Adsorption Properties of Surface Chemically Pure Sodium Perfluoro-n

Dec 24, 2014 - Technische Fachhochschule Wildau, D-15745 Wildau, Germany. Langmuir , 2015, 31 (3), pp 970–981. DOI: 10.1021/la503450k. Publication ...
0 downloads 0 Views 2MB Size
Article pubs.acs.org/Langmuir

Adsorption Properties of Surface Chemically Pure Sodium Perfluoro‑n‑alkanoates at the Air/Water Interface: Counterion Effects within Homologous Series of 1:1 Ionic Surfactants Klaus Lunkenheimer,*,† Dietrich Prescher,† Rolf Hirte,‡ and Katrina Geggel† †

Max-Planck-Institut für Kolloid- und Grenzflächenforschung, Department Adsorption Layers, Am Mühlenberg 1, D-16321 Potsdam, Germany ‡ Technische Fachhochschule Wildau, D-15745 Wildau, Germany S Supporting Information *

ABSTRACT: The unusual behavior of saturation adsorption calculated from experimental equilibrium surface tension (σe) versus logarithm of concentration (c) isotherms within the homologous series of aqueous sodium perfluoro-n-alkanoate solutions represents a particular problem in the adsorption of homologous ionic 1:1 amphiphiles at fluid interfaces. Special precautions were taken to guarantee surface-chemical purity for all solutions, avoiding falsifying effects by surface-active trace impurities. Surprisingly, all homologues’ adsorption isotherms reveal ideal surface behavior. The minimal surface area demand per molecule adsorbed for shorter-chain homologues slightly decreases with increasing chain lengths but then goes up steeply after having passed a minimum. A similar feature has been observed with the chemically quite different homologous series of the hydrocarbon surfactants of sodium-n-alkylsulfates. Comparing the corresponding 3D saturation concentrations in the boundary layer and in the bulk, it becomes evident that at high bulk concentrations when boundary layer and bulk concentrations are of the same order of magnitude the adsorption behavior may be treated as that of a pseudononionic surfactant. However, under conditions of the homologues’ strongest surface activity, adsorption seems to become increasingly governed by electrostatic repulsion, resulting in increasingly greater cross-sectional areas. Deviation from pseudononionic behavior sets in when the Debye length becomes distinctly greater than the adsorbent’s diameter at saturation. Formerly available theories on ionic amphiphiles’ adsorption deal either with electrical conditions of surfactant ions and counterions in the adsorption boundary layer or alternatively with pseudononionic behavior neglecting the former theories completely. Warszynski et al.’s novel theoretical model of the “surface quasi-two-dimensional electrolyte” seems to be capable of describing the adsorption of ionic amphiphiles at fluid interfaces in general. We conclude that the conditions of the two alternative approaches may be met within homologous series of ionic amphiphiles as limiting cases only.

1. INTRODUCTION

size, charge, solvation, and activity coefficient of the counterion,13−16, diffusion onto a charged monolayer,11,12 and specific adsorption within the boundary layer.3,12,16,22 Although the basic models on charge distribution at interfaces were set up a century ago,1−5,8,17,18 the fundamental understanding of the adsorption of ionic surfactants cannot be considered as being solved generally. Prosser and Franses have

Describing the adsorption of soluble ionic surfactants at fluid interfaces has remained a challenging task, even if it concerns that of the simplest ionic species, i.e., a symmetric 1:1 amphiphile. The first attempts to describe the electrochemical double layer were applied to a system of a simple 1:1 inorganic salt at a solid/liquid interface.1−3 Meanwhile, there are various approaches that have been extended to the more complicated ionic species of ionic amphiphiles. These models deal with quite different problems such as the surface equation of state,4−10, structure of the electrochemical double layer,6,10−12, © 2014 American Chemical Society

Received: August 28, 2014 Revised: December 24, 2014 Published: December 24, 2014 970

