Membrane Flexibility in a Dilute Lamellar Phase: Variation with

Jun 1, 1995 - Membrane Flexibility in a Dilute Lamellar Phase: Variation with Temperature and Composition. Per-Ola Quist. Langmuir , 1995, 11 (6), ...
0 downloads 0 Views 699KB Size
Download PDF
Langmuir 1995,11, 2201-2205

2201

Membrane Flexibility in a Dilute Lamellar Phase: Variation with Temperature and Composition Per-Ola Quist Condensed Matter Magnetic Resonance Group, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden Received November 28, 1994. I n Final Form: March 17, 1995@ The dilute regime of the lamellar phase in the SDS/pentanoYwater/dodecanesystem is investigated by 2Hand 23NaNMR. From the reduction ofthe quadrupole splitting on dilution,we determinethe temperature and compositionvariation in the bilayer bending rigidity K. We find an essentiallytemperature independent K = (9 f 1) x J in the range 0-60 “C.The variation in K with the bilayer composition displays an increasing rigidity on removing pentanol and water from the bilayer. The composition and temperature variation in K correlate with the extension of the lamellar phase in the phase diagram. The predictions ofrecenttheories for the molecularinteractionscontributingtoK-mainly the hydrocarbontail conformational entropy and the electrostatic interactions in the polar region-can account for the experimental results.

Introduction Two decades ago Brochard and Lennonl made the first determination of the bending rigidity ( K ) of a phospholipid membrane, by observing the well-known2 flicker phenomenon of human red blood cells. Contemporary, Helfrich3 proposed a n elastic theory of bilayers and introduced4the layer undulations as a sterically stabilizing interaction in lamellar lyotropic liquid crystal^.^^^ During the following decade, the phospholipid bilayer bending rigidity of several phospholipid bilayers was determined to the range K = (30-60)k~T((1.2-2.4) x J, k g is Boltzmann’s or to the range K = (5-15)kBT1’12’13(for the same lipids), by simply observing the shape fluctuations of vesicles. Simultaneously with these investigations, it was observed14 that in some ionic surfactantdalcohollwater. systems the lamellar phase could be diluted with brine to less than 10 wt % surfactant, i.e., to levels commonly not reached on aqueous dilution.6 Later, several groups observed that in some surfactant systems, the lamellar phase could be diluted by water, brine, or a n oily solvent to some few weight percent ~ u r f a c t a n t . l ~In - ~this ~ paper we investigate one of these systems, the SDSIpentanoll Abstract published in Advance A C S Abstracts, May 15, 1995. (1)Brochard, F.;Lennon, J. F. J. Phys. (Paris) 1976,36,1035. (2) Browicz, E. Zbl. Med. Wiss. 1890,28,625. (3) Helfrich, W. Z.Naturforsch. 1973,28c,693. (4) Helfrich, W. Z. Naturforsch. 1978,33a,305. (5) Luzzati, V. Biological Membranes; Chapman, D., Ed.;Academic Press: New York, 1968; Vol. 1,p 71. (6)Ekwall, P. Advances in Liquid Crystals; Brown, G. H., Ed.; Academic Press: New York, 1975; p 1. (7) Servuss, R. M.;Harbich, W.; Helfrich,W. Biochim. Biophys. Acta @

1976,436,900. ( 8 )Evans, E. A. Biophys. J. 1983,43,27. (9) Schneider, M. B.: Jenkins, J. T.; Webb, W. W. Bioph-ys. _ _ J. 1984, 45,891. (10)Beblik, G.; Servuss, R. M.; Helfrich, W. J.Phys. (Paris) 1986, 46., 1773. (11) Bivas, I.;Hanusse, P.;Bothorel,P.;Lalanne,J.;Aguerre-Chariol, 0. J. Phys. (Paris) 1987,48,855. (12) Sakurai, I.; Kawamura, Y. Biochim. Biophys. Acta 1983,735, ~~

*--. 1R Q

(13) Engelhard, H.; Duwe, H. P.;Sackmann, E. J. Phys. (PurisJLett. 1986,46,L-395. (14) Benton, W. J.; Miller, C. A. J. Phys. Chem. 1983,87,4981. (15) Larche, F.C.; Appell, J.; Porte, G.; Bassereau, P.; Marignan, J. Phys. Rev. Lett. 1986,56,1700. (16) Satoh. N.: Tsuiii. K. J. Phrs. Chem. 1987.91.6629. (17) Gomki, G.;Aipell, J.; Bassereau, P.;Marignan, J.; Porte, G. J. Phys. Chem. 1987,91,6203. (18) Bellocq, A. M.; Roux, D. Microemulsions: Structure and Dynamics; Friberg, S., Bothorel, P., Eds.; CRC Press: Boca Raton, FL, 1987. (19) Marignan, J.;Gauthier-Fournier,F.;Appell,J.;Akoum,F. ;Lang, J. J. Phys. Chem. 1988,92,440.

