871
J. Phys. Chem. 1985, 89, 871-874
+
+
ficiency k;/(kRS kMS k:) of deactivation is 2 times larger than the efficiency (kRs kMs)/(kRs kMs k,S) Of net reaction. The Arrhenius plot for aM/7is linear as shown in Figure 5d. The good linearity of the plot indicates that photoreduction through the molecular mechanism is negligible in both T2(n,?r*)and SI(?r.?r*l. From the sloDe we obtained AE, = 1590 cm-I which agrees with the value dbtained above. Therefore it is concluded that photoreduction through the molecular mechanism occurs only in S2(n,?r*). In a previous it was found that Tl(?r,?r*)reacts in MMA to yield R and the reaction efficiency does not change in the range of 200-290 K. Therefore we assume that the efficiency of R formation reactions in T2(n,7r*) and/or Sl(?r,a*)in ethanol does not depend on temperature above 170 K. Putting ORO/TO kR + k2kRT/(kzl+ kRT knT)= 5.5 X lo6 s-I, we obtained a linear relation for the plot of In (aR/7 - + R o / ~ o ) vs. 1 / T as shown in Figure 5c, plot 2. From the intercept and slope we obtained kRS = 3.5 X 10” s-l and AE4 = 1550 cm-’, respectively. The values for kRSand AE4 are consistent with the results obtained above. Using kR + k ~ k ~ ~+ /kRT ( k+ ~k?)~ = 5.5 X lo6 s-’ and 7 = 0.72 ns at 298 K, we calculated the quantum yield for the disappearance of acridine due to R formation in T2(n,7r*) and/or Sl(n,?r*)to be. 4 X which is much smaller than 0.043 which was reported by Koizumi et al.I5 Since the limiting value T~ is close to T at 77 K where photoreduction does not occur, kR k, is much smaller than kf kd + k l + k2. Although we could not evaluate kR and k2kRT/(kzl+ kRT knT)separately, the temperature-independent R formation reaction is considered to occur mainly through T2(n,?r*), because an n,?r* state is more reactive than a T,T*state. The conclusion given by Koizumi et al. that T2(n,?r*) reacts in ethanol to yield R was qualitatively confirmed. Using eq 2 and the rate parameters obtained above we can calculate cPcT at various temwrature. k, is considered to be much larger thank], judging from’the energy ;elation and the electronic character of T,(n,a*) and TI(*,^*). Since ki + k2 is 1.4 x lo7 s-I in PVA and 1.0 X lo7 s-l in water, k2 is estimated to be (10-1.4) X lo7 s-I in ethanol. However, the efficiency of T2(n,~*) T,(?r.?r*l internal conversion is reduced bv the R formation reacGbn1 Therefore, it may be assumed thit the Sl(x,?r*) Tz(n,a*) -* Tl(n,?r*) transition does not participate in aST above 170 K. The calculated curve for @ST on the basis of this assumption is shown in Figure 4b. A s t h e curve reproduces the \
I
+
experimental results, the above assumption seems valid. Since photoreduction and temperature-dependent intersystem crossing do not occur and T = 10 ns at 77 K, the following relation holds: kf + k,j + k2 = IO8 s-’
(8)
I
+
+
+
+
-
-
Putting k f = 4.2 X lo7 s-l in eq 8 we obtain kd + k2 = 5.8 X lo7 s-I, which is somewhat larger than 3.4 X lo7 s-’ in PVA22and 2.0 X lo7 s-l in water.23 As aST was not determined in ethanol at 77 K, we could not evaluate kd and k2 individually. When Tl(?r,a*) molecules were excited by the stepwise double-excitation technique3] which made complete excitation of Tl(n,?r*) molecules to T3(?r,?r*)possible, the original T1(?r,?r*) concentration was rapidly recovered after the Tl(?r,?r*) T3(?r,r*) excitation. This result indicates that the reaction in T3(?r,?r*)is negligible. Further it implies that the T3(?r,?r*) T2(n,?r*) transition is neglected in comparison with the T3(a,?r*) TI(a,a*)transition, because the reaction in T,(n,?r*) will inhibit the full recovery of Tl(?r,n*). In the present work, it was confirmed that photoreduction in ethanol occurs mainly through S2(n,7r*). The frequency factor of the l(n,r*) 3(?r,7r*) transition is much larger than that of the l ( a , x * ) 3 ( a , ~transition. *) Therefore, S2(n,n*) plays the most important role in both intersystem crossing and photoreduction when it is populated with the thermal activation of SI(7r,?r*). Since the rates of photoreduction in excited states along with the relative position of electronic energy levels depend on the nature of solvent, it is natural that the reaction or deactivation mechanism differs from solvent to solvent. The reaction and the deactivation of excited acridine in ethanol is satisfactorily explained by the deactivation mechanism shown in Figure 3 and the rate parameters listed in Table I.
