Kinetics of Ion Exchange under a Charged Surface - Langmuir (ACS

The clue was to use two ionic species with a very large electron density difference. Chloride was selected as the singly charged anion whereas the mul...
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Langmuir 1999, 15, 5547-5554

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Kinetics of Ion Exchange under a Charged Surface N. Cuvillier* and F. Rondelez Institut Curie, Laboratoire de Physico Chimie Curie, 11, rue Pierre et Marie Curie, 75231 Paris Cedex 05, France Received February 2, 1999. In Final Form: May 6, 1999 The exchange kinetics between monovalent and multivalent counterions under a charged Langmuir monolayer of eicosylamine has been monitored by X-ray reflectivity over a period of 24 h, at 5 min time intervals and with a spatial resolution of 5 Å. This time resolution is quite remarkable considering that the ionic layer contains 18.2 MΩ/cm). The water pH was adjusted to 3 by addition of concentrated hydrochloric acid (Prolabo, Normapur quality). Under such acidic conditions, the amino group of the amphiphile is ionized, since its pKa is about 10,14 and each molecule bears a positive NH3+ charge.15 After allowing some time for complete evaporation of the solvent, the monolayer is slowly compressed by a Teflon barrier to its final surface density, between 50 and 30 Å2/mol, depending on the experiment. Phosphotungstic acid16 (H3PW12O40 or PTA for short) was purchased from Aldrich and used as received without further purification. According to the manufacturer’s specifications, its purity is approximately 95%. Since it is very soluble in water, stock solutions at high concentration (ca. 2 mol‚L-1) were prepared and small aliquots were injected into the aqueous subphase until a final concentration of 3 × 10-3 mol‚L-1 of PTA was obtained. To avoid perturbing the Langmuir monolayer, the PTA was introduced in the subphase using a syringe that was dipped on the other side of the Teflon barrier, in the uncovered region of the Langmuir trough (see Figure 1). The evolution of the eicosylamine monolayer following this injection was then studied by measuring the surface pressure using a Wilhelmy balance with a filter paper blade (RieglerKirstein, Mainz, Germany), by Brewster Angle Microscopy and by X-ray reflectivity. 2.2. Brewster Angle Microscopy. Reflection of a p-polarized laser beam at an air/water interface is minimum when the angle of incidence is equal to the Brewster angle θΒ ) 53.17°. This reflectivity, however, will take a different value r(θB) if a monolayer is present at the interface. Assuming that the monolayer has a refractive index n(z) distinct from that of water nwater, one has

r(θB) ∝

+∞(n(z)

∫-∞

2

- nwater2)(n(z)2 - nair2) n(z)2

dz

(1)

in which z denotes the vertical axis, perpendicular to the interface. In addition, n(z) is a function of the in-plane coordinates if the monolayer density is not homogeneous. This property has been exploited by Meunier et al.17 to develop an optical microscope which is capable of imaging the monolayer structure in the plane of the interface. (12) Elemental Anal. Found for C20H43N: C, 79.6; H, 14.13; N, 4.72. Calcd: C, 80.8; H, 14.47; N, 4.72. (13) 1H NMR (CDCl3): δ ) 0.89 (3H, t, 20-H), 1.21-1.4 (34H, m, 3-17-H), 1.4-1.45 (2H, m, 2-H), 2.64-2.7 (2H, r, 1-H). (14) March, N. Advanced Organic Chemistry; McGraw-Hill: New York, 1977. (15) Zhao, X.; Ong, S.; Wang, H.; Eisenthal, K. B. Chem. Phys. Lett. 1993, 214, 203. (16) Keggin, J. F. Proc. R. Soc. London 1934, A144, 75. (17) He´non, S.; Meunier, J. Rev. Sci. Instrum. 1991, 62, 936.

Figure 1. Schematic of the experimental setup. The Langmuir trough is equipped with a Teflon barrier for compressing the eicosylamine monolayer and with a Wilhelmy balance to record the surface pressure isotherm. Brewster angle microscopy (BAM) or X-ray reflectivity measurements can also be performed in-situ. The syringe on the right-hand side of the barrier is used to inject aliquots of concentrated solutions of PTA (phosphotungstic acid, H3PW12O40). The aqueous subphase is 10-3 M HCl at pH 3.