0743-7463/95/2411-2201$09.00/0

water lamellar phase, which can be diluted by an oily blend of pentanol and dodecane.18 In several of these systems, including the present, scattering studies of the Bragg peak structure have established that the dilute lamellar phases are stabilized by the steric repulsion between the fluctuating bilayer^.^ With the stabilizing mechanism identified, it became interesting to determine the bending rigidity K of the bilayers, since this parameter influences the stability of the dilute lamellar p h a ~ e . Several ~ , ~ ~ techniques were introduced for this purpose: ESR (electron spin reso,~~ nance),28viscoelastic experiment^,^^ e l l i p ~ o m e t r yX-ray scattering,26dynamic light ~ c a t t e r i n gneutron ,~~ scattering,21Brillouin ~ c a t t e r i n gand , ~ ~ recently NMR (nuclear magnetic r e ~ o n a n c e ) .Unlike ~~ the other methods, the NMR method is simple to perform and oriented lamellar samples are not necessary. Hence, the results are easy to reproduce and the accuracy is good since the NMR method is very sensitive to K in the range K x (0-5)lz~T (cf. Figure 2, below). Typically the surfactant bilayer bending rigidity determined by these methods was in the range K = (0.23)kBT, with the spread mainly caused by experimental limitation^,^^ fluctuation induced s0ftening,3~andlor inaccurate theoretical modeling.33 For example, in the present (ESRZ8),K = ( 0 . 5 - 2 ) k ~ Tor, ~K~ system, K = (0.2 or 1)lz~T = (2 1 ) k ~ (X-ray P Bragg peak structure factor); K = (20) Imae, T.; Sasaki, M.; Ikeda, S . J. Colloid Interface Sci. 1989, 131,601. (21) Strey, R.;Schomacker, R.; Roux, D.; Nallet, F.;Olsson, U. J. Chem. SOC..Faradav Trans. 1990.86.2253. (22) Platz, G.;T h h i g , C.;Hoffman,’H.Ber. Bunsenges. Phys. Chem. 1992,96,667. (23) Bassereau, P.;Marignan,J.; Porte, G. J.Phys. (Paris) 1987,48,

-

672 .-.

(24)Row, D.; Safinya, C. R. J. Phys. (Paris) 1988,49,307. (25) Bassereau, P.; Marignan, J; Porte, G, May, R. Europhys. Lett. 1991,15,753. (26) Safinya, C . R.; Roux, D.; Smith, G. S; Sinha, S. K.; Dimon, P.; Clark, N. A,, Bellocq, A. M. Phys. Rev. Lett. 1986,57,2718. (27) de Gennes, P. G.; Taupin, C. J. Phys. Chem. 1982,86,2294. (28) di Meglio, J. M.;Dvolaitzky, M.;Taupin, C. J. Phys. Chem. 1986, 89,871. (29) Oswald, P.; Allain, M. J. Phys. (Paris) 1986,46,831. (30) Meunier, J. J . Phys., Lett. 1985,46,L-1005. (31) Nallet, F.;Row, D.; Prost, J. Phys. Rev. Lett. 1989,62,276and J. Phys. (Paris) 1989,50,3147. (32) Mangalamoalli, S.:Clark, N. A.; Scott, J. F.Phrs. Rev. Lett. 1991,67,2503. (33) Halle, B.; Quist, P.-0. J. Phys. II (Paris) 1994,4,1823. (34)Bassereau, P.;Appell, J.;Marignan, J. J. Phys. II (Paris) 1992, 2. 1257. (35) Gulobovic, L.; Lubensky, T. C. Phys. Rev. B 1989,39,12110. (36) Safinya, C. R.; Sirota, E. B.; Roux, D.; Smith, G. S. Phys. Rev. Lett. 1989,62, 1134. ’

0 1995 American Chemical Society

Quist

2202 Langmuir, Vol. 11, No. 6, 1995 Table 1. Composition of the Concentrated (@ = 1) Lamellar Phases in Weight Percent and Molar Ratios series wt % SDS wt %water wt % pentanol n,/nsDs I 30.6a 47.3b 22.1 24.8 19.4 I1 33.2 44.7c 22.1 16.6 41.4c 22.7 I11 35.9 IV 42.0 12.2 35.@ 22.4 a

np/nsDs

2.36 2.17 2.07 1.75

a-Deuterated SDS. HzO. Heavy water, DzO.

