Adsorption Properties of Soluble, Surface-Chemically Pure n-Alkanoic

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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 K. Lunkenheimer,*,† W. Barzyk,‡ R. Hirte,§ and R. Rudert| Max-Planck-Institut fu¨ r Kolloid- und Grenzfla¨ chenforschung, D-14424 Potsdam, Germany, Institute of Catalysis and Surface Chemistry, ul. Niezapominajek No. 8, PL 30-239 Cracow, Poland, Technische Fachhochschule Wildau, Friedrich-Engels-Strasse 63, D-15742 Wildau, Germany, and Bundesanstalt fu¨ r Materialforschung und -pru¨ fung, Unter den Eichen 44-46, D-12203 Berlin, Germany Received March 4, 2003. In Final Form: April 24, 2003 The adsorption properties of soluble, surface-chemically pure n-alkanoic acids at the air/water interface were investigated by evaluating equilibrium surface tension and surface potential versus concentration isotherms. There is no transition-like change in the adsorption isotherms of the n-alkanoic acids between n-pentanoic (C5) and n-undecanoic acid (C11). The isotherms are evaluated by the two-state approach to the adsorption equation and by the Gibbs equation. The nondissociated n-alkanoic acids’ surface area demand per molecule adsorbed is not constant within the homologous series but decreases with increasing chain length until it approaches the (almost constant) value of the insoluble homologues. The limiting surface area demand per molecule adsorbed of the soluble n-alkanoic acids is compared with the corresponding data of the insoluble homologues obtained from surface pressure versus surface area isotherms as well as from crystal structure analyses. Standard free enthalpies of adsorption, limiting cross-sectional areas, and surface interaction parameters reveal a distinct effect of alternation within the homologous series. Interestingly, also the Henry constants are subject to the even/odd phenomenon. This is explained by the even and odd homologues’ different surface arrangement of their terminal methyl groups with respect to the interface. The linear relationships describing the chain length dependences of the standard free enthalpy of adsorption and of the surface interaction parameter hold for chain lengths in the range 6 e nC e 11. n-Pentanoic acid has a somewhat different characteristic. Unlike the shorter chain homologues’ adsorption, the adsorption of n-dodecanoic acid cannot be described by a monotonically proceeding process but seems to include also processes of association.

1. Introduction n-Alkanoic acids have probably been the most frequently applied surface active agents in basic and applied research. Their longer chain sodium salts have been used as soaps since ancient times. There are several reasons for their widespread utility. They are easily available from natural sources, and they can simply be prepared from fat with low costs in a comparatively high purity, are nontoxic, and are biodegradable. Furthermore, with respect to surface chemistry, two different structures of surfactants can easily be prepared from them by changing the pH: the typical nonionic fatty acid at low pH, and the classical anionic surfactant, that is, the soaps, at high pH values. n-Alkanoic acids have become standard amphiphiles for insoluble and soluble monolayers in basic research. The pioneers of surface research like Traube,1 von Szyszkowski,2 Langmuir,3,6 Rehbinder,4 Frumkin,5 Harkins,7 and others used these amphiphiles. These inves* To whom correspondence should be sent. † Max-Planck-Institut fu ¨ r Kolloid- und Grenzfla¨chenforschung. ‡ Institute of Catalysis and Surface Chemistry. § Technische Fachhochschule Wildau. | Bundesanstalt fu ¨ r Materialforschung und -pru¨fung. (1) Traube, J. Liebigs Ann. Chem. 1891, 265, 27. (2) von Szyszkowski, B. Z. Phys. Chem. 1908, 64, 385. (3) Langmuir, I. J. Am. Chem. Soc. 1917, 39, 1848. (4) Rehbinder, P. Z. Phys. Chem. 1925, 11, 447. (5) Frumkin, A. Z. Phys. Chem. (Leipzig) 1925, 116, 466. (6) Langmuir, I. J. Am. Chem. Soc. 1937, 59, 2400. (7) Harkins, W. D. The Physical Chemistry of Surface Films, 2nd ed.; Reinhold Publishing Corporation: New York, 1954; Chapter 2.

tigations cover the adsorbed layers’ thermodynamic,1-21 kinetic,22-33 electric,5,8,12-14,20,34-41 optical,42-50 and surface(8) Stauff, J. Z. Phys. Chem. N. F. 1957, 10, 24. (9) de Witte, L. Kolloid Z. Z. Polym. 1965, 202, 147. (10) Pallas, N. R.; Pethica, B. A. Langmuir 1985, 1, 509. (11) Matuo, H.; Motomura, K.; Matuura, R. Chem. Phys. Lipids 1982, 31, 351. (12) Gaines, G. L., Jr. Insoluble Monolayers at Liquid-Gas Interfaces; Intersciences Publishers: New York, London, Sydney, 1966; Chapters 3-6. (13) Adamson, A. W. Physical Chemistry of Surfaces, 5th ed.; John Wiley & Sons New, Inc.: New York, 1990; Chapters 4-5. (14) Davies, J. T.; Rideal, E. K. Interfacial Phenomena, 2nd ed.; Academic Press: New York, London, 1966; Chapter 2. (15) Goncales da Silva, A. M.; Guerreiro, J. C.; Rodrigues, N. G.; Rodrigues, T. O. Langmuir 1996, 12, 4442. (16) Halperin, K.; Ketterson, J. B.; Dutta, P. Langmuir 1989, 5, 161. (17) Menger, F. M.; Wood, M. G.; Richardson, S. G.; Zhou, Q. Z.; Elrington, A. R.; Sherrod, M. J. J. Am. Chem. Soc. 1988, 110, 6797. (18) Baret, J. F.; Hasmonay, H.; Firpo, J. L.; Dupin, J. J.; Dupeyrat, M. Chem. Phys. Lipids 1982, 30, 177. (19) Yazdanian, M.; Yu, H.; Zografi, G. Langmuir 1990, 6, 1093. (20) MacArthur, B. W.; Berg, J. C. J. Colloid Interface Sci. 1979, 68, 201. (21) Matuo, H.; Cadenhead, D. A. Colloids Surf. 1989, 41, 287. (22) Ward, A. F. H.; Tordai, L. J. Chem. Phys. 1946, 14, 453. (23) Sutherland, K. L. Rev. Pure Appl. Chem. (Australia) 1951, 1, 35. (24) Ter Minassian-Saraga, L. J. Colloid Sci. 1956, 11, 398. (25) Defay, R.; Hommelen, J. R. J. Colloid Sci. 1959, 14, 411. (26) Hansen, R. S.; Wallace, T. C. J. Phys. Chem. 1959, 63, 1085. (27) Hansen, R. S. Trans. Faraday Soc. 1960, 64, 637. (28) Hansen, R. S. J. Colloid Sci. 1961, 16, 549. (29) Lunkenheimer, K.; Miller, R.; Fruhner, H. Colloid Polym. Sci. 1982, 260, 599. (30) Joos, P.; Bleys, G. Colloid Polym. Sci. 1983, 261, 1038. (31) Lin, Sh.-Y.; McKeigue, K.; Maldarelli, Ch. Langmuir 1991, 7, 1055.

