Varying the Counterions at a Charged Interface - Langmuir (ACS

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Varying the Counterions at a Charged Interface P. Koelsch and H. Motschmann* Max-Planck-Institute of Colloids and Interfaces, Am Mu¨ hlenberg 1, 14424 Golm/Potsdam, Germany Received August 5, 2004. In Final Form: November 27, 2004 The influence of different counterions on the adsorption behavior of the ionic soluble surfactant dodecyldimethylammonium-pyridimium bromide is investigated. The addition of potassium halogenides to aqueous solutions of the surfactant modifies the surface activity of the amphiphile and has a profound influence on the surface tension isotherms. The measured critical micelle concentration follows the order of the periodic table of elements which is in strong contrast to the surface excess. The number density of the adsorbed surfactants at the cmc does not depend on the amount of counterions in the solution but on the nature of the counterion. Furthermore, evidence is provided that the surface region is depleted on fluoride ions. Surface second harmonic generation and ellipsometry have been used to gain direct structural information which complement the thermodynamic considerations. The combination of both optical techniques yields the number density of the condensed counterions within the compact layer. A strategy to retrieve selected parameters of the ion binding model of Radke et al. is presented. The analysis of the optical data reveal the existence of a phase transition towards a surface condensed state with increasing salt condensation.

Introduction Charged surfaces are omnipresent in nature. Consequently, the distribution of ions at a charged surface is a fundamental problem of colloid and interface science.1,2 This topic received in the last years a renaissance, the progress in computational power enables more realistic modeling,3,4 novel experimental techniques provide a more detailed picture of the interfacial architecture5-7 and several advances in the theoretical description account for so-far neglected interactions.8 A very recent special issue of Current Opinion in Colloids and Interface Science is completely dedicated to ion distribution at interfaces and discusses the current state of art.9 Gouy and Chapman were the first who tackled this problem in a quantitative fashion.10,11 The ions were treated as point charges embedded in a continuum with given dielectric constants while the surface charge was considered to be continuously smeared out. The prevailing charge distribution generates a mean electrical potential in which the ions adopt a Boltzmann distribution. The combination of the Boltzmann distribution with the Poisson equation leads to a nonlinear second order differential equation for the electric potential ψ. The solution of the so-called Poisson-Boltzmann (PB) equation yields the number density of the counterions as a function * Corresponding author. mpikg-golm.mpg.de.

E-mail:

hubert.motschmann@

(1) Evans, D. F.; Wennerstro¨m, H. The Colloidal Domain; VCH Publishers: New York, 1994. (2) Adamson, A. W. Physical Chemistry of Surfaces; Wiley & Sons: New York, 1993. (3) Jungwirth, P.; Tobias, D. J. J. Phys. Chem. B 2000, 104 (2), 7702. (4) Jungwirth, P.; Tobias, D. J. J. Phys. Chem. B 2002, 106, 6361. (5) Koelsch, P.; Motschmann, H. Curr. Opin. Colloid Interface Sci. 2004, 9, 87. (6) Raymond, E. A.; Tarbuck, T. L.; Brown, M. G.; Richmond, G. L. J. Phys. Chem. B 2003, 107, 546. (7) Wang, J.; Caffrey, M. M.; Bedzyk, J.; Penner, T. L. Langmuir 2001, 17, 3671. (8) Lau, A. W. C.; Lukatsky, D. B.; Pincus, P.; Safran, S. A. Phys. Rev. E 2002, 65, 051502. (9) Curr. Opin. Colloid Interface Sci. 2004, 9, 1-197. (10) Gouy, G. J. Phys. 1910, 9, 457. (11) Chapman, D. L. Philos. Mag. 1913, 25, 475.

