J. Phys. Chem. 1983, 87, 1377-1385
radicals, are formed in the cavitation bubbles produced by ultrasound in aqueous solutions.
Summary Hydroxyl radicals and hydrogen atoms are produced by ultrasound in aqueous solutions. .OH and .H formed by ultrasound in aqueous solutions were spin trapped with DMPO and PYBN while with POBN the H-POBN adduct was obtained. Furthermore, sonolysis of D 2 0 solutions containing the same spin traps led to the formation of the D spin adduct. This is in good agreement with the previous work of Anbar and Pecht.lS These results were confirmed by investigating the competition reactions for .OH and .H between the spin traps (DMPO and POBN) and the .OH and .H scavengers (02, formate, thiocyanate, benzoate, Br-, bicarbonate, methanol, ethanol, 1-propanol,
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2-methyl-2-propano1, acetone, and MNP). The unusual effects of 02,acetone, and MNP indicate that .OH and .H are produced in the cavitation bubbles and not in the bulk of the solution. Registry No. DMPO, 3317-61-1;PYBN, 69396-86-7; POBN, 66893-81-0;MNP, 917-95-3;HO., 3352-57-6;H., 12385-13-6;02, 7782-44-7;DzO, 7789-20-0;HzO, 7732-18-5;COO-, 14485-07-5; CH,(OH)CH., 2348-46-1; D., 16873-17-9; OH-DMPO adduct, 55482-03-6; H-DMPO adduct, 40936-29-6; D-DMPO adduct, 80402-70-6; C02--DMP0 adduct, 84895-13-6; CH,CH(OH)DMPO adduct, 40936-18-3;OH-PYBN adduct, 69397-28-0;HPYBN adduct, 69397-35-9;D-PYBN adduct, 84895-14-7;H-POBN adduct, 81616-73-1;D-POBN adduct, 84895-15-8;COz-POBN adduct, 84895-16-9;CH,CH(OH)-POBN adduct, 8489517-0;formate, 71-47-6;thiocyanate, 302-04-5; benzoate, 766-76-7; methanol, 67-56-1; ethanol, 64-17-5; 1-propanol, 71-23-8; 2methyl-2-propanol,75-65-0; acetone, 67-64-1.
Structure of Micellar Solutions of Nonionic Surfactants. Nuclear Magnetic Resonance Self-Diff usion and Proton Relaxation Studies of Poly(ethy1ene oxide) Alkyl Ethers Per-Gunnar Nllsson," Hakan Wennerstrom,lb and Bjorn Llndman' Physical Chemistry 1, Chemlcal Center, Lund University, 5-220 07 Lund, Sweden, and Arrhenius Laboratory, Stockholm Universi@,S- 106 9 1 Stockhoim, Sweden (Received: March 4, 1982; I n Final Form: November 30, 1982)
Binary systems of water and nonionic surfactants of the dodecyl oxyethylene monoether type, C12H25(OCHzCH2),0H,have been studied by 'H NMR techniques. For n = 5, C12E5, and n = 8, C12E8,the self-diffusion coefficients of the surfactants in the isotropic, L1, phase have been measured by using the pulsed field gradient technique for a range of temperatures and concentrations. In addition, the line widths of the different proton signals have been monitored, and some samples of liquid crystalline character were also studied. Dramatic broadening of the methylene signals of the Clz chain is observed as the hexagonal liquid crystalline phase is approached in the ClzE5-water system, while only a small broadening is observed in the C12E8-watersystem, showing that at low temperatures there is a growth of C12E5 micelles to rods with increasing concentrations, while the C12E8micelles at low temperatures remain small in the whole concentration range. The self-diffusion coefficients of the surfactants decrease rapidly with increasing concentration until a minimum is reached after which there is a slow increase. The location of the minimum occurs at lower surfactant concentrations the closer the temperature is to the cloud point, where the system separates into two isotropic phases. In the line width studies, broadening is found at a certain temperature interval when the temperature is increased in the C12E5 system. These results taken together indicate that, in the C12E5 system, the surfactant aggregates grow in size as the cloud point is approached. The aggregates seem to be flexible and probably not of a definite shape close to the cloud point. In the C12E8system, the micelles are much less affected by an increase in temperature and micellar growth cannot be unambiguously established. The methylene signals of the ethylene oxide moieties consistently show narrower lH signals, showing that in the aggregates they are less ordered than the chain methylenes. The various changes in aggregate size and shape are correlated with the stability ranges of the isotropic and liquid crystalline phases according to phase diagrams from the literature. Both aggregate size and phase structures are in qualitative agreement with considerations based on the effective (as a result of coiling, hydration, and head group size) shape of the molecules at different temperatures and concentrations.
