0 Copyright 1991 American Chemical Society
The ACS Joumal of
Surfaces and Colloids APRIL 1991 VOLUME 7, NUMBER 4
Letters Interaction of Cations with a Fatty Acid Monolayer. A Grazing Incidence X-ray Fluorescence and Reflectivity Study J. Daillant,*lt L. Bosio,t J. J. Benattar,? and C.Blott Service de Physique d u Solide et de R6sonance Magngtique, Direction de la Physique, Centre d'Etudes NuclBaires de Saclay, 91191 Gif-Sur- Yvette Cedex, France, and Laboratoire Physique des Liquides et Electrochimie, ESPCI, 10 rue Vauquelin, 75321 Paris Cedex 05, France Receiued October 3, 1990.I n Final Form: January 24, 1991 The interaction of Mn2+ cations in the subphase with a behenic acid monolayer has been investigated as a function of surface pressure by using both grazing incidence X-ray fluorescence and X-ray reflectivity. The fluorescence probe provides an accurate determination of the number of cations attracted near the surface (0.47 f 0.06 per amphiphilic molecule),and the reflectivity experiments show that these cations are condensed within an extremely thin region (50.5nm). The complete structural parameters of the film and the surface roughness are compared to experimental data obtained with the same compound on pure water.
Introduction Monolayers of amphiphilic molecules adsorbed a t the air-water interface have drawn considerable attention, mainly focused on their phase tran~itions.l-~These transitions, revealed by kinks in the isotherms (n, A), where II is the surface pressure (n = ywater - y ) and A the molecular area, are conditioned by the chain statistics and by packing requirements.2p6 Monolayers on water are model systems for problems of biological importance such as the electrostatic properties of membranes (see e.g. the + Centre d'Etudes Nucleaires d e Saclay. t
ESPCI.
(1) Adam, N. K. The Physics and Chemistry of Surfaces, 3rd ed.; Oxford University Press: Oxford, 1941. Harkins, W. D. The Physical Chemistry of Surface Films; Rheinhold Publishing Corp.: New York 1952. Gaines, G. L. Insoluble Monolayers at Liquid-Gas Interfaces; Wiley-Interscience: New York, 1966. (2) Cadenhead,D. A.; Muller-Landau,F.; Kellner,B. M. J. In Ordering in Two Dimensions; Sinha, S. K., Ed.; North-Holland Amsterdam, 1980; p 73. (3) Albrecht, 0.; Gruler, H.; Sackmann, E. J. Phys. 1978,39, 301. (4) Lin, B.; Shih, M. C.; Bohanon, T. M.; Ice, G. E.; Dutta, P. Phys. Reu. Lett. 1990, 65, 191. (5) Daillant, J.; Bosio, L.; Harzallah, B.; Benattar, J. J. J. Phys. I I 1991, 1, 149. (6)Szleifer, I.; Ben-Shaul, A.; Gelbart, W. M. J.Phys. Chem. 1990,94, 5081.
0743-7463/91/2407-0611$02.50/0
review by MacLaughlin' and the references therein). In particular, their potential and the binding of charges affect the biological properties of membranes. In this paper we investigate the interaction of divalent Mn2+cations with a behenic acid monolayer as a function of surface pressure using near total external reflection fluorescence (NTEFP and X-ray r e f l e c t i ~ i t y . ~X-ray J~ reflectivity allows an accurate and independent determination of thicknesses and electron densities (i.e. structural parameters), as well as surface roughnesses, whereas NTEF" allows an absolute determination of the surface excess of the counterions. Both techniques used together yield unambiguous information that cannot be obtained separately (in ref 11, the ambiguousness was partly removed by means of an EXAFS experiment). This work follows an investigation of (7) MacLaughlin, S. Annu. Reu. Biophys. Biophys. Chem. 1989, 18, 113. (8) Eisenberger,P.;Marra,W. C.Phys.Reu.Lett. 1981,46,1081. Bloch,
J. M.; Sansone, M.; Rondelez, F.; Pfeiffer, D. G.; Pincus, P.; Kim, M. W.; Eisenberger, P. M. Phys. Rev. Lett. 1986, 54, 1039. Brunel, M. Acta Crystallogr., Sect. A 1986,42, 304. (9) Richardson, R. M.; Roser, S. J. Liq. Cryst. 1987, 2, 797. (10)Bosio, L.; Benattar, J. J.; Rieutord, F. Rev. Phys. Appl. 1987,22, 775. (11)Bloch, J. M.; Yun, W. B.; Yang, X.; Ramanathan, M.; Montano, P. A., Capasso, C. Phys. Rev. Lett. 1988, 61, 2941.