DOI: 10.1021/la503450k Langmuir 2015, 31, 970−981

Article

Langmuir

on surfactant adsorption basically require special measures to avoid artifacts caused by surface-active trace impurities.34−36 Unfortunately, these requirements have so far hardly been accepted in general.34 Besides particular aspects of application, fluorinated surfactants are of considerable interest for theoretical problems. Perfluoroalkanoic acids seem to be appropriate surfactants for various reasons. First, they reveal practically ideal surface behavior; second, their cross-sectional area is considerably greater than that of the corresponding hydrocarbon alkanoic acids; and third, they obviously reveal a particular pronounced counterion effect.40 Unlike hydrocarbon carboxylic acids, the perfluoroalkanoic acids are strong acids in aqueous solution. Thus, their alkali salts form completely dissociated 1:1 surfaceactive electrolytes in aqueous solutions. The sodium cation is that counterion that is mostly applied. After having presented the first results of our study,37 we extended the work of preparation and purification. Thus, we are now able to report on more and detailed results.

concluded that more reliable data for improving our fundamental understanding of the adsorption and tension behavior of ionic surfactants are needed.8 There are a few publications on this subject that review the recent state of the art on certain questions quite well.8,9,11,12,16 Originating from ample experience with chemical inadequacy in experimental studies on soluble amphiphiles’ adsorption, we looked for a favorable amphiphilic structure that seemed promising for investigating the adsorption of ionic surfactants. The homologous series of sodium-n-alkylsulfates, in particular, the sodium-n-dodecyl sulfate homologue (SDDS), has long been used as a standard ionic structure.4 Communications on it are so numerous that they shall not be enumerated here. However, investigations using alkylsulfates in the required grade of surface-chemical purity are rare.16,19−22 Meanwhile, it is known that alkali-alkylsulfates do hydrolyze in aqueous solution, producing the parent dodecanol whose surface activity is much stronger than that of the main substance sodium alkylsulfate.23−25 This process of degradation is especially favorable in acidic media. Nevertheless, early studies on sodium-n-octadecylsulfate spread on an acidic bulk water surface25 are still considered to be reliable experimental proof of the latest theoretical approach.10 However, an assumption of so-called ion−ion van der Waals forces between completely hydrophilic ions hardly seems reasonable from the point of view of chemistry.10,26 Recently, the rather complicate theoretical approach of ionic surfactant adsorption developed by Warszynski et al.12,21,22 has been improved by considering the penetration of counterions into the interfacial layer.27 This “surface-quasi-two-dimensional-electrolyte” (STDE) model seems promising for describing the adsorption of ionic surfactants in general. Unfortunately, the experimental studies so far applied to the few cationic surfactant systems are missing the required chemical qualification to serve the needs of ionic model amphiphiles. This has, in short, been the starting point of our investigation. Perfluoroalkanoic acids and their salts and derivatives are one of the most important groups of fluorosurfactants produced worldwide by several enterprises and applied by many industrial and scientific users. Only recently, a new procedure to produce perfluoroalkanoic acids was published by Clariant GmbH28 because of the great need for perfluorocarbonic acids in many different applications. Fluorosurfactants are a special group of fluorinated compounds. Their high chemical and thermal stability combined with their extraordinary surface activity is unique. In addition, they are very efficient at reducing the surface tension of aqueous and nonaqueous liquids. Therefore, fluorosurfactants are an important component of firefighting agents applied to burning fuels in, for example, aircraft crashes. Althougth the perfluoroalkanoic acids have often been described, the published data on these compounds differ considerably from each other, not only because of the different methods of measurement used. Thus, for example, comparing the data on surface tension and micelle properties given in refs 32 and 33, respectively, it soon becomes evident that the older data had obviously been obtained more carefully. Therefore, it was deemed necessary to investigate the properties of these compounds with special emphasis on their required purity. The main reason for the discrepancy between theoretical and experimental findings is due to too many unsatisfactory experimental results. As mentioned above, any experiments