Introduction With increasing temperature, dilute solutions of nonionic surfactants of the ethylene oxide variety split into two water-rich isotropic phases. This occurs throughout a region of coexistence, from above the lower to below the urmer critical temDerature. The Dhenomenon has been akributed to a deGydration of the surfactant head groups with increasing t e m ~ e r a t u r e . ~The - ~ changes in aggregate (1) (a) Physical Chemistry 1, Lund University; (b) Physical Chemistry, Stockholm University. (2) Lang, J. C.; Morgan, R. D. J . Chem. Phys. 1980, 73,5849.
structure accompanying this phase separation are still not well understood. Results from several experimental methods-light scattering,6s7membrane osmometry: sedimentation equilibrium? and visc~sity~~~-can be inter(3) Balmbra. R. R.:Clunie. J. S.: Corkill. J. M.: Goodman. J. F. Trans. Faraday i96zl581 1661: ' (4) Balmbra, R.R.;Clunie, J. S.; Corkill, J. M.; Goodman, J. F. Trans. Faradav sot, 1964, 60,979. (5) +iddy, G.J.'T. hhys. Rep. 1980,57, 1. (6) Attwood, D. J . Phys. Chem. 1968,72,339. (7) Elworthy, P. H.;McDonald, C. Kolloid-2. 1964,195,16. (8) Attwood, D.;Elworthy, P. H.; Kayne, S. B. J . Phys. Chem. 1970, 74, 3529.
0022-3654/83/2087-1377$01.50/00 1983 American Chemical Society
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Niisson et at.
isotropic aqueous solutions of the nonionic surfactants pentaethylene glycol dodecyl ether (C12E5) and octaethylene glycol dodecyl ether (ClzE8). Approximate phase diagrams of these systems are shown in Figure 1. 0
.
0
,
20
,
, 40
,
. 60
,
, 80
, xx)
%C12E3
%C12E6
04 0
I
, 20
,I
, 40
,
,'I,
60
4 8 O x x ) ,
%C12E5
%CtZE8
Figwe 1. Schematic phase dlagrams of the systems C,g3-H20 (from ref 5), CE , -,HO , (from: Harusawa et ai. Co//oidPolym. Sci. 1974, 252,613), C,,EB-H,O (from: Clunie et ai. Trans. Faraday Soc. 1969, 65,287), and C,&,-H20 (after: Shinoda, K. J . CdbH. Interface Sci. 1970, 3 4 , 278) (the cubic C, phase is not reported in the original reference). Hexagonal, lamellar, and cubic liquid crystalline phases are denoted by HEX., LAM., and CUB., respectlvely, and L, and L, denote isotropic solutions. I n regions denoted with S, solM surfactant is present.
Experimental Section Cl2E4,C12E5,C12E6,and ClZE8of high quality were obtained from Nikko Chemical Co. Ltd., Tokyo. C10E4was generously supplied as a gift from Dr. Robert Laughlin, Proctor and Gamble Co., Cincinnati, OH. The solvent used was D,O obtained from Ciba-Geigy and had >99.7 at. '70 isotopic purity. All components were used without further purification. Solutions were prepared by weighing the components. All concentrations will be given in percent by weight. The diffusion studies were performed on a Bruker 322s pulsed NMR spectrometer using 'H NMR at 60 MHz for the nonionic surfactant diffusion. The pulsed magnetic field gradient technique developed by Stejskal and Tanner22was used, the spectrometer being equipped with a specially made pulsed magnetic field gradient unit. With this technique, a spin echo is produced by a 90°-r-1800 pulse sequence and the magnetic field gradient, g, is applied during a time, 6, as two pulses, separated by a time A, one before and one after the 180" pulse. For a given chemical species, the diffusion attenuates the contribution, E , from the particular compound to the echo amplitude a t time 27 according to E = Eo exp(-(yg6)2D(A- 6/3)) (1)
preted as indicating that the size of the surfactant aggregates increases rapidly as the temperature is raised toward the cloud point. The validity of this interpretation as the sole explanation of the light-scattering experiments has, however, been questioned'*l2 and it has been s h ~ w n ' ~ ! ~ where ~ Eo is the contribution to the echo in the absence of that critical concentration fluctuations are responsible for field gradients and y is the magnetogyric ratio of the nuthe intense light scattering close to the cloud point. cleus studied. The self-diffusion coefficient, D, was deFurthermore, the interpretation of results obtained by termined by measuring E for a series of 6 values keeping using other methods is not unambiguous and it is possible g and A fixed (typically, A = 26 ms) at values suitable for that in some cases the observed behavior is due to the reliable determination of D. By minimizing E - Eo. presence of a critical point. It is also often difficult to exp[-Ba2(A - 6/3)] with a least-squares procedure, one distinguish between the effect of interactions between determines the diffusion coefficient from the optimal value small micelles and the effect of a growth in aggregate of B. size.l5-l7 Measurements to establish the absolute values of the