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Comments Comment on the Self-Diffusion in LSand Other Bicontinuous Surfactant Solutions Multicomponentmolecular self-diffusionhas been found to be very useful for a range of problems relating to surfactant self-assembly, including micellization, counterion binding, solvation, and micelle size and shape, not to mention the problem of distinguishing between uniand bicontinuous microstructures. It is also significant as a noninvasive technique for the study of droplet size and size distribution in emulsions. One interesting aspect concerns solution microstructure. Recently, Ott et ale1 have used this approach for the study of the so-called L3 phase formed in two-component and multicomponent surfactant systems. They report the quite remarkable observationthat over a wide surfactant concentrationrange the self-diffusion of a fluorescent amphiphilic probe is insensitive to composition, and this finding was taken as direct support for a bilayer continuous structure.2 The findings of Ott et al.' are in line with previous studies3of L3 phases in analogous surfactant systems. For example,as illustrated in Figure 1for systems of a nonionic surfactant and water, the diffusion of both components is quite rapid and composition invariant over wide ranges (from high dilution up to 50 w t % ! ). (Furthermore, both water and surfactant self-diffusion are close to 2/3 of the values of the diffusion of the neat ~omponenta.~) This behavior is very different from that of other surfactantwater solutions, and the observationsform the basis of an analysis of aggregate shape in the L3 phase. Later it has been convincingly shown that the diffusion data provide direct support for a connected bilayer structure, and a quantitative analysis of the diffusion has been made in terme of precisely defined bicontinuous structures.2 The self-diffusion data and theoretical calculations suggest a closestructural and topologicalanalogybetween L3 phases, bicontinuousmicroemulsions,and the class of bicontinuous cubic liquid crystalline phases. In particular, the analogy between L3 and bilayer continuous cubic phases was recently revealed in an NMR self-diffusion studyes Fourier transformpulsed-gradientspin-echo (FTPGSE) NMR6allows the simultaneous determination of the selfdiffusion coefficients of the different components of a complex mixture without any specific labeling or other perturbations. The technique has turned out to be a particularlyversatile, precise, and fast technique, not least for surfactant systems. However, the authors of ref 1 suggest that the NMR technique has severe limitations, in ita applicability for the problems considered here. The (1) Ott, A.; Urbach, W.; Langevin, D.; Hoffmann, H. Langmuir 1992, 8, 345. (2) Andereon, D. M.;WenneretrBm, H. J . Phys. Chem. 1990,!44,8683. (3) Nileeon,P.G.;Lindman,B.J.Phys. Chem. 1984,&?,4764.Nilsson, P.-G.; WennerstrBm, H.; Lindman, B. Chem. Scr. lSSS,25,67. (4) In the CBSB of surfactant diffusion a more relevant comparison is witha lamellar phase.'-2 The data,however,indicate a similarity between the self-diffusion constant in the neat liquid and the lateral diffusion constant in a f h . (5) Balinov, B.; Oleson, U.; SMennan, 0. J. Phys. Chem. 1991, 95, 5931. Oleeon, U.; Balinov, B.; SMennan, 0. In The Structure and Conformation of Amphiphilic Membranes; Lipowsky, R., Richter, D., Kremer, K., Eda.; Springer Proceedings in Physics; Springer-Verlag: Berlin, Heidelberg, 1992; Vol. 66, p 287. (6) For a comprehensive review of the NMR diffusion approach see: Stilbe, P. Frog. NMR Spectrosc. 1987, 19, 1.
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Figure 1. Relative surfactant (open symbols) and water (fiied symbols) self-diffusion coefficienta for the L3 phases of CHs ( C H Z ) I I ( O C H ~ C H ~ ) ~(ClZE3) OH (circles) and C H ~ ( C H Z ) ~ ~ ( c 1 2 4 ) (triangles). DOvaluee refer to reference (OCH~CHZ)~OH stateswhich are the neat liquid surfactant and water, respectively, at the same temperature. For water a correctiondue to hydration of the head groups has been used. Experimental data are taken from ref 3.
two aspects the authors of ref 1 discuss concem the influence of surfactant exchange processes and of the length scale probed by the experiment. We find this criticism unjustified, and since the NMR diffusion approach to study surfactant self-assembly has been very widely adopted, we find it essential to comment on these matters. The time scale of the NMR self-diffusion experiment' can be varied at will, and typical values are in the range of 0.1 to several seconds. The upper limit depends, in practice, on the transverse relaxation rate in combination with the concentration of the spins under observation. For L3 and bicontinuousmicroemulsionsthe typicallength scales probed by the technique are of the order of 10 pm (surfactant diffusion) and 100 pm (solvent diffusion). It should be noted that the particular length and time scales of the self-diffusion experiment on an isotropic solution are irrelevant as long as they are sufficiently long. In a properly performed experiment, the time scale is varied to ensure that the measured diffusion constant does not depend on the observation time, i.e., that the measured quantity indeed correspondsto the macroscopic diffusion constant. Furthermore, in many of our studies-inter alia the study which first could demonstrate microemulsion bicontinuitFwe combined the NMR studies with extensive experiments using the open-ended capillary tube method (with radioisotope labeling), with quantitative agreement between the techniques. In the capillary tube technique the diffusion lengths are of the order of centimeters. The invariance of the self-diffusion coefficients over diffusion times differing by a factor of more than 108 is gmtifying and gives support for an interpretation in terms of continuity. Another point of ref 1 concerns contributions from surfactant exchange between surfactant layers and nonassociated moleculesin a continuousmedium, or expressed differently the contribution to the average macroscopic surfactant displacement from monomerically solubilized (7) Stejskal, E. 0. J. Chem. Phys. 1966,43,3597. (8) Lindman, B.; Kamenka, N.; Kathopoulis, T-M.;Brun, B.; Nibron, P-G. J. Phys. Chem. 1980,84, 2485.