2. EXPERIMENTAL SECTION 2.1. Synthesis. The salts of the perfluoroalkanoic acids were prepared, as described earlier,39−41 from the corresponding acids by neutralization in aqueous solutions with equivalent amounts of alkali hydroxides. The resulting perfluoroalkanoates were purified by repeated recrystallization. Their purity was checked by paper chromatography (PC) according to the method described for alkanesulfonates.42 With respect to the aim of this investigation, it is important to know that perfluoroalkanoic acids produced by electrofluorination usually contain various impurities, such as small parts of homologous perfluoroalkanoic acids with a reduced and also with an elongated carbon chain length, as well as branched species.38,43,44 These impurities could be detected by PC. Thus, for example, homologues C6, C7, C9, and C10 could be detected in the parent product of the perfluorooctanoic acid as impurities. Therefore, the progress in the elimination of such contaminations by repeated recrystallization was controlled analogously by PC. The chemical identity of the resulting salts was proved by elementary analysis. 2.2. Preparation of Surface Chemically Pure Surfactant Solutions. Although thorough efforts had been undertaken to obtain the fluorosurfactant solutions in the particular grade of surfacechemical purity, this aim was reached by applying ordinary chemical purification techniques for sodium perfluorohexanoate only (cf. Figure 1). To reach the distinguishing surface-chemical purity allowing adsorption properties free of disturbing trace impurity effects for all homologues to be obtained, we prepared surface chemically pure stock solutions of each homologue by applying the special purification technique developed by Lunkenheimer et al.34,36 It is based on the principle of successively generating, compressing, and sucking off the adsorption layer repeatedly. The special meaning of purity for the perfluorinated surfactants is illustrated in Figure 1. Applying this technique, you can easily check the state of the surface chemical purity by the criteria described in ref 34. Following it, you plot the measured equilibrium surface tension values σe as a function of the number of purification cycles j. Generally, with rising number j the dependence σe(j) increases until it reaches a certain value σe(j) = constant. This is shown in Figure 1 for different homologues of sodium perfluoroalkanoates. However, for one original product of sodium perfluoro-octanoate it turned out that the characteristic became negative, i.e., dσe/dj < 0. Such strange behavior had never before been encountered when investigating normal hydrocarbon (n-alkyl-) surfactants. Presumably this unusual behavior is caused by some impurity component, the surface activity of which is greater than that of the main component, as commonly observed, but whose cross-sectional area is greater than that of the main n-perfluoroalkanoate one. It is known that synthesis via 971

DOI: 10.1021/la503450k Langmuir 2015, 31, 970−981

Article

Langmuir

excellent quality of the mathematical matching. This homologue’s characteristic may thus serve as a standard for fluorosurfactants. It turned out that the longer-chain homologues’ experimental measurement error is greater, although the solutions’ required grade of surface chemical purity was guaranteed. According to the theory of diffusioncontrolled surfactant adsorption kinetics, the establishment of adsorption equilibrium takes more time the longer the homologues’ chain length because the corresponding experimental σe versus log c isotherms are shifted toward lower bulk concentrations, cf. Figure 2.34 The adsorption times required to reach equilibrium for the highly concentrated solutions between 10−2 and 10−1 M are so short that they are established immediately after the first possible surface tension value could be measured, i.e., about 30 s after beginning. The lowerconcentration solutions between 10−3 and 10−4 M reached adsorption equilibrium on a time scale of seconds to minutes. Even lowerconcentration solutions ( 2 nm, the diffuse double layer might again get “filled up” by adding an inert electrolyte until the conditions of R ≈ 10 and/ or κ−1 ≤ 2 nm are established again.27 However, this option is of limited use because the longer-chain surfactants with κ−1 > 2 nm usually have low solubility and/or Krafft temperatures that are too high. Dissolving additional inert electrolyte would also further reduce the surfactants’ solubility. (v) The dynamic surface tension behavior of the solutions of the homologous sodium-n-perfluoroalkanoates also seems to be compatible with this hypothesis. As long as the Debye length is not greater than the molecular size, the surfactant’s adsorption kinetics seems to follow a diffusion-controlled mechanism, whereas longerchained surfactants obviously seem to disfavor the diffusioncontrolled adsorption kinetics but are increasingly governed by a mechanism due to electrostatic retardation. Thus, the dynamic surface tension behavior may also be useful for providing information on the nature of adsorption of ionic