In the present work, we try to avoid some of these difself-diffusion coefficients were performed on a reference ficulties by focusing on the motion of the surfactant glycerol sample with knownz3self-diffusion coefficients. molecules. The characteristic feature of the critical region For samples with lowest surfactant content, the spin echoes is the presence of long-range correlations. The amplitude were accumulated on a computer in order to obtain a better of the density fluctuations is, however, small and, for a signal-to-noise ratio. The temperatures are accurate to particular molecule (or aggregate), the short-range enviwithin i0.5 "C. ronment is virtually unaffected by the critical behavior, Due to exchange with the OH groups of the surfactant, as long as the molecule (or aggregate) is small relative to the heavy-water solvent is slightly contaminated with the correlation length. It has indeed been shown that both protons (cf. Figures 3, 6, and 8). These water protons proton NMR line widthsl8 and self-diffusion coeffiinterfere in principle with the measurements of surfactant cients18-2'are unaffected by critical fluctuations in binary diffusion. However, the water protons give only a small liquid mixtures. Thus, we have measured the self-diffusion contribution to the total intensity and the water diffusion coefficients of the surfactants, using the NMR spin-echo is fast, giving in general a negligible contribution from pulsed field gradient technique, and proton line widths in water to the echo amplitude in the presence of the strong field gradients often necessary for measurement of the surfactant self-diffusion. For DzO-rich samples, a con(9) Ottewill, R. H.; Storer, C. C.; Walker, T. Trans.Faraday SOC.1967, 63, 2796. tribution from water protons was sometimes observable (10) Herrmann, K. W.; Brushmiller, J. G.; Courchene, W. L. J. Phys. for short pulses, 6. These points were omitted and good Chem. 1966, 70, 2909. fits to eq 1 were obtained. (11) Corti, M.; Degiorgio, V. Opt. Commun. 1975, 14,358. (12) Wennerstrotn, H.; Lindman, B. Phys. Rep. 1979, 52, 1. Due to instrumental difficulties, the fitting to eq 1was (13) Corti, M.; Degiorgio, V. Phys. Rev. Lett. 1980, 45,1045. not perfect for water-rich samples in the C12E8-water (14) Corti, M.; Degiorgio, V. J. Phys. Chem. 1981,85, 1442. system at 69 "C. The accuracy of the measured D is lower (15) Elworthy, P. H.; Macfarlane, C. B. J. Chem. SOC.1963,907. (16) Tanford, C.: Nozaki, Y.: Rohde. M. F. J. Phys. Chem. 1977.81, for these samples, but this is of no consequence for the 1555. basically qualitative discussion presented below. (17) Staples, E. J.; Tiddy, G . J. T. J. Chem. SOC.,Faraday Trans. I The proton NMR spectra for the line width studies were 1978, 74, 2530. (18) Hamann, H.; Hoheisel, C.; Richtering, H. Ber. Bunsenges. Phys. recorded on a Jeol MH-100 spectrometer operating in the Chem. 1972, 76, 249. (19) M e g a , J. C.; Stein,A.; Allen, G. F. J. Chem. Phys. 1971,55,1716. (20) Anderson, J. E.; Gerritz, W. H. J. Chem. Phys. 1970, 53, 2584. (21) Lang, J. C.; Freed, J. H. J. Chem. Phys. 1972, 56, 4103.
(22) Stejskal, E. 0.;Tanner, J. E. J. Chem. Phys. 1965, 42, 288. (23) Tomlinson, D. J. Mol. Phys. 1973, 25, 735.
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
Micellar Solutions of Nonionic Surfactants I
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30
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L
n
0
N
3
**
204
0
1
1
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1
10
1
1
1
20
1
1
1
1
1
50
40
30
5
0
10
15
20
25
96 C12E5 Figure 2. Observed selfdiffusion coefficient of concentration.
;I( 1
1
C12E5
vs. the
1: 2 9 % 2: 219% 3: 29.5% 41 29.5% 5. 29.5% 6: 37.9% 7: 49.5%
2
C12E5
T ("C) Figure 5. Line width at half-height of the main proton NMR signal for the methylene groups of C12E5as a function of temperature for a 4.95% C12E5 solution.
244:%% 4.9"C 24.9% , 45.2OC 4.9"C 24.9OC
Il
1
4
I
5
e
I -1rI /
L
I-
-
? . / I
a b c d e f CHJCH~~CH,CH~CH,CH,)~OH, HOD
7
f
1
30
11
1)
b
I _
Figure 3. Selected proton NMR spectra for C1&. Percentage C,g5 and temperature are given in the figure. Sample 6 Is hexagonal llquid crystalline, and all other samples are micellar. The scale is the same as given for spectrum 1 for all spectra except spectrum 6.
Figure 6. Assignment of the proton NMR peaks of C12E5(after: Christenson, H.; Frlberg, S. J . CollOM Interface Scl. 1980, 75, 276).
o 45.2 C
60
A 35.0c 0
24.9'C 14.9C
L.
rN
40
c .
9 20
3
0
I
0
10
20
30
40
50
%C12E5
0
I
I
20
I
I
40
I
I
60
I
I
80
I
I
100
% C12E8
Flgure 4. Linewidth at haifhelght of the main proton NMR signal for the methylene groups of C12Esas a function of concentration.