0 1991 American Chemical Society
Letters
612 Langmuir, Vol. 7, No. 4, 1991 the phase transitions in monolayers on water using X-ray reflectivity.12J3 Due to the presence of ionizable groups, such surfaces may become charged and a diffuse double layer of counterions may form.14 The classical treatment of such systems is based on the Gouy-Chapman approach.' In the present case, this approach has to be modified in order to take into account the binding of ions.15 The reasons for the success of these models are reviewed in ref 7, and we shall discuss our results in relation to the recent model of Bloch and Yun.16 X-ray Optical Methods For X-ray wavelengths, the refractive index of matter n can be expressed as n = 1 - 6 - $3; the imaginery part of the index is proportional to the linear absorption coefficient17 ( p = 0.0126 X lo4 for water) and to the wavelength (Cu K q : X = 0.154 05 nm) and 6 is proportional to the electron density of the material (6 = 3.56 X 10-6 for water). Since the real part of the index is less than 1,total external reflection occurs for angles of incidence, 0, below a critical angle, Of = (26)'12 (here =2.67 mrad), and an evanescent wave is propagated at the interface. Beyond O,, the intensityof the beam reflected byasingle, ideal diopter followsthe Fresnel law of optics where the wave vector transfer q is perpendicular to the surface (q = qrz, qz = 47r sin O/A). For more complicated cases, the shape of the reflectivity curve results from interferences between the beams reflected by large electron density gradients, and one obtains information on the projection of the electron density p ( z ) normal to the surface.ls As in many similar cases, the present system can be described as composed of chemically homogeneous layers, and a model can be constructed by considering these layers as slabs of constant density. Then, one can take into account the standard deviation of the interface height (its roughness) ( P)lI2by smearing the model through a convolution with a Gaussian function. For amphiphilics on pure water,l8this roughness is due to thermally excited capillary waves and can be computed exactly without any adjustable parameter .13J8 The principle of a NTEF experiment is to use the evanescent wave in order to excite the fluorescence of a 0 of the given species of atoms. Since the limit as 0 penetration length of this evanescent wave (calculablefrom the Descartes-Snell law) is only 4.6 nm in the present case, the method is highly sensitive to the interface region. The fluorescence emission is incoherent, and the intensity is thus given by IF(O) 0: dz N(z)lE(z)l2,where E is the electric field and N ( z ) ,the concentration of the emitting atoms. The proportionality fador involves the fluorescence cross section and geometrical terms. A convenient way to compute the electric field inside the material is to use the matrix formalism of stratified media optics.'g The
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(12) Daillant, J.; Bosio, L.; Benattar, J. J. Europhys. Lett. 1990, 12, 715. (13) Daillant, J.; Bosio, L.; Benattar, J. J.;Meunier, J. Europhys. Lett. 1989, 8, 453. (14) Israelashvili, J. N. Intermolular and Surface Forces; Academic Press: London, 1985. (15) Grahame,D. C. Chem.Reo. 1947,41,441. Abramson,H. A.;Muller, H. Cold Spring Harbor Symp. Quant. Eiol. 1933, 1 , 29. Healy, T. W.; White, L. R. Ado. Colloid Interface Sci. 1978, 9, 303. McLaughlin, S.; Mulrine, N.; Gresalfi, T.; Vaio, G.; McLaughlin, A. J.Gen. Physiol.1981, 77,445. (16) Bloch, J. M.; Yun, W. Phys. Rev. A: Cen. Phys. 1990, 41, 884. (17) James, R. W. The OpticalPrinciplesoftheDiffractionofX-rays; Bell: London, 1948; p 135. (18) Daillant, J.; Bosio, L.; Harzallah, B.; Benattar, J. J. J. Phys.I1 1991, 1, 149. (19) Born, M.; Wolf, E. Principles of Optics, 6th ed.; Pergamon: London, 1980; p 491.
?