Table 2. Sample Composition and Bilayer Volume Fraction (6.at 26 "C) for the Investigated Samples series I11 series IV series I series I1 wt % solv f$ wt % solv f$ wt % solv f$ wt % solv 1 0 1 0 0 1 0 1 11.4 0.849 9.9 0.873 9.8 0.869 10.2 0.864 0.728 19.8 0.745 21.2 19.9 0.754 20.3 0.739 0.632 30.5 0.622 30.0 0.639 30.0 0.627 29.6 39.9 0.534 40.2 0.518 39.8 0.523 42.5 0.493 49.8 0.433 50.0 0.420 49.8 0.422 50.9 0.410 60.1 0.334 59.9 0.326 60.4 0.322 60.6 0.319 70.2 0.244 69.8 0.238 70.0 0.236 71.1 0.227 75.1 0.201 75.1 0.193 75.0 0.194 75.2 0.192 a a 80.1 0.158 80.0 0.153 80.1 0.153 a a 85.1 0.117 85.1 0.113 85.1 0.113 @J

(0.8 or 2 . 4 ) k ~ T(dynamic light scattenn$l); K = 0.8kBT (X-ray scattering, deviation from ideal swelling on dilution33,37); and K = (2.2 f 0 . 2 ) k ~ T(NMR33). In most of these studies the molar ratio pentanol to SDS in the bilayer was n P / n S D S = 2.4. Eliminating the methods that are internally inconsistent (ESR and dynamic light scattera Two-phase region with lamellar and isotropic phases. in$4) and methods barely sensitive to K (scattering, deviation from ideal swelling on dilution33),we find K % For series 1-111 it was possible to dilute the lamellar phase 2kBTfor the SDS/pentanol bilayer with molar composition to >85 wt % solvent (the samples made with 90 wt % solvent n p / n S D S = 2.4. were in a lamellar/isotropic two-phase region). For series IVthe transition to this two-phase region occurred in the range 75-80 Despite the obvious activity in this scientific field, there wt % solvent. is no study (to our knowledge) where the temperature NMRExperiments. The NMR experiments were performed dependence in K is determined, and very few where the variation in K with bilayer composition is ~ t u d i e d :For ~ ~ * ~ ~on a Nicolet Nic-360spectrometer equipped with avertical saddlecoil probe and operating a t 55.54 MHz (2H)and 95.70 MHz (23Na). an SDS/pentanol bilayer (with n p / n S D S = 2.9) ESR experiThe 2H spectra were recorded with the standard quadrupolar ments showed that K decreases by ca. 2/3 on addition of 10 echo pulse sequence, (n/2)~-r-(~/2)*~-~-acq., with 25 p s n/2 to 60% pentanoLZs The uncertainty in the experiments pulse and r = 100 ps. The 23Naspectra were obtained from the K of a was however large (cf. above). In a n other single-pulse free induction decays following a 20 ps n/2 pulse, phospholipid bilayer decreased from ca. 25k~Tforthe pure with the acquisition delay set to l/VQ (VQ is the quadrupole phospholipid bilayer to ca. lkBT on addition of pentanol splitting) to obtain in-phase satellite peaks. The magnetic field to n p / n p h = 2. Furthermore, in the SDS/C,-alcohollwater inhomogeneity was ca. 5 Hz. The sample temperature was controlled by an air-flow regulator (Stelar VTC91) yielding a lamellar phase K = (2 f 1)kBTfor n = 5-7 and K = (13 stability and temperature gradients off0.05 "C or better. Before f 3)kBT for n = 8-12.36 each experiment the sample was equilibrated in the probe and In this paper we report on the variation in K with the appropriate temperature for at least 10 min. In the temperature and bilayer composition, using the sensitive temperature-variation study the temperature was increased from NMR method33 on the system SDS/pentanoYwater 0 to 60 "C in steps of 10 "C, with 10 min equilibration a t each dodecane/pentanol, which is very precisely characterized step. in the dilute regime.l8 In the last section we relate these The quadrupole splitting VQ was measured directly as the variations to the phase diagram and to some recent splitting between the satellite peaks (arising from the 90" molecular theories for K. singularities) in the 2H doublet spectrum or as the separation