In our experiments, Brewster angle microscopy (BAM) will be used not only to detect the in-plane distribution of the eicosylamine molecules but also to provide information on the nature of the adsorbed counterions beneath the monolayer.18 Indeed, the refractive index of a concentrated solution of PTA (c ) 10 mol‚L-1) is 1.64 (as measured using an Abbe refractometer) and is significantly larger than that of a concentrated chloride solution. Therefore, an exchange of chloride ions by PTA ions within the interfacial double layer will increase the reflectivity. In our BAM setup, the light source was a 2 W argon laser operating at 5145 nm. The laser light was fed into a monomode optical fiber to allow an easy steering of the beam and facilitate the adjustment of the incidence angle at the air/water interface. The output of the fiber was placed at the object focal point of a 20× microscope objective mounted on a rotation stage. At the exit of the objective, a parallel beam was obtained whose incidence angle was carefully set at the Brewster value. It was then passed through a polarizer to select the p-polarization before reaching the water surface in the Langmuir trough. A CCD camera equipped with a Macrozoom objective was used to collect the reflected light, and the image was recorded on a VCR. The field of view of the camera was a full 3 × 3 mm2, but due to the oblique illumination, only a narrow stripe of 1 mm width was totally in focus. In this part of the image, the lateral resolution was approximately 10 µm. For further analysis, the videotape was digitized using an AV Macinstosh, and the resulting images were treated using the NIH Image software.19 2.3. X-ray Reflectivity. The X-ray reflectivity experiments were performed on a home-built reflectometer, which has already been described in details in ref 20 and 21. Therefore, only the main characteristics will be recalled here. The X-ray source is a classical 1.5 kW Cu tube mounted on one arm of a Huber goniometer, and two pairs of slits are used to reduce the angular divergence of the incident beam to better than 0.34 mrad. A graphite (18) Cuvillier, N.; Bernon, R.; Doux, J.-C.; Merzeau, P.; Mingotaud, C.; Delhae`s, P. Langmuir 1998, 14 (19), 5573. (19) Software obtained from http://rsb.info.nih.gov/nih-image/. (20) Cuvillier, N.; Bonnier, M.; Rondelez, F.; Parandjape, D.; Sastry, M.; Ganguly, P. Prog. Colloid Polym. Sci. 1997, 105, 118. (21) Cuvillier, N. Ph.D. Thesis, Universite´ Paris VI, 1997.

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monochromator set at the Cu KR wavelength (λKa ) 1.54 Å) is positioned on the other arm, and the reflected intensity is measured with a NaI scintillation detector. Since the adsorption process had to be followed for up to 24 h, the Langmuir trough was placed in an airtight aluminum box to minimize water evaporation and contamination of the surface by air-borne impurities. The relation between the reflectivity R(Qz) and the mean electron density profile F(z) perpendicular to the interface is22

∂F(z) 1 dz|2 R(Qz) ) Rf(Qz)| eiqzz Fwater ∂z

∫

(2)

where RF is the Fresnel reflectivity of the bare air/water interface, Qz is the scatttering wave vector in the z direction, and Fwater is the electron density of the water subphase. This relation cannot be inverted directly to yield the electron density F(z). The easiest method is to postulate a multilayer model for the interface, according to the Parrat’s formalism. This scheme has the additional advantage that it is valid even if there are large changes of electronic density between the various layers. The layers’ parameters were adjusted using a least-squares fit. The accuracy of the reconstructed profile depends on the number of points taken on the reflectivity curve. In the static measurements we have measured the reflected intensity at 50 different incidence angles over an angular span of 10 mrad. This provides a spatial resolution of approximately 3 Å in the vertical direction. In the kinetics experiments the acquisition time for a full scan has to be kept to a minimum in order to preserve the time resolution. We have therefore limited to eight the number of data points per scan. Fortunately, the overall shape of the reflectivity curve is simple enough in our experimental situation, so the full curve can still be unambiguously reconstructed. The typical time interval between two scans was 5 min. We have always considered in our analyses that the surface was homogeneous in the plane of the interface. This assumption is not as crude as it seems, even though our monolayer exhibits domain structures in certain ranges of surface densities. This is due to the fact that the coexistence is between a gaseous background (which is close to a bare air/water interface) and domains of long chain amines in the liquid condensed state. Numerical simulations of such heterogeneous surfaces show that the incoherent scattering from the domains leaves the shape of the reflectivity curves essentially conserved. The position of the oscillations still yields the height of the dense domains. There is only a change in their amplitudes, which are reduced, since the dense domains do not cover the whole surface. This consideration applies to the chloride ion subphase as well as to the PW12 ion subphase. 3. Results 3.1. Surface Pressure Measurements. 3.1.1. Equilibrium State. Figure 2 displays two surface pressure isotherms measured at room temperature for a monolayer of eicosylamine spread respectively on a subphase of diluted HCl at pH 3 (solid line) and on a subphase where PTA heteropolyanions (3 × 10-4 M) have been added to the HCl solution (dotted line). The data cover a range of areas per molecule A between 80 and 20 Å2. This (22) Braslau, A.; Pershan, P. S.; Swislow, G.; Ocko, B. M.; Als-Nielsen, J. Phys. Rev. A 1988, 38, 2457.

