Elemental Analysis within the Electrical Double Layer Using Total

Mar 23, 2007 - In contrast to the parent NTEF (near total external reflection X-ray fluorescence) method, TRXF uses a fixed angle of incidence (below ...
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J. Phys. Chem. B 2007, 111, 3927-3934

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Elemental Analysis within the Electrical Double Layer Using Total Reflection X-ray Fluorescence Technique Vladimir L. Shapovalov,*,† Mikhail E. Ryskin,‡ Oleg V. Konovalov,§ Antje Hermelink,| and Gerald Brezesinski| N. N. SemenoV Institute of Chemical Physics RAS, Kosygina 4, 119991 Moscow, Russia, UniVersal Laser Systems, Inc., 16008 North 81 Street, Scottsdale, Arizona 85260, ESRF, 6 rue Jules Horowitz, BP 220, 38043 Grenoble Cedex, France, and Max-Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany ReceiVed: October 20, 2006; In Final Form: January 17, 2007

A simplified total reflection X-ray fluorescence (TRXF) technique is proposed for the study of the electrical double layer (EDL) near charged monolayers at the air-water interface. In contrast to the parent NTEF (near total external reflection X-ray fluorescence) method, TRXF uses a fixed angle of incidence (below the critical one) and abandons both “spatial resolution” (which is poor anyway) and “absolute calibration” with the bulk reference. These modifications reduce both the duration of experiments and the complexity of the data treatment by 1-2 orders of magnitude and turn TRXF into a truly simple tool for elemental analysis within the EDL. A few TRXF experiments appear sufficient to disprove the model of simultaneous binding of alkali earth metal cations and inorganic anions to negatively charged phospholipid monolayers as proposed in literature. Direct experimental support was provided to the essential feature of the EDL near highly charged interfaces: The main amount of counterions is concentrated in the thin inner part of the EDL irrespective of the electrolyte concentration in the bulk. A study of the counterion competition for the participation in the EDL of highly negatively charged behenylsulfate (BS) monolayers (resulting from packing density limitations) revealed that univalent Cs+ is quite competitive with divalent Ca2+ and Ba2+ (which contradicts the classical GouyChapman model). If the univalent/divalent ion ratio in bulk is 9:1, the corresponding ratio in the EDL is ca. 1.5 for Cs+/Ca2+ and 0.5 for Cs+/Ba2+, whereas the model predicts 0.14 only. Bearing in mind packing density limitations, these values are consistent with a series of sizes for hydrated ions: Cs+ , Ba2+ < Ca2+.

Introduction Any charged surface exposed to water inevitably interacts with ions. The region of water next to the surface is highly enriched with counterions and depleted of co-ions. Together with the charged surface, ions form the electrical double layer (EDL)sa tiny space accommodating a strong electric field. This general phenomenon is responsible for a range of natural processes starting from the functioning of membrane proteins (biology) and ending with the precipitation of clays (geology). Countless technical and technological applications exploit the EDL as well. The EDL is highly inhomogeneous. The outer (diffuse) part moderately deviates from the surrounding electrolyte. The inner part (the few Ångstroms next to the charged surface) filled with an extreme electric field and crowded counterions is dissimilar to any bulk matter. Since the first physical description of EDL, given by Gouy and Chapman (hereafter GC model), the plausible conception of the outer part has practically not changed. In contrast, the inner part of the EDL still remains mysterious. Among numerous extensions of the GC model and independent sophisticated models, there is no one that is either widely used or generally accepted. The Stern extension of the GC model seems to be the single exception. Unfortunately, it * Author to whom correspondence should be addressed. Phone: +7 (495) 939-7345. Fax: +7 (495) 137-6130. E-mail: [email protected]. † N. N. Semenov Institute of Chemical Physics RAS. ‡ Universal Laser Systems, Inc. § ESRF. | Max-Planck Institute of Colloids and Interfaces.

is frequently used beyond the proper field of application, where it becomes a (illusive) means to describe virtually any experimental result (see extended discussion elsewhere1). Thus, the classical GC model remains in use in spite of the fact that many experimental observations remain in conflict with it (either moderate or dramatic). Pronounced differences in the properties of charged monolayers,1-5 micelles,6,7 and dispersions8,9 with different identically charged counterions (see more discussion elsewhere1) are a widespread example of “non-GC” behavior. Recently, we reported1 pronounced counterion size effect on the EDL near highly charged anionic Langmuir monolayers. The basic results contradicting the GC model were as follows:1 a dramatic decrease in the electric potential of the EDL for a series of alkali cations from Li+ to Cs+, unequal competition between counterions with the same charge but different size, and a capability of small univalent counterions to compete (for participation in the EDL) with large divalent ones. Because a specific chemical interaction (complexation) was excluded by the appropriate choice of monolayers and counterions, all of these effects have been qualitatively explained1 in terms of packing density limitations for counterions in the EDL. The rapid vanishing of counterion effects on the EDL potential with the decrease of surface charge density supported this explanation. Most of the results that concerned competition of counterions for participation in the EDL near highly charged interfaces were obtained in the previous study1 by means of the surface potential technique, which is highly sensitive and appropriate for mono-