of the distance to the interface. This approach defines the framework for many extensions of the theory. Netz et al. demonstrated by Monte Carlo simulations with charged hard spheres that this mean-field approach gives asymptotically the exact counterion density profile for monovalent ions and low charge densities at the interface.12,13 The oversimplification of the Gouy-Chapman approach was obvious from the beginning, and Stern was the first who pointed out that this theory predicts an unrealistic high concentration of counterions in the vicinity of the interface due to a neglect of the geometrical dimensions of the ions.14 Since then, many extensions of the theory have been put forward to account for the finite size of the ions,16 image forces,15 the dependence of the dielectric constant on the electric field17 or ion correlation.18,19 One striking deficiency of the treatment on this level is the prediction that ions of the same valence produce the same results, independent of their chemical nature. In contrast, experiments reveal pronounced differences between different ions. These ion-specific effects can be ordered in the so-called Hofmeister series of ions20 and any realistic theory must account for this observational effect. Two phenomena are of particular importance for understanding ion specificity, the van der Waals interaction between the ion and the interface and the ion hydration. Ninham et al. recognized that the van der Waals interaction at the interface is not screened by the electrolyte and can reach a significant magnitude.21,22 It can be accounted for by an additional ion-specific term Bi (12) Moreira, A.; Netz R. Eur. Phys. J. A 2002, 8 (1), 33. (13) Moreira, A.; Netz, R. Europhys. Lett. 2002, 57 (6), 911. (14) Stern, O. Z. Elektrochem. 1924, 30, 508. (15) Jonsson, B.; Wennerstrom, H. J. Chem. Soc., Faraday Trans. 2 1983, 79, 19. (16) Levine, S.; Bell, G. M. Discuss. Faraday Soc. 1966, 42, 69. (17) Spaarnay, M. J. Recl. Trav. Chim. Pays-Bas 1958, 77, 872. (18) Wennerstrom, H.; Jonsson, B.; Linse, P. J. Chem. Phys. 1982, 76, 4665. (19) Kjellander, R.; Marcelja, S. J. Chem. Phys. 1985, 82, 2122. (20) Collinns, K. D.; Washabaugh, Q. Rev. Biophys. 1985, 18, 323. (21) Bostrom, D. M.; Williams, R.; Ninham, B. W. Phys. Rev. Lett. 2001, 87, 168103. (22) Bostrom, M.; Williams, D. M. R.; Ninham, B.W. Langmuir 2001, 17, 4475.

10.1021/la0480179 CCC: $30.25 © 2005 American Chemical Society Published on Web 03/16/2005

Counterions at a Charged Interface

within the framework of an extended PB theory. A second key element for understanding ion specificity is the hydration of ions. So-called structure-making ions organize the water dipoles and, hence, are better accommodated in the bulk, whereas structure-breaking ions adsorb at the interface because this arrangement minimizes the impact on the water hydrogen bonding network. This simple concept is sufficient to predict depletion of ions at the interface. The surface tension of an aqueous electrolyte solution is usually higher than the one of pure water. According to Gibbs it means that the ions are depleted at the interface. Experiments establish a good correlation between the standard enthalpy of hydration and the modification of the surface tension by the electrolyte.23 The description of the interfacial architecture by first principles is complex, and, meanwhile, there is a zoo of decorations of the classical PB theory.24 The ion specificity with its diversity of effects is the manifestation of a subtle balance of several competing and evenly matched interactions. The complex interplay of electrostatics, dispersion forces, thermal motion, fluctuations, hydration, and ion size effects and the interfacial water structure makes it hard or may be even impossible to identify a universal law describing all systems. Hence, it is justified to adopt a more pragmatic point of view and describe the system behavior by an empirical approach. An excellent review of the current equilibrium models can be found in the review of Posser and Franses.25 Kralchevsky et al. developed a model that incorporates the effect of counterion binding using a counterion adsorption isotherm.26 Thermodynamic consistency criteria were presented for the adsorption isotherms of the surfactant and the counterion. Warszyski et al. developed a model that allows the penetration of counterions within the adsorbed surfactant layer.27 A recent extension of this approach takes into account the strong dependence of adsorption on the type of counterions present in solution.28 Kalinin and Radke extend the Borwabker and Wasan30 model to include the phenomena of counterion binding in a double (inner and outer) Stern layer arrangement.31,32 All these theories have some predictive power; for instance, they allow the variation in surface tension isotherms with the ionic strength of the solution to be described. However, a number of parameters are introduced to account for the complexity of the underlying processes. It’s not two surprising that the smooth variation of the surface tension isotherm can be excellently fitted with three to six parameters. Hence, it is more than desirable to have independent means to measure these parameters. Recently we could demonstrate that the combination of linear and nonlinear optical techniques provide a detailed picture of the interfacial architecture.29 For instance, the combination of ellipsometry and second harmonic generation (SHG) yields the number density of the condensed counterions. In this contribution we are using these optical (23) Johansson, K.; Eriksson, J. C. J. Colloid Interface Sci. 1974, 49, 469. (24) Manciu, M.; Ruckenstein, E. Adv. Colloid Interface Sci. 2003, 105, 63. (25) Prosser, A.; Franses, E. Colloids Surf., A 2001, 178, 1. (26) Kralchevsky, P.A.; Danov, K. D.; Broze, G.; Mehreteab, A. Langmuir 1999, 15, 2351. (27) Warszynski, P.; Barzyk, W.; Lunkenheimer, K.; Fruhner, H. J. Phys. Chem. B 1998, 102, 10948. (28) Para, G.; Jarek, E.; Warszynski, P.; Adamczyk, Z. Colloids Surf., A 2003, 222, 213. (29) Koelsch, P.; Motschmann, H. J. Phys. Chem. B 2004, 108, 18659. (30) Borwankar, R. P.; Wasan, D. T. Chem. Eng. Sci. 1988, 43, 1323. (31) Kalinin, V. V.; Radke, C. J. Colloids Surf., A 1996, 114, 337. (32) Karraker, K. A.; Radke, C. J. Adv. Colloid Interface Sci. 2002, 96, 231.