10.1021/la034379p CCC: $25.00 © 2003 American Chemical Society Published on Web 06/27/2003

n-Alkanoic Acids at the Air/Water Interface

rheological51-68 properties. (For the thermodynamic properties of insoluble monolayers we have included here only papers that were evaluated for the purpose of this work.) Although there has been such an enormous endeavor to find out the basic surface-chemical properties of this chemically simple amphiphilic structure, it seems surprising that some of these properties could not yet be determined unambiguously. To illustrate it, two of these questions are to be mentioned, namely: First, is the limiting surface area demand per adsorbed n-alkanoic acid molecule, Amin, really constant irrespective of the n-alkyl’s chain length? Second, do the soluble n-alkanoic acids adsorb by a diffusion-controlled adsorption mechanism? As it is uncertain whether these questions are caused by a lack of proper measuring conditions, by insufficient grade of surfactant purity, or by improper theoretical approaches to surface equations of state, we were eager to follow all necessary boundary conditions in our investigations about the soluble n-alkanoic acids. (32) MacLeod, C. A.; Radke, C. R. J. Colloid Interface Sci. 1993, 160, 435. (33) Chang, Ch.-H.; Franses, E. I. Colloids Surf. 1995, 100, 1. (34) Hansen, R. S.; Minturn, R. E.; Hickson, D. A. J. Phys. Chem. 1957, 61, 953. (35) Baikerikar, K. G.; Hansen, R. S. J. Colloid Interface Sci. 1975, 52, 277. (36) Damaskin, B. B.; Petrii, O. A.; Batrakov, V. V. Adsorption organischer Verbindungen an Elektroden; Akademie-Verlag: Berlin, 1975. (37) Dynarowicz, P.; Paluch, M. J. Colloid Interface Sci. 1989, 129, 379. (38) Retter, U. Langmuir 2000, 16, 7752. (39) Retter, U.; Avranas, A.; Lohse, H.; Siegler, H.; Lunkenheimer, K. Langmuir 1999, 15, 3661. (40) Avranas, A.; Retter, U.; Lunkenheimer, K. J. Colloid Interface Sci. 2000, 227, 398. (41) Dudnik, V.; Lunkenheimer, K. Langmuir 2000, 16, 2802-2807. (42) Mann, J. D.; Baret, J. F.; Dechow, F. J.; Hansen, R. S. J. Colloid Interface Sci. 1971, 37, 14. (43) Rusanov, A. I. Prog. Surf. Membr. Sci. 1971, 4, 57. (44) Zhao, X.; Goh, M. C.; Eisenthal, K. B. J. Phys. Chem. 1990, 94, 2222. (45) Daillant, J.; Bosio, L.; Benattar, J. J. Europhys. Lett. 1990, 12, 715. (46) Shih, M. C.; Bohanon, T. M.; Mikrut, J. M.; Zschak, P.; Dutta, P. Phys. Rev. A 1992, 45, 5734. (47) Overbeck, G. A.; Mo¨bius, D. J. Phys. Chem. 1993, 97, 7999. (48) Earnshaw, J. C.; Nugent, Ch.; Lunkenheimer, K. Langmuir 1997, 13, 1368. (49) Teer, E.; Knobler, Ch. M.; Lautz, C.; Wurlitzer, S.; Kildae, J.; Fisher, T. M. J. Chem. Phys. 1997, 106, 1913. (50) Peterson, I. R.; Brezesinski, G.; Struth, B.; Scalas, E. J. Phys. Chem. B 1998, 102, 9437. (51) Stuke, B. Chem.-Ing.-Tech. 1961, 33, 173. (52) Lucassen, J.; Hansen, R. S. J. Colloid Interface Sci. 1966, 22, 32. (53) Thiessen, D.; Schwartz, P. Z. Phys. Chem. 1967, 236, 363. (54) Kretzschmar, G.; Lunkenheimer, K. Ber. Bunsen-Ges. Phys. Chem. 1970, 74, 1064. (55) Hansen, R. S.; Ahmad, J. Prog. Surf. Membr. Sci. 1971, 4, 1. (56) Mayer, E.; Eliassen, J. D. J. Colloid Interface Sci. 1971, 37, 228. (57) Mann, J. A.; Du, G. J. Colloid Interface Sci. 1971, 37, 2. (58) Hedge, M. G.; Slattery, J. C. J. Colloid Interface Sci. 1971, 35, 183. (59) Lucassen, J.; van den Tempel, M. J. Colloid Interface Sci. 1972, 41, 491. (60) Lucassen, J.; van den Tempel, M. Chem. Eng. Sci. 1972, 27, 1283. (61) Pierson, F. W.; Whitaker, S. J. Colloid Interface Sci. 1978, 63, 129. (62) Maru, H. C.; Wasan, D. T. Chem. Eng. Sci. 1979, 34, 1295. (63) Panaiotov, I.; Dimitrov, D. S.; Ivanova, M. G. J. Colloid Interface Sci. 1979, 69, 318. (64) Wantke, K.-D.; Miller, R.; Lunkenheimer, K. Z. Phys. Chem. (Leipzig) 1980, 261, 1177. (65) Lucassen-Reynders, E. H. In Anionic Surfactants; LucassenReynders, E. H., Ed.; Marcel Dekker: New York, Basel, 1981; p 173. (66) Langevin, D. J. Colloid Interface Sci. 1981, 80, 412. (67) Earnshaw, J. C.; Nugent, C. P. J. Phys. Condens. Matter 1993, 5, 1769. (68) Sakai, K.; Takagi, K. Jpn. J. Appl. Phys. 1993, 32, 2199.

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We report on investigations about the adsorption properties of surface-chemically pure n-alkanoic acids of the formula CnH2n+1COOH (4 e n e 10) that shed light on their adsorption behavior. These investigations comprise surface tension and surface potential measurements of their aqueous, surface-chemically pure solutions in 0.005 M hydrochloric acid (HCl). Aiming at a plausible molecular explanation of the resulting findings, the results are compared with monolayer properties and with crystallographic data of the insoluble members of this homologous series. 2. Experimental Section 2.1. Substances. The substances used were obtained from various suppliers: n-pentanoic acid, Merck-Schuchardt (for synthesis); n-hexanoic acid, Fluka puriss., p. a., standard for GC; n-heptanoic acid, Schuchardt; n-octanoic acid, Arco (pure) and Fluka (puriss. p. a., standard for GC). These substances were fractionated by vacuum distillation. The fractions of the best GC analysis were used. n-Nonanoic acid (Fluka, purum, 100% GC) was used as received; n-decanoic was prepared from the methyl ester of decanoic acid. This was fractionized. The gas chromatographically pure decanoic acid methyl ester was saponificated, and the n-decanoic acid was recrystallized. nUndecanoic (for biochemistry) was obtained from Merck, and n-dodecanoic (puriss., p. a., standard for GC), from Fluka. They were used as received. 2.2. High-Performance Purification. Aqueous stock solutions of the alkanoic acids in 0.005 M hydrochloric acid were purified by the high-performance purification apparatus as described in ref 69. The grade of surface-chemical purity (scp) was checked by surface tension measurements in the solutions’ progressing states of purity according to the thermodynamic criterion derived in ref 70. 2.3. Surface Tension Measurement. Surface tension measurements were performed with the du Nou¨y ring tensiometer Lauda TE 1C taking into account necessary modifications for the measurement of surfactant solutions.71,72 The measurements were performed at 295 K. 2.4. Surface Potential Measurements. The electric surface potential was measured by using the vibrating plate (VP) method. The surface potential meter SV 1000 SPD together with the software (LB 5000) were provided by the firm KSV, Helsinki. The probing “electrode” was an induction type sensor with a disk of stainless steel of 0.5 mm thickness and of about 2 cm diameter. It was perforated to diminish the air drag during vibration. The plate (VP) was made to vibrate above the solution surface by a loudspeaker with a constant frequency close to 90 Hz. As the KSV-SP-measuring head was originally designed for working with a Langmuir trough, for the application of this apparatus to free surfaces of solutions (adsorbed surfactant layers), the development of a new procedure of measurement was required. A glass dish was used to assemble the measuring cell. A height regulation table was constructed using a micrometer screw by means of which the cell was located precisely beneath the vibrating plate. Prior to each measurement the gap between the vibrating plate and the solution surface was adjusted at a constant distance in the range between 0.5 and 1 mm. The dependence of the surface potential, ∆V, on the air gap distance was checked occasionally in the measuring system. It was usually maintained within the range 1-5 mV/mm. The surface potentials were determined as the potential difference between two values taken in series: one for the supporting electrolyte (0.005 M HCl for the alkanoic acid solutions) and the second one for the surfactant solutions in the supporting electrolyte. Each pair of measurements was performed taking care not to lose the apparatus’ zero level when the reference (69) Lunkenheimer, K.; Pergande, H.-J.; Kru¨ger, H. Rev. Sci. Instrum. 1987, 58, 2313. (70) Lunkenheimer, K.; Miller, R. J. Colloid Interface Sci. 1987, 120, 176. (71) Lunkenheimer, K.; Wantke, K.-D. Colloid Polym. Sci. 1981, 259, 354. (72) Lunkenheimer, K. Tenside Deterg. 1982, 19, 272.

