D. J. Phillies, J . Chem. Phys., 60, 976 (1974). (18) N . A. Mazer, G. B. Benedek, and M. C. Carey, J. Phys. Chem., 80, 1075 (1976). (19) M. Corti and V. Degiorgio, J . Phys. Chem., 85, 711 (1981). (20) P. J. Missel, N. A. Mazer, G. B. Benedek, and C. Y. Young, J. Phys. Chem., 84, 1044 (1980).
The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 2997 TABLE I: Critical Micelle Concentrations for a Homologous Series of Sodism Alkyl Sulfates in H20 and D20at 25 OC 8 136 130
cmc, mM (H20) cmc, mM (D20)
no. of carbon atoms 10 12 8.20 33.6 7.60 31.4
14* 2.21 1.97
Measured at 40 OC.
6ool 0 XHzO= 1
0
T = 25°C
550
0 XHzO= 0 0
2
450
Y
4001
350
t
3001
6
I
I
I
1
7
6
9
10
c x i o 3 (mole liter) Figure 1. Specific conductivity as a function of SDS concentration in solutions containing various ratios of H20/D20.
was recrystallized from 95% ethanol to remove dodecanol. The effectiveness of this procedure for a similar batch of surfactant from the same manufacturer has been verified by surface tension measurements,21although no surface tension measurements of the batch used here were made. Surfactant purity was also verified by gas chromatography, which showed that the sample consisted of >99.1% CI2. The C8, Clo, and CI4sodium alkyl sulfates were purchased from Eastman Kodak and purified by recrystallization from 95% ethanol. Reagent grade NaCl was from Mallinckrodt, and D 2 0 (>99.9% D) was from Norell Inc. B. Cmc Measurements. The critical micelle concentrations were measured in a constant-temperature water bath at either 25.00 f 0.01 or 40.00 f 0.01 OC with an Orion conductivity bridge (Model 101) and a Pyrex cell from Yellow Springs Instrument (cell constant 1.04 cm). Each measurement was recorded after the conductivity had not changed for at least 5 min. C. QLS Measurements. The light source was a Spectra-Physics Model 165 2-W argon laser operating at 488 nm. The average scattered intensity and the time-dependent homodyne autocorrelation function of the scattered intensity were measured at a scattering angle 0 = 90'. The signal count rate was between 15 and 80 kHz for all measurements. SDS solutions in 0.2 M NaCl were prepared at room temperature and stored in a water bath at 25.00 f 0.01 OC. SDS solutions in 0.6 and 0.8 M NaCl were likewise prepared and stored in a water bath at 40.00 f 0.01 OC for several hours to allow for equilibration (the cmt is 26.6 OC in H 2 0and 28.4 OC in D 2 0 in 0.6 M NaCl compared to 29.3 OC in H 2 0 and 31.3 OC in D 2 0 in 0.8 M NaCl). The sample cells used for light scattering were 2-cm-diameter ultraprecision glass cylindrical cells made from N M R tubes. Solutions for light scattering were filtered twice by gravity through a 0.22-pm filter unit (Millipore) directly into the scattering cell. The cell was held in a thermostated block during measurement, anU temperature was maintained to within f0.05 OC. The autocorrelation function was analyzed by the cumulant method.22 The average hydrodynamic radius of micelles is related to the apparent diffusion coefficient via Rh= kT/6x7Dapp,where 7 is the viscosity of solvent, k is Boltzmann's constant, and T is the temperature. The viscosities of H 2 0 and D 2 0 containing various amounts of NaCl have been tabulated.23 (21) E. W. Kaler, J. E. Puig, and W. G . Miller, J. Phys. Chem., 88, 2887 (1984). (22) D. E. Koppel, J . Chem. Phys., 57, 4814 (1972).