10.1021/jp066894c CCC: $37.00 © 2007 American Chemical Society Published on Web 03/23/2007

3928 J. Phys. Chem. B, Vol. 111, No. 15, 2007 layer studies. For the particular task, this method is indirect because it observes variations in the EDL potential (resulting from alteration of counterion distribution) but not the counterions themselves. Even the X-ray reflectivity (XR) technique used there1 for the “direct” determination of the ratio of different counterions in the EDL is indirect in the strictest sense. Indeed, it senses only spatial distribution of total electron density and cannot discern between different atoms. Below, we will give an example of such a failure of this technique in an attempt of a “chemical analysis at the surface”. X-ray fluorescence (XF) at total reflection conditions is a surface sensitive technique capable of distinguishing different atoms that have different X-ray fluorescence spectra. In the present study, we used this ability of XF and investigated directly the competition between counterions for participation in the EDL. It was done, in particular, for such counterions and their combinations, which cannot be resolved with the XR technique. We also experimentally confirmed one of the basic features of the EDL near highly charged surfaces: The structure of the inner part of the EDL is virtually independent of the bulk electrolyte concentration. This seems to be quite important but is not generally recognized. Besides, we tested the recently reported10,11 surprising binding of Cl- anions to negatively charged phospholipid monolayers. The two last experiments are not directly related with counterion competition but clearly demonstrate the capability of the XF technique in interaction studies of ions with Langmuir monolayers. The particular realizations of the XF technique in applications to Langmuir monolayers12-15 imply a variation of the incident angle of the exciting X-ray beam from very low to higher values substantially above the critical angle for total external reflection (so-called NTEF technique12,13,16). In this way, the experiment gives 15-100 data points (or data sets)sfluorescence intensity (or fluorescence spectrum) against the angle of incidencesand needs many hours to complete a single sample. The use of bulk reference samples12,13 (solutions with known concentrations of analyzed atoms), which undergo the same procedure, further prolongs the experiments. NTEF data treatment (intended to determine the surface concentration of analyzed atoms) is complex and time-consuming: It includes fitting of experimental curves with model ones where adjustable parameters are the concentration of analyzed atoms and optical parameters of the sample. It is worth noting that the resulting accuracy of the surface concentration obtained in such laborious ways appears quit modest: Less than a 20% error is reported in one publication,12 and a 10% standard deviation can be estimated from figures presented in another publication.13 Attempts to obtain the location of fluorescent atoms in the direction normal to the interface from NTEF experiments14-16 (with variable angle of incidence) reveal the low spatial resolution of this method. A value of (300 ( 100) Å was found for the parameter characterizing the concentration profile near the surface.16 The choice of one model (the first) between two models, which differ in distance between the fluorescent atoms residing inside the monolayer and the water surface (7 versus 2.5 Å), made in another publication,14 looks surprising rather than convincing. It seems very unlikely that an evanescent wave with a 50 Å decay length can constitute a measuring tool with a 5 Å resolution (at least that for general applications). In the present study, we greatly simplified the NTEF approach for the particular task: quantitative detection of ions in the EDL near charged Langmuir monolayers. In our TRXF (total reflection X-ray fluorescence) experiments, we used a fixed angle of incidence below the critical one and abandoned both “spatial