Figure 2. Pressure-area isotherms for a monolayer of eicosylamine spread on two different aqueous subphases, both at pH 3 and room temperature. The solid line corresponds to a subphase containing 10-3 mol‚L-1 HCl whereas the dashed line is for a subphase containing PTA (phosphotungstic acid, H3PW12O40) at 3 × 10-4 mol‚L-1 in addition. At pH 3, the amine groups of the amphiphile are ionized and interact strongly with the anions dissolved in the subphase.

corresponds to surface charge densities between 0.2 and 0.8 C.m-2, respectively. In the case of the HCl subphase, one observes a plateau in the surface pressure between 30 and 80 Å2. This plateau region is characteristic of a biphasic state with liquid condensed domains in coexistence with a gaseous phase within the monolayer. The corresponding pressure is nonzero and of the order of 1.5 mN/m. For areas per molecule less than 30 Å2, the surface pressure is a strong function of A and increases steeply up to 60 mN/m for A ) 24 Å2/mol. In this region, the monolayer is monophasic and liquid condensed. In the case of the mixed HCl and PTA subphase, the pressure-area isotherm is markedly different. The plateau region exists only for areas larger than 65 Å2, and the corresponding pressure is zero. For smaller areas, the surface pressure is finite and varies strongly with the surface density, which indicates the existence of a monophasic state in a region which was biphasic in the earlier case. The compressibility of this new phase is relatively large, however, and definitely higher than the one measured in the liquid condensed phase on pure HCl. At about 40 Å2, a hump is observed in the isotherm: the monolayer is no longer in equilibrium, and the shape of the isotherm depends on the compression speed. In general, we observe a slight decrease in the surface pressure, which is always followed by a reincrease around 20 Å2/mol. At this stage, the hard-core interactions between the aliphatic chains become important and the monolayer reaches its liquid condensed incompressible state. 3.1.2. Time Evolution. Figure 3 shows the time evolution of the pressure at constant surface density when PTA is added to a subphase, which initially contained HCl only. The area per molecule is 28 Å2, corresponding to a monophasic, liquid condensed, state of the monolayer, and the starting surface pressure is 3 mN/m. Three regions can be identified in the curve. First, there is a small pressure drop down to 1 mN/m, which stabilizes after a time T0π (in the present case, T0π ≈ 5 min). This

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Figure 3. Temporal evolution of the surface pressure of the eicosylamine monolayer after injection of PTA (phosphotungstic acid, H3PW12O40) into the subphase. The inset is a blowup of the evolution at short times.

regime is followed by a long time interval (T0π < t < Tincπ) during which there is no significant evolution of the surface pressure. This period can vary between 0.5 and 2 h, depending of the experiment.23 At the end of this incubation regime, the pressure shoots up abruptly and reaches pressure values as high as 25 mN/m in 20 min. Such values are comparable to the ones observed at equilibrium on a mixed HCl and PTA subphase and shown in Figure 1. At longer times, the surface pressure continues to evolve very slowly to reach an asymptotic value of 28 mN/m. The final state of the monolayer has now been reached. If one repeats the experiment at an area per molecule larger than 30 Å2, similar features are observed although the monolayer is initially in a biphasic state. The only difference is that the initial pressure drop is missing, which is consistent with the fact that the starting pressure is already low. 3.2. Brewster Angle Microscopy. Figure 4 displays several snapshots of the interface morphology, which have been taken at different times before and after injecting the PTA salt in the aqueous subphase. Initially the eicosylamine film was in its biphasic state (A ) 50 Å2/mol and π ) 1.5 mN/m), and this allows us to work with wellcontrasted images. As shown in Figure 4A, bright liquid condensed (LC) domains, which are small and uniformly distributed throughout the film, are observed to coexist with a continuous gaseous phase, which appears dark. The LC domains are characteristically elongated rather than circular. Although it is hard to tell from the printed image, their typical size is 50 × 10 mm2, in agreement with the results of ref. 24. A few minutes after the PTA injection, the morphology of the monolayer has started to change and has become more complex and heterogeneous. Domains of macroscopic size and of uniform brightness are now separating regions in which the biphasic structure has been maintained. As can be observed in Figure 4B, these domains can be either totally dark or extrabright. (See the thin bright line in the (23) This large discrepancy in the latency time is due to the injection process that introduces turbulence into the trough. (24) Cuvillier, N.; Rondelez, F. Thin Solid Films 1998, 327-329 (12), 19.