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Figure 1. Ion binding model using a triple layer structure consisting of a plane of adsorbed surfactant ions, a plane of partially dehydrated contact-bound counterions, and the diffuse layer with fully hydrated counterions.

techniques to study adsorption layers of ionic surfactants. In particular we are interested in the influence of different counterions on the adsorption behavior. The data are used for a comparison with the ion binding model of Radke et al. because we feel that this model contains the decisive ingredients. The paper presents a brief discussion on the ion binding model and the meaning of the parameters. Furthermore, the key features of the optical techniques are outlined. Background 1. Ion Binding Model. The ion distribution model of Radke et al. is sketched in Figure 1. The following triple layer interfacial structure was proposed: a plane of adsorbed surfactant ions, a plane of partially dehydrated contact-bound counterions, and a plane of hydrated counterions where the diffuse layer, as given by the GouyChapman theory, begins. The adsorption is characterized by an equilibrium exchange reaction between the empty surfactant sites [M], the positively charged amphiphile [S+], and the adsorbed amphiphiles [MS+]

M + S+ h MS+

(1)

The corresponding equilibrium constant accounts for the Frumkin lateral interaction parameter ω between the surfactant tails and the prevailing electrical potential ψ0

KS )

(MS+) (M)[S+]

exp

(

)

ωΘ - eψ0 kT

(2)

Θ is the fractional coverage of surfactants at the interface, k is the Boltzmann constant, T is the absolute temperature, e is the elementary charge, the parentheses denote surface concentrations (m-2), and the brackets denote bulk concentrations [m-3]. In analogy the ion binding of the counterions A- is introduced by an additional equilibrium reaction between the mobile counterions far from the surface and the adsorbed surfactants and MS+A- stands for a bound counterion (ion pair) at the interface.