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surfactant molecules in the bulk. This contribution w i l l clearly be determined by the solubility of surfactant in the solvent (or in the two solvents for a surfactant-oilwater system) and thus vary strongly with the hydrophobicity (amphiphobicity)of the surfactant. This additional diffusion process is a genuine contribution to the translational diffusion, and it is present independently of the experimental technique. The measured self-diffusion constant corresponds to macroscopic molecular displacements. Microscopic heterogeneities,for example, involving aggregated and monomeric (nonaggregated) states of the surfactant, are averaged out on the experimental time scale, and in principle, only an average diffusion constant is recorded. In bicontinuous microemulsions and L3 phases the concentrationof monomericsurfactant is oftenvery low, which is one reason why these phases can be very dilute. The surfactant diffusioncau be modeled in variousways, but one thing remains clear: From a low monomer concentration together with a high diffusion constant in the aggregated state (for a continuous surfactant film this corresponds roughly to the lateral surfactant diffusion constant within the film)it followsthat the contributions to the observed diffusion constant from monomeric surfactant are small and often negligible.oJ0 To take an example, for the c12E3system studied in ref 3 the effect of surfactant exchange can be calculated to affect D by at most 0.04% for the higher concentrations and by less than 1% at the lowest concentrations. For the particular microemulsion system referred to in ref 1(ref 11)an estimate of the monomeric concentrationlz in the (9) See for example: Lindman, B.;Brun, B. J. Colloid Interface Sci. 1973,42,388. (10) Within a twesite dmrete exchange model we may estimate the
relative contribution from monomeric (nonasaociated)Surfactant mol-
ecules to the observed diffusion constant to equal PD-JD, where P is n in the fraction of monomeric surfactant, D,, b the d ~ i o coefficient the monomeric state,and D is the observed diffusion coefficient. In the
limit of emall P,D = D, where D, is the diffusion coefficient in the aggregated state. In a bicontinuous microstructure we have in addition the conditionthatD and D,, differ by only a smallfactor which implies that the contributio?ii of the order of P (notethat this ale0 implies that the observed diffusion constant b rather ineensitive to P). (11) Chatenay, D.; Gu6ring.P.; Urbach, W.; Cazabat, A.-M.; Langevin, D.; Meunier, J.;Uger, L.;Lmdman, B. In Surfactants in Solution; Mittal, K. L., Bothorel, P., Eds.; Plenum: New York, 1988, Vol. 6, p 1373. (12) In the presence of alcohol, the SDS monomer concentration in water is very low; nee: J o h n ,I.; Olofseon,G.; Lmdgren, M.; J h w o n , B.J.Chem.Soc.,Faraday Trans.1 1989,86,4211. T h e a d d i t i d p m n c e thii value even further. of d t ia expected to dep(13) NMR relaxation can be used to obtain information on the lateral mobility in nelf-arrsembledsurfactant systems. Recent relaxation studies on spherical micelles1* and cylinders in a hexagonal liquid crystalline phase16 c o n f i i that the diffusion process, aseociated with the observed diffusion coefficientof dodecyl sulfate in bicontinuous microemulsions,11 b dominated by lateral diffusion.
Comments aqueous microdomain implies that ale0 here the monomeric contribution to the D value is less than 1%. The dominating reason for the observed difference between the surfactant and the probe reported in ref 11is due to the intrinsic mobilityl3 of the respective species, not the surfactant exchange. We note that the NMR measurements are clearly more informative ale0 in this case. In conclusion, we f i d that the broadly applicable and versatile NMR technique to study self-diffusiondoes not have the limitationscompared to thefluorescencerecovery after fringe pattern photobleaching (FRAPP)technique which are claimed in ref 1. On the contrary, the diffusion lengths probed are comparable in the two techniques and are more easilyvaried in N M R experimemts. Furthennore, the influence of surfactant exchange is basically identical in the two methods as it is determined by the molecule probed in the diffusion experiment. This can be varied much more broadly in NMR thanin the FRAPPtechnique, the latter requiring the addition of a foreign fluor-nt probe. Furthermore, although the total system perturbation from the addition of trace quantities of dye may be low, one should clearly note the inherent problem in all approachesusing "probe molecules": regardleaeof probe concentration, the probe approach will give information on a system (e.g., micelle) containing at least one probe molecule. The presence of a large dye molecule is thus likely to impose a major perturbation on most selfassembled surfactant systems regardla of probe concentration. On the other hand, there are other limitations of the NMR self-diffusion approach. Occasionally, depending on chemical or micelle structure (frequently for strongly elongated micelles),the relaxationrate is high. Generally, the sensitivity is low in NMR,but for surfactant systems this is no limitation in practice. B. Lindman,' U. Olrmn, and E.Wennerrtr(lm Physical Chemistry 1, Chemical Center, Lund University, Box 124, S-221 00 Lund, Sweden P. Stilbr Department of Physical Chemistry, Royal Institute of Technology, 5-10044 Stockholm, Sweden Received June 22,1992 In Final Form: October 19,1992 (14) Sdderman, 0.; Carletrdm, G.; O h n , U.; Wong, T. C. J. Chem. Soc., Faraday Trans. 1 1988,84,4476. (15) Quiet, P.-0.; Halle, B.;Fur4 I. J. Chem. Phys. 1991,96, 694S.