Cuvillier and Rondelez

diagonal of the image and the large black stripe adjacent to it. The triangular domain in the top left corner is also extrabright but appears fainter than the central line due to image vignetting.) The same features continue to be observed in Figure 4C, 36 min after the initial injection. Figure 4D illustrates a second significative change in the morphology of the monolayer, namely the progressive disappearance of the biphasic LC domains. In this new state, the extrabright regions are now intimately and uniformly mixed with the black domains, which have all the characteristics of a gaseous phase. Figure 4E confirms this observation, the only difference being that some of the dark domains have coalesced, which has induced a large polydispersity in their sizes. One notices that the small bubbles are perfectly circular, contrary to the larger ones, which are deformed and have therefore not yet reached their equilibrium shape. The extrabright regions grow at the expense of the dark regions and gradually invade the whole monolayer. Figure 4F, taken 15 min after Figure 4E, shows that, in its final state, the monolayer contains only a few remnants of the black phase. Eventually, the remaining black spots will disappear and the whole field of view will be white. With the BAM setup we have measured the variations in the brightness of this monolayer as a function of the elapsed time. Even if the field of view is limited, we think that the measurements are representative of the whole monolayer because of the surface drifts which tend to average the measurements over a large part of the monolayer. Figure 5 shows the average intensity received by the optical detector after the PTA has been injected below the monolayer. The dotted line is a guide for the eyes which provides an estimate of the average intensity as a function of time. It helps to smooth out the spikes in luminosity, which result from the drift of one of the macroscopic domains shown in Figure 4B through the region of observation. In the first approximation, the measured intensity is proportional to the surface fraction of the monolayer occupied by the extrabright phase. As in the surface pressure data, one observes an incubation period of duration TincBAM ≈ 40 min followed by a region of sharp, almost linear, increase that terminates after 20 min. After that (t > TendBAM), the light intensity remains constant at a value which is four times the initial one. In the range of surface densities where the monolayer is initially monophasic (i.e. below 30 Å2/mol), the BAM images are featureless. However, a gradual increase with time of the averaged luminosity can be observed, corresponding to the adsorption of PTA ions. This has also been shown in ref 18 on a slightly different system. 3.3. X-ray Reflectivity. 3.3.1. Steady States. Figure 6 shows the normalized X-ray reflectivity as a function of the scattering wave vector Qz for a monolayer of eicosylamine at an area per molecule of 50 Å2 and on the two different subphases, both at pH 3. The squares are for the pure HCl subphase prior to the injection of PTA in the trough, and the circles are for the mixed HCl and PTA subphase. In this latter case, the reflectivity has been measured after the end of all detectable evolution of the monolayer, 8 h after the injection of PTA. The curve obtained in the presence of PTA has much more prominent features and exhibits a very sharp and high maximum at Qz ) 0.17 Å-1 and a slight shoulder around 0.45 Å-1. By comparison, the oscillations on the curve obtained on HCl are much more subdued and the normalized intensity never goes above 1. The solid curves correspond to least-squares fits with two-box models, one box for the amphiphilic layer and one box for the counterion layer, and an excellent

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Figure 4. Brewster angle microscopy images of the eicosylamine monolayer spread on an HCl subphase and after injection of PTA (phosphotungstic acid, H3PW12O40) at time t ) 0. (The white bar corresponds to 500 µm.) (a) t ) 0; the initial state of the layer is biphasic, with coexisting liquid condensed (LC) and gaseous (G) domains. (b) t ) 10 min. (c) t ) 36 min. Three different morphologies can be distinguished: gas bubbles (in dark), extrabright domains (in white), and regions where the morphology remains unchanged (in gray). (d) t ) 46 min. The coexistence LC/G has disappeared and has been replaced by a mixture of extrabright domains and gaseous phases. (e) 55 min. The extrabright regions invade the field of view and force the gaseous domains to coalesce. (f) 65 min. The whole monolayer is occupied by an almost uniform extrabright region, and the monolayer has reached its final equilibrium state.