MS+ + A- h MS+A+

KA )

-

(MS A ) +

-

(MS )[A ]

(

exp -

)

eψβ kT

(3) (4)

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Ψβ is the electrostatic potential at the inner Helmhotz plane. This approach includes all interactions in the equilibrium constants. This model predicts the surface coverage of surfactants and bound counterions as a function of the salt concentration. Furthermore, by applying classical Gibbs thermodynamics an expression for the surface tension can be retrieved. The ion binding model demands three systemspecific parameters, the equilibrium constants, KS and KA, and the interaction parameter ω. So far, these parameters have been fitted by using the surface tension data only. We outline a strategy for how KA and KS could be retrieved by optical measurements. 2. SHG. SHG is a nonlinear optical second order χ(2) process; the generation of frequency doubled light is the result of the interaction of a high-power laser pulse with matter. It has been used for decades to extend the frequency range of laser light sources using noncentrosymmetric crystals. SHG as a surface-specific tool exploits the fact that there is no generation of SHG light in centro-symmetric media. At the interface of two isotropic media the centrosymmetry is broken and SHG light is generated within the transition region of both adjacent media.34,35 In favorable cases, the analysis of polarization-dependent SHG measurements allows the determination of the symmetry of the interface, the number density N of the amphiphiles within the topmost layer, and the orientation of the molecules in the interfacial layer. Depending on the hyperpolarizability β of the adsorbed molecules, a submonolayer sensitivity of about 1/100 of a monolayer can be achieved.36,37 Unfortunately, only certain molecules give rise to a SHG signal and to fully exploit the potential offered by SHG it is necessary to design a suitable model system with a high hyperpolarizability. The SHG signal is then determined by the dipolar contribution, and combinations of various components of the macroscopic susceptibility tensor χ(2) are measured in reflection mode. The relation between the individual elements of the susceptibility tensor χ(2) and the corresponding molecular quantities is provided by the oriented gas model38

χ(2) ∝

β ∝ N〈β〉 ∑ mol

(5)

It states that the susceptibility χ(2) is the sum of the hyperpolarizabilities β of all molecules. This can also be expressed in terms of the number density of the SHG active molecules N and their corresponding orientational average 〈β〉 as denoted by the brackets. A detailed description of SHG theory in reflection mode and the algorithm which has been used for analysis of our data can be found in ref 39. Here it is important to denote that SHG measures selectively the number density of the adsorbed surfactants (MS+) and (MS+A-) of the ion binding model. (33) Teppner, R.; Haage, K.; Wantke, D.; Motschmann, H. J. Phys. Chem. B 2000, 104, 11489. (34) Shen, Y. R. Annu. Rev. Phys. Chem 1989, 40, 327. (35) Corn, R. M.; Higgins, D. A. Chem. Rev. 1994, 94, 107. (36) Bae, S.; Haage, K.; Wandtke, D.; Motschmann, H. J. Phys. Chem. B 1999, 103 (7), 1045. (37) Vogel, V.; Mullin, C.; Shen, Y. R.; Kim, M. W. J. Chem. Phys. 1995, 95, 4620. (38) Prasad, P.; Williams, D. J. Introduction to Nonlinear Optical Effects in Molecules and Polymers; Wiley: New York, 1991. (39) Harke, M.; Ibn Elhaj, M.; Mo¨hwald, H.; Motschmann, H. Phys. Rev. E 1998, 57, 1806.

3. Ellipsometry Used for the Investigation of Adsorption Layers of Soluble Surfactants. Ellipsometry is an optical technique which measures and analyzes changes in the state of polarization of light upon reflection. These changes can be expressed by two measurable quantities, Ψ and ∆, which are related to the ratio of the complex reflectivity coefficients for sˆ and pˆ polarization by the basic equation of ellipsometry:41

tan ψei∆ )

rp rs

(6)

This analysis of ellipsometric data requires the translation of the interfacial architecture in the corresponding refractive index profile. The reflectivity can then be calculated by Fresnel theory.42 The correct treatment of charged interfaces requires the explicit consideration of the counterion distribution and their corresponding refractive index profiles.29 In the thin film limit ellipsometry measures only a single parameter that is proportional to the following integral of the dielectric function  across the interfacial region43

η)

∫

( - 0)( - 2) dx 

(7)

and

∆≈

4x02π cos φ sin2 φ

1 η (0 - 2)[(0 + 2) cos φ - 0] λ

(8)