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solution was replaced by the surfactant solution in the cell. The measurements were started after having assured that the purity of the measuring cell containing the sample of water obeyed the criterion of negligible shift with time. Under the conditions applied, the reproducibility of the measurements was better than (5 mN/m. The first surface potential values, ∆V, discussed in this paper, were determined after having formed the free surface of the solution by aspirating. The values taken after 60 min were used as equilibrium surface potentail values, ∆Ve, used for the evaluation of the adsorption isotherms. The dynamic surface potential behavior, ∆V(t), of n-dodecanoic acid solutions was discussed in ref 41.

3. Evaluation of Equilibrium Surface Tension versus Concentration Isotherms The σe versus log c isotherms were evaluated by the two-state approach derived in detail originally in refs 73 and 74. This approach uses the well-known adsorption equation of Frumkin and of Henry to describe the experimental σe versus log c dependences. However, our experience made us conclude that one of the basic assumptions of the original Frumkin equation5,75 may not be fulfilled within the entire adsorption range. Unlike this, it is assumed that the adsorbant’s surface conformation does not remain unaltered but changes with the adsorption coverage. Hence, we applied the original Frumkin equation only to that concentration region of higher concentrations attributed to the amphiphile’s upright surface conformation. The highly diluted concentration region is described by the simple Henry law, due to the adsorbed amphiphile’s flat surface conformation. It expands to the range of coverage below 10%. However, for the interval of medium concentrations, we assume that the two alternative surface states are present as a mixture, and the ratio of their concentrations is described according to assumptions about the characteristic of the transition interval. Meanwhile, support for an essential change in surface conformations of extended chain amphiphiles within the transition interval was given by investigations on surface laser light scattering76-78 and surface potential.41,78,79 However, it is not yet possible to decide whether there are only two alternative surface conformations or whether the extended chain possesses a propensity to exist in a variety of conformations within the transition interval, as it was suggested in ref 81. The latter suggestion was incorporated in another approach of Warszynski and Lunkenheimer.80 This approach modeling the n-alkyl chains’ conformation at the interface uses the distribution of conformations calculated by Vold81 for n-alkanoic acid molecules in a vacuum. This is discussed below. With respect to the evaluation of the experimentally determined σe versus c isotherm, we have the relation

∆σ ) R∆σ1 + (1 - R)∆σ2

(1)

∆σ ) σw - σe stands for surface pressure with σw the surface tension of pure water and σe the equilibrium surface tension of the surfactant solution. (73) Lunkenheimer, K.; Hirte, R. J. Phys. Chem. 1992, 96, 8683. (74) Hirte, K.; Lunkenheimer, K. J. Phys. Chem. 1996, 100, 13786. (75) Lucassen-Reynders, E.-H. Prog. Surf. Membr. Sci. 1976, 10, 311. (76) Earnshaw, J. C.; Nugent, Ch.; Lunkenheimer, K.; Hirte, R. J. Phys. Chem. 1996, 100, 5004. (77) Earnshaw, J. C.; Grattan, M.; Lunkenheimer, K.; Rosenthal, U. J. Phys. Chem. B 2000, 104, 2709. (78) Lunkenheimer, K.; Earnshaw, J. C.; Barzyk, W.; Dudnik, V. Prog. Colloid Polym. Sci. 2000, 116, 95. (79) Barzyk, W.; Lunkenheimer, K.; Warszynski, P.; Pomianowski, A. Bull. Pol. Acad. Sci., Chem. 2000, 48, 153. (80) Warszynski, P.; Lunkenheimer, K. J. Phys. Chem. B 1999, 103, 4404. (81) Vold, M. J. J. Colloid Interface Sci. 1984, 100, 224.

The function ∆σ1 denotes the Traube/Henry equation,

∆σ ) Kc ) RTΓ(c)

(2)

and ∆σ2 stands for the Langmuir/Szyszkowski equation,

∆σ ) RTΓ∞ ln(1 + c/aL)

(3)

and/or the Frumkin equation

∆σ ) -{RTΓ∞ ln(1 - Γ/Γ∞) + Γ∞Hs(Γ/Γ∞)2} (4a) with

c ) aLΓ/(Γ∞ - Γ) exp(-2HsΓ/RTΓ∞)

(4b)

Γ, Γ∞, aL, and Hs denote surface concentration, saturation surface concentration, half saturation concentration (“surface activity”), and surface interaction parameter, respectively. K is called Henry’s constant. R denotes the transition function changing from 1 to 0. There is one constant for R ) 1 (Henry’s constant K), two for 1 e R e 0 (concentration of transition and width of transition interval), and three for R ) 0 (adsorption parameters aL, Γ∞, and Hs). The four parameters and the transition function are calculated by an iteration procedure using eqs 1-4, as described in ref 73. Standard free energy of adsorption is calculated as

∆G°ad ) RT ln aL

(5a)

in which aL is given in concentration (mol/dm3). If one uses mole fractions, x, the corresponding standard free energy refers to the standard state of x2 ) 1. (x ) 1 stands for the solvent water, and x ) 2 for the surfactant component.) The relation between ∆G°ad and the related value of ∆µ0,s is then given by

∆µ0,s ) RT ln xa ) RT ln aL - RT ln 55.6 ) ∆G°ad RT ln 55.6 (5b) (xa is the constant of half saturation of the Langmuir equation given in mole fractions.) At room temperature one gets ∆µ0,s = ∆G°ad - 10 kJ/mol as a good approximation. For comparison, the surface excess versus concentration isotherm, Γ(c), is calculated separately from the Gibbs adsorption equation

Γ)-

1 dσe RT d ln c

(6)

Γ was calculated by the first derivative of a spline function which includes the next two adjacent measuring values of the experimental σe versus log c isotherm at either side of the value under consideration according to eq 6. 4. Results and Discussion 4.1. Surface Potential. Figure 1 shows the equilibrium surface potential, ∆Ve, in dependence on concentration for n-decanoic acid. Three different regions can be discriminated in this isotherm. The first one covers the region of low adsorption coverage, Θ ) Γ/Γ∞ < 10%, characterized by a weak increase of the surface potential on concentration up to 37 mV. The second one extending over the concentration range close to saturation reveals