surfactants. (vi) So far there have been two alternative approaches to describing the adsorption parameters of ionic surfactants. On the one hand, there were the various models that originate from the well-established “classical” theories of the electrical double layer.1−3 On the other hand, there was the approach of Fainerman and Lucassen-Reynders,9 which disregards contributions of the diffuse double layer completely. Recently there has been a promising theoretical approach of the quasi-two-dimensional-electrolyte (STDE), developed by Warszynski et al., which seems capable of describing the adsorption of ionic surfactants in general.22,27 Thus, the STDE theory might be capable of harmonizing the two different kinds of approaches. As a consequence, every approach should have its own validity but within appropriate boundary conditions. The STDE theory should also be able to predict the boundary conditions for transition from pseudoionic to ionic behavior. However, to reach this aim, further experimental studies with appropriate model surfactants obeying the entire requirements for reliable experiments are necessary. Applying the STDE theory to the results of this contribution ought to be promising to understand better the adsorption of ionic surfactants with respect to their particular molecular properties such as the influence of the kind and charge of counterions and effects of divalent or multivalent amphiphiles and excess electrolyte, respectively. As a first attempt, we dealt with another investigation of the role of alkali counterions of perfluoro-n-alkanoates to see what information about the nature of the counterion could be gained from the adsorption parameters of ionic surfactants under conditions of κ−1 < 2 nm (R ≤ 10). This will be communicated in a subsequent report.



ASSOCIATED CONTENT

* Supporting Information S

Synthesis techniques. This material is available free of charge via the Internet at http://pubs.acs.org.

■ ■

AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS We are grateful to Mrs. Antje Storek for having carefully performed surface-chemical purification and surface tension measurements. We very much regret that Prof. Dr. Rolf Hirte died during the work on this subject on March 8, 2012.



REFERENCES

(1) Gouy, G. Sur la constitution de la charge électrique a la surface d’un électrolyte. J. Phys. Radium 1910, 9, 457−468. (2) Chapman, D. L. A Contribution to the Theory of Electrocapillarity. Philos. Mag. 1913, 25, 475−481. (3) Stern, O. Zur Theorie der elektrolytischen Doppelschicht. Z. Elektrochem. 1924, 30, 508−516. (4) Davies, J. T.; Rideal, E. K. Interfacial Phenomena; Academic Press: New York, 1966; p 196. (5) Kohler, H. Surface Charge and Surface Potential. In Coagulation and Flocculation; Dobiás,̌ B., Ed.; Marcel Dekker, Inc.: New York, 1993; Chapter 2, p 37. (6) Kalinin, V. V.; Radke, C. R. An ion-binding model for ionic surfactant adsorption at aqueous-fluid interfaces. Colloids Surf., A 1996, 114, 337−350. (7) Kralchevsky, P. A.; Danov, K. D.; Broze, G.; Mehreteab, A. Thermodynamics of Ionic Surfactant Adsorption with Account fort the 979

