4764
J . Phys. Chem. 1984,88, 4764-4769
Modeling the (91/92) ratio curve by RRKM calculations shows, first, that a statistical-model interpretation can easily account for the magnitude and energy dependence of the ratio, and second that within such a model the activation energy for m / e 91 formation must be approximately 0.6 eV higher than that for m / e 92 formation. An excellent RRKM fit was found with activation energies near recent literature values for mle 91 (benzyl) and m / e 92 (methylenecyclohexadiene). Activation energy values near 1.1 ( m / e 92) and 1.7 eV ( m / e 91) seem reasonable, but within the constraint that their difference must be near 0.6 eV, there is
considerable latitude in their choice.
Acknowledgment. The support of the National Science Foundation and of the donors of the Petroleum Research Fund, administered by the America1 Chemical Society, is gratefully acknowledged. Construction of the instrument was made possible by a gift from SOHIO. We thank Prof. John E. Bartmess for invaluable discussion and suggestions about the thermochemistry of the methylenecyclohexadiene ions. Registry No. Butylbenzene, 104-51-8.
Nuclear Magnetic Resonance Self-Diffusion and Proton Relaxation Studies of Nonionic Surfactant Solutions. Aggregate Shape in Isotropic Solutions above the Clouding Temperature Per-Gunnar Nilsson and Bjorn Lindman* Physical Chemistry 1 , Chemical Center, Lund University, S-220 07 Lund, Sweden (Received: June 6, 1983;
In Final Form: April 1I, 1984) In certain systems consisting of water and a nonionic surfactant of the alkyl oxyethylene monoether type an isotropic phase is found at temperatures above the cloud-point temperature, sometimes existing as an isotropic island in the miscibility gap. The self-diffusion coefficients of both the surfactant and water (D20) have been measured in this phase, termed the L3 phase, for the systems triethylene glycol dodecyl ether (C12E3)-D20and tetraethylene glycol dodecyl ether (CI2E4)-D20by means of the NMR pulsed field gradient spin-echomethod. In addition, proton NMR spectra have been recorded. For the Cl2E4-D20 system measurements have also been performed in the isotropic L1phase existing at lower temperatures. The water self-diffusion coefficients are interpreted in terms of aggregate obstruction and surfactant hydration. From the obstruction term, which is different for different aggregate geometries, it is inferred that the aggregates present in the L3 phase are large and oblate in both systems investigated while the results from the L1 phase are consistent with spherical or prolate aggregates. Spherical aggregates are, however, excluded from the broad proton NMR spectra observed in the L1phase. For the L3 phase a considerable broadening of the proton NMR signals is found at low concentrations giving evidence for large aggregates. The surfactant diffusion is rapid and can be referred to interaggregate exchange rather than aggregate motions. A low barrier to fusion and fission provides a mechanism for rapid long-range surfactant diffusion. The different observations provide evidence for large flexible oblate aggregates which attract each other. These results are consistent with deductions from the phase diagrams.
Introduction Aqueous solutions of nonionic surfactants of the poly(ethy1ene oxide) variety (C,E,, denoting an alkyl chain of n carbon atoms and x ethylene oxide groups) possess a miscibility gap over a certain concentration and temperature range. For nonionic surfactants with a relatively short poly(ethy1ene oxide) chain, the two-phase region of two isotropic solutions is sometimes transformed into a two-phase region of an isotropic phase and a liquid crystalline phase as the temperature is increased. In such system, an additional isotropic phase may be found in a certain temperaturecompition range in the miscibility gap, where it sometimes exists as an isotropic island. Such a phase was first reported by Harusawa et ala1for the system ClzE5-water. The phase has since then been found in several other systems2 and has been termed the anomalous phase3 or the L3 phase.4a In Figure 1 schematic phase diagrams of the systems ClzE3-water and C12E4-water are presented.2 In the C12E4 system, the L3 phase exists as an isotropic island in the phase diagram while in the C12E3 system the regions of the L3 phase and of the isotropic L2 phase are connected. It has been shown by Harusawa et al.' that for the C12E5 system ~~
~
(1) Harusawa, F.; Nakamura, S.;Mitsui, T. Colloid Polym. Sci. 1974, 252, 613. (2) Mitchell, D. J.; Tiddy, G. J. T.; Waring, L.; Bostock, T.; McDonald, M. P. J. Chem. Soc., Faraday Trans. I 1983, 79, 975. (3) Lang, J. C.; Morgan, R. D. J. Chem. Phys. 1980, 73, 5849. (4) (a) Bostock, T. A.; McDonald, M. P.; Tiddy, G. J. T.; Waring, L. "Surface Active Agents"; Society of Chemistry and Industry: London, 1979;
p 181. (b) Bostock, T. A.; Boyle, M. H.; McDonald, M. P.; Wood, R. M. J. Colloid Interface Sci. 1980, 73, 368.