I
i20t a
gL tI
LL
0
0. 19
\
I
\
LC
\
\
0. 21 0. 23 0. 25 molecular orea (nn2)
I
0. 27
Figure 1. Measured isotherm for the behenic acid monolayer on a 10-3 mol/L MnClz subphase (pH = 7.5).
interfacial region is broken into laminae characterized by a unimodular transfer matrix which relates the electromagnetic field a t both sides of the lamina. (Note that this method allows, as well as the Born approximation,20 a calculation of the reflectivity.) The complete analysis of the results therefore consists of first obtaining an electron density profile from the measured reflectivity curves in order to compute the electromagnetic field for the treatment of the NTEF data, which in turn are used to refine the reflectivity analysis. The error bars were estimated by assuming Poisson statistics for each independent counting process and according to the contour Ax2 = x 2 - X2min = 1 in the space of parameters for each fit. Experimental Section The diffractometer and the Langmuir trough have been described elsewhere.21 The Cu Ka1 radiation is selected by using a flat LiF (200) monochromator. For recording reflectivity curves, we used a 50-pm collimating slit followed by an antidiffusion slit and a 50 pm X 10 mm analysis slit, leading to a low divergence (0.23 mrad). The angular scale accuracy is f0.05 mrad. The reflected beam is scanned at each incident angle to determine the specular reflectivity and the background. The NTEF signal is recorded a t grazing angles ranging on both sides of 8,. This requires a lower divergence which is fixed by means of a 6-pm thin slit. At each incident angle, the Mn K a fluorescence was recorded with a Si(Li) detector (80mm2aperture) placed =l mm above the surface, whereas the reflected beam was scanned as a proof of the beam positioning accuracy (which is critical due to the meniscus). For this study of a monolayer on an ionic solution, we chose a fatty acid, behenic acid, which we previously studied intensive1y,l3J8andthe Mn2+cation (the fluorescent Mn K a radiation (5898 eV) can be excited by using Cu Kal radiation (8047 eV)). Behenic acid was purchased from Fluka (purissimum, for gas chromatography) and used asobtained. The pH ofthe l@3mol/L solution of manganese(I1) chloride (Prolabo 99% min) in ultrapure water from a Millipore system was adjusted to 7.5 by using concentrated NaOH. The isotherm of a behenic monolayer on the mol/L mn2+solution is represented in Figure 1.
Results and Discussion NTEF curves are reported in Figure 2; Figure 2a was recorded on the bare 10-3 mol/L Mn2+ solution without any monolayer and Figure 2b was recorded with a behenic (20) Braslau, A,; Pershan, P. S.; Swislow,G.; Ocko, B. M.; Als-Nielsen, J. Phys. Rev. A: Gen. Phys. 1988.38, 2457. (21) Bosio, L.; Corks, R.; Folcher, G.; Oumezine, M. Reo. Phys.Appl. 1985, 20, 437.
Letters
Langmuir, Vol. 7, No. 4, 1991 613
ow0 1 J
' . " ,
2
'
3
0 (mradl
4
I
5
-
0.5 0.20
0.25 0.30 0.35 0.40 molecular area (m2)
Figure 2. Mn Kal fluorescence intensity as a function of the angle of incidence: (a) mol/L MnC12 solution; (b) behenic acid monolayer compressed a t II = 17 mN/m on the 10-3 mol/L MnCll subphase; (c) Mn2+cations surface excess calculated from NTEF data as a function of molecular area of behenic acid.
