Analysis of Electron Transfer Processes across Liquid/Liquid Interfaces: Estimation of the Equilibrium Free Energy of Activation S. Harinipriya and M. V. Sangaranarayanan* Department of Chemistry, Indian Institute of Technology, Madras 600 036, India ReceiVed: July 16, 2003; In Final Form: September 17, 2003 The equilibrium free energy of activation for electron-transfer processes across liquid/liquid interfaces is estimated using the desolvation energies, interfacial solvation numbers, and inner potential difference between the bulk and the interface for the ionic species and dielectric permittivities. The analysis employing a sharp boundary model is shown to yield a quantitative expression pertaining to the free energy of activation, solvent reorganization energy, and the rate constant. The methodology is applied to the electron transfer of [Fe(CN) 6 ] 3- /[Fe(CN) 6 ] 4- with (i) [Lu(biphthalocyanine)] 4+ /[Lu(biphthalocyanine)] 3+ and (ii) TCNQ/TCNQ - redox couples in water/1,2 dichloroethane interface. 1. Introduction The analysis of charge-transfer phenomena across liquid/ liquid interfaces is a frontier area of research on account of its fundamental importance in ion transport across membranes, 1 fabrication of ion-selective electrodes, 2 photoinduced processes, 3 phase transfer catalysis 4 etc. Despite this extensive role, a rigorous formulation and quantitative interpretation is rendered difficult in view of the necessity to incorporate satisfactorily, the interfacial potential distribution, ionic solvation energies and dielectric permittivities in conjunction with the nature of the boundary existing between the immiscible electrolyte solutions. Although the experimental studies in this context employ diverse techniques such as cyclic voltammetry, 5a scanning electrochemi- cal microscopy (SECM), 6 second harmonic generation (SHG), 7 etc., the rationalization of the data in terms of the system parameters with the help of the constituents of the interface has remained elusive. In this Article, a phenomenological thermodynamic approach for evaluating the equilibrium free energy of activation pertain- ing to electron transfer processes across liquid/liquid interfaces is suggested, using a sharp boundary model. A sharp boundary model becomes valid when the two solvents are highly immiscible. A notable feature of the formalism consists of the explicit incorporation of various extent of interfacial desolvation of the reactants, inner potential differences of the species involved, dielectric permittivity of the nonaqueous solvent, and bulk solvation numbers of ions in aqueous and organic phases. The qualitative validity of the procedure is demonstrated for the redox reactions occurring at the water/1,2 -dichloroethane (1,2 DCE) interface; TCNQ denotes 7,7,8,8-tetracyanoquinodimethane. 2. Composition of the Equilibrium Free Energy of Activation Using a Sharp Boundary Model For a general redox reaction Ox 1 + Red 2 T Ox 2 + Red 1 , where Ox 1 and Ox 2 refer to the oxidant in the aqueous and organic phase respectively, Red 1 and Red 2 being the reduced species, the equilibrium free energy of activation (ΔG eq,sharp q ) may be represented (cf. Scheme 1) as 8 In eq 3, w r1 denotes the work done in bringing the reactants (Ox 1 and Red 2 in the aqueous and organic phases) from bulk to the interface, w p1 being the work involved in the transfer of products. 8 ΔG et1 denotes the free energy change involved in the electron transfer between the reactants. The above equation is reminiscent of the Marcus theory 9 of electron-transfer processes wherein the overall free energy of activation is partitioned into different contributions involving the reactants and products mediated by dipolar polarization. 2.1. Work Terms and Interfacial Solvation Behavior of Ions. The work term pertaining to the reactants, w r1 may be written as where ΔG Ox 1 -s 1 inter and ΔG Red 2 -s 2 inter refer to the interfacial Gibbs free energy of solvation of Ox 1 and Red 2 in the solvents denoted as s 1 and s 2 , respectively. An exact estimate of these parameters is rendered difficult in view of the electrostatic potential profiles and diverse nature of interfacial interactions. 10 However, one may anticipate that ΔG inter should be considerably diminished at the interface from the bulk value because desolvation of ions is a prerequisite for electron-transfer processes in general. However, the precise extent of desolvation of ions is not known at metal/electrolyte as well as at liquid/liquid interfaces. Consequently, we introduce a parameter SN Ox 1 inter /SN Ox 1 bulk that reflects the extent of desolvation of Ox 1 during its transport from bulk to the interfacial region. Analogous considera- tions apply for other species Ox 2 , Red 1 , and Red 2 . Assuming such a strategy to be valid, ΔG Ox 1 -s 1 inter and ΔG Red 2 -s 2 inter may be * Corresponding author. E-mail: mvs@chem.iitm.ac.in. [Fe(CN) 6 ] 3- + [Lu(biphthalocyanine)] 3+ T [Fe(CN) 6 ] 4- + [Lu(biphthalocyanine)] 4+ (1) [Fe(CN) 6 ] 3- + TCNQ - T [Fe(CN) 6 ] 4- + TCNQ (2) ΔG eq,sharp q ) (w r 1 + w p 1 )/2 + ΔG et 1 (3) w r 1 ) ΔG Ox 1 -s 1 inter + ΔG Red 2 -s 2 inter (4) 1660 J. Phys. Chem. B 2004, 108, 1660-1666 10.1021/jp036063w CCC: $27.50 © 2004 American Chemical Society Published on Web 01/09/2004