Chang and Kaler
2998 The Journal of Physical Chemistry, Vol. 89, No. 14, 1985 TABLE II: Critical Micelle Concentration for SDS in Solutions of Various Ratios of HzO/DzO at 25 and 40 OC vol fraction of H20in s o h 0 0.25 0.5 0.75 1.0 7.95 8.1 8.2 cmc, mM (25 "C) 7.6 7.6 cmc, mM (40 "C) 7.95 7.9 8.1 8.4 8.6
Results A. Cmc Measurements and the Standard Free Energy Change of Micellization. The total (negative) free energy change of micellization (AGO) is balanced by two terms: a negative portion due to hydrophobic interactions (AGoHI) and a positive portion due to electrostatic charge repulsion and hydration of the polar groups at the micelle-water interface (AGoR).zk26 Thus, AGO = AGOHI AGOw AGO is related to the experimentally measured cmc by21,28
TABLE III: The Free Energy Change of Micellization in H20and D20SDS Solutions at 25 OC AGO,,,,, cal/mol AGO,,, cal/mol AGOR, cal/mol H20 -4910 f 20 -8600 f 40 3690 f 50 D20 -4980 f 20 -8700 f 40 3720 f 50 TABLE I V Ouasi-elastic Light Scattering Data at 25 and 40 O C T, OC x,,, IO*D,,, cm2/s kD, cm"g R ~A, 0.975 25 1.o 7.77 24.7 0.5 0.826 6.94 26.1 0.25 0.766 8.39 26.7 0.0 0.732 7.78 26.7 1.o 0.5 0.25 0.0
40
+
AGO = (2
- P)RT In cmc
(1)
where p is the degree of dissociation of counterions from the micelle. For completely ionized micelles, @ = 1 ; for neutral micelles, /3 = 0. Here concentration has units of mol/L, corresponding to a 1 m ideal solution standard state. Equation 1 is valid under the assumption that the micelles are effectively monodispersed, which is justified here because the surfactant and salt concentrations are low. Table I presents the cmc's determined from specific conductance data (Figure 1) for a homologous series of sodium alkyl sulfates from C8 to CI4in DzO and H20. The linear least-squares fits of data below and above the cmc were made neglecting the region of curvature close to the cmc. The concentrations measured (Figure 1) varied from approximately 30% below the reported cmc value to 30% above it. Our cmc result in DzO is about 5% lower than that in ref 10, while the results in HzO.are within 1%. We do not have a satisfactory explanation for this, but we find our results reproducible and self-consistent. The cmc's of SDS in solutions containing various ratios of H 2 0 / D 2 0 are shown in Table 11. The ionization constant, @, in eq 1 can be evaluated with the following relation:29 PzM/3(1000SI - ANa)
+ @A,,
= 1OOOS2
(2)
Here, SI and Szare slopes of the specific conductivity-concentration curve (Figure 1) below and above the cmc, respectively. ANa is the limiting conductance of sodium counterions, and N is the aggregation number of a micelle. At 25 OC, ANa in HzO and D 2 0 is 50.19 and 41.62 cm2/(ohm equiv), respectively.M B k u s e the value is not sensitive to the aggregation number in eq 2, the aggregation number is taken to be 65 in both HzO and DzO. The calculated p values are 0.275 in HzO and 0.277 in DzO. The experimental accuracy is estimated to be f5%. It should be mentioned that the presence of charged micelles makes the solution nonideal, even at low concentrations, and the use of eq 2 to determine the absolute value of @ may not be rigorously justified. The free energy change associated with transfer of a methylene group from the solvent to the oillike interior of the micelle, AGO(-CH,-), can be estimated by taking the derivative of eq 1 with respect to the number of carbon atoms in the surfactant nc:31 AGo(-CH,-)
a In cmc
= (2 - 8 ) R T -
an,
(3)
(23) F. A. Goncalves, Water Steam: Their Prop. Curr. Ind. Appl., Proc. Int. Conf. Prop. Steam, 9th, 1979, 354 (1980), and CRC handbooks. (24) K. S. Birdi in "Micellization, Solubilization, and Microemulsions", K. L. Mittal, Ed., Plenum Press, New York, 1977. (25) M. F. Emerson and A. Holtzer, J . Phys. Chem., 71, 1898 (1967). (26) C. Tanford, J. Phys. Chem., 78, 2469 (1974). (27) P. Mukerjee, J . Phys. Chem., 66, 1375 (1962). (28) J. N. Phillips, Trans. Faraday SOC.,51, 561 (1955). (29) H. C. Evans, J . Chem. SOC.,579 (1956). (30) C. G. Swain and D. F. Evans, J . Am. Chem. Soc., 88, 383 (1966).