0022-3654/84/2088-4764$01.50/0
the Lzand L3 phases are separate in the pure surfactant-water system but become connected upon addition of dodecane. It is interesting to notice that, in all systems studied where an L3 phase appears (also where the surfactant is not of the poly(ethy1ene oxide) ~ a r i e t y ) the , ~ L3 phase is found to be in equilibrium with a lamellar liquid crystalline phase over a certain temperature interval. The maximum temperature of existence of the L3 phase is closely the same as that of the lamellar liquid crystalline phase for most systems studied suggesting that the solution structure of the L3 phase and the lamellar structure are closely related. The solution structure of the L3 phase has been investigated in some previous studies. Thus Bostock et al? measured the self-diffusion coefficients of both amphiphile and water as well as the conductivity (NaCl added) in the system C12E4-water. It was suggested that the L3 phase consists of secondary aggregates of ellipsoidal micelles but the data were not interpreted in detail. In other the authors suggest that the L3 phase consists of rather small oblate micelles in an aqueous continuum. Lang and Morgan3 found for the system Clo E4-water that flow birefringence can be generated readily in the L3 phase and that the L3 phase is not stable to ultracentrifugation; the two phases formed upon ultracentrifugation are aqueous surfactant solution and lamellar liquid crystal. These both findings suggest that the aggregates present in the L3 phase are large. (The authors also (5)Ja) Persson, P. K. T.; Stenius, P., to be published. (b) Laughlin, R. G. In Advances in Liquid Crystals", Brown, G. H., Ed.; Academic Press: New York, 1978; p 41. (c) Laughlin, R. G. In "Advances in Liquid Crystals", Brown, G. H., Ed.; Academic Press: New York, 1978; p 99.
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4765
N M R Study of Nonionic Solutions
40542846847.552.154.9-
v-
u)
N
A
E 2-
\
A
D20 in PEG/D20
A A
A
A
A
0)
A
A
0 7
A
A
A
1-
A
D20 in C12E3/D20
ol
1
I
1
20
0
1
80
-1"
40
0
3
n
3c
A
AA
4
2 20
40
60
80 100 % C12E 3
Figure 2. The self-diffusion coefficient of D20in the L2/L3 phase of the system ClzE3-D20(A). For the same value of the abscissa as a certain surfactant sample, the self-diffusion coefficient of D 2 0 in the system PEG-D20 is also plotted (A). This sample has the same molar ratio DzO/ethyleneoxide groups as the surfactant sample. The self-diffusion coefficient of neat D20is also presented (0). The self-diffusion coefficients plotted at the same value of the abscissa are measured at the same temperature given at the top of the figure.
WtL2
Ya ' W
A
A
:
0
k a
A A
20bl ,I ,
,
0 0
20
40
60
80
100
% C12E4
Figure 1. Schematic phase diagrams of the systems ClzE3-water and C12E4-water(redrawn from ref 2). LAM denotes lamellar liquid crystalline phase, W denotes water with a very small amount of surfactant, and S denotes solid surfactant. L1,L2,and L3 denote isotopic solution phases. In the C1,E3-water system the Lz and L3 phases are connected and the whole phase region is denoted L2.