2

where 0 and 2 are the dielectric constants of the adjacent bulk phases, in our case air and water, respectively, φ is the angle of incidence, and λ is the wavelength of light. The condensed counterions reduce the surface charge density and influence the counterion distribution in the diffuse layer. The distribution of the counterions is a function of the effective surface charge density σnet. The counterion distribution within the diffuse layer is given by the solution of the PB equation. Because there is a linear relation between the dielectric function and the concentration in the diffuse layer we can translate the ion distribution in a refractive index profile:

(z) ) 2 + c(z)

d d 1 ) 2 + dc 2πlBNA(z + b)2 dc

(9)

where NA is Avogadro’s constant. The number density decays to 0 algebraically with the characteristic GouyChapman length b ) e/2π|σ|l ) wkBT/2πe|σ|, where l ) e2/wkBT ≈ 7 Å is the Bjerrum length in water at room temperature. The Bjerrum length defines the distance where the thermal energy is balanced by the electrostatic interaction. To quantify the impact of the counterion distribution in the diffuse layer on the ellipsometric angle ∆ we separate the integral over the interface in eq 7:

η)

( - 0)( - 2) dz + 

∫0d

) ηSL + ηDL

∫ad

( - 0)( - 2) dz  (10)

(40) Hirose, C.; Akamatsu, N.; Domen, K. Appl. Spectrosc. 1992, 6, 1051. (41) Azzam, R. M.; Bashara, N. M. Ellipsometry and Polarized Light; North-Holland Publication: Amsterdam, 1979.

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Figure 2. Chemical structure of the cationic amphiphile C12DMP bromide.

where the second term ηDL describes the influence of the counterions in the diffuse layer on the ellipsometric angle ∆. The length d is the thickness of the compact layer. Inserting eq 9 in ηDL and solving the integral leads to

ηDL ) -

(x

[

d σnet π e + k0 - arctan dc eNA 2 σ

2NA

)]

2πlB(d/dc) (11)

with

k)

x

d/dc 2πlBNA2

(12)

This equation gives the desired relation between the measurable quantity ∆ und the effective surface charge density σnet of the compact layer σ. It contains only direct measurable quantities and can be used to determine (MS+A-), (MS+), and (MS+A-) of the ion binding model. Experimental Section Materials. The chemical formula of the soluble cationic amphiphile 1-dodecyl-4-dimethylaminopyridinium bromide, C12DMP bromide, used in this study is presented in Figure 2. The SHG activity is provided by the cationic headgroup with the dimethyl amino group N(CH3)2 acting as an electron donor. Details about the synthesis, analysis, and various physical properties can be found in ref 44. Sample Preparation. An aqueous solution of the surfactant at a concentration close to the critical micelle concentration (cmc) was prepared using bi-distilled water. This solution was then purified with the aid of a fully automated device described in ref 45. The purification scheme ensures the removal of any surfaceactive impurities by repeated cycles of (a) compression of the surface layer, (b) its removal with the aid of a capillary, (c) dilation to an increased surface area, and (d) again a formation of a new adsorption layer. The cleaning cycles are repeated until the equilibrium surface tension σe levels off in a plateau which indicates that all surface-active trace impurities are completely removed. Solutions of different concentrations were prepared by diluting the stock solution. To study the impact of counterions on the adsorption behavior, we add to each solution 100 mmol of KF, KCl, and KBr. Therefore, we effectively increase the amount of different counterions in the solution. Surface Tension Measurement. With a ring tensiometer (model K11, Kru¨ss) the surface tension was recorded until a constant equilibrium value, σe, was established. The cmc was determined on the basis of the adsorption isotherm. The cmc values of the members of the homologous series strictly follow the Stauff-Klevens equation.46 (42) Lekner, J. Theory of Reflection; Martinus Nijhoff Publishers: Boston, 1987. (43) Motschmann, H.; Teppner, R. Ellipsometry in Interface Science. In Novel methods to Study Interfacial Layers; Miller, R., Moebius, D., Eds.; Elsevier: New York, 2001. (44) Haage, K.; Motschmann, H.; Bae, S.; Gru¨ndemann, E. Colloids Surf. 2001, 183, 583. (45) Lunkenheimer, K.; Pergande, H. J.; Kru¨ger, H. Rev. Sci. Instrum. 1987, 58, 2313. (46) Stauff, J. Kolloidchemie; Springer: Berlin, 1960.