agreement can be found. The width and average electron density for the two layers which characterize the interface are shown in the inset. When a finite interfacial roughness is introduced, the boundaries are no longer steplike and smoother profiles are obtained. In both cases, the width and the electron density of the amine layer are almost identical. On the contrary, the ionic layer is markedly different. For the pure HCl subphase, it is almost indiscernible from the water whereas it is very conspicuous with the mixed HCl-PTA subphase. This difference reflects the ionic exchange of chloride ions by PTA ions. 3.3.2. Time Evolution. Figure 7 shows the X-ray reflectivity scans successively taken on a single monolayer after the injection of PTA in a subphase initially containing HCl only and with a surface density of 50 Å2 per amine. The 3D representation summarizes 100 scans and evidences the drastic changes occurring at the interface over a time period of 5 h. Immediately after injection, the reflectivity curve is similar to the one observed on pure HCl, the only difference being that the limited number of data points per scan prevents the observation of the shallow oscillations shown in Figure 6. This incubation period lasts for a time TincRX of approximately 80 min. It is followed by a brief period of dramatic changes in which the reflectivity is multiplied

by almost an order of magnitude in less than 20 min. In addition, a new, intense, peak appears at Qz ) 0.13 Å-1. It is relatively broad, with a full width at half-maximum of 0.07 Å-1, and its position is observed to remain the same for the following 100 min. The interface structure detected by the X-ray technique appears to be quasistationary. However, the final equilibrium state at the interface has not yet been reached. A second significant evolution in the reflectivity is observed at times longer than 200 min. Its main feature is a shift of the previous peak by 0.06 Å-1 toward larger Q values. The peak position is now at Qz ) 0.19 Å-1, which is identical to the one observed on the high-resolution reflectivity curve observed in static conditions on the pure PTA subphase. The transition between two regimes is evident in the horizontal projection of Figure 7, in which two different ridge regions can be clearly distinguished. It corresponds to a decrease in the overall thickness of the interface at long times. This set of scans has been analyzed more quantitatively using a one-box model. Despite its relative crudeness, this model allows us to extract the essential characteristics of the interface, namely its thickness and its average electron density. A two-box model would not be justified anyway because of the limited spatial resolution of the present experiments. The time evolution of these two parameters

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Figure 5. Time evolution of the optical reflectivity of the monolayer averaged over the whole field of view of the images shown in Figure 4. The large spikes are due to random displacements of the monolayer under the microscope objective. The dashed line is a guide to the eye and shows the transition between the two states of the monolayer when the chloride ions are replaced by the PTA ions.

Figure 6. X-ray reflectivity for a monolayer of eicosylamine at 50 Å2‚mol-1 and for two different subphases. The squares are for a subphase containing 10-3 mol‚L-1 HCl. The dots are for a mixed subphase of PTA (3 × 10-4 mol‚L-1) and HCl (10-3 mol‚L-1). The data have been taken only after the monolayer has reached its final equilibrium state. The continuous lines are the best fit to two-box models shown in real space in the inset. The zero depth has been arbitrarily set at the head group position.

is represented in Figure 8. Both display sharp discontinuities in two specific time regions. The characteristic times are marked as TincRX, TadsRX and TreorgRX. Below TincRX ) 80 min, the electron density is almost equal to that of pure water and the monolayer is hardly detectable. The corresponding value of the surface layer thickness is 35 Å; however, this figure should not be taken too much for granted because of the very large uncertainty in the measurement due to the lack of electron contrast. In the time period between TadsRX and TreorgRX, the electron density quickly increases by a factor of 1.9 and then saturates.

Cuvillier and Rondelez

Figure 7. 3D plot of the time evolution of the X-ray reflectivity of the interface after injection of PTA in the subphase. The mean area per amine is 50 Å2. The scattering vector Qz increases from right to left, and the time after injection, from left to right. The scale of grays goes from 0 to 10. The x-y projection reveals the successive appearance of two sharp peaks at different positions.