Shapovalov et al. resolution” (which is too low for the EDL anyway) and “absolute calibration” with the bulk reference sample (replaced with a reference monolayer). The proposed approach substantially reduces the duration of the experiment and simplifies the subsequent data treatment as well. We also demonstrated that, with the proper choice of the reference monolayer, data treatment can be further greatly simplified. Materials and Methods Chemicals and Monolayer Preparation. Behenylsulfate (BS) tetramethylammonium salt n-C22H45OSO3- N+(CH3)4 was synthesized and purified as described previously.1 The organic salt of BS was chosen because of a higher solubility compared with that of the sodium salt. 1,2-Dipalmitoylphosphatidylglycerol (DPPG) from Sigma was used without additional purification. Purified eicosylamine (ECA) n-C20H41NH2 was kindly provided by Professor T. Richardson (University of Sheffield, U.K.). Alkali and alkali earth metal chlorides were all of analytical grade and used without further purification. Subphase solutions were prepared from ultrapure water with 18.2 MΩ cm specific resistance. Monolayers were spread from chloroform-methanol (4:1 w/w) solutions of amphiphiles with concentrations of 0.51 mM. Experimental Setup. The Langmuir trough for the X-ray experiments was equipped with a moveable single barrier. The trough dimensions are 170 × 438 mm2 with the short side along the beam. The surface pressure π was measured using a NIMA tensiometer PS4 and was kept constant during the measurement. All measurements were carried out at 20 °C. The total reflection X-ray fluorescence (TRXF) measurements were performed at the beamline ID10B at ESRF, Grenoble, France. The synchrotron X-ray beam coming from the undulator was monochromated at photon energy 22.5 keV by a double crystal monochromator using symmetric Bragg reflection (220) from two diamond crystals. Higher harmonics were rejected by a platinum-coated double mirror system. Both mirrors reflect in the vertical plane and keep the X-ray beam in the horizontal plane. The down stream mirror was bent to focus the X-ray beam at the sample (6 m from the mirror). The beam was deflected from the horizontal plane by rotation of the deflecting Ge crystal around the incident beam with keeping the Bragg reflection condition for Ge (111) reflection. The deflected beam (0.017 mm height, 1 mm width) touches the liquid surface at a grazing angle of 0.022° that is 40% of the critical angle of total reflection for the water surface. A scintillation (NaI) detector for the reflected X-ray beam was used for the height adjustment of the liquid surface. The fluorescence signal was measured by the Peltier cooled ROENTEC silicon drift detector (SDD) with an entrance window placed parallel to the liquid surface at a distance of 22 mm. The axis of the incident beam and the view directions of the NaI and ROENTEC detectors were lined up so that they crossed at the same point. The surface of the liquid was moved to this point before each measurement of the fluorescence signal. Background of the Method. The fluorescence intensity Ifi of an element i with a concentration profile ci(z) (along the direction normal to the interface) can be written as

Ifi ) bi

∫ Iex(z) ci(z) dz

(1)

where Iex(z) is the exciting X-ray intensity at a distance z from the surface and bi is a constant. It depends on the experimental conditions, X-ray absorbance of the particular element, and

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fluorescence yield for a particular line but not on the structure and composition of the monolayer. The absorption of fluorescence inside the sample, included into the integrand in an earlier publication,12 can be safely neglected for the case of total external reflection. Therefore, the determination of concentration of ions at the interface from experimental X-ray fluorescence data requires knowing both the intensity distribution of the exciting X-ray and the ion distribution near the interface. In this article, we evaluate both distributions theoretically and for the particular case of studying the EDL near charged monolayers finally reduce the data treatment procedure to simple arithmetic. Iex(z) and its dependence on parameters of the system can be estimated in a framework of a well-known model for X-ray reflection at the interface.12,14,17 A charged Langmuir monolayer is represented by two layers on the top of the bulk water subphase: upper, “organic” layer of thickness L1, comprising the amphiphilic molecules and lower, “ion-rich” layer of thickness L2, containing counterions. Each layer is characterized by its individual complex refractive index n (at the wavelength of the exciting X-ray): n ) 1 - δ - iβ, where the values of δ and β are functions of X-ray wavelength λ and the chemical composition of the layer.12 For hard X-rays, the coefficient β is several orders of magnitude smaller than δ and can be neglected without substantial loss of accuracy (see below). The value of δ is proportional to the electron density Fe of the matter: δ ) reλ2Fe/2π, where re ) 2.82 × 10-5 Å is the classical electron radius. The electron density of composite matter is given by the relation: Fe ) ∑ cjNj, where cj is the concentration and Nj is the total number of electrons per molecule for each component. The exciting X-ray radiation undergoes reflection and refraction on each of the three boundaries between the layers. Therefore, the electric field in each layer is a sum of two waves, incident and reflected, except in the water layer, where only the incident wave is present. The amplitudes of these seven waves are coupled to each other by a system of six linear equationsstwo per each boundary. The first equation represents the continuity of the tangential component of the electric field, and the second represents the continuity of the tangential component of the magnetic field.18 Below are the equations for the case of an incident wave polarized normal to the plane of incidence:

A0 + R0 ) A1q1-1 + R1q1 (A0 - R0) sin(R0) ) (A1q1-1 + R1q1)n1 sin(R1) A1 + R1 ) A2q2-1 + R2q2 (A1 - R1)n1 sin(R1) ) (A2q2-1 + R2q2)n2 sin(R2) A 2 + R2 ) A 3 (A2 - R2)n2 sin(R2) ) A3n3 sin(R3)

(2)

where A0 ... A3 and R0 ... R3 are the amplitudes of the incident and reflected (propagating backward) waves in each layer, respectively (Figure 1). The q parameters in these equations are phase factors for each layer: q1 ) exp(-ik1zL1); q2 ) exp(-ik2zL2), where k0z ... k2z are z-components of wave vectors in two adjacent layers, R0 is the angle of incidence and R1 ... R3 are the angles of refraction. Values of kjz are functions of the refractive indexes of layers and the angle of incidence: kjz

) k0z xn2j -cos2(R0).

