On the Adsorption Kinetics of Octanoic Acid at the Mercury/Electrolyte Interface U. Retter,* ,† A. Avranas, H. Lohse, K. Siegler, and K. Lunkenheimer § Bundesanstalt fu ¨ r Materialforschung, Rudower Chaussee 5, D-12489 Berlin, Germany, Aristotle University of Thessaloniki, 54006 Thessaloniki, Greece, and Max-Planck-Institut fu ¨ r Kolloid- und Grenzfla ¨ chenforschung, Rudower Chaussee 5, D-12489 Berlin, Germany Received September 8, 1998. In Final Form: December 21, 1998 The adsorption kinetics of octanoic acid at the mercury/electrolyte interface was investigated by means of capacity-time transients. For low concentrations of octanoic acid and for the short-term region, the transients can be theoretically well described with a diffusion-controlled adsorption process according to the Delahay-Trachtenberg law. The long-term transients for higher concentrations of octanoic acid exhibit an increase of the capacity with time, which can be modeled with an adsorption-controlled replacement of a condensed adsorption state by a hemimicelle adsorption state. Criteria are derived for which an increase of the double-layer capacity with time can be expected. Introduction In recent times, the formation of surface hemimicelles from adsorption layers at the interfaces metal/electrolyte 1-5 and air/water 6-9 has been intensively discussed. This problem is of fundamental interest, because mostly two- dimensional phase transitions in adsorption layers were found but not transitions from monolayers to three- dimensional microstructures. Furthermore, the question arises whether the estab- lishment of the adsorption equilibrium is always combined with a decrease of the double-layer capacity at the metal/ electrolyte interface or whether, for certain conditions, an increase can be expected. Interestingly, in this context, Jehring 10 already found in 1971 that the double layer increases with time when butanol molecules will be displaced by poly(ethylene glycol) (PEG) 1000 molecules at the interface mercury/electrolyte in the establishment of the adsorption equilibrium. The present paper is therefore aimed at clarifying the two problems mentioned. As an example, we selected the adsorption of octanoic acid at the interface mercury/ electrolyte. In two previous papers we have investigated the adsorption of octanoic acid at the air/electrolyte and mercury/electrolyte interfaces using surface tension and double-layer capacity measurements. 11,12 In the first paper we clearly showed the influence of the surfactant’s purity on its adsorption behavior while in the second one we calculated the surface area, adsorption energy, and lateral interaction energy of adsorbed octanoic acid molecules. The present paper aims at the investigation of short- and long-term capacity-time dependencies for adsorption of octanoic acid at the mercury/electrolyte interface. When short-term capacitance transients corresponding to dif- fusion-controlled adsorption were analyzed, it was found that the square root law (momentary surface concentration proportional to the square root of time) was only valid for very short times. 13 More refined models should be applied here, which also include surface concentrations which are close to the equilibrium ones. The long-term capacitance transients can reveal rela- tively small changes of the double-layer structure, and only recently has an increase of this capacity with time been observed, 3 the reason of which is not yet quite clear. Therefore, in the present paper octanoic acid was included in these investigations. Theory Model A: Diffusion Control according to the Delahay-Trachtenberg Model. Diffusion of neutral molecules to the electrode can be described by the Delahay-Trachtenberg law: 14 D is the diffusion coefficient, c e is the bulk concentration of the surfactant, and erfc(x) represents the complement of the error function erf(x). Here, the degree of coverage Θ e corresponds to the adsorption equilibrium, and Γ m is the surfactant’s maximal possible surface concentration. In the following, a way is shown how to determine erfc- (Kt ). The Gaussian error integral is: * To whom correspondence should be addressed. Bundesanstalt fu ¨ r Materialforschung. Aristotle University of Thessaloniki. § Max-Planck-Institut fu ¨ r Kolloid-und Grenzfla ¨ chenforschung. (1) Nikitas, P.; Andoniou, S. J. Electroanal. Chem. 1994, 375, 339. (2) Gorman, C.; Biebuyck, H.; Whitesides, G. Langmuir 1995, 11, 2242. (3) Sotiropoulos, S.; Avranas, A.; Papadopoulos, N. Langmuir 1997, 13, 7230. (4) Bizzoto, D.; Lipkowski, J. Prog. Colloid Polym. Sci. 1997, 103, 201. (5) Ivosevic, N.; Zutic, V. 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Θ t ) Θ e [1 - exp(K 2 t) erfc(Kt)] (1) K ) (Dc e 2 /Θ e 2 Γ m 2 ) 1/2 (2) 3661 Langmuir 1999, 15, 3661-3665 10.1021/la981179i CCC: $18.00 © 1999 American Chemical Society Published on Web 04/22/1999