+

Experimental Section Sample Preparation. The experiments were performed on four series of samples in the lamellar phase of the quaternairy system sodium dodecyl sulfate (SDS)/pentanol/water/dodecane, the phase diagram of which was thoroughly studied a t 2 1 "C in a previous study.1s The samples were made by diluting four different concentrated lamellar phases, containing SDS, pentanol, and water, by a solvent mixture of91.0 wt % n-dodecane (>99%,Aldrich) and 9.0 wt % 1-pentanol (>99%, Aldrich). The compositions of the concentrated lamellar phases are given in Table 1. For series I, we used a-deuterated SDS (Synthelec, Lund), doubly distilled HzO, and pentanol. For series 11-IV, we used ordinary SDS ("speciallypure", BDH Chemicals),heavy water (DzO, > 99.9 atom % 2H, Sigma), and pentanol. Approximately 12 g was made of each concentrated lamellar phase, which were mixed with a slowly rotating magnetic stirrer for 2 weeks (at ca. 22 "C).During this mixing each sample was kept in a glass vessel, tightly sealed with a screw cap. The samples used for the NMR experiments were prepared by weighing appropriate amounts of the concentrated lamellar phase and the solvent into Pyrex tubes, which were flame sealed immediately and then gently mixed for 1 to 2 weeks. Since the bilayer composition is essentially invariant under dilution (cf. ref 33 and below), the bilayer volume fraction 4 was calculated as the volume fraction of the starting lamellar phase in the final sample, using specificvolumes (mug) of 1.002 (HzO), 0.905 (DzO), 0.85 (SDS), 1.228 (pentanol), and 1.336(dodecane). The bilayer volume fractions calculated in this way are given in Table 2. (37) R o w , D.; Nallet, F.; Freyssingas, E.; Porte,G.;Bassereau, P.; Skouri, M.; Marignan, J. Europhys. Lett. 1992, 17,575.

between the central and satellites peaks in the 23Na triplet spectrum. In general, there was a tendency for the samples in the dilute regime to align with the optical axis perpendicular to the magnetic field. However, this partial alignment has no effect ~ ~ on the determined VQ and thus the layer bendingrigidity K . The uncertainty in VQ is estimated to fO.l-0.2 kHz.

Results and Analysis Temperature Variation. The temperature variation in the bilayer bending rigidity K was investigated by a 2H-NMRstudy of the quadrupole splitting of aJH-SDS in series I. The results of this investigation are shown in Figure l.38With some few exceptions, V Q decreases with increasing dilution and temperature. To determine the rigidity K from the variation in VQ with the bilayer volume fraction 4, we use the recently derived relations33between VQ, 4, and K (which are valid for a sterically stabilized dilute lamellar phase)

and (38)There is an error in Figure 2 of ref 33. The SDS quadrupole splitting for the 4 = 1sample should be 20.43 kHz. The error does not influence the analysis in ref 33.

Layer Fluctuations in a Dilute Lamellar Phase I

I

I

Langmuir, Vol. 11, No. 6, 1995 2203 1

I

0.8

00

0.6

> \

0

> 0.4 0.2

11

' 0

1

I

I

0 0.1

I

0.2 0.4 0.6 0.8 1 Bilayer volume fraction, Q Figure 1. Quadrupole splitting of the a-deuterated SDS for series I vs the bilayer volume fraction for temperatures T/"C = 0.0, 10.0,20.0,30.0,40.0,50.0, and 60.0. The lines are simply guides to the eye. In general, V Q decreases with increasing temperature and decreasing 4.

0.3 0.5 0.7 0.9 Bilayer volume fraction, $ Figure 2. VQ/WQO vs the bilayer volume fraction 4 for K /kBT = 1, 2,and 4 and d/a = 4. 26