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Figure 2. Equilibrium surface tension (σe) versus log concentration (c) isotherms of aqueous solutions of n-alkanoic acids in 0.005 M hydrochloric acid: (1) pentanoic; (9) hexanoic; (b) heptanoic; (2) octanoic; ([) nonanoic; (+) decanoic; (×) undecanoic acid. The lines are a guide to the eye. Figure 1. Equilibrium surface potential, ∆Ve, versus concentration isotherm of aqueous solutions of n-decanoic acid in 0.005 M hydrochloric acid. The curve R(c) is the theoretical transition function according to eq 1. The solid line of ∆Ve(c) is a guide to the eye.

also a sigmoid dependence on concentration with positive slope. In the medium part, the surface potential changes are very big, with a slope about 10 times higher than that in the adjacent regions. The dependence of surface potential on concentration can also well be described by a transition function similar to that of eq 1. Comparing the experimental data of the ∆Ve versus log c isotherm with the dependence of surface coverage, Θ ) Γ/Γ∞, on concentration c, calculated by the two-state approach, eqs 1 and 4, it comes out that the shape of the ∆Ve versus c isotherm fairly well reflects the Θ(c) dependence, in which the steepest change, covering the medium region of 10% < Θ < 45%, contains the changes in ∆Ve between 37 and 202 mV. As this region exactly covers the transition region, one can conclude that it reflects the main change in the orientation of the adsorbate molecules that occurs within the adsorption isotherm. The data accessible at present let us propose the following model. In the diluted region there is enough place available to align the n-alkanoic acid molecules flat with their dipoles compensated by hydration water. Thus, having the effective amphiphile’s dipole vector close to zero, this does not contribute to the surface potential drop. Consequently, there are only small changes in the surface potential, presumably due to disorientation of water molecules. The steepest change in ∆Ve(c) occurs in that particular region which was called the transition region.73,74 In this region the adsorbates are thought to turn progressively from a flat to an upright orientation. As the main contribution to the surface potential is to be expected from the chain’s terminal methyl component,82 the overwhelming change in surface potential is brought about within the transition range. In the limiting region close to saturation, the adsorbed molecules assume an extended chain conformation oriented perpendicular to the surface. Since surface concentration is already close to saturation and as there is no reorientation possible, there is a comparatively weak (82) Vogel, V.; Mo¨bius, D. J. Colloid Interface Sci. 1988, 126, 408.

increase of surface potential left with increasing concentration. The steep increase of ∆Ve within the transition region hints to the fact that it is the terminal methyl group with positive partial charge expulsed to the air phase which, due to the low permittivity on the air side of the boundary, is mainly contributing to the surface potential.82,83 The conformational changes that occur in the adsorption layer were also confirmed for n-decanoic acid by surface laser light scattering experiments.76 These findings prove experimentally that conformational changes are not appropriately considered in the original adsorption equations of Langmuir/Szyzskowski and of Frumkin. 4.2. Adsorption Isotherms. Figure 2 represents the equilibrium surface tension (σe) versus log concentration (c) isotherms of the n-alkanoic acids from n-pentanoic to n-undecanoic acid. The isotherm of n-dodecanoic acid covers a limited concentration interval only, owing to its solubility limit. It is not contained in the figure. All isotherms show a continuously increasing slope with rising concentration. Except for dodecanoic acid, there is no discontinuity that would indicate phase transition, as was prompted in ref 85 for n-octanoic acid. The adsorption parameters of the evaluation of these isotherms calculated by the two-state approach73 are presented in the following figures. Figure 3 shows the surface excess, Γ, in dependence on concentration, as calculated by eqs 1-4 by using the adsorption parameters concerned. Figure 4 presents the standard free energies of adsorption, ∆G°ad, in dependence on the number of carbon atoms per molecule, nC. The dependence of the odd-numbered homologues is slightly, but significantly, different from that of the evennumbered ones; that is, the surface activity of the odd members is a little stronger compared to that of the even homologues. This will be discussed below in the context of the alkanoic acids’ Henry constants. The dependence of the standard free energy of adsorption on the chain length is given by the linear relationships (7): (83) Barzyk, W.; Pomianowski, A.; Lunkenheimer, K. Bull. Pol. Acad. Sci., Chem. 1997, 45, 189. (84) Lunkenheimer, K.; Haage, K.; Hirte, R. Langmuir 1999, 15, 1052. (85) Aratono, M.; Uryu, Sh.; Hayami, Y.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1984, 98, 33.

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odd-numbered n-alkanoic acids: ∆Gad ) -2.555nC + 1.84 (7 < nC < 11)

(7a)

even-numbered n-alkanoic acids: ∆Gad ) -2.595nC + 2.60 (6 < nC < 10)

(7b)

The values are given in kJ/mol. For n-dodecanoic acid it was not possible to determine the entire σe versus log c isotherm with equal reliability because of two problems. There is first the limited solubility of dodecanoic acid in 0.005 M HCl. Because of it, the lowest surface tension value measured of this isotherm was only 58 mN/m. Second, it turned out that the determination of the equilibrium surface tension values within the remaining small concentration interval was extremely difficult. Thus, sometimes a distinctly different measuring value, far exceeding the measuring accuracy, was obtained for the same solution under like conditions. For a few of the σe values, the scatter was up to 1.5-2 mN/m. Hence, we suggested that these solutions can hardly form a well-defined, soluble adsorption layer, but the formation of a homogeneous adsorbed layer is presumably disturbed by another process of association, as known for the adsorption of n-octanoic acid at the mercury/water interface.38,40 Nevertheless, we tried to evaluate the σe versus log c isotherm obtained to get some hint for the reason for this fact. Evaluating the σe versus log c isotherm of n-dodecanoic acid either by the classical Frumkin equation, eq 4, or by the two-state approach of this equation, eq 1, resulted in two characteristic findings. The value of the interaction parameter Hs was always well above that critical value of interaction, that is, (Hs)cr ) 2RT, for which a 2D-phase separation is predicted. In addition, the resulting Amin values were as small as 19-20 Å2/molecule. Applying the two-state approach to the evaluation of the n-dodecanoic isotherm was not reasonable because of the low number of reliable measuring data. Any attempt of matching produced a break in the calculated isotherm, resulting in a negligible width of the transition interval with a value of the interaction Hs > (Hs)cr. This means that also this attempt hints to phase transition. Figure 5 shows the dependence of the limiting surface area demand per molecule adsorbed, Amin, on nC. Unlike the general assumption, the cross-sectional areas of the soluble n-alkanoic acids, that is, nC e 11, are not constant but depend decidedly on the hydrocarbon chain length. With increasing chain length the Amin values decrease. Interestingly, the relationship Amin(nC) of the odd members is significantly different from that of the even homologues. The linear relationships are given below:

odd-numbered n-alkanoic acids: Amin ) -1.11nC + 34.03 (5 < nC < 11)

(8a)

even-numbered n-alkanoic acids: Amin ) -0.58nC + 30.90 (6 < nC < 10)

(8b)

The data are given in Å2/molecule. The slope of the Amin(nC) dependence of the odd homologues is almost twice that of the even ones. It is remarkable that a like trend was also observed for the corresponding Amin(nC) dependences of the soluble nalkyldimethylphosphine oxides although these surfactants do not reveal any measurable interaction within their adsorption layers.84

Figure 3. Adsorption isotherms of n-alkanoic acids in 0.005 M HCl: surface excess, Γ, in dependence on concentration, c, calculated from the two-state approach, eqs 1-4. (O) n-pentanoic acid; (2) n-hexanoic acid; (]) n-heptanoic acid; (>) n-octanoic acid; (g) n-nonanoic acid; (9) n-decanoic acid; (3) n-undecanoic acid. The solid lines are the best-fit curves.

Figure 4. Standard free enthalpies of adsorption, ∆G°ad, of the n-alkanoic acids in dependence on the number of carbon atoms per molecule, nC.