Figure 3. Surface tension isotherms of C12-DMP bromide for the pure solution (stars) and the solutions where 100 mmol/L of KBr (triangles), KCl (circles), and KF (squares) was added to each concentration of the surfactant. The cmc observed for different counterions follows the order of the periodic table of elements. SHG. SHG experiments were carried out in reflection mode at a fixed angle of incidence of 53°. Details on the experimental setup can be found in ref 47. Ellipsometry. All relevant design features of the ellipsometer (Multiskop, www.optrel.de) are discussed in ref 48. We used the Null ellipsometer mode of the ellipsometry module in a laser, polarizer, compensator, sample, analyzer arrangement at an angle of incidence of 56°.

Results and Discussion The experimental equilibrium surface tension isotherms (surface tension γ versus bulk concentration) of the cationic amphiphile C12-DMP bromide is represented by the stars in Figure 3. The amphiphile is a strong electrolyte, and the conductivity follows the prediction of the DebyeHu¨ckel theory.33 The surface tension isotherm shows a cmc at a surface tension of 43 mN/m. Our interest is in particular the investigation of the influence of indifferent electrolytes on the system behavior. For this reason we added KBr, KCl, and KF to a portion of the purified stock solution and measured again the equilibrium surface tension isotherms. The total concentration of the indifferent electrolyte was 100 mmol/ L, exceeding the concentration of the amphiphile by a factor of 100-1000. The indifferent electrolyte has a strong impact on the corresponding isotherms as shown in Figure 3: bromide (triangles), chloride (circles), and fluoride (squares). The salt increases the surface activity; the cmc is shifted to lower concentrations and occurs at different surface tensions: 35 mN/m for KBr, 42 mN/m for KCL, and 45 mN/m for KF. Obviously there is an ion specificity in the system behavior. The decrease in the surface tension comparing the different added counterions follows the order of the periodic table of elements. Fluoride has the smallest impact on the surface tension followed by chloride and bromide. Because most molecular properties such as ion radius, polarizability and hydration energy possess a monotonic behavior within a period one can speculate about a fundamental correlation. The surface excess can be retrieved by analyzing the isotherm in the framework of Gibb’s equation. The slope (47) Mo¨ller, G.; Schrader, S.; Motschmann, H. Langmuir 2000, 16, 4594. (48) Harke, M.; Teppner, R.; Schulz, O.; Orendi, H.; Motschmann, H. Rev. Sci. Instrum. 1997, 68 (8), 3130.

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Figure 4. Derivative of of the suface tension isotherms. The values for the pure solution were normalized by the factor m. The order at the cmc does not follow the periodic table.

of the surface tension isotherm is proportional to the total surface excess:2

( )

Γ)-

∂γe ∂µ

dγe ) -1/(mRT) T d ln a

(13)

where µ is the chemical potential of the solute component in the bulk solution, m is the number of independent components, and a is the activity of the solute. Because the concentration range for soluble surfactants in the range below the cmc is very low it is justified to replace the activity by the bulk concentration c.2 In absence of an indifferent electrolyte the rigorous thermodynamical treatment requires a factor of m ) 2 for a 1:1 ionic surfactant provided that the system is completely dissociated in the surface phase following an ideal behavior. The derivative of the interfacial tension as a function of the bulk concentration is presented in Figure 4 on a linear scale. The most surprising finding is that the surface excess does not follow at all the order of the periodic table of elements as the surface tension does. It is remarkable that the functional dependence of the slope of the surface excess for flouride matches the values of the pure solution. This implies that obviously fluoride has negligible impact on the adsorption of the surfactant despite the fact that the slope of the surface tension isotherm is changed. Furthermore, it is noticeable that the surface excess at the cmc seems to be independent of the amount of counterions because the surface excess for the solution with added counterions of bromide matches the one of the pure solution. To gain a more detailed picture of the interfacial architecture we performed linear and nonlinear optical measurements. As outlined, surface SHG is a nonlinear optical technique with an inherent surface specificity. Only the adsorbed surfactant molecules that contribute to the signal and bulk contributions are suppressed. The SHG response is completely dominated by the surfactant headgroup because this moiety dominates the hyperpolarizability due to the π push-pull system. Polarizationdependent SHG measurements36 reveal that (a) the orientational order of the headgroup is independent of the surface coverage with a tilt angle of 59° of the long chromophore axis with respect to the surface normal and (b) the symmetry of the molecular arrangement of the headgroup belongs to the point group C∞v which is