--
--
Acknowledgment. The present work was supported by a Grant-in-Aid for Scientific Research (No. 56430001) from the ~ ~ Ministry of Education, science, and Culture, J Registry No. Acridine, 260-94-6. (31) Kobayashi, S.; Kikuchi, K.; Kokubun, H. Chem. Phys. Lett. 1976,42,
..
AO, A
(32) Periasamy, N. Chem. Phys. Lett. 1983, 99, 322.
Determination of the Rigidlty Constant of the Amphiphiiic Film in “Birefringent Microemulsions”: The Role of the Cosurfactant Jean-Marc Di Meglio,* Maya Dvolaitzky, and Christiane Taupin Laboratoire de Physique de la Matiere CondensZe,t College de France, 75231 Paris Cedex 05, France (Received: June 22, 1984; In Final Form: September 7 , 1984)
The amphiphilic lamellae of “birefringent microemulsions”are known to exhibit undulations. The results of a quantitative study of the corresponding angular disorientation are well explained by competition between the high flexibility of the film and the interactions between layers. We thus determine for the first time the rigidity constant of the interfacial film and evidenced that one role of the cosurfactant is to lower the interfacial rigidity.
Lyotropic systems containing oil and water have been widely studied for a few years1 Two main situations occur: either oil and water are organized in a periodic array or they form isotropic dispersions called microemuisions.2 Recently, the flexibility of the interfacial film has been invoked to explain the variety of these +EEluiDe de Recherche Asswit% au ‘Micrkmulsions” du C.N.R.S.
C.N.R.S. (No. 542). GRECO
structures3 and much interest has been devoted to special lamellar phases which appear in the vicinity of microemulsions in the phase diagram for a smaller amount of alcohol (co~urfactant).~In a (1) Ekwall. P. In “Advances in Liauid Crystals”: Brown, G. H.. Ed.: Academ’ic Press: New York, 1975; Vol: 1, p 1: (2) Hoar. T. P.: Schulman. J. H. Nature 1943. 152. 102. (3) de Gennes, P. G.; Taupin, C. J . Phys. Chem. 1982, 86, 2294
0022-3654/85/2089-0871$01.50/00 1985 American Chemical Society
~
~
.
872 The Journal of Physical Chemistry, Vol. 89, No. 5, 1985
Di Meglio et al.