4.3. Adsorption and Insoluble Monolayer Behavior. Using these dependences, one ought to be able to extrapolate to the Amin values of the carbon numbers, nC, of the insoluble homologues, that is, to nC > 12 (cf. Figure 5). The straight lines should meet the cross-sectional area values of the insoluble homologous fatty acids. We expected these to be well-known from surface pressure (π) versus surface area (A) isotherms. However, having a more thorough look into the literature, it came out that there was poor agreement about the data on the limiting surface areas per molecule of the insoluble members. This was rather astonishing because insoluble n-alkanoic acids are the classical substances used already by the pioneers of film balance measurements such as Langmuir, Harkins, or Adams. The Amin values of long-chain carboxylic acids found in the literature were scattered in an interval between 19 and 26 Å2/molecule. This seems to be due to various reasons. First of all, there is no agreement to which state (“surface phase”) of the monolayer the limiting surface area is to be attributed. (Usually a value A0 is


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Figure 5. Limiting surface area demand per molecule adsorbed, Amin, of the n-alkanoic acids in dependence on carbon number, nC. Ac values determined from surface area (A) versus surface pressure (π) isotherms of spread n-alkanoic acid monolayers (cf. Table 1): (3) even-numbered homologues; (×) odd-numbered homologues; (9) most reliable Ac value taken from ref 10; (b) data taken from crystal structure analysis. The solid lines are calculated by the best-fit, eqs 8a and 8b, respectively. The dash-dot line is calculated by eq 9.

used which is obtained by extrapolation of the linear part of the solid phase of the π versus A isotherms to zero surface pressure.) Furthermore, and even more important, as Pallas and Pethica have convincingly demonstrated,10 most of the data published are missing a sufficient purity of the alkanoic acids. Mainly due to it and also due to inadequate monolayer techniques and poor humidity control, these experimental π versus A isotherms are qualitatively and quantitatively falsified. Thus, misleading conclusions about the thermodynamic characterization of the monolayers and, consequently, incorrect A0 values were obtained. Pallas and Pethica gave unambiguous evidence that the liquid-expanded to liquid-condensed phase transition in monolayers of really pure n-pentadecanoic (at 25 and 30 °C) and n-hexadecanoic (at 30 °C) acid at the air/aqueous hydrochloric acid interface is simply first order,10 characterized by a distinct plateau in the transition region of the π versus A isotherm at rather low surface pressures. Reconsidering the literature data on the background of these results and following the authors’ conclusions, we have to note that reliable π versus A isotherms and, thus, reasonable A0 values that can be compared with the Amin values of the soluble homologues are rare. We searched for such π versus A isotherms of insoluble fatty acids that reveal a plateau, at least a small one, in the region of transition from liquid to solid surface phase, although it seems to be clear that for none of them was the purity as good as that used in refs 10 and 11. These data are compiled in Table 1. (However, in the majority of the papers evaluated, the corresponding π versus A isotherms did not show a plateau at all.) From the isotherms selected, we determined (by extrapolation after magnification of the figures) the area which belongs to the cross-point where the linear dependence of π(A) of the isotherm’s solid-phase meets the plateau value, πpl, of the phase transition region. These values are denoted Ac values here. They are usually a little smaller than the A0 values that are obtained by extrapolation of the measured π(A) dependence in the solid state to zero surface pressure. These A0 values are generally considered to represent the molecules’ crosssectional area for the upright surface conformation.7,12-14 However, we think the Ac values are rather comparable to the corresponding Amin values of the soluble homologues, since they relate to the equilibrium condition of saturation adsorption that is reached at a certain surface pressure

Table 1. Ac Values of Spread n-Alkanoic Acid Monolayers Determined from Various Referencesa alkanoic acid

ref

Ac (Å2/molec)

temp (°C)

pH

tetradecanoic acid (myristic acid)

(a) 88 (b) 11 (c) 18 (d) 89 (a) 90 (b) 10 (c) 21 (d) 91 45

23.0 18.6 22.8 20.2 25.4 21.8 20.6/20.9/21.0 24.3 26.4

22.3 25.2 20 21 21.7 25 25 25 22

2 3 2 2 2 2 2 7 2

19.3 ≈21 12.9 ≈16 4.5 7.3 7.0-7.5 5.9 ≈0

(a) 92 (b) 15 (a) 18 (b) 17 (c) 19 93

22.0 24.7 22.6 18.9 21.8 23.6

25 25 20 23 25 22

2 7 2 1.5 2 2

∼17 ≈0 ≈0 ≈23 ≈0 18

pentadecanoic acid

hexadecanoic acid (palmitic acid) heptadecanoic acid octadecanoic acid (stearic acid) docosanoic acid a

π at Ac

Cf. explanations in section 4.3 and Figure 5.

of a nonsolid (fluid) surface film, instead of to the idealized (hypothetic) condition of a solid surface film at zero surface pressure. The obtained Ac values still scatter between 19 and 25 Å2/molecule. All values are compiled in Table 1. We have included investigations in the temperature interval between 20 and 25 °C. As long as there does not occur a change in the phase behavior of the spread monolayer within this temperature interval, the influence of temperature on the Ac value is much less than the scatter observed between the Ac values of the various investigations evaluated. This is supported by the results of refs 10 and 15. In ref 15 the Ac values obtained for 15 and 25 °C differed only negligibly. The average of all Ac values evaluated amounts to 22.6 Å2/molecule, indicated by a dashed line in Figure 5. Interestingly, this value is close to that value of Pallas and Pethica’s work being the most reliable of all. Thus, we can conclude that the most probable value of the cross-sectional area of the insoluble homologues of the nondissociated n-alkanoic acids should be within the interval 21-23 Å2/molecule (Table 1). Unfortunately, the rather big scatter in the Ac values does not enable us to conclude definitely whether they are independent of the hydrocarbon chain length. However, within the limits of error, there is no trend detectable other than Ac ≈ constant. This should be true for nC g 14,