Figure 1. Schematic illustration of the optical model of the sample. The z-axis is directed downward; the surface of the monolayer corresponds to z ) 0. The amplitudes of the refracted (propagating forward) and reflected (propagating backward) waves within the i-th layer are Ai and Ri accordingly.

Figure 2. The intensity of the X-ray wave inside the layered sample as a function of the incidence angle R and the distance from the surface z for the case of L1 ) 25 Å, Fe1 ) 0.32 je Å-3, L2 ) 2 Å, Fe2 ) 1.28 ej Å-3, Fe3 ) 0.33 je Å-3. Selected distances are 25 (solid line), 50 (dashed), 100 (dotted), and 200 Å (dashed-dotted). X-ray absorption in all media is neglected (see text for discussion).

The values of A1 ... A3 and R0 ... R2 have been found by numerically solving the linear system (2) for the chosen set of physical parameters and A0 ) 1 using MathCAD software. The relative intensity of X-ray excitation at a given distance from the interface z was calculated as a square of the total amplitude of the incident and reflected waves. For example, the intensity of X-rays within the “ion-rich layer” is represented by the formula Iex(z) ) |A2 exp[-ik2z(z - L1 - L2)] + R2 exp[ik2z(z L1 - L2)]|2. Analogous formulas can be written for each layer. Some results of these calculations are presented in Figures 2 and 3. The electron densities of particular layers required for these calculations were estimated as follows: The organic layer was represented as the matter with a density of 0.9 g cm-3 and a chemical formula (CH2)n, resulting in Fe ) 0.32 ej Å-3, which is in agreement with X-ray reflectivity data for the same monolayer1 and other studies.13,19 For the water layer, the usual value1,12 Fe ) 0.33 je Å-3 was reproduced in the same manner. For the ion-rich layer, the average concentration of univalent counterions (deduced from neutrality of the total system) is 10-3/ (NaSL2), where Na is the Avogadro number and S is the area per unit charge in the monolayer. Taking L2 ) 2 Å (roughly the doubled Pauling radius for an alkali cation), one can determine for the ion-rich layer that Fe ) 1.28 ej Å-3 for Cs+ counterions, 0.63 ej Å-3 for K+, and 0.36 ej Å-3 for Li+. As a matter of fact, the value L2 is not a deciding factor for X-ray intensity distribution Iex(z) (see below). Figure 2 demonstrates the dependence of X-ray intensity at several distances from the open surface versus the angle of incidence. The plots look very similar to previously published12,16 ones, but in our case, the maximums are much sharper. The simple analysis shows that the difference results from substantially less absorbance of hard X-rays (in our case). Note

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Figure 3. The intensity of the X-ray wave inside the layered sample as a function of the distance from the surface z and electron density of the ion-rich layer. The angle of incidence R ) 0.022° is near 40% of the critical one. The electron density of the ion-rich layer Fe2 (corresponding to one ion per 25 Å2) is 0.33 (no ions, solid line), 0.36 (Li+ ions, dashed), 0.63 (K+ ions, dotted), and 1.28 ej Å-3 (Cs+ ions, dashed-dotted). All other parameters are same as in the legend to Figure 2. Note that solid and dashed lines overlap completely.

Figure 4. Plots of electric potential (a) and counterion concentration (b) for the GC model of the EDL. Horizontal axes are broken to show both inner and outer regions of the EDL. Parameters taken for simulation are as follows: surface charge density, -1 ej/25 Å2; dielectric constant, 80; concentration of 1-1-electrolyte (mmole dm-3), 100 (solid lines), 10 (dashed), 1 (dotted), 0.1 (dashed-dotted).

that in our case the variation of the imaginary part of refractive indexes produces, within reasonable limits, no substantial effect on the X-ray intensity distribution, and for that reason, we neglect this term in our calculations. Figure 3 represents the decay of X-ray intensity with the distance from the open surface for different counterions. It is worth noting that the spread of intensity (for any given distance) does not exceed 10% even for extreme cases of Li+ and Cs+. Variations of L2 in the range 1-10 Å (Fe changes accordingly) gives no observable effect on the intensity decay curves (data not shown). Variations of L1 within the range 15-30 Å produce only a 3% spread of intensity (data not shown). The determination of the total amount of ions at the interface from X-ray fluorescence experiments, which is the primary interest of the current study, requires knowing the ci(z)sthe ion distribution along the normal to the surface (see eq 1). Because there are no direct experimental approaches to this distribution, it can be evaluated only theoretically. Different theoretical

Shapovalov et al.