Figure 8. Time evolution of the overall thickness and mean electron density of the interfacial layer after injection of PTA in the subphase. The electron density is observed to increase by a factor of 3 in two consecutive steps while the thickness decreases from 27 to 13 Å. The discontinuities are observed at identical times on both curves.

The corresponding thickness is 27 ( 2 Å. At the time TreorgRX, a new jump in the electron density is observed. It now reaches three times that of water. In the meantime, the thickness drops to 13 Å.25 This marks the end of the evolution of the interface. 4. Discussion 4.1. Steady States. The results obtained by all three different methods prove the existence of fundamental differences in the behavior of the monolayers depending on whether they are spread on chloride solutions or on (25) These data were analyzed using a one-box model, instead of a two-box model, imposed by the higher resolution, for the steady-state measurements. Therefore, the thicknesses derived from these two sets of experiments could not be directly compared.

Kinetics of Ion Exchange under a Charged Surface

mixed chloride-PTA anion solutions. They also allow a precise description of the structure of the long chain amine monolayer and of the layer of associated counterions. In the case of chloride solutions, the surface-pressure isotherms display features which are characteristic of strong electrostatic interactions between the charged head groups of the long chain amines. They are not found with fatty acid amphiphiles which are electrically neutral at similar pHs. First, the pressure on the liquid condensedgas coexistence plateau, at areas between 80 and 30 Å2, has a nonzero value of 1.5 mN/m. This reflects the lower cohesive energy of the liquid condensed phase because of the electrostatic repulsion between the charged head groups. Second, the limiting area at zero pressure of this phase is shifted from the classical 20 Å2 value to a much larger value of 30 Å2. This indicates that the effective cross section of the head group is not the geometrical core value but a “dressed” value, which includes the width of the repulsive electrostatic barrier. The 50% increase is quite compatible with a rough estimation of the DebyeHuckel screening length. In a bulk 10-3 M chloride solution, the Debye screening length is about 100 Å. At the interface, the value is smaller because of the high local concentration of chloride anions. Taking the electrical dielectric constant to be 10 at the interface, we obtain a screening length of 5 Å. When the mean distance between amines becomes less than this characteristic length, electrostatic forces become significant. The liquid condensed phase remains compressible, however, because of the important free volume. The surface pressure isotherm shows that the monolayer can be mechanically compressed down to 22 Å2/mol. At this point, the pressure is 60 mN/m, corresponding to a very small interfacial tension γ ) π γwater ) 12 mN/m with γwater ) 72 mN/m. These long range electrostatic forces are also evident in the morphology of the monolayer. The Brewster images show that the liquid condensed domains are elongated. This shape results from a competition between the electrostatic energy, which tends to stretch the domain, and the line energy, which tends to minimize its perimeter and therefore favor a circular shape.26,27 The orientation of the molecule in the liquid condensed phase can be extracted from our X-ray reflectivity data. Using a two-box model, a best fit yields a total length of 13 ( 2 Å for the aliphatic chains. For an aliphatic chain of 20 carbon atoms, the molecular length in the all-trans configuration is 26.8 Å.28 This implies that the chains are largely tilted. We find an angle of 60° relative to the normal to the interface. The reflectivity data yield an estimate for the concentration of chloride counteranions below the charged head groups. The best fit gives an electron density of 1.1 times that of water and a layer thickness of approximately 8 Å. This corresponds to about one chloride anion per amine, as indeed required by electroneutrality. The counterion layer is not diffuse and is of atomic thickness. When the monolayer is spread on a mixed solution of chloride and PTA anions, quite substantial differences are observed which point to the replacement of the small, monovalent, chloride ions by the large, multivalent PTA. The X-ray reflectivity data recorded at 50 Å2/mol allow a precise description of the electrical properties of the monolayer. Using a two-box model for the interface, the best fit to the data points of Figure 6 indicates that the (26) Yee, K.; Lee, C.; McConnell, H. M. J. Phys. Chem. 1993, 97, 9532. (27) Stine, K. J.; Statmann, M. Langmuir 1992, 8 (10), 2510. (28) Deutsch, M.; Wu, X. Z.; Sirota, E. B.; Sinha, S. K.; Ocko, B. M.; Magnussen, O. M. Europhys. Lett. 1995, 30, 283.