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although, by measuring surface pressure with a Wilhelmy plate in parallel and perpendicular directions, Halperin et al. concluded that pentadecanoic acid monolayers still behave as a fluid whereas those of octadecanoic and tetracosanoic acids behave as typical solid monolayers.16 However, the Ac values of the four evaluated papers dealing with myristic acid11,18,88,89 and the four of pentadecylic acid10,16,21,90,91 scatter between 18.6 and 23 Å2/molecule and 20 and 25 Å2/molecule, respectively. Thus, these findings could give grounds to assume that the Ac values of all insoluble homologues included are constant. Unfortunately, due to the rather big scatter in the Ac values, it is also not possible to conclude about the phenomenon of alternation between the insoluble even and odd members. The Ac values obtained in ref 10 for n-pentadecanoic and n-hexadecanoic acids are practically identical. Thus, one should suggest the absence of the even/odd effect. However, answering this question unambiguously would necessitate taking into account more homologous members and carefully considering the required boundary conditions, in particular that of purity. It is important to underline the necessity of well-defined boundary conditions because our evaluation of the literature data showed another surprising result. Even when we considered only the isotherms in which a plateau, or at least an indication of one, was detectable, there were significant differences in the reported surface pressures, πpl, at that plateau or break point. Thus, for example, for octadecanoic acid at almost identical pH and temperature, Menger et al.17 found a break in the isotherm at a surface pressure of about 23 mN/m, whereas Baret et al.18 and Yaszdanian et al.19 observed this for negligible surface pressure. The latter result is in agreement with that of Harkins.7 This can be seen from a comparison of the data collected in Table 1. In addition, in some cases, neutral substrate water (pH 7) was used although it is known that n-alkanoic acids dissociate weakly in water and the dissociated alkanoate ion possesses surface properties different from those of the parent nondissociated fatty acid. Furthermore, another conclusion is suggested from the literature search. Recently, a number of new techniques, including fluorescence microscopy, Brewster angle microscopy (BAM), X-ray reflectivity, and grazing incident (GI), have revealed novel details of the internal structure of the “condensed” (solid) phase.50 However, on the basis of the evaluation discussed above, the question arises whether the different novel solid phases (at least up to four according to Peterson et al.50) might be induced at least to some extent by impurity effects. In any case, it would be interesting to perform similar investigations under conditions of sufficient purity, as undertaken by Pallas and Pethica.10 Extrapolating the odd characteristic to Amin values between 21 and 23 Å2/molecule, one arrives at a carbon chain length nC ) 11, that is, at undecanoic acid. This result is well in agreement with the results about the π(A) investigations of the odd insoluble fatty acids, as nundecanoic acid in 0.005 M HCl still behaves as a soluble amphiphile. Thus, there seems to be a distinction between soluble and insoluble monolayer behavior possible for odd (86) Abrahamsson, S.; von Sydow, E. Acta Crystallogr. 1954, 7, 591. (87) Malta, V.; Celotti, G.; Zanetti, R.; Martelli, A. F. J. Chem. Soc. B 1971, 548. (88) Adam, N. K.; Jessop, G. Proc. R. Soc. (London) 1926, A112, 362. (89) Agrawal, M. L.; Neuman, R. D. J. Colloid Interface Sci. 1988, 121, 355. (90) Harkins, W. D.; Boyd, E. J. Phys. Chem. 1941, 45, 20. (91) Moore, B. G.; Knobler, C. M.; Akamatsu, S.; Rondelez, F. J. Phys. Chem. 1990, 94, 4588.

Lunkenheimer et al.

alkanoic acids in 0.005 M HCl at 295 K according to nC e 11 corresponding to soluble and nC g 13 corresponding to insoluble monolayer behavior. Extrapolating the even Amin(nC) characteristic to Amin values of 21-23 Å2/molecule, you arrive at insoluble monolayer behavior at chain lengths between nC ) 14 and nC ) 16, that is, at myristic and/or palmitic acid. However, as discussed above, the investigations with n-dodecanoic acid solutions in 0.005 M HCl showed that already their adsorbed layers must no longer be considered as homogeneous. As it is a well-established fact that already myristic acid reveals typical insoluble monolayer behavior,7,18,20,21 one has to conclude that a clear discrimination between soluble and insoluble monolayer behavior is not possible. The transition from soluble to insoluble behavior of the even-numbered alkanoic acids occurs between lauric and myristc acid. On the other hand, this gives grounds for the assumption that the odd-numbered tridecanoic acid should still maintain some feature of a soluble adsorption layer. Finishing this question, it should be mentioned that the discrimination between soluble and insoluble monolayer behavior cannot be answered unequivocally on the basis of the Amin(nC) characteristic, because there remains some uncertainty about the exact value of the insoluble homologues’ cross-sectional area. In the textbooks of surface chemistry these values are given between 20 and 21 Å2/molecule. However, the average of the most reliable values chosen by us amounts to 22.6 Å2/molecule. This, in turn, would mean that insoluble behavior of the evennumbered alkanoic acids sets in with myristic acid already. This result is in good agreement with experimental observations. 4.4. Crystal Structures. To better assess the limiting surface area per alkanoic acid adsorbed, we have evaluated literature data about crystal structures of alkanoic acids. With respect to the monolayer behavior of the soluble and insoluble alkanoic acids, these data are very informative. More than 40 crystal structures of unbranched long chain saturated fatty acids (chain length longer than 10) are known from single crystal and powder diffraction experiments. The crystal structures consist of stacked layers. With few exceptions the molecules in each layer are arranged with parallel chains, with the headgroup pointing to one face of the layer and the terminal methyl group pointing to the other. The molecules form dimers with two carboxyl groups connected by two hydrogen bonds and the whole dimer ranging over two neighboring layers. These two layers constitute a bilayer, with the terminal methyl groups pointing to the outer faces. A different structure was found in one type of lauric acid crystals. This crystal has bilayers with interdigitated chains. In such a structure there is enough space between the alkyl chains to allow the chains of the neighboring bilayer to fill out the space. For each compound there seems to exist a large variety of crystal structures that differ in chain tilt, tilt direction, and headgroup conformation, depending on the conditions of crystallization. Because of the difficulties of growing single crystals from long chain fatty acids, only one small fraction of all possible crystal structures is known. The most common type is the so-called type C.86,87 Table 2 shows the areas per headgroup for this structure type. The angle between the chain axis and the layer plane in the C form of fatty acids is about 55° (observed in stearic acid). The area per headgroup shrinks slightly with increasing chain length. In Figure 5 the cross-sectional areas of several evennumbered homologues obtained from the crystal structure


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Table 2. Area per Head Group in Crystal Structures of Fatty Acids of Structure C86,87 alkanoic acid

nC

Amin (Å2/molecule)

n-dodecanoic acid (lauric acid) n-tetradecanoic acid (myristic acid) n-octadecanoic acid (stearic acid)

12 14 18

n-docosanoic acid n-hexacosanoic acid

22 26

23.92 ( 0.07 23.62 ( 0.07 23.19 ( 0.07 23.17 ( 0.10 23.01 ( 0.07 22.91 ( 7

analyses are also given. Taking into account the considerable scatter in the Ac values, the Amin values suit very well the former ones determined by us from the selected π(A) isotherms of insoluble monolayer studies as described above (cf. Table 2). The average of the Ac values amounts to 22.6 Å2/molecule. The proposed Ac values do better represent the characteristic behavior of the solid film than the corresponding A0 values of the literature, which refer to (extrapolated) negligible surface pressure, π f 0. It is therefore the Ac value that represents the real monolayer behavior rather than the A0 value. Pallas and Pethica’s conclusion about the direct transition of these monolayers’ surface behavior from a liquid into a solid film state seems to be correct. The Ac value reflects already the peculiarity of a 2D solid body. It is interesting to note that the Amin values of the insoluble homologues’ crystal structure analysis seem to still maintain a slight tendency of reduction with increasing chain length. If this were true, one could include it into the observed behavior of Amin(nC) of the soluble homologues. Thus, it becomes possible to describe the entire dependence for 5 e nC e 26 (!) by the following simple exponential function

Amin ) Amin,0 + k1 exp{nC/k2}

(9)

The constants amount to k1 ) 14.80 Å /molecule and k2 ) 5.43. Amin,0 ) 22.67 Å2/molecule. The correlation factor is R2 ) 0.95. This result is very interesting. Following on from this, we must conclude therefore that there is a gradual transition from soluble to insoluble monolayer behavior although, of course, the homologues concerned represent discrete steps in this feature. Hence, the limiting surface area demand of the insoluble fatty acids would indeed only be reached for rather long chain lengths. Thus, for example, one could discriminate a typical soluble behavior from a typical insoluble monolayer behavior by the following inequality 2

(dAmin/dnC)soluble , (dAmin/dnC)insoluble

(10)

According to it, for the even-numbered fatty acids the decrease in the characteristic Amin value with increasing chain length amounts to roughly 2.2 Å2 per ethylene group for the soluble homologues but only to about 0.3 Å2 per ethylene group for the insoluble members. In agreement with the results obtained from the thermodynamic evaluation, the intermediate homologues of chain lengths between nC ) 12 and nC ) 14 should also reveal soluble and insoluble monolayer behavior, possessing intermediate values of dAmin/dnC. Interestingly, the limiting value of Amin,0 ) 22.67 Å2/ molecule is practically identical to the average of the Ac values (see above), obtained from the evaluation of the insoluble fatty acids’ π versus A isotherms. Unfortunately, there are no investigations available about crystal structure analyses of odd-numbered fatty acids. It would be very interesting to know whether the phenomenon of alternation does exist in the 3D-crystal