TABLE I: ComDosition of the SsmDles
A Gauss1 O/W ratio 1
sodium dodecyl sulfate (surfactant), g tridistilled water, mL 1-pentanol (cosurfactant), mL I-pentanol required to obtain an isotropic microemulsion, mL
2
0.4
0.4 1 1 0.23 0.32 0.54 0.69
23
4
8
0.4
0.4 1 1 0.43 0.72 1 1.6
22
21
io
io
40
io
60
io T ~ C ]
Figure 2. Variation with the temperature of the extreme splittings for (p) a powder spectrum and ( 0 ) an oriented spectrum. 2T< 2T)i
I
1 1
8
2
(radian2)
1
Figure 1. (a) "Powder spectrum" obtained with a spherical sample container (isotropic distribution of the lamellae). (b) "Oriented spectrum" obtained with a parallel glass wall container. Note the discrepancy between the two extreme splittings. previous paper,5 it was shown by the spin-labeling method that these lamellae are undulated, the angular disorientation amplitude of the undulations increasing with the degree of swelling (Le., the oil/water ratio) of the phase. In this paper, these undulations are quantitatively studied in the frame of de Gennes' calc~lations,~ who present them as resulting from competition between the flexibility of the film and interlamellar interactions. This allows us to measure the constant of rigidity K and to verify the predictions of the model with regards to swelling. We evidenced for the first time the effect of the cosurfactant upon film flexibility. Experimental Part The compositions of the samples are given in Table I. The amount of alcohol corresponds to the minimum amount required to obtain the transparent birefringent phase. Samples with a slightly higher quantity of alcohol have also been investigated (see Effect of Cosurfactant). All these phases show classical lamellar textures when observed with a microscope between crossed polarizers; their homogeneity has been checked with a phase contrast setup. The labeled surfactant of formula C H3-
( C H 2 )11-
C -(
/ \ O
q
C H 2 13-N
'b,
CH~SOQ-
L../
0
resides exclusively in the interfacial film6 and was used at a molar fraction of around 0.1% with respect to SDS. The spin-label measurements have been performed on a Varian E-9 EPR spectrometer. Two types of sample containers were used5 which ~
(4) Dvolaitzky, M.; Ober, R.; Billard, J.; Taupin, C.; Charvolin, J.; Hendricks, Y.C. R. Acad. Sci. 1981, 295, 45. ( 5 ) di Meglio, J. M.; Dvolaitzky, M.; Ober,R.; Taupin, C. J. Phys. Lett. 1983, 44, L-229. (6) Dvolaitzky, M.; Taupin, C. Nouu.J. Chim. 1977, 1 , 355.
01
8
20
io
40
50
sb
I
io ~ p )
-
Figure 3. Variation with the temperature of the square angular spread of the normal to the lamellae (dashed line: 0 7'). give rise either to a homeotropic orientation (checked by observation with a microscope between crossed polarizers) or to an isotropic distribution of the lamellar domains. The spectra of these samples differ from those of usual lamellar phases (as, for instance, smectic thermotropic liquid crystals); the main effect is a discrepancy between the extreme splittings measured either on an oriented spectrum or on the corresponding powder spectrum (Figure 1). This indicates that, in spite of the homeotropic aspect, a significant fraction of the surfactant molecules is not parallel to the magnetic field; this is due to a continuous angular spread around a mean orientation corresponding to smooth undulations of the lamellae.5 This angular spread can be determined by the synthesis of the oriented spectrum using the line widths and splittings deduced from the synthesis of the powder spectrum according to classical procedures.' Effect of Temperature on Angular Distribution The spectra of a sample with a 4:l oil-to-water ratio have been recorded as a function of the temperature between 20 and 70 OC. The temperature was controlled within f0.2 OC in the cavity of the EPR spectrometer by a Varian E-257 variable accessory. Figure 2 represents the extreme splittings measured on oriented (0)and on isotropic (or powder (p)) spectra. According to the procedure described above, first used in ref 5, we have determined the square of the spread angle 0 as a function of the temperature. 10-2Trad (Figure 3). We found that O2
-
(7) "Spin Labelling"; Berliner, L. J., Ed.; Academic Press: New York,
1976.
The Journal of Physical Chemistry, Vol. 89, No. 5, 1985 873
Rigidity Constant of Interfacial Films
0
',
\ \ \ \ \ \ \ \ \ \ \ \ w \\\\\ \\',\\\\' Figure 4. Geometry used in the model.
Interpretation: The Role of the Flexibility In order to understand this behavior, we use the model described in ref 3 for multilamellar systems. We assumed the lamellae to be water lamellae separated by cyclohexane as shown in Figure 4. The free energy per unit area is written as follows: F = '/K(V,2z)2 '/ZUfk2 (1)
Figure 5. Plot of 82 vs. log of the distance between lamellae.