Figure 5. TRXF spectra of 10 mM KBr subphase with and without charged monolayers (intermediate range of 4 to 11 keV, containing no lines is not shown, vertical scale at the right is highly extended to accommodate strong lines). Without a monolayer (solid line), only the fluorescence of atmospheric Ar is observable. In presence of a charged monolayersanionic BS (dashed line) or cationic ECAs(dotted line) strong emission of counterions appears (see labels and text for details).

models of the EDL give a variety of distributions starting from the enormously sharp distribution with physically irrelevant concentrations given by the classic GC model (see Figure 4) and ending with a flattened one reproducing the close packing of counterions.20 Fortunately, even in the last case, the thickness of the layer containing 95% of counterions is less than 5 Å (for the case of simple inorganic ions in a hydrated state). Within so narrow a layer, the intensity of the exciting X-ray wave changes only slightly (see Figure 3) and can be considered as a constant within 10% accuracy, which allows us (with the same accuracy) to reduce the integral expression for fluorescence to a product of counterion amount per unit surface area and an average X-ray intensity within the 5 Å layer. As a matter of fact, the maximum error resulting from that simplification is less than 5%. The last value results from a comparison of two extreme distributions: uniform distribution within a 5 Å interval (i) and a sharp one when all ions are located just at the beginning of that interval (ii). Moreover, within an accuracy better than 10%, the fluorescence signal of a particular ion can be treated as independent of the presence of other ions (compare X-ray intensity curves for different ions in Figure 3). All the above considerations allow the application of a simple calibration procedure utilizing monolayers with known charge density on subphases that contain only one type of counterions as “standard samples”. In the above considerations, the monolayer head groups were advisedly not described as a separate layer for the following reasons. Head groups consisting of only light atoms (H, C, N, O) can be regarded as a part of the organic layer12 because they have similar electron densities. For the case of head groups containing heavier atoms (S, P, etc.), simulations with a model that includes one more layer reveal that they can be included into the ion-rich layer as an additional component (with appropriate correction of layer thickness). Intensity distributions for “exact” and simplified models are practically indistinguishable. The noticeable difference appears only in reflectivity curves R0(R) far above the critical angle (data not shown). Results and Discussion Figure 5 illustrates the applicability of the TRXF technique for observations of ions in the EDL of a charged Langmuir monolayer in the presence of the same ions (in moderate concentration) in the bulk subphase. In the X-ray fluorescence spectrum of the subphase solution (10 mM of KBr in water) without a monolayer on top, the only strong line is the KR1,2 line of Ar (see Table 1), originating from ca. 1% of argon in the surrounding air. The KBr electrolyte in the subphase produces a weak KR1,2 line

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TABLE 1: X-ray Emission Lines (Photon Energy in keV) for Selected Elements in the Range between 2 and 15 keVa element P S Cl Ar K Ca Br Cs Ba

Lγ1

Lγ2,3b

15 2.01 2.14 16 2.31 2.46 17 2.62 2.82 18 2.96 3.19 19 3.31 3.59 20 3.69 4.01 35 11.9 13.3 55 3.80 4.28 4.62 4.94 5.28 56 3.95 4.46 4.83 5.16 5.53