Figure 6. Surface interaction parameter, Hs, of the n-alkanoic acids in dependence on the number of carbon atoms per molecule, nC. The lines are used as a guide to the eye.

properties, too. If so, one could reasonably conclude about its appearance in the insoluble monolayer behavior. 4.5. Surface Interaction. Illustrating the differences between even and odd members, we include the discussion of the surface interaction parameters concerned. This is shown in Figure 6. The corresponding relationships are given by eqs 11a and 11b:

odd-numbered n-alkanoic acids: Hs ) 0.288nC - 1.88 (7 < nC < 11)

(11a)

even-numbered n-alkanoic acids: Hs ) 0.500nC - 2.57 (6 < nC < 10)

(11b)

The data are given in kJ/mol. From them the effect of alternation becomes quite obvious although the scatter in the interaction parameters is not better than (0.6 kJ/mol on average. The interaction between the adsorbed alkanoic acids is relatively stronger for the even-numbered homologues by more than 100%. The difference even seems to diverge with increasing chain length. The linear dependence of Hs(nC) is well-determined for the even-numbered homologues. This is also true for the odd-numbered homologues in the case where pentanoic acid was excluded. For the odd members’ surface interaction characteristic, two noticeable findings were obtained. The whole adsorption isotherm of heptanoic acid was repeated three times using freshly purified stock solutions. Negligible interaction was always obtained by the fits. Opposite to this, the surface interaction value of pentanoic acid cannot be neglected. (A small but distinct interaction was always found.) The reason for this is obviously due to conditions in the pentanoic acid’s adsorbed layers that are different from those valid for the homologous members between C6 and C11. Pentanoic acid does not obey the general trend of the adsorption parameters observed for these homologues. The following facts hint to this. Pentanoic acid is the only homologue for which no improvement of the isotherm’s best fit was found whether the two-state approach or only the original, single Frumkin equation (4a/4b) was applied. This suggests an invariable

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Lunkenheimer et al.

surface conformation within the entire adsorption range. In addition, the experimental value of the standard free energy of adsorption of pentanoic acid (see Figure 4) is roughly 10% lower than that one extrapolated from the relationship ∆G°ad(nC), eq 7a, for which the experimental value of pentanoic acid is excluded. This means that the surface activity of pentanoic acid is less than expected from the general relationship valid for the other oddnumbered homologues. According to Tanford,94 weaker surface activity means less protrusion of the n-alkyl chain from the aqueous bulk phase. Furthermore, the highest value of all cross-sectional areas of the soluble alkanoic acids in the adsorption layer was found for the shortest chain length measured, that is, for pentanoic acid. This value amounts to 28-29 Å2/molecule. This area per molecule is obviously sufficient to still allow a conformational freedom under conditions of saturation adsorption. Thus, the alkyl chains will then still have some contact with the aqueous bulk phase, resulting in comparatively lower surface activity. The fact that pentanoic acid’s Henry constant well obeys the relationship observed for all oddnumbered members also supports this conclusion (cf. eq 12a). Nevertheless, a residual, non-negligible surface interaction parameter is observed for pentanoic acid (Hs ) 0.5 kJ/mol). This excess surface interaction might be due to some contribution of hydrogen bonding between the carboxylic acid groups of the adsorbed short chain pentanoic acid molecules, because the stronger surface interaction usually hints to more favorable packing conditions. Thus, the odd-numbered homologues’ surface conformation is less favorable for good packing, although the trend observed for the cross-sectional areas would suggest the opposite. However, the effect of alternation in Amin(nC) in comparison to that of Hs(nC) is weak, amounting to about 10% at maximum. 4.6. Phenomena of Alternation (Even/Odd Effects). The phenomenon of even/odd alternation in the adsorption and micellar properties of surface-chemically pure surfactant systems represents a well-established fact now.95-101 Even/odd phenomena in a crystal lattice induced by different packing structures were already investigated by Marcelja in ref 102. This work gives ample evidence that the effect of alternation is also characteristic of adsorbed layers of soluble n-alkanoic acids. The relative extent of this effect is widely varying in various homologous series. As was reported recently, for certain homologous amphiphilic hemicyanine dyes, the alternation may extend up to almost 100%.99 Compared to this, the effect of alternation is comparatively small for the n-alkanoic acids.

The reason for the even/odd effects is not yet understood well, although it has been known for long for bulk properties of homologous compounds. From the effect of alternation, which occurs in the different surface parameters, it follows that the even homologues’ stronger surface interaction can not simply be explained by a higher adsorption density. Investigations on the melting point alternation in the short chain n-alkanes showed that the way in which the molecules are packed laterally does not play any role in the differences in the packing density of the even- and oddnumbered triclinic n-alkanes,103 but the intermolecular distance between the end methyl groups is responsible for the alternation in the densities. Thus, the evennumbered n-alkanes have optimal intermolecular contacts at both ends, whereas the odd ones possess these at one end, and at the other end the distances are longer. This leads to a less dense packing of the odd n-alkanes. Trying to evaluate the n-alkanoic acids’ alternation by this concept, one has to take into consideration that not only is their molecular structure more complicated than that of the n-alkanes, insofar as they possess one methyl group at one end but one polar carboxyl group at the other, but also the phenomenon does occur at the boundary layer between liquid and air phase. Therefore, we also have to consider the behavior of the polar group in the interface. Previously, we attempted to understand the wellpronounced even/odd phenomenon of the nonionic 2-nalkyl-5-hydroxy-1,3-dioxanes100 by Gutmann’s concept of donor-acceptor-approach.104 There was good reason for this to occur. Recently, there is an interesting investigation considering this effect of the nonionic structure of dimethyl-nalkylphosphine oxides in terms of different conformations of the adsorbate by SFG (sum frequency generation). By it the different cross-sectional area values of even and odd homologues might be understood in terms of the adsorbates’ varying surface orientations.105 The fact that the surface activities of the odd-numbered members are relatively stronger (more negative ∆G°ad values) than those of the even members points to the different alkyl chains’ protrusions from the aqueous bulk phase. This could well be consistent with a difference in their surface orientation. Thus, there seems to be a fundamental theoretical effort necessary to satisfactorily explain the even/odd phenomena in adsorbed layers by appropriately taking into account the various factors possible. In this respect, it is interesting to note that also the Henry constants of the adsorption isotherms reveal the effect of alternation. This is shown in Figure 7. The linear relationships K(nC) for the even and the odd homologues are given in eqs 12a and 12b.