indicate that preliminary light-scattering results suggest the aggregates to be very large.) The purpose of the present work was to obtain more information about the solution structure of the L3 phase. We have thus measured the water and surfactant self-diffusion coefficients in the L3 phase for the systems ClzE3-D20 and CI2E4-DZO. For the C12E4system, a few measurements have also been performed for the isotropic L1 phase, which exists at temperatures below the miscibility gap, in order to clarify the difference between this phase and the L3 phase. The water self-diffusion coefficients are interpreted in terms of obstruction and hydration effects according to a model suggested in an earlier paper? For the surfactant different diffusion mechanisms are discussed. In addition to the diffusion studies proton N M R spectra have been recorded to obtain information on the solution structure from the line widths. Experimental Section CI2E3and CI2E4of high quality were obtained from Nikko Chemicals, Tokyo, Japan. Poly(ethy1ene glycol) (PEG M R = 20000, for gas chromatography) was obtained from Merck. DzO was obtained from Ciba-Geigy and was of >99.7 atom % D isotopic purity. All components were used without further purification. Solutions were prepared by weighing the components. All concentrations are in percent by weight unless otherwise indicated. The diffusion studies were performed on a Bruker 3228 pulsed N M R spectrometer using the pulsed field gradient method innovated by Stejskal and Tanner? The experimental data were fitted to the following equation E / E o = exp[-(ygS)*D(A
- 6/3)]
(1)
except for the cases indicated below. All symbols have their usual ( 6 ) Nilsson, P.-G.; Lindman, B. J . Phys. Chem. 1983, 87, 4756. (7) Stejskal, E.0.; Tanner, J. E. J . Chem. Phys. 1965, 42, 288.
For a more detailed description of the experimental aspects, see ref 6 and 8. The heavy water was slightly contaminated by protons and it was necessary to correct for this contamination in the 'H studies of surfactant diffusion a t the highest experimental water concentrations. In these cases a fit was made to an equation of the following type E / E o = C exp[-(yg 6)*0,(A - 8/31] + (1 - c) exp[-(yg 6I20,(A - v 3 ) 1 (2)
0,is the amphiphile or polymer self-diffusion coefficient and 0, the water self-diffusioncoefficient (from the 2H studies). C, which depends on the relative concentrations of protons in the two species as well as on relaxation effects, is varied to give the best fit. The D20 self-diffusion data must be corrected for the influence of exchangeable hydroxy hydrogens of the surfactanL6 For solutions in the L3 phase with more than 50% D 2 0 (by weight) the correction was in all cases less than 2% while the correction increases to 15% for the solutions with the lowest contents of D20. In the L1 phase the corrections were estimated since the corresponding amphiphile self-diffusion coefficients were not measured. In the polymer-water system no correction is needed. The proton N M R spectra were recorded on a Jeol MH-100 N M R spectrometer operating in the continuous wave (CW) mode at 100 MHz. Experimental Results The analysis of the self-diffusion coefficients of the L3 and L1 phases is partially based on a comparison with data for reference systems, namely, neat D 2 0 and surfactant and solutions of poly(ethy1ene glycol) (PEG) in DzO. The fact that temperature and composition cannot be varied independently for the L3 phase puts demands on the planning of the experiments for the reference systems. Thus, for each sample in the C12E3-Dz0and C12E4-D20 systems, a P E G D z O sample was prepared with the same molar ratio DzO/ethylene oxide groups. The polymer samples were measured at the same temperature as the corresponding aqueous surfactant sample. Neat DzO and surfactant samples were also measured at each of these temperatures. The observed self-diffusion coefficients of D 2 0 in the Lz/L3 phase of the system CI2E,-D2O are plotted in Figure 2 vs. the weight percentage of amphiphile. The self-diffusion coefficients of DzO in the PEG-D20 system and of neat D,O are also plotted in the same figure. At a certain value of the abscissa there are plotted (1) the self-diffusion coefficient of DzO in the L3 phase (8) Nilsson, P.-G.; Wennerstrom, H.; Lindman, B. J . Phys. Chem. 1983, 87, 1377.
4766
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 401442745.741452154.9
-
Nilsson and Lindman
"C 20 5
-
N
-
F r
-
v)
E
.