acid monolayer adsorbed at the interface and compressed at II = 17 mN/m. The increase in fluorescent intensity in Figure 2a is due to the increase in the penetration length vs 8 at 8,. Due to the very low value of the penetration length below the critical angle, the striking enhancement of the fluorescence intensity below and near Be in Figure 2b is due to the presence of Mn2+ cations near the surface. Reflectivity curves for bare water, behenic acid on pure water at n = 15 mN/m, and behenic acid on the mol/L Mn2+ at 20 and 37.5 mN/m, are represented in Figure 3. The presence of the Mn2+cation leads to a much better contrast of the interference pattern than on pure water, implying the presence of a well-defined (dense) layer near the interface. The reflectivity data are in any case inconsistent with an Mn2+layer extending to more than 1 nm from the surface, and it is therefore possible to separate the fluorescence signal into only two contributions (which can be calculated from the formula given for IF): the first arising from the bulk (with a Mn2+concentration mol/L) and the second from the surface (with an unknown surface excess r M n 2 + ) . The experimental NTEF curve is a linear combination of the two curves, and a fit thus allows the determination of the absolute value of rMn2f as the coefficient of the surface contribution. The measured variations of this surface excess, r M n 2 + , as a function of the molecular area of behenic acid are represented in Figure 2c. One observes a decrease of the surface excess with increasing area consistent with a l / A law, i.e. the number of Mn2+ cations per amphiphilic molecule is a constant (0.47 f 0.06) over the range of molecular areas investigated. Since the C1 K a (2622 eV) fluorescence intensity does not exhibit a peak vs 8 at the critical angle (only an increase in fluorescence intensity due to the increase in penetration length is observed, with rather large error bars =*20%), the species attracted to the surface should be Mn2+and not MnCP as sometimes suggested.22 This means that the excess charge on the layer (due to ionization of the carboxylic group) is completely compensated for by condensation of divalent Mn2+cations. The overall electric neutrality implies that half of the amphiphilic molecules are C21H43C00- anions (and the other half C21H43COOMn2+). By use of the Poisson-Boltzmann equation, taking into account the chemical binding of the cations Na+, H+, and Mn2+23 on the layer,l6 it is expected that the Mn2+ ions react with the ionized monolayer and that the fraction of C21H43COOH or CzlH43COONa+is less than 0.15% that of (22) Vogel, C.; Corset, J.; Billoudet, F.; Vincent, M.; Dupeyrat, M. J . Chim. Phys. 1980, 77,947. (23) We used a constant KM",~+ = 104.02 L/mol for the reaction C21Hd200- + MnZ+ C2lHaCOOMn+) according to Martell, A. E.; Smith, R. M. Critical Stability Constants, Volume IV; Plenum: New York, 1977; the other constants are given in ref 16 above.
CzlH43COOMn+.24 This is in agreement with the NTEF data and this question will now be further examined by using X-ray reflectivity, which provides information about the depth distribution of the cations. In fact, in the leastsquares analysis of the reflectivity data, the parameters of the head and Mn2+regions are correlated and no determination can be obtained without additional information. This additional information is provided firstly by the NTEF data detailed above and secondly by the reflectivity data for behenic acid on pure water.13 In this analysis, we used a three-laminae model (chains, heads, Mn2+). The head (carboxylic group) parameters are held fixed at the values obtained for a similar molecular area ~ 0= , 0.3 nm).13J8Only on pure water (i.e. Phead = 1 . 6 ~ ~lhead two roughnesses are considered, one common for the (air/ chain) and (chain/heads) interfaces characterizing the chains, and the other for the (head/Mn2+)and (Mn2+/ bulk) interfaces, characterizing the Mn2+region. These structural parameters and the roughness of the behenic acid monolayer and of the Mn2+ region are reported in Table I. As previously observed,lB the chain density remains constant within the condensed phases of amphiphilic films Consequently, adsorbed on water ( p , = (0.97 f0.03)p~~o). the aliphatic medium thickness increases upon compression (or for these condensed layers, the tilt angle decreases) in order to compensate for the diminishing available area, here from approximately 25" to 0" within the liquid condensed (LC) region of the isotherm. A most interesting parameter is the thickness of the (1.90 f 0 . 