+
where K is the rigidity constant of the interface? z the local displacement of the water layer with respect to the reference flat plane (Figure 4), and U" the curvature of the interaction potential between layers. The geometry of the Figure 4 is the simplest one we can imagine which allows us to vary the distance between layers and thus to destroy the lamellar order. The first term of (1) represents the energy needed to curve the interface and the second term is determined by the interactions between layers. We have evaluated U f ffrom the following two competitive interactions (see Appendix for the detailed computation U" = Uf:dW + Uffrep). (1) van der Waals attractive interactions, which lead to a collapse of the lamellar structure, can be represented as Uf:dW = -A/7r(l/d4 + l / ( d 2e)4 - 2 / ( d e ) 4 )
+
+
where A is the Hamaker constant for water embedded in cyclohexane (= A131(H20,C6H12)), d the distance which separates two lamellae, and e the thickness of a lamella (Figure 4). (2) Steric repulsive interactions, which were first introduced by Helfrich: can be represented as Ut:, = +5.04(k7')2/(Kd4) We think that these interactions are stronger than the van der Waals because of the low expected value for K. This hypothesis will be checked further. erg.1° The Hamaker constant was taken equal to 1.5 X d and e were deduced from geometrical calculations by taking an area per polar head of around 60 At;" this leads to d = 160 A and e = 40 A for the studied sample. This theoretical approach allows to estimate the average 82: = kT/(TK) log (€,/a) (2) where f , is a characteristic length equal to (K/U'91/4 and a a molecular size of around 10 14.) Thus the experimental behavior (e2 7') is in good agreement with the model. This allows us to estimate the rigidity constant K from the following formula by an interation procedure (recall that f u = (K/U")1/4): K = kT/(7r02) log ( [ , / a )
-
(We assume that K is fairly independent of the temperature.12) We find K = 6.4 X lo-'* erg, taking a = 10 A. The assumption that repulsive interactions were greater than the van der Waals is thus well checked: UNq/UflydW = 70. This value is much lower than the value obtained for lecithin lamellar systems (4, = 2 X ergI3); we may understand that by the fact that, in lecithin (8) Helfrich, W. Z . Naturforsch. C 1973, 28C, 693. (9) Helfrich, W. Z . Naturforsch. A 1978, 33A, 305. (10) Visser, J. Ado. Colloid Interface Sei. 1972, 3, 331. (11) Dvolaitzky,,M.; Guyot, M.;Lagues, M.;Le Pesant, J. P.; Ober,R.; Sauterey, C.; Taupin, C. J. Chem. Phys. 1978, 69, 3279. (12) Cantor, R. Macromolecules 1981, 14, 1186.
O/W
Figure 6. Line width used in the synthesis of the high-field peak in a powder spectrum as a function of the swelling rate.
systems, interactions inside the interfacial film are much stronger-electrostatic interactions between polar heads are not screened by the cosurfactant and steric interactions in the hydrophobic part of the film may be strong because of the two alkyl chains per surfactant molecule. Effect of Swelling Recall that it was shown in ref 5 that the local order parameter of the surfactant molecules is independent of the degree of swelling (S = 0.40); furthermore, the amounts of cosurfactant needed to obtain the samples correspond to a straight line in the phase diagram. These two experimental facts prove that the chemical composition in the film does not changeI4 with the degree of swelling, hence the rigidity must remain the same. It is thus of interest to study the influence of the swelling of the phases on the angular spread since it constitutes a fine test of the model: U" is in a very good approximation proportional to 118 and then O2 must be linear with log d 82 = kT/?rK log d + constant This is shown in Figure 5; the agreement between theory and experiment is good and leads to another determination of K which is independent of the previous one. We find K = 4 X erg. Dynamical Effects on the Spectra. Figure 6 represents the line width used in the synthesis of the high-field part of the spectra vs. the degree of swelling; it is clear that a dynamic effect is correlated with the oil to water ratio. Because of the flexibility, the interfacial film is locally curved and when the surfactant molecules diffuse laterally on this curved surface, they undergo a disorientation of their mean axis.ls If the time of disorientation is of the same order that the characteristic time of ESR experiments s), this will promote a broadening of the spectral lines.7 The curve of Figure 6 can thus be easily understood: for small swelling rates (O/W < 4), the dispersion angle of the lamellae (13) Servuss, R. M.; Harbich, W.; Helfrich, W. Biochim. Biophys. Acra 1976, 436,900. (14) Graciaa, A.; Lachaise, J.; Martinez, A.; Bourrel, M.; Chambu, C. C. R. Acad. Sci. Ser. B 1976, 282, 547. (15) Seelig, J.; Limacher, H. Mol. Crysr. Liq. Crysr. 1974, 25, 1051.