I
9.96 8.46 10.2 8.68
1.40 1.18 1.09 1.07
24.6 25.2 27.4 26.8
I
I
I
I
I
0.2
0.4
0.6
0.8
1.0
I
C (gmidl) Figure 2. Light scattering by solutions of SDS in H 2 0 and D,O with 0.2 M NaCl at 25 OC.
Note that this equation assumes that the values of @ are the same for each sodium sulfate surfactant used. Reported variations of @ as estimated with eq 2 are within our experimental error.29 Calculation shows that there is a free energy change per methylene group of -717 f 4 cal in HzO compared to -725 f 4 cal in D,O. The free energy change due to the hydrophobic interactions of the hydrocarbon chain, AGOHI, can than be estimated as n, times AGo(-CHz-). The differences between AGO and AGOHIin D,O and in HzO are small, but they are definite and consistent. Comparison of the hydrophobic part of the free energy change (AGOHI) with the total free energy change (AGO) calculated from eq 1 shows that the repulsive part of the free energy change (AGOR) is the same in HzO and D 2 0 within experimental error (Table 111). B. Light Scattering. (i) SDS in 0.2 M NaCl Solutions. In aqueous solutions of low ionic strength, the interactions between micelles and the repulsions between surfactant head groups can be compared by analysis of both static and dynamic light scattering data. We can determine the weight average molecular weight of the micelle Mw and the second virial coefficient B from the data using the equation H ( C - cmc) 1 = - + 2B(C - cmc) (4) I - I, M W Here H is a calibration constant, Z is the intensity of the scattered light, and Io is the intensity of the scattered light at the cmc. Debye plots for SDS in 0.2 M NaCl in H 2 0or D 2 0 are shown in Figure 2. The two straight lines have the same slope; hence the solutions have the 'same second virial coefficient. The weight average molecular weight of micelles is found to be 31 200 in D 2 0 and 28 500 in HzO. The estimated uncertainty is 10%. (31) M. S. Ramadan, D. F. Evans, and R. Lumry, J . Phys. Chem., 87, 4538 (1983).
SDS Micelles in Solutions of H20 and D20 I
The Journal of Physical Chemistry, Vol. 89, NO. 14, 1985 2999 I
T = 25°C 40'C 0
0
'H20=
C (gm/dl)
Figure 5. Apparent diffusion coefficient plotted as a function of SDS concentration in H20and D20with 0.8 M NaCl at 40 OC. TABLE V Aggregation Numbers and Hydrodynamic Radii Calculated for SDS Micelles in H20 and D 2 0 at 40 OC Rh, A
%a 0.71
I
0.5
I
[NaCI], M
I
I
3
2 C (gddl)
1
Figure 3. Apparent diffusion coefficient plotted as a function of SDS concentration in solutions containing various ratios of H 2 0 / D 2 0with 0.2 M NaCl at 25 and 40 OC. 8
,
I
I
I
I
I
T = 40°C
0 XHz0= 1.0 0 XHzO = 0.5
9
0.21 0
I
'
I
1
I
I
2
I
I
3
1
C (gmdl)
Figure 4. The same as Figure 3, with 0.6 M NaCl at 40 OC.