I

I

I

I

22

2 In eqs 1-3 UQO is the hypothetical quadrupole splitting in the absence of bilayer curvature fluctuations ( = 01, n l is the perpendicular (to the mean orientation) component of the local layer director, kg is Boltzmann's constant, K is the Qilayerbending rigidity, 6 is the bilayer thickness (ca. 35 A (series I) to ca. 27 8, (series W ) )a, is the short-wavelength cutoff (below which the continuum description fails, a2 should be of the order of the area of a surfactant molecule in the bilayer), and 4 is the volume fraction bilayer in the sample. For eqs 1-3 to be valid, it is assumed that (i)the dilute lamellar phase is sterically stabilized, which we know is true from scattering studies,l5?23-26 (ii) the layers are incompressible and only interact weakly, which limits the analysis to bilayer volume fractions 9 x 0.65 or less, and (iii) the bilayer fluctuations are in the weak crumpling limit, which restricts the analysis to 4 = 0.10 or more.33 Inspection of eqs 1-3 reveals that VQ depends on four parameters, viz. UQO, K/k&",dla, and 4. The ratio dla is limited to the range 1.5 < dla < 8,33independently of temperature, a n uncertainty that hardly affects K since Y Q ( ~varies ) strongly with K , which we illustrate in Figure 2. It is this strong variation in VQ(@) with K that makes the NMR method so sensitive to K-if K is in the range 0-5 kgT. As we will see below, the uncertainty in dla is the major source for the uncertainty in the obtained K. Yet, it is possible to determine K to within &lo%. Furthermore, since UQO for a-2H-SDSis essentially independent of the bilayer c o m p o ~ i t i o nand ~ ~ the bilayer composition is constant in the dilute regime (cf.below), UQO is also constant in this region. So far, we have regarded the volume fraction 4 as temperature independent, which is not strictly true. However, since the temperature variation of the specific volumes of the components are similar (except for water in the range 0-10 0C),40-42 4 is essentially temperature (39)Quist, P.-0.; Fontell, K.; Halle, B. Liq. Cryt. 1994,16,235, and references therein. (40) CRC Handbook of Chemistry and Physics; Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1993;Vol. 74.

18

0

>

14

10

0

0.2 0.4 0.6 0.8 1 Bilayer volume fraction, Q Figure 3. Best nonlinear least-squares fit of eqs 1-3 to the vQ(a-2H-SDS) vs 4 data of series I at 30.0 "C. d/a = 4.The error bars indicate the uncertainty in the experimental splittings. Filled data points were used in the fit, whereas the open data points were omitted (see text). independent. Although the deviations from 425"c in Table 2 are small, the variation in 4 was taken into account in the fits. (The shift in K on neglecting this correction was insignificant .) In Figure 3 we show the best nonlinear least-squares fit of eqs 1-3 to the vQ(a-2H-SDS)vs 4 data of series I a t 30 "C assuming dla = 4. From this fit we obtain K = (2.18 f 0.Ol)kBT and VQO = 25.4 f 0.1 kHz, where the experimental uncertainty in VQ is the source of the uncertainty. Of course, this 1%uncertainty in K is too small-if we actually knew dla, the small systematic errors in 4 and the small variations in UQO with 9 would contribute to the uncertainty, yielding something like f 2-3%. However, dla is not exactly known but in the range 1.5 I dla i 8, we thus obtain K = (2.18 f 0.17)kgT and UQO = 25.4 f2.2 kHz, taking the uncertainty in 61a into account. Since dla is the major source for the uncertainty in K , the NMR method is rather sensitive to changes in K with, e.g., composition and temperature-if the variation of the (41)Beilstein Handbook; Springer Verlag: Berlin, 1918-1980; 4. Ad.-V Suppl. series. (42)Hagsliitt, H.; Sodeman, 0.;Jonsson, B. Liq. Cryst. 1992,12, 667.

Quist

2204 Langmuir, Vol. 11, No. 6, 1995 Table 3. Temperature Variation in the Bilayer Bending Rigidity K for Series I TI "c K / k B p K/10-21 Ja UQ'flrHz' VQ(@=l)flrHZ 20.4f0.2 8.7 f 0 . 8 25.7 f 2 . 1 0.0 2.31 f 0 . 2 1 20.5f0.2 8.8 f 0 . 7 25.8 f 2 . 2 10.0 2.25f0.19 20.5 f 0 . 2 9.0% 0.8 25.6 f 2 . 2 20.0 2.22f0.19 2 0 . 4 f 0.2 9.1 f 0.7 25.4f2.2 30.0 2.18 f 0 . 1 7 20.2 f 0.2 9.2 f O . 8 25.2 f 2 . 3 40.0 2.12 f 0 . 1 8 20.0f 0.2 9.5 f 0 . 8 24.4f2.2 50.0 2.14f0.17 24.2 f 2 . 3 19.8f 0.2 60.0 2.06 f 0 . 2 0 9.5 f O . 9 a