874 The Journal of Physical Chemistry, Vol. 89, No. 5, 1985
6
E2
-o/w = 0.5 -....qw=4
Figure 7. Powder spectrum of a 4:1 O/W sample (dashed line) compared to a powder spectrum of a 0.91 O/W sample (full line). Note the discrepancy between the line widths.
Di Meglio et al. Effect of Cosurfactant (Alcohol) We have performed experiments on samples (O/W = 4 ) in which the alcohol was up to 80% in excess of the amount required to obtain the birefringent phase. The samples are still homogeneous and present lamellar structures (oily streaks) when observed with a microscope. The angle of dispersion increases with an excess of cosurfactant. The added quantities do not change the mean distances between lamellae; this indicates a decrease in the rigidity due to a modification of the chemical composition in the film. Figure 8 represents the ratio K/K,,, vs. the excess of alcohol. Conclusion The smooth undulations observed in “birefringent microemulsions”are shown to be a consequence of the competition between the high flexibility of the interfacial film and lamellar interactions. The validity of the model3 is verified by studying both the influence of temperature and the oil-to-water ratio. It has been shown that the role of the cosurfactant is indeed to lower the rigidity of the film which permits us to explain the transition from organized phases toward isotropic microemulsions. Acknowledgment. We thank Jean-Francois Joanny and Loic Auvray for many helpful discussions, and also one of the referees for a remark about the physics of the interaction potential. This research has received partial financial support from PIRSEM (C.N.R.S.) under AIP No. 2004.
0
10
20
30
40
50
60
70 Yo
EXCESS OF ALCOHOL
Figure 8. Plot of the K/K- vs. the excess of alcohol (excess with respect to the amount needed to obtain the ‘birefringent microemulsions”).
is very small and does not lead to a strong disorientation of the labeled surfactant while for strong swelling rates (O/W > 4), the dispersion angle becomes important and the mean axis of the label molecule may disorient itself by more than 1 rad during the time scale of the experiment. This phenomenon allows us to evaluate the radius of curvature of the interfacial film according to the procedure developed in ref 16 for the sample with a 4:l oil to water ratio. Taking as a reference the spectrum where the interfacial film is almost flat (O/W = 0.5) (Figure 7), we estimate from a simulation methodI7 an angular correlation time of around 5 X s; the lateral diffusion constant Dlatis also estimated from ESR experiments according to the procedure developed in ref 18 and found equal to 3 X cmz/s-’. This gives a radius of curvature of around 80 A (R2= 4D,at7R(ref 16)) which is comparable to the correlation length deduced from eq 2 (with a mean value for K of 2.3 X erg, 5 = 60 A). (16) di Meglio, J. M.; Paz, L.; Dvolaitzky, M.; Taupin, C. J . Phys. Chem. 1984, 88, 6036. (17) McCalley, R. C.; Shimshick, E. S.; McConnell, H. M. Chem. Phys. Lert. 1972, 13, 115. (18) Devaux, P.; McConnell, H. M. J . Am. Chem. SOC.1972, 94,4475. Sackmann, E.; Triuble, H. J. Am. Chem. Soc. 1972, 94, 4492.
Appendix: Computation of U” We have taken into account both van der Waals and steric interactions between one layer and its two nearest neighbors. We have for the energy W per unit area (W = WC + W ) = - A / ( 1 2 ~ ) ( l / ( d - z ) ~l /+( d - z + 2 e ) 2 - 2 / ( d z + e)2) 0 . 4 2 ( k q 2 / ( K ( d- z ) ~ ) (upper layer)
+
W = - A / ( 1 2 ~ ) ( l / (+ d z)’ z
+ l / ( d + z + 2e)2 - 2 / ( d + + e)Z)+ 0.42(kT)2/(K(d+ z ) ~ ) (lower layer)
Assuming that z