1 5 ) p ~ dense ~o Mn2+region, which we find to be 0.30 f 0.15 nm (Table I and Figure 4). This implies that the cations are tightly bound to the layer (the radius of the hydrated Mn2+cation is 0.438 nmz5). Note also that, according to the Poisson-Boltzmann model the concentration of Mn2+ cations attracted by the small uncompensated charge remaining on the layer (these cations form the diffuse part of the double layer) falls to half its maximum value (at z = 0) within 0.38 nm (to be compared to the Debye length on the order of 5.5 nm in the subphase). From the resulting high concentration near the surface, it should follow that a high fraction of C21H43C00molecules react to create CzlH43COOMn2+,and this is consistent with the previous analysis. Since the molecular area and the number of Mn2+ions per amphiphilic molecule are known, one can calculate the average number of water molecules with the head/ Mn2+region: The results of Table I imply the presence of 3.5 f l molecules of water per amphiphilic molecule in this dense region, to be compared with the primary hydration number for Mn2+(4.2).26 Note that it has been suggested that dehydration should determine the dynamics of the monolayer deposition onto a solid substrate.27 The values of the chain and Mn2+region roughnesses are also given in Table I. Note that the roughness of the Mn2+ layer is almost equal to that of the chains ( C T M ~ Z=+ (1.05 f O . O ~ ) C T , I , ~ ~the ~ ~ )ratio , slightly decreasing to 1upon compression. As for fatty acid films on pure water, the
(24) According to ref 16, the ratio of monovalent (H+) ions to divalent = (Mnz+) ions condensed on the monolayer is KH+QH+/(K~(~z+QM~z+)~/~ 104.56X IO-7.6/(lO4.02x lO-3)1/2= 3.5 X lO-4(theKvaluesare theconstants of reaction as defined in ref 23 and the Q bulk concentrations). This ratio is even smaller for Na+ ions. This behavior comes from the square root in the divalent ions contribution, which reflects their higher efficiency, basically related to the law of mass action. (25) Nightingale, E. R. J.Phys. Chem. 1959, 63, 1381. (26) Conway, €3. E. Ionic Hydration in Chemistry and Biophysics; Elsevier: Amsterdam, 1981; p 582 (27) Petrov, J. G.; Kuhn, H.; Mbius, D. J. Colloid Interface Sci. 1980, 73, 66.
614 Langmuir, Vol. 7, No. 4 , 1991
Letters
Table I. Structural Parameters and Roughness of the Behenic Acid Monolayer and the Mn2+ Region as a Function of Surface Pressure (n. mN/m) 0
5mN/m
10mN/m
15mN/m
20mN/m
25mN/m
28mN/m
35mN/m
37.5mN/m
2.4 0.39 1.3 1.25 0.25
2.4 0.4 1 1.40 0.42
2.32 0.47 1.3 1.60 0.42
2.4 0.52 1.2 2.1 0.24
2.45 0.52 1.1 2.0 0.23
2.48 0.53 1.1 1.85 0.22
2.59 0.37 1 1.7 0.15
2.6 0.415 1 1.7
2.55 0.44 1 2.00 0.33
(k0.5) Itail, nm utail, nm
(k0.05) (kO.2) UM~>+/V~~~ ( iIO . 1 ) P M ~ ' + / P H ~ O (kO.2) h+, nm (*0.05)
loo
3
0.35
2. 0 1.5
h
,KO \
4
-
0.5
-
-
1o+ -4
-3
-2
-1
0
1
2
depth (nm)
'LC
CL \
1o
Figure 4. Electron density profiles for behenic acid on water
-~
(dashed line) and on the 10-3mol/L MnC12 subphase (solid line). The positive depths are toward water.
IO-' \
I I 1 I
I
I
I
I
I
1
1
4
-
1
roughness first increases on compression dlie to the decreasing in surfacetension, and then abruptly decreases in the less compressible phase (to 0.44 f 0.02 nm at 35 mN/m) due to the appearence of a high bendingrigidity.l8 The drop in the roughness is larger that that for behenic acid on pure water.13 This is due either to a larger value of the bending rigidity modulus or to significant structural changes. The higher value of the roughness implies that an intrinsic short-wavelength roughness of the monolayer
is to be added in the present case to the roughness solely due to capillary waves. This behavior can be attributed to a particular configuration (analogous to that of twodimensional micelles of ref 28) of the headgroups (COOor COOMn+)in order to minimizetheir electrostatic energy (approaching the positive and negative charges closest to each other implies a shifting of hydrophobic tails). In particular,the short range order of Mn2+cations segregated to a stearic acid monolayer reported in ref 11could affect the chain packing. These results are consistent with the observation of ref 10 that the roughness increased with the fraction of ClaH&OOPb+ and also with the results of Richardson and RoserQwho found a larger roughness at pH = 7 when Cd2+cations are bound to their behenic acid monolayer. Note however that the absolute values of the roughness given in refs 9 and 10 are not directly comparable to the present ones, due to a broader resolution function. Acknowledgment. We wish to thank A. Braslau and
0. BBlorgey for a critical reading of the manuscript. (28) Ter-Minassian-Saraga, L. In Progress in Surface and Membrane Scieme, Volume 9; Cadenhead, D. A., Dianelli,J. F., Ed.; Academic Press: New York, 1979; p 223.