Figure 5. Number density of the surfactants measured by surface SHG. Flouride has no impact on the adsorption behavior of the surfactant. The number density at the cmc for the pure solution is equal to the one where KBr was added.

characteristic for an isotropic azimuthal arrangement within the adsorption layer. The absolute number density of the cationic amphiphile requires the evaluation of SHG intensities. There is a direct relation between SHG intensity and number densities of the headgroup; however, the underlying expression is complex because of the difficulty to account for local field corrections. A rock solid alternative has been developed in ref 36. The SHG signal is properly calibrated using a Langmuir monolayer of the water-insoluble C20 representative of the homologous series. The number density of a quasi-two-dimensional Langmuir layer is directly given by the preparation, and also all effects and inherent ambiguities are then eliminated. The results are presented in Figure 5. It shows the number density of the surfactant headgroup as a function of the bulk concentration. SHG records the adsorbed headgroups without a discrimination between adsorbed ion pairs and adsorbed amphiphile. In terms of the ion binding model of Radke et al. SHG measures the sum of (MS+) and (MS+A-). The formation of the ion pairs does not form new species with a new electronic signature at optical frequencies; hence, the hyperpolarizibility is not changed by the formation of ion pairs. The SHG measurement goes nicely along with the analysis of the surface tension isotherm. The SHG intensity measurements reveal that the surfactant surface coverage of the pure surfactant is not altered by adding fluoride as the counterion. Furthermore, the limiting value for the surfactant surface coverage is independent of the amount of counterions in the solution, because the values for the pure solution and the solution with the added bromide are nearly identical at the cmc. This is in accordance with the analyses of the surface tension isotherms, only chloride as a counterion decreases the surface coverage. Further details on the ion distribution can be retrieved by ellipsometry which records the complete transition region between air and the aqueous surfactant solution. The ellipsometric isotherm of the system is displayed in Figure 6. The optical isotherms are showing a monotonic increase with the bulk concentration. The difference to the SHG isotherms is obvious because in the limiting values it depends on the nature of the counterion. Specifically, the ellipsometric angle ∆ of the pure solution and the solution with fluoride as a counterion at the cmc is significantly lower as compared to that of bromide. It

Counterions at a Charged Interface

Figure 6. Ellipsometric angle ∆ as a function of the concentration of the surfactant. The values for the pure solution and the solution where flouride was added are significantly lower in comparison to the number density measured by SHG. A comparison leads to the fraction of condensed counterions in the compact layer at the interface.