, ,

The uncertainties include the uncertainty in the ratio dfa.

bilayer thickness 6 is known and taken into account. This is because we expect the cut-offlength ( a )to be essentially independent of composition and temperature (for a particular system). The hypothetical quadrupole splitting in absence of bilayer fluctuations, VQO,of the a-2H-SDScan be used as an independent check of the derived K . For aliphatic deuterons in a surfactant hydrocarbon chain, VQO can be reduced to43 (4) where x = 170 kHz is the quadrupole coupling constant for the aliphatic deuterons a n d S the local order parameter. For a-deuterated anionic surfactants (like SDS) the local order parameter is essentially independent of composition, S= interfacial curvature, and t e m p e r a t ~ r e .Typically ~~ 0.18-0.24 for a-2H-SDS. With VQO = 25.4 f 2.2 kHz and x = 170 kHz we obtain S = 0.20 f 0.02 from eq 4, which fits nicely into the expected range and thus certifies the derived K . Repeating the analysis at 0, 10, 20, 40, 50, and 60 "C yields the results displayed in Table 3. As expected from the literature39 VQO decreases weakly with increasing temperature. More surprisingly, perhaps, is the hardly significant increase in K with temperature. We discuss this feature in the next section. A comparison of vQoand V Q ( @ = ~ ) yields a temperature independent ratio V Q ( ~ = ~ )= /V 0.80 Q ~f 0.11. Because of the limited space for bilayer undulations at 4 = 1we expect / V1.Q ~Consequently, the (n:) 0 and thus V Q ( ~ = ~ ) x deviation of VQ(~I=~)/VQO from unity cannot be caused by bilayer undulations. A conceivable source for the deviation is structural defects (on the nanometer length scale) in the most concentrated samples of the lamellar phase. Defects ofthis kind (e.g., aqueous pores or channels in the bilayer) were observed in other similar systems39,44,45 in the same region of the lamellar phase.ls In the present system, the defects obviouslydisappears on dilution (since VQO equals the expectedvalue for 4 5 0.651, which possibly is caused by a n uptake of pentanol to the bilayer (since addition of alcohol to the bilayer removes the structural defect^).^^,^^ Thus, the bending rigidities in table 3 (and 4, cf. below) may correspond to a bilayer with slightly more pentanol than the original concentrated (4 = 1) lamellar phase (cf. below). Another source for the deviation of VQ(~=~)/VQO from unity is a minor decrease in the local order parameter to S = 0.16 a t 4 = 1. However, since this is outside the otherwise observed regime S = 0.18-0.24, we regard it as a less probable explanation. Composition Variation. The variation in K with composition was investigated at 20.0 "C, using the 23Na quadrupole splitting ofthe Na+ counterions in series I-IV. In Figure 4 we show the experimental results. Since the (43) Davis, J. H.Biochim. Biophys. Acta 1983, 737, 117. (44) Hendrikx,Y.; Charvolin, J.; Kbkicheff, P.; Roth, M. Liq. Cryst. 1987,2,677. (45) Quist, P.-0.; Halle, B. Phys. Rev. E 1993, 47, 3374.

I

I

I

I

'0

0.2 0.4 0.6 0.8 1 Bilayer volume fraction, 4 Figure 4. 23Naquadrupole splittings vs the bilayer volume fraction 4 for series I-IV at 20.0 "C:series I, circles; series 11, squares; series 111, diamonds; series IV, triangles. The lines are simply guides to the eye. Table 4. Variation in K with the Bilayer Composition at 20 "C Series

I I1 I11

IV a

nwf?ZsDs nP/?ZSDS

24.8 19.4 16.6 12.2

2.36 2.17 2.07 1.75

K/kBp

Ug0flrHZa

2.103~0.23 10.1 f 1.1 2.34f 0.22 9 . 6 f 1.1 2.37 f 0.22 9 . 8 f 1 . 1 2.96f 0.21 10.7 f 1.1

YQ(@=l)flrHZ

9.1 f 0.2 8.5 f 0 . 2 8.4f0.2 8 . 9 5 0.2

The uncertainties include the uncertainty in the ratio 61a.