DOI: 10.1021/la503450k Langmuir 2015, 31, 970−981

Article

Langmuir Counterion Binding: Effect of Salts of Various Valency. Langmuir 1999, 15, 2351−2365. (8) Prosser, A. J.; Franses, E. I. Adsorption and surface tension of ionic surfactants at the air-water interface: review and evaluation of equilibrium models. Colloids Surf., A 2001, 178, 1−40. (9) Fainerman, V. B.; Lucassen-Reynders, E. H. Adsorption of single and mixed ionic surfactants at fluid interfaces. Adv. Colloid Interface Sci. 2002, 96, 295−323. (10) Middleton, S. R.; Pallas, N. R.; Mingins, J.; Pethica, B. A. Thermodynamics of Ionized Monolayers: Surface Manometry on Very Low Density Spread Monolayers of Sodium Octadecyl Sulfate at the Air/Water Interface and Analysis of Ionic Double Layer Contributions to the Isotherms. J. Phys. Chem. C 2011, 115, 8056−8063. (11) MacLeod, C. A.; Radke, C. J. Charge Effects in the Transient Adsorption of Ionic Surfactants at Fluid Interfaces. Langmuir 1994, 10, 3555−3566. (12) Warszynski, P.; Barzyk, W.; Lunkenheimer, K.; Fruhner, H. Surface Tension and Surface Potential of Na-n-Dodecyl Sulfate at the Air-Solution Interface: Model and Experiment. J. Phys. Chem. B 1998, 102, 10948−10957. (13) Weil, I. Surface Concentration and the Gibbs Adsorption Law. The Effect of the Alkali Metal Cations on Surface Behavior. J. Phys. Chem. 1966, 70, 133−140. (14) Wang, Ch.; Morgner, H. Effects of Counterions on Adsorption Behavior of Anionic Surfactants on Solution Surface. Langmuir 2010, 25, 3121−3125. (15) Vlachy, N.; Jagoda-Cwiklik, B.; Vacha, R.; Touraud, D.; Jungwirth, P.; Kunz, W. Hofmeister series and specific interactions of charged headgroups with aqueous ions. Adv. Colloid Interface Sci. 2009, 146, 42−47. (16) Gilanyi, T.; Varga, I.; Meszaros, R. Specific counterion effect on the adsorption of alkali decyl sulfate surfactants at air/solution interface. Phys. Chem. Chem. Phys. 2004, 6, 4338−4346. (17) Verwey, E. J. W. In The Physical Chemistry of Surface Films; Harkins, W. D., Ed.; Reinhold Publishing Corporation: New York, 1952. (18) Adamson, A. W. Physical Chemistry of Surfaces, 2nd ed.; Interscience Publishers: New York, 1967. (19) Elworthy, P.H.; Mysels, K.J. The Surface Tension of Sodium Dodecylsulfate Solutions and the Phase Separation Model of Micelle Formation. J. Colloid Interface Sci. 1966, 21, 331−347. (20) Lunkenheimer, K.; Czichocki, G.; Hirte, H.; Barzyk, W. Novel Results on the Adsorption of Ionic Surfactants at the Air/Water Interface - Sodium-n-alkyl Sulfates. Colloids Surf., A 1995, 101, 187− 197. (21) Warszynski, P.; Wantke, K. D.; Fruhner, H. Theoretical description of surface elasticity of ionic surfactants. Colloids Surf., A 2001, 189, 29−53. (22) Warszynski, P.; Lunkenheimer, K.; Czichocki, G. Effect of Counterions on the Adsorption of Ionic Surfactants at Fluid − Fluid Interfaces. Langmuir 2002, 18, 2506−2514. (23) Eagland, D.; Franks, F. Preassociation and the Thermodynamics of Hydrophobic Hydration in Dilute Solutions of Surfactants. Proceedings of the 4th International Congress on Surface Activity; Brussels, 1967; pp 535−544. (24) Lunkenheimer, K.; Fruhner, H.; Theil, F. Adsorption-catalyzed hydrolysis of sodium n-dodecyl sulfate at solid/liquid interfaces. Colloids Surf., A 1993, 76, 289−294. (25) Pethica, B. A.; Few, A. V. The surface potentials of long chain sulfates and their relation to dispersion stability. Faraday Soc. Discuss. 1954, 18, 258−267. (26) Ninham, B. W.; Yaminsky, V. V. Ion Binding and Ion Specifity: The Hoffmeister Effect and Onsager and Lifshitz Theories. Langmuir 1997, 13, 2097−2108. (27) Para, G.; Jarek, P.; Warszynski, P.; Adamczyk, Z. Effect of electrolytes on surface tension of ionic surfactant solutions. Colloids Surf., A 2003, 222, 213−222.