Flgure 7. Observed selfdlffuslon coefficients of C,?E, vs. the concentration of C1&
continuous-wave (CW) mode a t 100 MHz. The temperature was measured with a calibrated copper-constantan thermocouple which was placed in an NMR tube with water. The temperatures are accurate to within h0.5 OC.
solution regions; lower critical temperatures are approximately 31 and 74 "C for the two surfactants, respectively. Figure 2 shows the self-diffusion coefficients of C12E6. In Figure 3, selected proton NMR spectra are presented for this surfactant, and the proton NMR line widths a t half signal h e a t for the main methylene signal of the C12chain are summarized in Figure 4. Figure 5 shows the lime width for a 4.95% C12ESsolution a t several different temperatures. Figure 6 shows a more detailed 'H NMR spectrum
Results Amphiphile self-difision and proton NMR spectra were studied for C12E6and C12Esas a function of temperature and concentration over the extensions of the isotropic
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Niisson et al.
,
l 4
A
E 5 1 : 3 . 0 % , 5.0;C
u L
i
3 2 ': 3:0%.%6:%"! 30% 4 4: 29.4%' 5.0" 5 : 29.4%'24.9'
1
I
8 ,
38:.2;66.8: 8 . 69.8%: 63:0'!
jLL
$i!
Figure 8. Selected proton NMR spectra for C,& Percentage C l g 8 and temperature are given in the figure. Sample 7 1s cubic iiquM crystalline, and all other samples are micellar. The scale Is the same for all spectra.
A
a
66.8.C 50.0.C 24.9.C
01 0
I
I
10
l
l
20
1
I
30
l
l
40
I
50
%C12E5 Flgure 10. Apparent radius of C12Esmicelles calculated from the selfdiffuslon data given In Figure 2.
In surfactant-water systems, there is always a finite monomer concentration and these monomers can contribute significantly to the observed average diffusion. The observed self-diffusion coefficient can for a micellar system be written as (3)
V
I
0
I
I
20
I
I
40
I
I
60
I
I
I
I
80 100 90 C12E8
Figure e. Line width at halfheight of the main proton NMR signal for the methylene groups of C,2E8 as a function of concentration.
of a C12E5solution, so assignment of the different peaks can be given. Figures 7-9 show the self-diffusion, selected NMR spectra, and the line width of the methylene signal, respectively, for the C12E8system. The assignments of the NMR signals correspond to those in Figure 6.
Discussion Self-Diffusionin Surfactant Systems. General Considerations. Because the translational mobilities are greatly affected by association phenomena, observed amphiphile self-diffusion coefficients can be of considerable help in the determination of solution structure^.^^ With the NMR pulsed field gradient method, the diffusion is monitored over a characteristic distance, 1, given by 1 = ($)1/2 = ( D A ) 1 / 2 (2) For D = 10-l' mz/s and A = 26 ms, 1 N 0.7 pm and the molecular motion has to occur over distances of several thousand angstroms to contribute to the observed D. For a molecule confined to an aggregate with an extension smaller than 1, the observed D value will mainly reflect the slow diffusion of the aggregate itself. On the other hand, for a molecule that is free to move over large distances, the diffusion is fast, i.e., corresponding to molecular diffusion. (24) Lindman, B.; Kamenka, N.; Brun, B.; Nilsson, P. G. In 'Microemulsions"; Robb, I. D., Ed.; Plenum Press: New York, 1982; p 115.
where P,, and Pmicare the fractions of amphiphile in monomeric and micellar states, respectively, and Dmn and Dmicare the self-diffusion coefficients of the monomeric and micellized amphiphiles, respectively. The largest effect of monomer diffusion is, of course, observed at the lowest amphiphile concentrations and for the lowest DmiC The critical micelle concentration (cmc) is very low for the nonionic surfactants studied in this work (for example, cmc = 7.1 X 10" for C1&Z8at 25 OCZa) making the contribution to D from the free monomers small except for the cases with low Ddc and low surfactant concentration. Thus, for ClZE5,the free monomers may significantly contribute (by approximately 10% in the worst cases) to the observed self-diffusion coefficient at the lowest concentrations while, for C12E8,the monomer contribution is only a few percent a t the lowest concentration because of the higher Dmic. The analysis of the experimentally determined diffusion coefficients is in the present case complicated but is made interesting by the fact that the aggregate structure in the solutions is partly unknown. In order to clarify the discussion, we will adopt an assumed solution of noninteracting (except for a hard-sphere part) spherical micelles as a reference system. In such a reference system, there will be a small decrease in D with increasing concentration due to the obstruction caused by the repulsive short-range micelle-micelle interactions. More importantly, there is a sizable temperature dependence of D due to the nonspecific temperature dependence of any transport property in a solution. To eliminate this factor, we have calculated Stokes-Einstein radii, rapp,from
rapp = kT/( 6 d )
(4)
where q is the viscosity of the medium taken to be that of the pure solvent. (it should be noted that no contributions from the presumably small increase in viscosity in the vicinity of the critical point are included in this viscosity.) The calculated rappvalues for the two systems (25) Meguro, K.; Takasawa, Y.; Kawahashi, N.; Tabata, Y.; Ueno, M. J. Colloid Interface Sci. 1981,83, 50. (26) Ueno, M.; Takasawa, Y.; Miyashige, H.; Tabata, Y.; Meguro, K. Colloid. Polym. Sci. 1981,259, 761.