5.55 5.80

Z

KR1,2

Kβ

Llb

a Data taken from handbook.23 energies.23

LR1,2

b

Lβ1

Lβ2

Calculated from electron binding

of Br, and the KR1,2 line of K is possibly seen as a weak shoulder, overlapping with the Kβ1 line of Ar. In the presence of a condensed (π ) 25 mN m-1) negatively charged BS monolayer, there appear a strong KR1,2 and weaker Kβ1 lines of K, originating from K+ counterions in the EDL. The additional peak near 2.3 keV originates from the S atom in the head group (see Table 1). In the presence of a condensed (π ) 25 mN m-1) positively charged monolayer of protonated ECA (pH adjusted to ca. 4 with HCl), there appear strong KR1,2 and weaker Kβ1 lines of Br manifesting a significant amount of Br- anions in the EDL of the positively charged monolayer. Full protonation of ECA at pH ) 4 and millimolar salt concentration was proved in supplementary surface potential experiments (data not shown). Thus, it has approximately the same absolute value of surface charge density as the BS monolayer (ca. 1 elementary charge per 25 Å2). It is worth noting that the relative intensity of the fluorescence signals of Br from the clean subphase and the BS monolayer (referenced to that from the ECA monolayer) is 1.5-3 times stronger than theoretically estimated according to eq 1 (supposing ion distributions given by the GC model). We have checked various hypotheses but failed to find a satisfactory explanation until now. Figure 6 provides direct experimental support for the important feature of the EDL near highly charged interfaces, resulting from the GC model. According to the model, the main amount of counterions is concentrated in the thin inner part of the EDL irrespective of the electrolyte concentration in bulk (see Figure 4). The well-known “Debye screening length”, inversely proportional to the square root of electrolyte concentration, determines the thickness of the outer part of the EDL, where the electric potential (relative to the bulk) is below the “thermal potential” φT ) kT/ej (k is the Boltzmann constant, T is absolute temperature, ej is elementary charge). The outer part of the EDL at moderate electrolyte concentrations contributes to material balance for co-ions but is inessential for that of counterions (according to the GC model). Direct comparison of counterion surface concentrations for the same surface charge density (see below) and different electrolyte concentrations supports this model prediction. Indeed, peak (or integral) intensities of Cs fluorescence in Figure 6 (determined by eq 1) coincide within ca. 10% (close to experimental accuracy) for a range from 0.01 to 10 mM of CsCl concentration in the subphase, whereas Debye length changes roughly from 1000 to 30 Å accordingly. Subtraction of the background signal from the bulk subphase (significant for 10 mM CsCl only) can further improve the quality of coincidence. Taking into account that the decay length for X-ray intensity inside the sample is near 50 Å (see Figure 3), this coincidence suggests that the outer part of the EDL gives only a negligible contribution to the total amount of counterions in the EDL. It is worth noting that direct comparison of fluorescence signals (without correction factors) is valid, because

Figure 6. TRXF spectra of an anionic BS monolayer on subphases with different concentrations of CsCl (given in mM): 10 (solid line), 1 (dashed), 0.1 (dotted), and 0.01 (dashed-dotted). All lines in the shown range belong to Cs (see labels for attribution). Lines, except of solid one, overlap strongly. For the last case, it is worth it to subtract the background signal from bulk subphase (solid line at the bottom).

Figure 7. TRXF spectra of DPPG (solid line), BS (dotted), and ECA (dashed) monolayers on 10 mM BaCl2 subphase. The DPPG monolayer is the system under investigation; BS and ECA are “standard samples” for Ba and Cl accordingly. Labels give attribution of fluorescence lines (for Ba only the two most intense lines are labeled for simplicity). For the ECA monolayer, the subphase pH was adjusted to 4.0 to ensure full protonation.

the charge density in BS monolayers is independent of the alkali chloride concentration in a wide range of concentrations. This was shown in a previous study1 for LiCl and KCl (0.01 to 100 mM range in the last case) and theoretically explained. Therefore, there are no reasons to suppose that for CsCl the situation is different. As one can see, the TRXF technique demonstrates both its power and simplicity in application to the EDLsthe final result can be extracted from Figure 6 practically with naked eye. The results presented in Figure 7 clarify the situation with binding of alkali earth metals to negatively charged phospholipids. In several publications,10,11 Loesche et al. arrived at the conclusion that the amount of Ba2+ cations bound to anionic monolayers of DPPG and DMPA (1,2-dimyristoyl-phosphatidic acid) on the surface of a BaCl2 solution exceeds that necessary for electric neutrality. In order to maintain final electric neutrality, the authors assumed complimentary binding of Clanions from the BaCl2 subphaseseither individual or in the form of monovalent cations BaCl+. In spite of the fact that this model is based on multiple highly precise XR experiments accompanied with sophisticated data treatment,10,11 it looks highly debatable from general chemical positions. Nevertheless, we checked it in a direct way by means of the TRXF technique, preserving all experimental conditions reported in the original publication.10 The information presented in Figure 7 is necessary and sufficient to disprove the model. It is worth noting that both

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Figure 9. TRXF spectra of a BS monolayer on subphases containing individual alkali earth metal chlorides (“calibration samples”) and their mixture (system under investigation). Subphase compositions are as follows: BaCl2/CaCl2 1:1 (solid line), BaCl2 (dashed), and CaCl2 (dotted). The total salt concentration is 10 mM in all cases. Labels give the attribution of the most intense fluorescence lines. Figure 8. TRXF spectra of a BS monolayer on subphases containing individual alkali metal chlorides (“calibration samples”) and their mixtures (systems under investigation). Subphase compositions are as follows: KCl/CsCl 1:1 (part a, solid line); LiCl/CsCl 9:1 (part b, solid); CsCl (parts a and b, dashed); and KCl (part a, dotted). The total salt concentration is 10 mM in all cases. Labels give the attribution of the most intense fluorescence lines (see part a).