is already established that in the case of nonionic surfactants the ellipsometric angle ∆ is proportional to the surface coverage.43 This must not be the case for ionic surfactants because ellipsometry is also sensitive to the distribution of the counterions. The ellipsometric isotherm can be used to retrieve the number density of the condensed counterions. The procedure for the determination of the ion distribution on the basis of eq 11 can be reduced to a simple recipe: First, determine the surface coverage Γ(c) as a function of the surfactant concentration with an independent technique. The desired quantity Γ(c) is, for instance, given by the derivative of the surface tension isotherm or alternatively by the square root of the SHG signal. A Fresnel analysis proves a linear relation between the prevailing surface coverage and the ellipsometric angle ∆ provided that there are no changes in the ion distribution with an increase of the surface concentration. Hence, a linear relation can be established if all counterions are located in the diffuse layer and a linear relation holds if all ions are condensed. As a next step measure the ellipsometric isotherm. Deviations from the linearity of the simulated ∆(Γ) dependence can be attributed to changes in the counterion distribution and yield directly the effective surface charge.29 The corresponding plot is given Figure 7 showing the deviation of the measured ellipsometric signal ∆ - ∆0 from the simulated one with a fixed ion distribution. The deviations are very pronounced for the pure surfactant and the surfactant solution with added fluoride ions. Both show a semi-quantitative agreement. The data clearly indicate a redistribution of the ions with increasing surfactant concentration. The addition of chloride and bromide leads immediately to a condensed state at all concentrations, and the ellipsometric data match the simulated dependence with all counterions condensed. The data can be further quantified. Figure 8 shows the charge per molecule as a function of the surface coverage of the surfactant without any added electrolyte. A charge per molecule of one means that all counterions are located in the diffuse layer; a value of zero implies that all counterions are condensed. The plot reveals a sharp transition between a free and a condensed state within a narrow concentration regime. This transition resembles all features of a second-order phase transition. The ion binding model of Radke et al. does not capture such a

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Figure 7. Ellispometric signal ∆ - ∆0 changing in a linear fashion with the surface coverage if all ions remain in the diffuse layer. The deviation of the measured ellipsometric signal ∆ ∆0 from the corresponding simulated dependence with a fixed ion distribution indicates changes in the ion distribution. The pure solution (stars) and the one with fluoride (squares) show a transition from a diffuse to a condensed state. The corresponding functional dependence of KBr (triangles) and KCl (circles) matches the one of a condensed state at all concentrations.

Figure 8. Charge per molecule as a function of the surface coverage of the surfactant without any added electrolyte. A charge per molecule of one means that all counterions are located in the diffuse layer; a value of zero implies that all counterions are condensed. The plot reveals a sharp transition between a free and a condensed state within a narrow concentration regime.

behavior and needs further extensions to address this remarkable observational fact for our model system. The ion binding model predicts instead a steady increase of the condensed counterions with the bulk concentration. The observed ion specificity as well as the condensation cannot be captured by a pure electrostatic theory and is the manifestation of a subtle interplay of several competing evenly matched interactions. A similar ion specificity has been identified in the counterion binding of bromide and chloride ions to micellar solutions of hexadecyltrimethylammonium choride and bromide. NMR investigations reveal a pronouncedly preferential binding of Br- ions to spherical and rodlike micelles.49,50 (49) Fabre, H.; Kamenka, N.; Khan, A.; Lindblom, G.; Lindman, B.; Tiddy, G. J. Phys. Chem. 1980, 84, 3428. (50) Ulmius, J.; Lindman, N.; Lindblom, G.; Drakenberg, T. J. Colloid Interface Sci. 1978, 65, 88.

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Langmuir, Vol. 21, No. 8, 2005

Conclusion The influence of an indifferent electrolyte on the adsorption behavior of a cationic soluble surfactant has been investigated by surface tension measurements, ellipsometry, and surface SHG. Each technique probes different structural elements, and the combination of all the techniques provides a sound picture of the interfacial architecture. The techniques measure directly structural parameters which are commonly introduced in the thermodynamic description of surface tension data. The analysis of our data provide evidence for an ion-specific effect which cannot be categorized according to the periodic table of elements. The combined data prove the existence of a phase transition between a free and a condensed state of the counterions with an increase of the bulk concentration. The number density and the surface excess at the cmc are equal for the pure solution and for the solution with

Koelsch and Motschmann

the added counterions of the same species, whereas the surface tension of the surfactant with the added counterions is significantly lower. This could be a hint that the structure of water, or to be more precise the dipole moment of water molecules at the interface, is changed for different electrolyte concentrations in the solution and, therefore, effectively changes the surface tension. To further support this concept molecular dynamic simulations would be very valuable. Fluoride has an exceptional role in our measurements and is depleted on the surface. Further investigations are required to see if this turns out to be a general effect or has an ion-specific origin. Acknowledgment. The authors thank Prof. Mo¨hwald for his continuous and steady support and stimulating discussions. LA0480179