dilution does not influence the bilayer composition in the range 0.10 5 4 5 0.65 (cf. below), the composition of the polar region is unchanged under dilution. Thus, we can regard v~'('~Na)as independent of 4 in the dilute regime. Repeating the analysis, using eqs 1-3, yields the bilayer bending rigidities listed in Table 4. For series I we obtain K = 2.10 f 0.23 from the 23Na data, which agrees with K = 2.22 f 0.19 obtained from a-2H-SDSa t 20 OC-as expected. Furthermore, the ratio Y Q ( ~ = ~ )= / v0.87 Q ~ f 0.12 for the 23Nasplittings, which is slightly closer to unity than V Q ( ~ = ~ )obtained / V Q ~ from aJH-SDS. Although the difference is small (and hardly significant), it is interesting to notice that the splitting ratio V Q ( $ J = ~ ) is / Vlarger Q ~ for 23Na than for a-2H-SDS. Since VQ is composition independent for a-2H-SDS, but not for 23Na+,we can conclude that (i)the composition of the bilayer does not change in the range 0.10 5 4 5 0.65, since we obtain the same K from the aJH-SDS and 23Na splittings, (ii) the composition of the bilayer (in the range 0.10 5 4 5 0.65) probably differs from the composition in the original concentrated (4 = 1)lamellar phase, and (iii) since v ~ ( ~ ~4N=a1), decreases on pentanol addition,46the difference in Y Q ( ~ = ~ ) / for V Q23Na ' and a-2H-SDS corresponds to an increased pentanol concentration in the bilayer of ca. 0.4 units when diluting from 4 = 1to 4 I 0.65 (i.e., from np/nsDs = 2.36 to ca. 2.8 for series I, etc.). Discussion In this section we compare the temperature and composition variation in K to the phase diagram and to some recent molecular theories for K. An inspection of Table 4 reveals a rather interesting composition variation in the bilayer bending rigidity--rc- is essentially constant for series 1-111 and then increases by ca. 30 % in series IV. A comparison with the phase (46) Quist, P.-0. Unpublished results.

Layer Fluctuations in a Dilute Lamellar Phase diagram, where the lamellar phase in series 1-111 can be diluted to 85-90 wt % solvent but series IVto only 75-80 wt %, shows that an increased K destabilizes the dilute lamellar phase-as p r e d i ~ t e d . ~ Following the arguments of de Gennes et al.,27 a n increased cosurfactant concentration in the bilayer should decrease K , which is also observed. Furthermore, these authors predict that with K larger than a certain threshold (K,) the dilute lamellar phase is stable, but with K < K~ a transition to a microemulsion should occur. However, according to Bellocq et a1.18the water-to-surfactant ratio (n,lnsDs) in series IV is the lowest possible for the dilute lamellar phase to exist-at ratios n,lnsDs -= 12.2 there is only a wide microemulsion phase in the dilute region of the phase diagram. Thus, the prediction of de Gennes et aLZ7of the phase sequence on changing K cannot be supported by our results, where a n increasing K is a precursor for a transition from the dilute lamellar phase to the microemulsion phase. As we noticed in the previous section, the temperature dependence in K is hardly significant (Table 3). Thus, with increasing temperature the ratio dkgT decreases, thereby increasing the bilayer crumpling to finally yield a transition to a two-phase region, with the lamellar phase in equilibrium with a n isotropic phase, as postulated by de Gennes et al.27 Second, the temperature invariance in K implies that the molecular interactions governing K increases approximately linearly with the temperature. There are essentially two kinds of interactions being discussed in connection to K ; the conformational entropy of the flexible hydrocarbon chain^^^,^^ and the electrostatic interactions in the polar r e g i ~ n . ~Of~ these, , ~ ~ explicit calculations show that the contribution from the hydrocarbon chain flexibility ( K ~ Jdominates the contribution from the electrostatics ( ~ ~ 1in) the present system. In the mean-field limit, the electrostatic contribution to in a lamellar phase with high surface charge density and no added salt is given by50

where the constant q x 0.06, d is the intermembrane separation (width of tbe aqueous region), and IB is the Bjeaum length (ca. 7 A). With cl 18 (series I) to ca. 11A (series IV),we thus obtain ~~1 = (0.2-0.3)k~T. For series IV, with a rather narrow polar region, it is however doubtful if the mean-field result (5) is valid. Thus, the increase in K on going from series I11 to series IV may be of electrostatic origin (although the hydrocarbon region can account for it too, cf. below). The contribution from the hydrocarbon chain conformational entropy to the bilayer bending rigidity has been calculated by Szleifer et From these calculations Khc depends strongly on the headgroup area, the hydrocarbon chain length (Cn),the molecular composition in the twocomponent blend, and the (postulated) molecular restrictions in the bilayer. In the present lamellar phase the mean area per molecule is ca. 25 Az,which together with the results of Szleifer et al.4s rules out two of the three models considered, since they predict too large bending rigidities: the “blocked exchange”, where the molecules are not allowed to rearrange, and the “constant area” (47)Szleifer,I.; Kramer, D.; Ben-Shaul, A,; R o w , D.; Gelbart,W. M. Phys. Reu. Lett. 1988,60,1966. (48) Szleifer, I.; Kramer, D.; Ben-Shaul, A,; Gelbart, W. M.; Safran, S. A. J. Chem. Phys. 1990,92,6800. (49) Pincus, P.; Joanny, J. F.; Andelman, D. Europhys. Lett. 1990, 11, 763.