in the original10 and in the present experiment no buffer was added to the subphase, resulting in an arbitrary pH in the range of 5 to 6. Fortunately, this is of no importance because DPPG is fully ionized at pH > 4 at the given concentration of salt.21 The X-ray fluorescence spectrum of the DPPG monolayer (π ) 20 mN m-1) on the 10 mM BaCl2 subphase exhibits a set of Ba lines, the line of atmospheric Ar and a poorly visible line of the P atom from the head group of DPPG (see labels in Figure 7 and Table 1 for attribution). Lines of Cl (essential for the Loesche model) in the 2.6-2.8 keV region are not observable. This result, already fatal for the model, can be further strengthened. According to Loesche et al.,10 the area per DPPG molecule is ca. 48 Å2 at π ) 20 mN m-1 and the number of Cl- anions per head group is roughly 0.35, which results in 0.675 Ba2+ per head group (from the condition of electric neutrality). The fully protonated ECA monolayer (dashed spectrum in Figure 7) on the same subphase (with pH adjusted to 4 by addition of HCl) has, at π ) 25 mN m-1, an area per molecule of ca. 23 Å2 and 1.0 Cl- ions per head group (from the condition of electric neutrality). In this case, the fluorescence signal of Cl- near 2.7 keV is clearly observable (see Figure 7). Now, using the ECA monolayer as a “standard sample”, one can estimate the relative intensity of the Cl fluorescence, resulting from the Loesche model as a ratio: (0.35‚23)/(1.0‚ 48) ≈ 0.17 (referenced to the intensity of the Cl peak of the ECA monolayer). Comparing the fluorescence curve of the DPPG (solid line) in the region between 2.5 and 2.8 keV with that of the ECA monolayer (dashed line), one can ensure that the Cl peak intensity of DPPG is not 17% of that for ECA but practically zerosthe curve overlaps with that of the BS (dotted line) monolayer in this energy region. The dotted spectrum in Figure 7 belongs to the BS monolayer at π ) 25 mN m-1, which has an area per molecule of ca. 24 Å2. Using this monolayer as a “standard sample” for Ba2+ with 0.50 Ba2+ cations per head group, one can estimate the relative intensity of Ba peaks for DPPG resulting from the model: (0.675‚24)/(0.50‚48) ≈ 0.675 (referenced to the intensity of the Ba peak for the BS monolayer). However, the experimental value is 0.5 ( 0.05 (the

Figure 10. TRXF spectra of a BS monolayer on subphases containing individual alkali and alkali earth metal chlorides (“calibration samples”) and their mixtures (systems under investigation). Subphase compositions are as follows: CsCl/CaCl2 9:1 (part a, solid line); CsCl/BaCl2 9:1 (part b, solid); CsCl (parts a and b, dashed); CaCl2 (part a, dotted); and BaCl2 (part b, dotted). Total salt concentration is 10 mM in all cases. Labels give the attribution of the most intense fluorescence lines. Individual components of the composite spectrum (part b) are shown with thin solid lines.

spectrum of the ECA monolayer, which repels cations, is used as background signal), which corresponds to 0.5 ( 0.05 Ba2+ cations per DPPG head group. This value is in good agreement with the absence of Cl-, and both findings oppose the published model.10,11 The last three figures are devoted to “non-Gouy-Chapman” behavior resulting from finite size of counterions.1 Because the GC model treats electrolyte ions as point charges, predicted concentrations of counterions near highly charged interfaces (see Figure 4) appear physically irrelevant, conflicting with packing density restrictions.1,23 Recently, we published an extensive study1 testing this “weak point” of the classic model in application to charged Langmuir monolayers. The essential feature of the EDL near highly charged Langmuir monolayers resulting from packing density limitation is the unequal competition of counterions with the same charge but different size. Preferential participation of smaller counterions in the EDL of highly negatively charged BS monolayers was demonstrated1

Elemental Analysis within EDL

J. Phys. Chem. B, Vol. 111, No. 15, 2007 3933

TABLE 2: Comparative Characteristics of XR, NTEF (Previous), and TRXF (Proposed) Techniques (for the Case of Highly Brilliant Synchrotron X-rays) characteristic

XR

NTEF

TRXF

standard sample spatial resolution (Å) sensitivity (atom/Å2) elemental selectivity duration of experiment (s) data treatment

none 5-7 0.01(Cs)-0.03(K) none ∼104 complicated

bulk solution ∼50a 1(Cs)-5(K) × 10-3 fullc ∼104 complicated

monolayer inapplicableb 1(Cs)-5(K) × 10-3 full (P to U) ∼102 simple

a Only spatial parameter of prescribed fluorescent atom distribution can be obtained. b The surface density and average location of fluorescent atoms appear non-separable. c The range of elements is limited by the excitation photon energy.