(92) Do¨rfler, H.-D.; Rettig, W. Colloid Polym. Sci. 1982, 260, 1126. (93) Hasmonay, H.; Hochapfel, A.; Boidart, M.; Peretti, P. Mol. Cryst. Liq. Cryst. 1990, 185, 155. (94) Tanford, C. The Hydrophobic Effect: Formation of Micelles and Biological Membranes, 2nd ed.; Krieger Publishing Company: Malabra, FL, 1991; Chapters 3-5 and 10. (95) Prescher, D.; Lunkenheimer, K. J. Fluorine Chem. 1992, 58, 207. (96) Lunkenheimer, K.; Holzbauer, H.-R.; Hirte, R. Prog. Colloid Polym. Sci. 1994, 97, 116. (97) Lunkenheimer, K.; Czichocki, G.; Hirte, H.; Barzyk, W. Colloids Surf., A 1995, 101, 187. (98) Goebel, A.; Lunkenheimer, K. Langmuir 1997, 13, 369. (99) Lunkenheimer, K.; Laschewsky, A.; Hirte, R. J. Colloid Interface Sci. 2002, 246, 260. (100) Lunkenheimer, K.; Burczyk, B.; Piasecki, A.; Hirte, R. Langmuir 1991, 7, 1765. (101) van Os, M.; Haak, J. R.; Rupert, L. A. M. Physico-Chemical Properties of Selected Anionic, Cationic and Nonionic Surfactants; Elsevier: Amsterdam, London, New York, Tokyo, 1993. (102) Marcelja, S. J. Phys. Chem. 1974, 60, 3599.

odd-numbered n-alkanoic acids: log Kodd ) 0.38nC + 0.87 (5 < nC < 11) (12a) even-numbered n-alkanoic acids: log Keven ) 0.38nC + 1.66 (6 < nC < 10) (12b) The Henry constant K can be considered in terms of a partitioning constant between the bulk and the surface phase. The difference in the alkanoic acids’ partitioning (103) Boese, R.; Weiss, H.-C.; Bla¨ser, D. Angew. Chem., Int. Ed. Engl. 1999, 38, 988. (104) Gutmann, V. The Donor-Acceptor-Approach to Molecular Interaction; Plenum Press: New York, London, 1978. (105) Fazio, V.; Lunkenheimer, K.; Mo¨hwald, H.; Motschmann, H. Submitted.


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this results in

(∆µ0)odd - (∆µ0)even ) RT ln Keven/Kodd

(17)

By it the difference between the odd and even surface states in the Henry region can be estimated. As for the n-alkanoic acids Keven/Kodd ≈ 1.29 (cf. Figure 6), this results in

(∆µ0)odd = (∆µ0)even + 0.6 kJ/mol

Figure 7. Henry constants, K, of the n-alkanoic acids’ adsorption isotherms in dependence on the number of carbon atoms per molecule, nC.

constants is a useful hint to differences in the protrusion of the n-alkyl chains’ terminal methyl group in the adsorbed layer’s gaseous state. According to Abraham, the increments of the hydrophobic effect are different whether you have a -CH2- (methylene) and/or a terminal -CH3 (methyl) group.106,107 Assuming a flat arrangement of the extended chain in the adsorbed layer, this means that the interaction of the terminal methyl group with water should be different for even- and odd-numbered homologues. To underline it, we can use the Henry constants, K, to calculate differences in the standard free enthalpies of adsorption, ∆G°ad, of the even and odd homologues using Betts and Pethica’s definition of surface fugacity π*108 with

µs ) µ0s + RT ln π*

(13)

π*A ) πfsA ) RT

(14)

and

µ , f , and π ≡ ∆σe denote surface chemical potential, surface activity coefficient (fs ) 1 for the Henry region), and equilibrium surface pressure, respectively. Using the chemical bulk potential s

s

µb ) µ0b + RT ln c

(15)

the standard free enthalpy of adsorption is given by

∆µ0 ) µ0s - µ0b ) RT ln 1/K

(16)

Now, defining by eq 16 the standard free enthalpy of adsorption for the even and the odd homologues each, (106) Abraham, H. M. J. Chem. Soc., Faraday Trans. 1 1984, 80, 153. (107) Abraham, H. M.; Matteoli, M. J. Chem. Soc., Faraday Trans. 1 1988, 84, 1985. (108) Betts, J. J.; Pethica, B. A. Proceedings of the 2nd International Congress on Surface Active Substances; Butterworth: London, 1957; p 152.

This small difference is not only of the order of magnitude of typical differences in amphiphiles’ molecular conformations,81 but it is also consistent with the structural arrangement of an amphiphile’s extended hydrocarbon chain in the surface. This means that in the gaseous surface state the even members’ terminal methyl groups have less contact with bulk water than the corresponding methyl groups of the odd members. Thus, whereas the terminal methyl group of the even homologues is suggested to be completely protruded from the aqueous phase, it will still partially remain in contact with water for the odd homologues. It shall only be mentioned here that the standard free energy of adsorption, which is approximately related to half saturation with upright surface orientation, as given by eqs 4, shows an opposite feature, insofar as the ∆G°ad values of the odd members are slightly more negative (stronger surface active) than those of the even members. Thus, having upright orientation in the adsorption layer, the odd members’ hydrocarbon chains ought to have comparatively less contact to bulk water left than their related evennumbered homologues. 5. Concluding Remarks Finishing the discussion, we would like to come back to the problem of evaluating the n-alkanoic acids’ experimental σe versus log c isotherms appropriately. There is no doubt that the two-state approach results in a much better matching of these isotherms. It is also evident from surface potential and surface laser light scattering investigations that the hypothesis of the surfactant’s transition from a flat to an upright surface orientation during adsorption has a sound physical basis. To further prove it, we compared the adsorption densities calculated by the two-state approach with those calculated by the Gibbs equation, eq 6. As a matter of fact, the surface excesses, Γ, in the concentration regions outside the transition region were always identical. However, this is usually not true for the Γ values obtained within the transition interval. The Γ values of the transition region calculated by the Gibbs equation are determined by using a cubic spline function using the next two adjacent measuring values of the experimental σe versus log c isotherm. As the latter procedure may not be sufficient to exactly determine the slope of the σe versus log c isotherm at the few measuring data of the transition interval and as the change in slope is the strongest within this region, it is not sure whether these differences are thermodynamically sound. However, within the framework of this work, this question is not important, as the calculation of the adsorption parameters is related either to the true Frumkin region and/or to the separate Henry region of the adsorption isotherm. What matters only is the question how far these “nonmixed” regions do really extend. Surface potential measurements prove that the transition region calculated from the two-state approach covers the region of the steepest change of the ∆Ve versus c isotherm. This

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helps to identify the separate surface states of equal orientation. Thus, we can be sure of the validity of the adsorption parameters calculated in this work. The question whether it is reasonable to take into consideration further surface conformations in addition to the two hypothesized alternative surface orientations still remains open. It is to be elucidated by evaluating also the said experimental adsorption isotherms by the approach put forward by Warszynski and Lunkenheimer80 recently. Applying these two approaches, which have in common the basic feature of a transition region, to various homologous series of extended chain surfactants will shed light on this problem. This is to be performed in subsequent work. Concerning the evaluation of the numerous investigations on insoluble monolayers, the conclusions drawn in ref 10 that there is no additional intermediate phase between the liquid-expanded and liquid-condensed (solid) phases should carefully be taken into account. It should be clarified whether this conclusion can be generalized. To answer these questions, it is no use to collect further results obtained with substances of insufficient purity,

Lunkenheimer et al.

but to seriously check not only the physical but also the chemical boundary conditions. These investigations have shown that there is a continuous transition from soluble to insoluble monolayer behavior that is in line with basic chemistry. The intermediate homologues between lauric (nC ) 12) and myristic (nC )14) acids possess still soluble and already some insoluble features. For typical soluble monolayer behavior the decrease in the limiting surface area demand per ethylene group with increasing chain length is much greater than the almost negligible one for the typical insoluble homologues. It is astonishing that the data of the 3D crystal structure analysis well suit the monolayer properties. This indicates that the Ac value really reflects properties of a solid 2D body. It would be interesting to investigate crystal structures of odd-numbered n-alkanoic acids in a quality of sufficient purity. This should help to answer the question whether the phenomenon of alternation will also be met in solidlike monolayers. LA034379P

Adsorption Properties of Soluble, Surface-Chemically Pure n-Alkanoic

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