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ionic layer is of very large electron density, about 3 times that of pure water, and that its thickness is 9 Å. This is compatible with a single layer of nearly close-packed PTA anions. Indeed the molecular size of PTA is 10 Å, according to the literature.29 From these data one can also calculate that there is approximately 2.9 long chain amines per anion, which is close to what is expected from electroneutrality.30 One can view that each PTA anion is connected to three aliphatic amine chains on average. As the molecular cross section of PTA is 100 Å2, there is obviously a limit to the surface density of charged amphiphiles, which can be electrically compensated by PTA anions contained in a single layer. One expects a change in behavior in the ionic layer when the area per amine is less than one-third of the molecular cross section of PTA. We have indeed observed the formation of ionic multilayers below 40 Å2/molecule. This point will be discussed in detail in a future paper.31 The gradual replacement of the PTA anions over the chloride ions following the injection of PTA in the monolayer subphase is also manifested by the increase in the brightness of the Brewster images (compare Figure 4A and F). The optical reflectivity is proportional to n2d2, where n is the refractive index and d is the overall thickness of the interfacial layer. The optical index of refraction for a PTA ionic layer at 60% volume fraction is calculated to be 1.6. On the other hand the index of refraction of the amine layer is 1.5. The two values are sufficient to say that in the first approximation one has to compare the reflectivity of an interfacial layer which is the sum of the amine and the PTA layer in one case and a bare amine layer in the other case. Taking 10 + 9 ) 19 Å in the first case and 13 Å in the second case, one expects a reflectivity change of 800/380 ) 2.1. In Figure 5, the reflectivity observed at long times is 4 times higher than the initial reflectivity when PTA is absent. Finally, the preferential adsorption of PTA anions over the chloride anions under the charged long chain amine surface explains well the features of the surface pressurearea isotherms observed at long times in the case of the mixed HCl and PTA subphase. For instance, one striking feature is the shift of the low-density end of the liquid condensed-gas coexistence region to much larger areas per molecule, typically from 30 to 62 Å2. We believe that is due to the steric hindrance between the PTA counterions localized in the electrical double layer. The possibility of an increase of the electrostatic repulsion between the positively charged amine head groups is disproved by the X-ray reflectivity data. The Debye screening length estimated from the measured local ion concentration is lower for PTA than for chloride anions because of the difference in valency. At 50 Å2/mol, the thickness of the amine layer measured by X-ray reflectivity is approximately 10 Å, which is much less than the all-trans chain length. At these large surface densities, the chains either tilt up to an angle of 70° in order to come into contact and to maximize their van der Waals chain-chain interactions or are disordered. That makes this phase highly compressible, as shown on the (29) Spirlet, M. R.; Busing, W. R. Acta Crystallogr. 1978, B34, 907. (30) We believe that the difference between 2.9 and 3 is significant and therefore that the interface appears as globally negatively charged if PTA anions only are considered: such charge inversion phenomena are frequently observed with multivalent counterions (Adamson, A. W. Physical chemistry of surfaces, 5th ed.; Willey-Interscience: New York, 1990. Shaw, D. J. Introduction to Colloid and Surface Chemistry, 2nd ed.; Butterworths: London, 1970). In our case, the charge excess is probably compensated by the adsorption of H3O+ cations, which are invisible to X-ray reflectivity due to lack of contrast with water. (31) Cuvillier, N.; Rondelez, F. To be published.