A
-
0 0
O
C12E4 in C12E4 D20
0
/
O
n
0
neat C12E4
A
A
PEG in PEG/D20
A
0
,
A
PEG in PEG/D20 ,
,
I
I
I
I
A
A
A
A
A
A
A
0 I
'
A
,
1
A 1
1
I
c d
-
I
t
1
f 2
0
10
20
30
40
0
50
%C12E4 Figure 4. The self-diffusion coefficient of D20 in the L3 phase of the system Cl2E4-D2O(A). For the same value of the abscissa as a certain
surfactant sample, the self-diffusion coefficient of D20 in the system PEG-D20 is also plotted (A). This sample has the same molar ratio D20/ethylene oxide groups as the surfactant sample. The self-diffusion coefficient of neat D20 is also presented (0).The self-diffusion coefficients plotted at the same value of the abscissa are measured at the same temperture given at the top of the figure. at the indicated concentration (A);(2) the self-diffusion coefficient of D 2 0 in the system PEG-D20 (A)(This sample has the same molar ratio D20/ethylene oxide groups as the surfactant sample.); (3) the self-diffusion coefficient of neat D 2 0 (0). All three samples are measured at the same temperature which is given in the figure. In Figure 3, the self-diffusion coefficient of CI2E3in the L2/L3 phase, the self-diffusion coefficient of PEG in the system PEGD20, and the self-diffusion coefficient of neat CI2E3are plotted. The principles of presentation are the same as in Figure 2. Hence a t a certain surfactant concentration there are plotted ( 1 ) the self-diffusion coefficient of Ci2E3in the L2/L3 phase at the indicated concentration (A);(2) the self-diffusion coefficient of PEG in the system PEG-D20 (A) (This sample has the same molar ratio D20/ethylene oxide groups as the surfactant sample.); (3) the self-diffusion coefficient of neat C12E3 (0). In Figures 4 and 5 the corresponding data for the C12E4 system are presented. The observed self-diffusion coefficients of C12E4 and D 2 0 in the L3phase are consistent with the results presented in ref 4. In Figure 6, the self-diffusion coefficient of D20 at 3.0 OC in the L1 phase of the system C12E4-D20 (A)and in solutions of PEG in D 2 0 (A)is plotted in the same way as in the previous figures. Figure 7 shows the echo amplitude of a sample in the L3phase plotted vs. I?~(A- 6/3). The concentration is 30.4% c& and the temperature 63.3 O C . The dotted line shows the fitting
10
20
30
1 50
40
% C12E4 Figure 6. The self-diffusion coefficient of D20 at 3.0 O C in the L, phase of the system C12E4-D20(A). At a particular value for the abscissa is also plotted the self-diffusion coefficient of D20 for a sample in the
system PEG-D20 which has the same molar ratio D,O/ethylene oxide groups as in the surfactant sample (A). 1 .o
0.8
0.6 0
W \
W
0.4
0.2
0 0
1
2
3
4
5
6*(8-6/3).
6
lo7, s3
Figure 7. The echo amplitude of a sample in the L, phase vs. a2(A - 6/3). The concentration is 30.4% C12E4 and the temperature 63.3 OC. The dotted line shows the best fit to eq 1 while the full drawn line shows eq 5 for the case that the fitting is good for low gradient strengths.
to eq 1 from which the presented self-diffusion coefficient was calculated. The full drawn line shows eq 5 (two-dimensional diffusion, see below). In Figures 8 and 9 the proton NMR line widths a t half signal height for the main methylene signal of the C12chain are presented for various conditions in the two systems. Because of the narrow temperature-composition region of existence of the L, phase of the C12E4system it was difficult to perform measurements on
4767
N M R Study of Nonionic Solutions
201
,
O
,
O
;
,
0
, o ,
, o ,
0
0
I
f
60
80 100 Yo surfactant Figure 8. Line width at half-height of the main proton NMR signal for the methylene groups. The experimental temperature is 1.8 OC for the LI(CI2E4)samples. For the L3(C12E3)samples the experimental temperature is varied between 43.2 and 54.9 "C. 20
40
% surfactant
50 N
I
40
.