The Journal of Physical Chemistry, Vol. 87, No. 8, 1983
Micellar Solutions of Nonionic Surfactants
I2
4
A
0
I
I
I
I
I
I
I
l
l
are shown in Figures 10 and 11. In extensive concentration-temperature regions, raPpis clearly larger than what is reasonable for spherical micelles, considering the molecular structure of the surfactant. The real systems thus deviate markedly from the reference system. These deviations could be caused either by strong micelle-micelle interactions or by a micelle growth or by both. Proton Relaxation. It has been demonstrated that the proton NMR line shape for large surfactant aggregates results from a superposition of Lorentzian lines of different Under certain assumptions, the line shape can be calculated and it is possible then to obtain the rotational correlation time for the aggregates, and hence the aggregate size, from a comparison between theoretical and experimental spectra. This procedure is applicable only for line widths larger than those generally encountered in the present study, and we present here mainly a qualitative discussion of the data obtained for the half-width of the main methylene signal of the alkyl chain. The ethylene oxide peak consists of several signals with small chemical shift differences, and, therefore, broadening cannot easily be separated from changes in the chemical shift. Furthermore, the observed effects are much more dramatic for the alkyl chain signals than for the ethylene oxide signals (see Figures 3 and 8). Although the width of a signal a t half-height does not give a faithful description of transverse relaxation for large aggregates andcannot, therefore, be used to deduce values of the correlation time, they do provide qualitative insight into micellar growth. As the surfactant aggregates increase in size, it takes a longer time for the aggregate to rotate as well as for a molecule to diffuse around the micelle surface. The long rotational correlation time for large surfactant aggregates will make the proton NMR line widths larger than for simple solutions containing small speciesa2' In addition to the correlation time, the actual line width will be affected by the local order parameter of the alkyl chains, S = 1/2(3cos28 - l ) ,where 8 is the angle between the normal to the micelle surface and a H-H vector. Figures 3 and 4 show that, for the C12E5-water system a t low temperatures, the main methylene signal gets broader when the amphiphile concentration increases. These broad signals demonstrate that there is growth into large micelles with increasing concentration for this system in the low temperature range. For the broadest signals, the methvlene and methvl signals overlap and the line width at kalf-height for the methylene signal is taken as (27) Ulmius, J.; Wennerstrom, H. J.Magn. Reson. 1977, 28, 309.
1381
twice the low-field half of the methylene signal. For temperatures close to or above the critical point temperature (the minimum in the cloud point curve, all measurements refer to the one-phase region), the signals17are narrower, indicating shorter correlation times or smaller order parameters. The signals are, however, at least at 25 "C, still broader than those normally encountered for a solution consisting of small micelles. For the C12E8-water system, the proton NMR signals are quite narrow a t all temperatures and concentrations (see Figures 8 and 9). This shows that micellar growth of the kind that is encountered in the C12E5system does not occur or occurs to a much lesser extent in the C12E8system. A striking observation is the rather narrow peaks ob-
alkyl methilene ones and are even narrower than the methyl signal. It seems that, throughout, the ethylene oxide chains are on the average in a less extended conformation than the alkyl chains. Miceliar Size, Shape, and Hydration in Dilute Solutions. Of the two surfactants studies, C12E8shows the smallest deviation from the reference system and reasonable apparent radii are in fact obtained at low concentrations. As indicated above, the monomer diffusion cannot be ignored a t low amphiphile concentration. The micellar diffusion coefficients were calculated from eq 3. D,, was assumed to be 3.5 X m2/s at 25 "C and to vary with temperature according to q D / T = constant, where 7 is the viscosity of water. P,,, is calculated from interpolated values of literature values of the cmcaZ5If an extrapolation of the micellar diffusion coefficients to infinite dilution is done for C12C8,one obtains a micellar radius of 30.3 A at 5.4 OC, 31.0 A at 25.2 "C, and 30.5 A at 49.1 OC from eq 4. At 69 "C, a trustworthy extrapolation cannot be done because of the rapid decrease in apparent radius with decreasing amphiphile concentration that probably occurs a t low surfactant concentration. The extrapolations are rather crude and the differences between the obtained radii are not significant. We will, . in our calculations. therefore, use an average value of 31 & The micellar hydration can be estimated by subtracting the volume occupied by the amphiphile from the micelle volume. We thus assume a spherical micelle with an approximate experimental radius of 31 A and use the density 1.0 g/cm3 for C12E8and 1.1g/cm3 for DzO. The length of the fully extended hydrocarbon chain in the amphiphile can be calculated to be 16.7 A.28 If the hydrocarbon core radius is taken as the length of the fully extended hydrocarbon chain of the amphiphile, the micelle aggregation number will be 55.28 One obtains then a hydration of approximately six water molecules per ethylene oxide group from these data. This value can be compared with the result obtained from D20 self-diffusion studies29 in nonionic micellar solutions where the hydration was found to be approximately four to five water molecules per ethylene oxide group for approximately 10% solution and decreasing with increasing surfactant concentration. It should be noted that the concept of a hydration number is a questionable simplification and that "hydration" is defined somewhat differently depending on the experimental method used. Since water is the solvent, water (28) Tanford, C. "The Hydrophobic Effect"; Wiley-Interscience: New York, 1973. (29) Nilsson, P. G.; Lindman, B., to be submitted for publication.