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pressure isotherms. There is much free volume between the aliphatic chains, and the counterions are not rigidly fixed to the charged head group. To conclude the discussion about the steady state of the monolayer, our data provide unambiguous evidence for the preferred adsorption of PTA ions over chloride ions in the case of the mixed HCl and PTA subphase. The driving force is entropic rather than enthalpic. Indeed, because of the difference in valency, fewer ions are needed to ensure electroneutrality when they are multiply charged. A simple calculation shows that there is a gain of about 2kT per ion. 4.2. Time Evolution. The pressure isotherm and the X-ray reflectivity allow us to identify three stages in the exchange process when PTA anions are injected in an aqueous subphase initially containing chloride ions. They will be called the incubation stage, the adsorption stage, and the reorganization stage, respectively. During the incubation stage, the main feature is the absence of pressure change with time, except for a small initial pressure drop. The overall concentration of PTA counterions underneath the monolayer remains extremely small, as shown by the X-ray reflectivity signal that is analogous to that of a pure amine monolayer. The concentration of PTA in the sublayer is not zero, however. We believe that the small initial pressure drop is indicative of a condensation of the amine molecules induced by the multivalent PTA ions. Such an effect has been analyzed in detail by Clemente-Leon et al.32 on a similar system. The presence of some PTA ions in the sublayer is also revealed by the high contrast between the gaseous regions and the liquid condensed domains in the Brewster images taken at the end of this period (compare Figure 4A and D). The incubation period lasts for a time Tincπ on the order of 40 min, which largely exceeds the time necessary to distribute evenly the ions in the horizontal plane. They are injected in the subphase under turbulent conditions in order to speed up the diffusion process. The efficiency of this injection method has been checked separately using aliquots containing colored markers. Therefore, this regime is not limited by mass transport of PTA, at least in the first approximation, and adsorption can start immediately after injection. One difficulty, however, is due to the density difference between the HCl subphase and the PTA solutions. This may create a vertical distribution of the PTA ions, and it cannot be excluded that a small part of the adsorption is diffusion-controlled. The main adsorption stage occurs after this incubation period and covers a very narrow time span during which the saturation of the adsorption is reached. It lasts 20 min only and is finished at the time TadsRx. The experiments performed at the amine density 50 Å2, where liquid condensed domains are initially in coexistence with gaseous regions, reveal that the adsorption takes place preferentially under the liquid condensed domains where the amine density is the largest. This is proved by the Brewster images in which the liquid condensed domains are shown to grow at the expense of the gaseous regions. At 30 Å2, where the layer is homogeneous and monophasic, a strong increase in the interfacial electron density is detected by X-ray reflectivity during this period. It again (32) Clemente-Leon, M.; Agricole, B.; Mingotaud, C.; Gomez-Garcia, C. J.; Coronado, E.; Delhaes, P. Langmuir 1997, 13, 2340.

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shows that the counterion layer reaches its PTA saturation level in 20 min. Although the PTA concentration has now reached its saturation, the ionic layer has not yet reached its equilibrium state. At the time TreorgRx, strong condensation is observed to occur within the ionic layer. There is a characteristic decrease of the overall layer thickness by a factor of 2, from 27 Å down to 13 Å. The total number of ions remains unchanged, however. This has the effect of drastically increasing the electron density, which jumps to 3 times that of pure water. This reorganization which does not change the number of counterions within the sublayer, is favorable with respect to the electrostatic attractions with the positively charged amine head groups. It is as if the ionic layer was collapsing on itself and changing from a disordered structure to a compact one, loosing entropy but gaining enthalpy in the process. Here again, the narrow time span of 15 min over which this reorganization phenomenon takes place could be indicative of the existence of a cooperative process. The final thermodynamic state is one in which a single layer of PTA counterions of approximately 8 Å is in immediate contact with the amine head groups. The volume fraction, which was initially 35%, now reaches 60%, corresponding to a close-packed state for these spherical ions. An inplane X-ray diffraction experiment would allow us to see if there is long range lateral order between the counterions. Unfortunately, the large size of the counterions put the expected peak position very near the specular reflection, which makes the experiment quite difficult. 5. Conclusion We have used three complementary in-situ techniques to study the kinetics of counterion exchange between singly and multiply charged ions under a charged Langmuir monolayer of long chain fatty amines at low pH. This system provides an ideal archetype for a charged planar surface in contact with an electrolyte. It lends itself to the investigation of the structure of the ionic double layer with atomic resolution. The particular choice of chloride and phosphotungstate anions also allows achieving high temporal resolution in the X-ray reflectivity experiments. The buildup and the structure of the electrical double layer have been monitored almost continuously, and we have observed the complete replacement of the chloride anions by the phosphotungstate anions over the course of time. The driving force for the exchange is the overall gain in translational entropy, since the adsorption of each trivalent anion permits release of three monovalent ions. The kinetics process could be split into three stages. In the first phase, the concentration of PTA in the vicinity of the interface remains low and spatially heterogeneous. After this latency period, which may last as long as 1 h, the adsorption rate speeds up drastically and quickly leads to the formation of a disordered and relatively thick (15 Å) layer of adsorbed PTA. In a third maturation stage, the number of adsorbed PTA molecules no longer evolves (the exchange process is finished) but the counterion layer gets more organized, leading to the formation of a close-packed monolayer of monomolecular thickness (8 Å). This structure is indefinitely stable and corresponds to the new equilibrium state of the electrical double layer. LA990104R