\ N
i
Q
20 AA
10
A
-
A
A A
A A
A A
0 50
55
60
65
70 TIC
Figure 9. Line width at half-height of the main proton NMR signal for the methylene group vs. the experimental temperature. The samples were measured in the two-phase region W + L3in the system C12E4-D20.The approximate compositions of the L3 phase are given at the top of the
figure. single-phase samples. However, in practice this did not cause any problems since in the two-phase regions only surfactant molecules in the L3 phase contribute significantly to the N M R spectrum. Thus the other isotropic phase (W) has an extremely low surfactant concentration while the lamellar phase gives very broad signals due to residual nonaverage dipolar couplings. Measurements on the CI2E4system were, therefore, made as a function of temperature for two-phase samples.
Discussion Water Self-Diffusion. The observed self-diffusion coefficient of water in a nonionic surfactant solution is lower than that of neat water. Our model6 assumw that this decrease in self-diffusion coefficient is caused by a combination of two phenomena: obstruction and hydration. The interaction between water and the poly(ethy1ene oxide) chains is described by a single parameter, Pb, which gives the fraction of bound water as given by the translational mobilities. W e divide thus the water into two populations and assume that the "bound" water molecules have the same translational mobility as the surfactant molecules (which may be in monomeric or micellar state) and that the free molecules have the same translational mobility as in neat water except for the obstruction effect. The hydrocarbon core of the micelle is considered as an excluded volume for the water molecules and is described by an obstruction term. Combining the two effects gives (3)
where D, is the observed water self-diffusion coefficient, and Df and Db are the self-diffusion coefficient of free and bound water,
0.60
I
I
I
obstructing volume
I
1
(vel.%)
Figure 10. The theoretical obstruction term A for some different particle shapes vs. the volume fraction obstructing particles (from ref 9).
respectively. A , which describes the obstruction effect, is dependent on the aggregate shape and volume fraction of obstructing particles. A has been calculated for different spheroidal particle shapes in ref 9 and results for some particle shapes are shown in Figure 10. The small obstruction effect for spherical and different prolate shapes is striking, and one should also notice the large obstruction even at low concentrations for oblates with large axial ratios. Hence, if A could be calculated from eq 3 it would be possible to obtain information about the aggregate shape. It should at least be possible to distinguish between spherical and prolate aggregates on one hand and oblate aggregates on the other. D,, Df, and Db are all measurable and the only term to determine experimentally is Pb. In an earlier article6 we showed that Pb is to a very good approximation only determined by the temperature and the molar ratio D20/ethylene oxide groups while it seems to be quite independent of the particular system. For a solution of poly(ethy1ene oxide), A is equal to unity and eq 3 becomes (4)
By measuring D,, Df, and Db (or assuming that Db can be put equal to zero, the case applicable for long polymers), Pb can be deduced. If the polymer sample has the same molar ratio D20/ethylene oxide groups as a certain surfactant sample and both samples are measured at the same temperature, Pb from the polymer system can be used in the calculation of A for the surfactant system. Figure 6 shows that the self-diffusion coefficients of D 2 0 are quite similar in the L1 phase of the C12E4system and in the PEG system for the same ratio D20/ethylene oxide groups. This is also found for the Ll phase in the systems C12E5-D,0 and C12E8-D20.6 This shows that the obstruction term A is close to unity in the L1 phase. In the L3 phase, on the other hand, the self-diffusion coefficient of D,O is, at a certain molar ratio D20/ethylene oxide groups, considerably lower in the L, phase than in the PEG system as seen in Figures 2 and 4. As a dramatically larger hydration in the L3 phase is unlikely, the difference in observed self-diffusion coefficient must come from a difference in the obstruction term. Values of A , for both the L1 and L3 phases, calculated from eq 3 and 4, are presented in Figure 11. The A values for the L1 phase are calculated by assuming the self-diffusion coefficient of the amphiphile and the polymer to be zero. The error in A introduced by this approximation is of the order of 1-2%. It is seen that the values of A are close to unity for the Ll phase strongly indicating that the aggregates are spherical or prolate in this phase. The values of A for the L3 phase are close to 2/3 (Le., the limiting value for large oblates) for both the Cl2E3 system and the ClzE4system strongly indicating that the aggregates present in this phase are oblate. From Figure 10 it can be inferred that the axial ratio has to be at least of the order (9) Jonsson, B.; Lime, P.;Nilsson, P.-G., to be published.
4768
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 1.2 1.0