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molecules will be close to the micelles even if they are not bound to the micelles. In the D 2 0 self-diffusion studies, the hydration is defined as the water molecules effectively moving with the micelles as a kinetic entity. The different definitions can be the explanation for the slightly different values of the hydration. Another explanation is that the micelles are not spherical. Tanford et a1.16 drew this conclusion from geometrical considerations, and they suggested that the micelles are disklike. If nonspherical micelles are assumed, the hydration calculated from the geometrical considerations decreases. It should be noticed that the hydration calculated from micellar size is very strongly dependent upon the micellar radius and small errors in the radius can give considerable effects in the calculated hydrations. The length of the fully extended ethylene oxide chain in C12E8 is approximately 30 A. If the C12E8 micelles were spherical and with a hydrocarbon core radius of 16.7 A, the experirmental average length of the ethylene oxide chain in the micelle would be approximately 14 A. If the micelles were nonspherical, the length of the ethylene oxide chain would be even lower. This suggests that the ethylene oxide chains are far from an extended configuration and that the order of the ethylene oxide chains must be low. This agrees with the observed narrow proton NMR signals for the ethylene oxide groups (see above). It should be stressed that, also when broadening is found for the methylene signal, the ethylene oxide signals remain quite narrow (see Figure 3). For C12E5, trustworthy extrapolations cannot be done a t any temperature because of the rapid decrease in apparent radius with decreasing amphiphile concentration. The corresponding calculations for C12E5 cannot, therefore, be accomplished. The deviation from the behavior of the reference system is so large even a t the lowest concentration studied that, if there were intact spherical micelles in the system, they must interact strongly. The presence of a critical point shows that the interaction should be attractive and one has to invoke extensive formation of oligomeric aggregates to explain the diffusion data. However, the rather broad proton NMR line widths found even at low concentrations show that the aggregates present are larger than spherical micelles. Changes in Solution Structure on Approaching the Cloud Point. It is seen from Figures 10 and 11 that, for low surfactant concentrations, the apparent radius increases faster with increasing surfactant concentration the higher the temperature is. This increase in apparent radius with temperature shows that there is either a strong increase in the micellar interaction or an increase in aggregate size as the cloud point is approached. Figure 5 shows that, for an approximately 5 % ClzE5 solution, the halfwidth of the methylene signal increases with increasing temperature up to approximately 15 "C, which gives a direct demonstration of a growth of the aggregates with increasing temperature. Figure 4 shows that, even for lower surfactant concentrations, the methylene signal is broader at 15 "C than at 5 "C. One generally expects (without major changes in aggregate size) a decreasing line width with increasing temperature as a result of accelerated molecular and aggregate motion; a decreasing order parameter also contributes to a decrease in line width. Above 15 "C, the decreased line width may result from a markedly decreased order in the aggregates. The phase diagram indicates that, close to the cloud point, the preferred aggregate shape may be an intermediate between a disk and a rod. Our conjecture is then that the aggregates do not have a definite preferred shape close to the cloud
point and that there may be large fluctuations in aggregate size and shape. Combined with a relatively low intrinsic order of the alkyl chains, the fluctuations in shape could explain why the aggregate growth is not accompanied by an extensive broadening of the NMR signals close to the cloud point. A possible alternative explanation of the data in the high temperature range is in terms of strong interactions between rather small micelles. It is on the whole more difficult, but not impossible, to account for the experimental data on the basis of this idea. One could ask if the distinction between strongly interacting small micelles and large aggregates with a fluctuating size and shape reflects a difference in point of view rather than a difference in opinion about the physical properties of the system. For C&8, the aggregates present in the solution gennerally seem to be smaller than for C12E5 under corresponding conditions (distance from the cloud point). Because of the small aggregate size, the changes in proton NMR line width with temperature are much less dramatic than in the CI2E5system. It is difficult to assess, on the basis of the present data, whether the clear deviations in properties from those of the reference system with noninteracting spherical micelles are due to micelle-micelle interactions or whether they are caused by micellar growth. If micellar growth exists in this system, the growth must be rather small. Due to the higher temperature, the thermal agitation leads to a preference for smaller aggregates, other factors being equal. For the higher temperature, we also expect a stronger aggregate-aggregate interaction. Solution Structure at Higher Concentrations. For ionic surfactant systems, it is sometimes found that the surfactant aggregates increase in size with increasing surfactant c o n ~ e n t r a t i o n . ' ~ , ~Also ~ * ~for ~ nonionic surfactant systems, an increasing aggregate size has sometimes been inferred.32*33 With increasing concentration, we find both from selfdiffusion and from proton NMR line widths clear evidence for micellar growth for C12E5 a t low temperatures. There is a continuous broadening in proton NMR until the relatively narrow two-phase region L1 hexagonal phase is reached. These observations taken together suggest that at low temperatures there is a growth of C12E5 micelles into long rods with increasing concentrations. For CI2Esat low temperatures, the apparent radius remains quite small up to rather high concentrations. (The dramatically increasing apparent radius at high surfactant concentrations is probably caused by repulsive interactions between the aggregates.) There is, above all, essentially no broadening in proton NMR line widths even at the highest concentrations in the L1 phase. Comparing Figures 4 and 9, one infers that the broadening is 1 order of mangitude greater for C12E5 that for CI2Es. For C12E8, there is a cubic liquid crystalline phase succeeding the micellar phase a t low temperatures as the concentration is increased. The location of the phase, as well as its self-diffusion behavior (see below), suggests that it is built up of small closed amphiphile aggregates in a water continuum (cf. ref 34). The different observations seem to demonstrate that the CI2E8micelles at low temperatures
+
(30)Mazer, N.A.;Benedek, G. B.; Carey, M. C. J . Phys. Chem. 1976, BO, 1085. (31)Lindman, B.; Wennerstrom, H. Top. Curr. Chem. 1980, 87, 1. (32) Bcatmk, T. A.; McDonald, M. P.;Tiddy, G. J. T.; Waring, L. Surf. Act. Agents, Symp. 1979, 181. (33)Hoffman, H.; Kielman, H. S.; Pavlovik, D.; Platz, G.; Ulbricht, W. J. Colloid Interface Sei. 1981, 80, 237. (34)Bull, T.; Lindman, B. Mol. Cryst. Liq. Cryst. 1974, 28, 155.