(50)Higgs, P.G.; Joanny, J. F. J. Phys. (Paris) 1990,51, 2307.

Langmuir, Vol. 11, No. 6, 1995 2205 model, where the headgroup area of the molecules in the bilayer is constant. The only model that may account for the observed K (with the restriction of a mean headgroup area of ca. 25 k )is the physically pleasing “free-exchange” model, where the molecules are allowed to rearrange until the free energy reaches a minimum. With a mean headgroup area of 31.6 k the “free exchange” model predicts bending rigidities of pure c16, (212, cg, and C5 (extrapolated) bilayers of KhJkBT sz 2.5, 1.2,0.4, and 0.3, r e s p e ~ t i v e l yoHowever, .~~ decreasing the headgroup area from 31.6 to 25 A2increases Khc by a factor of ca. 6 in the “free exchange” model (for a C16 chain).4s We should thus expect KIkBT x 15, 7, 2.5, and 2, respectively, for these pure bilayers. With these adjustments, we can estimate the variation of Khc with the molar ratio for the CdC5 blend, by a comparison with a CdC8 blend with a mean headgroup area 31.6 A2(Figure 14c in ref 48). We thus estimate Khc/kBT 7 and 2 for pure cl2 and C5 bilayers, respectively, and KhdkBTx 2 for the blends in series I-IV. For the “blockedexchange” and “constant area” models we expect K = (20-40)k~T,with’ similar arguments. Even though the estimate is rough (a serious calculation would not harm) it is good enough to identify the major interaction governing K-the conformational entropy of the flexible hydrocarbon tails of the surfactant and cosurfactant in the bilayer. Furthermore, the observed increase in K on decreasing the pentanol-to-SDS ratio (Table 4) is predicted by Szleifer et al.:4s In the “freeexchange”model for a cl&g blend (with a mean headgroup area of 31.6 Az), Khc is essentially constant in the range 00 > ncdnc16 > 1.75 and then starts to increase with -a similar to what we decreasing cg ~ o n t e n t ~ ~variation observe experimentally (cf. Table 4). Finally, we expect a weak variation in K with temperature, since the conformational statistics of the hydrocarbon chains is governed, primarily, by packing considerations (i.e., head group area), while temperature variations play a secondary To conclude, the microscopic models for the bilayer bending ~4gidity4~t~O can account for the observed bilayer bending rigidity as well as for the variation with the bilayer composition. We can, however, not reproduce the rapid decrease in K with increasing pentanol-to-SDS ratio observed in a previous ESR study.28 Note Added in Proof. In a recent publication, the NMR method is used to determine K for bilayers in the lamellar phase in the systems SDSIalcohoUwaterdiluted with water or brine. (Auguste, F. et al. J. Phys. IZ (Paris) 1994,4,2197.) The results are similar to ours, taking the different chain lengths into account: dkBT = 6-2 for a molar ratio nc$nCl2 = 1.2-2.9 and K/kBT = 1.3-13 for bilayers with c6-clo alcohols and nc,lnc,, = 2.4. In another recent publication the temperature dependence of K for a phospholipid bilayer is determined (Niggemann, G. et al. J . Phys. ZZ (Paris) 1995,5, 413). In this system, K decreases dramatically with temperature--from ca. 9 kBT a t 12 “cto ca. 2 kBT a t 33 “C, which is quite different from our results.

Acknowledgment. I am grateful to Dr. B. Halle for his comments on the manuscript. The financial support from the Swedish Research Council for Engineering Sciences (TFR)and the Swedish Natural ScienceResearch Council (NFR) is acknowledged. LA9409384 (51)Szleifer, I.; Ben-Shad, A.; Gelbart, W. M. J. Chem. Phys. 1986, 85,5345.