The apparent diffusion coefficients measured at 25 and 40 OC are presented in Figure 3. The apparent diffusion coefficient at the cmc, Do, the quantity kD defined via Dapp= Do[l + kD(C- cmc)]
H20
D20
0.25 0.5 1 2
66 92 127 185
70 122 21 1 320
0.8
0.125 0.25 0.5 0.75 1
216 398 502 588
194 416 666 785 928
H20 25 28 33 39 41 60
70 77
D20 26 32 42 53 40 61 83 93 105
micellar solutions in 0.6 M NaCl and 0.8 M NaCl at 40 O C plotted as before. Note that the curves are no longer straight lines. Under these conditions of ionic strength and temperature, the micelles are thought to have a rodlike shape.32 The aggregation number obtained by assuming a prolate ellipsoidal micelle, together with the mean hydrodynamic radius, is listed as a function of surfactant concentration in Table V. The value of the semiminor axis (the length of the paraffin chain) is taken to be 17 A in this calculati~n.)~
A XH20 = 0.0
\\
[SDS],g/dL
0.6
(5)
and the hydrodynamic radius Rhevaluated from Do are given in Table IV. The cmc term in eq 5 is small, and it is neglected without introducing appreciable error. The basic assumption of constant micelle size underlying this equation is discussed below. (ii) SDS in 0.6 and 0.8 M NaCl Solutions. The dependence of apparent diffusion coefficient on the concentration of surfactant is due in general to both intermicellar interactions and changes of micelle size with the change of surfactant c ~ n c e n t r a t i o n .At ~~ high ionic strength, intermicellar interactions are less important as a result of screening of the electrical double layers, and changes in diffusion coefficients are indications of changes in micelle size.20 Figures 4 and 5 show respectively the light scattering results for
Discussion In this section, micellar interactions and micelle size in H 2 0 or D 2 0 are discussed. First, note that eq 5 is based on the assumption that micelles do not change size or shape with the addition of surfactant and that changes in the apparent diffusion coefficient as the surfactant concentration increases are due to steric and electrical interactions between micelles. Corti and Degi6rgiolg calculated the pair interaction potential based on DLVO theory and showed that the effect of intermicellar interactions still dominates the change of apparent diffusion coefficient of micelles with concentration in 0.2 M NaCl solutions. Furthermore, Hayashi and Ikeda34 reported from light scattering measurements that the sphere-to-rod transition in SDS solutions occurs at a salt concentration greater than 0.45 M, thus justifying the assumption that micelles do not grow with increasing concentration in 0.2 M NaCI. Earlier in this paper it was shown that the degree of ionization of the micelle is the same in H 2 0 as it is in D 2 0 . Also kD, a measure of the interparticle forces between micelles and the hydrodynamic effect of surrounding micelles, is roughly constant in solutions of various ratios of H 2 0 / D 2 0 (Table IV). From the similarity of kD, @, and dielectric constants in the two solvents, as well as the closeness of the calculated values of AGOR in both (32) C. Y. Young, P. J. Missel, N. A. Mazer, G. B. Benedek, and M. C. Carey, J. Phys. Chena., 82, 1375 (1978). (33) C. Tanford, J. Phys. Chem., 76, 3020 (1972). (34) S. Hayashi and S . Ikeda, J. Phys. Chem., 84, 744 (1980).