Micellar Solutions of Nonionic Surfactants
remain small and spherical or roughly spherical in the whole concentration range. As discussed below, the different behavior of C12E5and C12E8is in qualitative agreement with simple geometrical considerations. To illustrate further the suggestion that large micelles are formed from nonionic amphiphiles with a small ratio of ethylene oxide chain to hydrocarbon chain, we measured the half-width of the methylene signal for a few concentrated solutions (>15%) of C&4, C12E4, and C12E6 a t approximately 5 "C. For all samples, the signals were broader than for C12E8(not much in the case of C12E6 close to 15%) supporting this suggestion. Unfortunately, no surfactants with longer ethylene oxide chain were available for measuring. For some temperatures, isotropic solutions are stable also a t high surfactant concentrations (cf. Figure l),making it possible to measure D in a region where there is little excess water. At the higher temperatures, the observed D values seem to extrapolate smoothly toward the value for the pure liquid surfactant at the corresponding temperature (see Figures 2 and 7). This indicates that, in the concentrated systems, the surfactant diffusion is markedly influenced by diffusion mechanisms other than aggregate diffusion. Either the aggregates are, on the average, larger than the characteristic diffusion length or the aggregateaggregate interactions are so strong that monomers exchange between different aggregates or there are no identifiable aggregates in the system under these conditions. Because of the low micellar self-diffusion coefficients, exchange of monomers between different aggregates can contribute significantly to the observed self-diffusion coefficients even if the probability for exchange is low. For temperatures slighty below the cloud point, 24.8 "C for C12E5 and 69.2 "C for C12E8,the diffusion coefficients have been measured over a continuous wide concentration range. In this way, one can follow the transition from the low-concentration to high-concentration regime. As is seen in Figures 2 and 7, respectively, there is a minimum in D at -4% surfactant for C12E5 and around 10% surfactant for C12EB.Since we have an interpretation of the diffusion mechanism in the two extremes of low and high concentration, the natural explanation of the occurrence of a minimum in D is that there is a gradual changeover in the diffusion mechanism. At low concentrations, D, is determined by the aggregate diffusion, which decreases with increasing concentration due to aggregate growth and/or interactions. At some concentration, the other diffusion mechanism becomes more efficient and D increases again. If Figures 10 and 11 are compared, it is seen that the concentration dependence of the apparent radius of C12E5 micelles at 5 "C does not at all resemble the curve obtained a t the same temperature for the C12E8micelles. There is, on the other hand, an approximate resemblance with the curve obtained a t 49 "C for the CI2E8system except that larger apparent radii are obtained throughout for the C12E5 system. It is interesting to notice that these temperatures are both approximatley 25 "C below the respective cloud points (the minimum in the cloud point curve). The same correspondence also holds for higher temperatures. Thus, the curves a t 25 "C for C12E5 and 69 "C for C12E8a!so resemble each other except for the larger apparent radius for the C12E5 system. Both these temperatures are approximately 5 "C below the respective cloud points. Consequences of Amphiphile Geometry on Micelle Shape cnd Phase Equilibria. Three properties of the surfactant aggregates are of special importance when considering the formation of a particular structure in a surfactant system, i.e., the elimination of the unfavorable
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hydrocarbonwater contact, head group interactions (steric factors, electrostatic interactions, hydration, etc.), and interaggregate interactions (van der Waals, electrostatic, etc.). For dilute micellar solutions, where intermicellar interactions are of minor importance, the shape of the micelle that best satisfies the first two demands depends on the relative size of the alkyl chains and the head groups. Even for concentrated micellar solutions and liquid crystalline phases, where interaggregate interactions cannot be neglected, simple geometric considerations are important when judging the merits of one structures over the It is possible to understand the main features of the phase equilibria in nonionic surfactant systems by using purely geometrical considerations. Steric repulsion between the head gruops gives stability in the order sphere > cylinder > bilayer, while the elimination of hydrocarbon-water gives stability in the order bilayer > cylinder > sphere. The head group repulsion term becomes more important for surfactants with large head grup cross-sectional area such as when the head group is strongly hydrated and when the head group is coiled. From these crude considerations in combination with the observed coiling of the ethylene oxide chains, we expect that, when the number of ethylene oxide groups in the nonionic surfactant increases (at a constant hydrocarbon chain length), a