(28) Grottenmüller, R.; Knaup, W.; Probst, A.; Dullinger, K. Process for the preparation of perfluorcarboxylic acids. Eur. Pat. Appl. EP1172350 A2 20020116, 2002. (29) Para, G.; Hamerska-Dudra, A.; Wilk, K. A.; Warszynski, P. Mechanism of cationic surfactant adsorption − Effect of molecular structure and multiple charge. Colloids Surf., A 2011, 383, 67−72. (30) Para, G.; Hamerska-Dudra, A.; Wilk, K. A.; Warszynski, P. Surface activity of cationic surfactants, influence of molecular structure. Colloids Surf., A 2010, 365, 215−221. (31) Wilk, K. A.; Frackowiak, R.; Luczynski, J.; Warszynski, P. Cleavable Gemini Cationic Surfactants: Experimental and Theoretical Description of Adsorption. Chem. Lett. 2012, 41, 1096−1098. (32) Schiz, L. A.; Safronova, N. A.; Rebinder, P. A.; Maksimov, B. N. O nekotorych powerch nostnych i objomnych swoistwach rastworov soljei kalia i natria ftorsameschtschonnych alifatitscheskich kislot. Dokladi Nauk UdSSR 1968, 2, 416−419. (33) Lopez-Fontan, J. L.; Sarmiento, F.; Schulz, P. C. The aggregation of sodium perfluoro-octanoate in water. Colloid Polymer Sci. 2005, 283, 862−871. (34) Lunkenheimer, K.; Miller, R. A Criterion for Judging the Purity of Adsorbed Surfactant Layers. J. Colloid Interface Sci. 1987, 120, 176− 183. (35) Lunkenheimer, K. Surface-Chemical Purity of Surfactants: Phenomena, Analysis, Results, and Consequences. In Encyclopedia of Surface and Colloid Science, 2nd ed.; Taylor & Francis: New York, 2006; Vol. 8, pp 5879−5906. (36) Lunkenheimer, K.; Wienskol, G.; Prosser, A. J. Automated HighPerformance Purification of Surfactant Solutions: Study of ConvectiveEnhanced Adsorption. Langmuir 2004, 20, 5738−5744. (37) Prescher, D.; Lunkenheimer, K. Investigations on the adsorption properties of surface-chemically pure sodium salts of perfluoroalkanoic acids. J. Fluorine Chem. 1992, 58, 207. (38) von Werner, K. Hoechst-Gendorf, private gift. (39) Shinoda, K.; Nakayama, H. Separation determination of the surface excesses of surface-active ions and of gegenions at the airsolution interface. J. Colloid Sci. 1963, 18, 705−712. (40) Amorim da Costa, A. M; Santos, E. B. H. Structure and conformation analysis on perflu- ordecanoic acid and its lithium, sodium and ammonium salts as studied by Raman spectroscopy. Colloid Polym. Sci. 1983, 261, 58−63. (41) Lines, D.; Scutliffe, H. Preparation and properties of some salts of perfluorooctanoic acid. J. Fluorine Chem. 1984, 25, 505−512. (42) Püschel, F.; Prescher, D. High-molecular-weight aliphatic sulfonic acids. VII. Paper chromatography of sulfonates and some alkyl sulfates. J. Chromatogr. 1968, 32, 337−345. (43) Gramstadt, T.; Haszeldine, R. N. Perfluoroalkyl derivatives of sulfur. VII. Alkyltrifluoromethanesulfonates as alkylating agents, trifluoromethanesulfonic anhydride as a promoter for esterification, and some reactions of trifluoromethanesulfonic acid. J. Chem. Soc. 1957, 2640−2645. (44) Klein, H. G.; Meußdoerffer, J. N.; Niederprüm, H. Fluorinecontaining surfactants based on electrochemical fluoridation and possibilities for introducing them in surface treatment techniques. Metalloberfläche 1975, 29, 559−567. (45) Klein, H. G.; Meußdoerffer, J. N.; Niederprüm, H.; Wechsberg, M. Tetraethylammoniumperfluorooctanesulfonate, a versatile fluorosurfactant with many uses. Tenside Deterg. 1978, 15, 2−6. (46) Bryce, H. G. Industrial Aspects of Fluorine Chemistry. In Fluorine Chemistry; Simons, J. H., Ed; Academic Press: New York, 1964; Vol. 5, 297−314. (47) Lunkenheimer, K.; Wantke, K.-D. Determination of the Surface Tension of Surfactant Solutions Applying the Method of Lecomte du Noüy (Ring-Tensiometer). Colloid Polym. Sci. 1981, 259, 354−366. (48) Lucassen-Reynders, E. H. Anionic Surfactants − Physical Chemistry of Surfactant Action. Surfact. Sci. Ser. 1981, 11, 173−216. (49) Lunkenheimer, K.; Hirte, R. Another Approach to Surface Equation of State. J. Phys. Chem. 1992, 96, 8683−8686. 980