Chang and Kaler
3000 The Journal of Physical Chemistry, Vol. 89, No. 14, 1985
,
I
I
T = 40°C
120-
OH,O A D,O
-
K=2.3x108/
6ol A
40
t
1
, , I
0
I
I
I
I
,
,
,
/
I
Mole fraction SDS Figure 6. Hydrodynamic radius as a function of SDS concentration in H 2 0 and D 2 0 with 0.8 M NaCl at 40 O C . Solid curves represent the fit of the theory of Missel et aLZ0
cases, we conclude that the intermicellar interactions and head group repulsions are the same in light and heavy water. Tables IV and V display the data concerning the size of SDS micelles in H 2 0 / D 2 0 solvents. Note that in 0.2 M NaCl the micellar radius in D 2 0 is only about 10% larger than that in HzO, but in 0.8 M NaCl the radii differ by approximately 40%. This difference can be rationalized as follows. At low ionic strength, the data indicate that the micelles are nearly spherical. The intermicellar interactions and head group repulsions, which have been shown to be the same in HzOand DzO in the previous section, are the dominant factors in determination of the micelle size. Thus, the micelle sizes are comparable in the two solvents. On the other hand, at high ionic strength, the head group repulsions are reduced, the density of head groups a t the micelle surface increases, and the micelles assume a prolate shape. As the micelles elongate, each monomer associated into the cylindrical region of the micelle will only slightly increase the repulsive part of the free energy change. As a result, the hydrophobic interactions masked by the head group repulsions at low ionic strength become relatively more important in determining the length of the micelles. Under these conditions a small difference in hydrophobic interaction may make a large difference in aggregation number, and hence in micelle size. Therefore, larger micelles form in DzOdue to the stronger hydrophobic interactions therein. A quantitative model of SDS micelle growth at high ionic strength has been proposed by Missel et aL2O They show that R T In K = pow - n,po (6) where pow and n,,po are the chemical potentials of n, monomers in a spherical cap and in the cylindrical region of a micelle, respectively. K is a parameter which measures the tendency for the n,monomers to associate into the cylindrical part of a micelle
rather than to form an independent spherical micelle. In other words, the larger the value of K is, the higher is the tendency for micelle growth. The comparison of theory to data taken at 40 OC is shown in Figure 6. The solid line is calculated from the theory with the parameter K set equal to 2.3 X lo8 for D 2 0 and 8.2 X lo7 for H20. The larger value of K in D 2 0 is consistent with the previous argument. The data fit the theory, however, only,at the intermediate range of surfactant concentration. The inconsistency observed at low surfactant concentration is likely due to the fact that the model assumes that the value of K is constant above the cmc. That is, the tendency for micelle growth is assumed to be the same at all surfactant toncentrations above the cmc. However, as mentioned above, Hayashi and Ikeda34have shown that the sphere-to-rod transition in micellar solutions of SDS occurs a t NaCl concentrations >0.45 M only when the SDS concentration is well above the cmc. Evidence for the lack of growth of micelles at low SDS concentrations is given in Table V, which shows that the micelles formed in 0.6 M NaCl by 0.25% suffactant (approximately 16 times the cmc) are nearly identical in size to those formed in 0.2 M NaCl. It is apparent that the pryicted micelle size is too high at low surfactant concentration since the tendency of micelle growth is lower at these concentrations. The incQnsistency at higher surfactant concentrations is likely due to the effect of intermi'cellar interactions, which are neglected in the theory. Finally, recall that salt has a dramatic effect on the cmc for ionic ~ u r f a c t a n t .It~ is ~ possible that the remarkable difference between the micelle size in HzO and D2O at high ionic strength may 6e due to an enhancement of the small difference in hydrophobic interactions in HzOand D 2 0 measured in the absence of added salt.
Conclusions Analysis of the static and dynamic light scattering and electrical conductivity data indicates that the electrical interactions between SDS micelles are the same in light and heavy water. From the comparison of micelle sizes in H 2 0 and D20, it seems that the mechanism of the change of micelle structure is similar in both solvents. At high ionic strength the micelle size changes dramatically with surfactant addition in both solvents when the SDS concentration is well above cmc; the D20 micellar solution behaves like its H 2 0counterpart at higher salt concentrations. The difference in micelle size, which is greatest at high ionic qtrength, illustrates the important role that small differences in hydrophobic interactions between HzO and DzO play in determining the micelle structure. Further investigation of surfactants containing longer hydrocarbon chains should show more evidence of this phenomenon. Acknowledgment. This research was supported by the National Science Foundation under Grant CPE-8307 188. Registry No. D20,7789-20-0; SDS, 151-21-3; sodium decyl sulfate, 142-87-0; sodium octyl sulfate, 142-3 1-4; sodium tetradecyl sulfate, 1 191-50-0.