in a direct way with a X-ray reflectivity technique. Unfortunately, this method is sensitive to the total electron density in the EDL but unable to distinguish different atoms. Because of accuracy limitations, only the extreme cases of Cs+-Li+ and Cs+-Mg2+ competition were tested.1 The point is that the ion ratio in the EDL can be obtained with a good accuracy from X-ray reflectivity data only for ions with very different numbers of electrons. The TRXF technique eliminates this limitation. Indeed, even Cs+ and Ba2+ with the same number of electrons (54) can be distinguished in the fluorescence spectrum (see below). Figure 8a illustrates the case of practically equal competition for participation in the EDL of BS monolayer between K+ and Cs + cations. Relative intensities of K and Cs fluorescence for the case of the 1:1 K+/Cs+ ratio in bulk are both ca. 0.5 (referenced to “standard samples”sBS monolayers on subphases with K+ and Cs + alone). Taking into account that for “standard samples” the area per molecule under the experimental conditions (π ) 25 mN m-1) differs by ca. 15%,1 one can safely estimate the K+/Cs+ ratio in the EDL as 1.0 ( 0.15 (with the plausible assumption that the monolayer on the mixed subphase has some intermediate value of area per molecule). Thus, the K+/Cs+ ratio in the EDL of the BS monolayer is roughly the same as that in the bulk. Very similar radii of hydrated K+ and Cs+ cations (3.31 and 3.29 Å according to the literature24) are in a good agreement with this result. Figure 8b demonstrates highly unequal competition of Cs+ with a large Li+ cation (3.82 Å radius24). Unfortunately, Li is “invisible” not only with the X-ray reflectivity technique1 but with TRXF as well (it has emission near 0.05 keV, which is absolutely inaccessible for our experimental arrangement). Nevertheless, the amount of Li+ can be estimated as a supplement to electric neutrality, providing that other counterions are detectable. The relative intensity of Cs+ fluorescence for the BS monolayer on Li+/Cs+ 9:1 mixed subphase is approximately 0.5 (referenced to “standard sample” with only Cs+ in the subphase). Taking into account that the areas per molecule at π ) 25 mN m-1 for these two samples are practically the same,1 0.5 is the estimate for the Cs+ fraction in the EDL as well. This result is in accordance with a value of 0.5-0.6 extracted from X-ray reflectivity data.1 It is worth noting that in contrast to the K+/Cs+ system, the fraction of Cs+ in the bulk for this experiment was only 0.1. Thus, in the EDL of the BS monolayer, Cs+ competes equally with K+ (having similar size), and it has strong preference with respect to Li+, which is substantially larger. Divalent alkali earth cations Ca2+ and Ba2+ also demonstrate highly unequal competition for participation in the EDL of the BS monolayer (Figure 9). In the presence of both cations with a 1:1 ratio, fluorescence lines of Ba have almost the same intensity as in the absence of Ca. In contrast, Ca fluorescence is roughly 10-fold decreased. Thus, Ba2+ cations have roughly 10-fold preference for participation in the EDL of the BS

monolayer compared with Ca2+ cations. Bearing in mind the relatively small difference of Ca2+ and Ba2+ radii in the hydrated state (4.12 and 4.04 Å, respectively24), this result looks surprising and can be unlikely explained by packing density limitations in the inner part of the EDL alone. Further discussion requires extended studies with other methods providing complimentary data (XR, surface potential, etc.), which are now in progress. The most striking effect resulting from packing density limitations for counterions near highly charged surfaces is the capability of small univalent counterions to compete effectively with large divalent ones. Such a competition between Cs+ (the smallest alkali cation) and Mg2+ (the largest alkali earth cation) having radii of 4.28 and 3.29 Å, respectively,24 was demonstrated earlier1 with the X-ray reflectivity technique. For a 1:1 Cs+/Mg2+ ratio in bulk, that in the EDL region was estimated to be 1.3 to 2 (compared with ca. 0.04 resulting from the GC model1). Two more examples of competition between uni- and divalent counterions obtained with TRXF technique for the same BS monolayer are presented in Figure 10. The relative intensity of Cs+ fluorescence peaks for the case of the 9:1 Cs+/Ca2+ mixture in bulk (panel a, solid line) is 0.42, referenced to the “standard sample” with only Cs+ in the subphase (dashed line). The corresponding value for Ca2+ is 0.57 (fluorescence of “standard sample” for Ca2+ is shown by dotted line). Neglecting the small difference (