DOI: 10.1021/la503450k Langmuir 2015, 31, 970−981

Article

Langmuir (50) Lunkenheimer, K.; Haage, K.; Hirte, R. Novel Results on the Adsorption Properties of n-Alkyldimethylphosphine oxides at the Air/ Water Interface. Langmuir 1999, 15, 1052−1058. (51) Lunkenheimer, K.; Barzyk, W.; Rudert, R.; Hirte, R. Adsorption Properties of Soluble, Surface-Chemically Pure n-Alkanoic Acids at the Air/Water Interface and the Relationship to Insoluble Monolayer and Crystal Structure Properties. Langmuir 2003, 107, 6140−6150. (52) Tasaki, T.; Hattori, M.; Sasaki, J.; Nukima, K. Studies of Aqueous Sodium Dodecyl Sulfate Solutions by Activity Measurements. Bull. Chem. Soc. Jpn. 1975, 48, 1397−1403. (53) Woolley, E. M.; Burchfield, T. E. Thermodynamics of Ionic Surfactant Solutions. Fluid Phase Equilib. 1985, 20, 225−232. (54) Mukerjee, P.; Korematsu, K.; Oekawauchi, M.; Sugihara, G. Effect of Temperature on the Electrical Conductivity and the Thermodynamics of Micelle Formation of Sodium Perfluorooctanoate. J. Phys. Chem. 1985, 89, 5308−5312. (55) An, S. W.; Lu, J. R.; Thomas, R. K.; Penfold, J. Apparent Anomalies in Surface Excess Determined from Neutron Reflection and the Gibbs Equation in Anionic Surfactants with Particular Reference to Perfluorooctanoates at the Air/Water Interface. Langmuir 1996, 12, 2446−2453. (56) Li, X.-S.; Lu, J.-F.; Li, Y.-G. Study on ionic surfactant solutions by SAFT equation incorporated with MSA. Fluid Phase Equilib. 2000, 168, 107−123. (57) Andersson, G.; Krebs, T.; Morgner, H. Activity of surface active substances determined from their surface excess. Phys. Chem. Chem. Phys. 2005, 7, 136−142. (58) Menger, F. M.; Shih, L.; Rizvi, S. A. A. Reevaluating the Gibbs analysis of surface tension. J. Am. Chem. Soc. 2009, 131, 10380−81. (59) Laven, J.; de With, G. Should the Gibbs equation be revised? Langmuir 2011, 27, 7958−7962. (60) Xu, H.; Li, P. X.; Ma, K.; Thomas, R. K.; Penfold, J.; Lu, J. R. Limitations in the Application of the Gibbs Equation to Anionic Surfactants at the Air/Water Surface: Sodium Dodecylsulfate and Sodium Dodecylmonooxyethylenesulfate Above and Below the CMC. Langmuir 2013, 29, 9335−9351. (61) Kortuem, G. Lehrbuch der Elektrochemie, 2nd ed.; Verlag Chemie GmbH, Weinheim, 1957. (62) Kuester, F. W.; Thiel, A.; Fischbeck, K. Logarithmische Rechentafeln; Walter de Gruyter & Co.: Berlin, 1958. (63) Reshetnyak, E. A.; Chernysheva, O. S.; Nikitina, N. A.; Loginova, L. P.; Mchedlov-Petrosyan, N. O. Activity Coefficients of Alkyl Sulfate and Alkylsulfonate Ions in Aqueous and Water-Salt Premicellar Solutions. Colloid J. 2014, 76, 358−365. (64) Defay, R.; Prigogine, I.; Bellemans, A.; Everett, D. H. Surface Tension and Adsorption; Longmans, Green and Co. Ltd: London, 1966. (65) Mann, J. A. Jr., Porzio, K. C. Capillarity: The Physical Nature of Fluid-Fluid Interfaces Including the Problem of Biomembrane Structure. In Physical Chemistry; Kerker, M., Ed.; Butterworth, London - Boston: 1975; Series 2, Vol. 7, pp 47−160. (66) Guggenheim, E. A. Thermodynamics; North-Holland: Amsterdam, 1988. (67) Handbook of Chemistry and Physics, 44th ed.; Hodgman, Ch. D., Ed.; The Rubber Publishing Company: Cleveland, OH, 1963. (68) Jones, M. N. The relationship between surface charge density and double layer potential in soap films. Kolloid-Z. Z. Polym. 1968, 230, 236−240. (69) Shinoda, K.; Hato, M.; Hayashi, T. The Physicochemical Properties of Aqueous Solutions of Fluorinated Surfactants. J. Phys. Chem. 1972, 76, 909−914. (70) Collazo, N.; Shin, S.; Rice, St. A. Molecular-dynamics studies of the structure and properties of monolayers of perfluorinated amphiphiles. J. Phys. Chem. 1992, 96, 4735−4742.

981

DOI: 10.1021/la503450k Langmuir 2015, 31, 970−981