change in aggregate stability occurs in the direction bilayer cylinder sphere. This trend is exemplified by the phase diagrams in Figure l.46It is seen that a large lamellar phase exists in the Cl2E3-water system. Because of the short ethylene oxide chain, no micellar phase exists in this system, but, instead, there is a dispersion of lamellar phase in water at low concentrations. A lamellar phase also exists in the C12E5-water system, but there is also a hexagonal phase and an isotropic micellar phase. For the C12E6-water system, the extension of the lamellar phase has decreased somewhat, while the extension of the hexagonal phase is increased compared to C12E5. For C12E8,the lamellar phase has disappeared, while the hexagonal phase extends over a rather large part of the phase diagram. Cubic phases are also found in this system. For both C12E6 and C12E8,an isotropic phase extends over large parts of the phase diagram. The stability of the liquid crystalline phases changes in the expected direction when the head group size is increased. It is, of course, possible to understand the phase behavior in more detail by considering factors other than purely geometrical ones, but the above examples show that geometrical factors have a considerable influence on phase equilibria. It can be expected that geometrical considerations can also be fruitful when considering the micellar shape in the isotropic phases. This means that large micelles (prolate or oblate) can be expected for nonionic surfactants with a small ratio of ethylene oxide chain to hydrocarbon chain, while, for nonionic surfactants with a larger ratio of ethylene oxide chain to hydrocarbon chain, there should be a strong tendency to retain small spherical micelles.39 As is seen from the phase diagrams, the temperature has a dramatic effect on the phase equilibria. Most striking is perhaps the separation into two isotropic phases that occurs at elevated temperatures. This is a rather common
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(35)Israelachvili, J. N.; Mitchell, J. J.; Ninham, B. N. J. Chem. SOC., Faraday Trans. 2 1976, 72, 1525. (36)Israelachvili, J. N.;Marcelja, S.; Horn, R. G. Q.Reo. Biophys. 1976, 13, 121. (37) Wennerstrom, H. J. Colloid Interface Sci. 1979, 68, 589. (38) Jonsson, B.; Wennerstrom, H. J. Colloid Interface Sci. 1981, 80, 482. (39) Jonsson, B.; Nilsson, P. G.; Lindman, B.; Guldbrand, L.; Wennerstrom, H. In 'Surfactants in Solution"; Mittal, K. ., Lindman, B., Eds., in press.
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finding in aqueous binary systems, such as water-trimethylamine, water-nicotine, water-poly(ethy1ene oxide), and water-alkylphosphine oxide. This general behavior indicates that water becomes a relatively poorer solvent for hydrophilic groups as the temperature increases. It is tempting to correlate this property with the anomolously rapid decrease of the dielectric constant of water with increasing temperature. For the ethylene oxide surfactants, the NMR data show that the ethylene oxide chain is strongly coiled. The palisade layer of the surfactant agregate resembles a concentrated poly(ethy1ene oxide) solution. Kjellander and F1orin4O have shown that the resulting interaction when two ethylene oxide segments approach each other is repulsive compared to hydration at low temperatures but becomes attractive with increasing temperature. Such an effective dehydration with increasing temperature is confirmed by water self-diffusion studies.29 This should lead to a decrease of the effective area per polar group, which in turn leads to a tendency for a decrease in the curvature at the aggregate surface, and an increased tendency for the aggregates to grow in size39with increasing temperature. Liquid Crystalline Phases. For phases with cubic structure, NMR self-diffusion studies are straightforward, while the anisotropic liquid crystalline phases cannot be studied directly with the standard technique. It is well established that some fundamentally different types of cubic phases exist and one can distinguish between those having continuous amphiphilic regions extending over macroscopic distances and those with closed amphiphilic regions.41 With the NMR spin-echo method, the selfdiffusion is measured over macroscopic distances (several thousand angstroms). An amphiphile discontinuous cubic phase will, therefore, be characterized by a very low amphiphile self-diffusion coefficient, as it is unlikely (because of the low free-monomer concentration) that monomers will pass over from one aggregate to another. An amphiphile continuous cubic phase, on the other hand, will have a high self-diffusion coefficient as the amphiphile molecules can move freely over macroscopic distances in this structure. It may be recalled that the amphiphile aggregates have a liquidlike nature. In the system ClzE8-water, two different cubic phases exist, one (C,) between the isotropic low-viscositysolution and the hexagonal phase, and one (C,) between the hexagonal phase and the concentrated surfactant solution (see Figure 1). Two samples (35.0% and 39.8% C12E8) investigated belong to the C1 phase a t 5 "C. The amphiphile self-diffusion coefficients for these samples were too low to be measured with our spectrometer (
