Solvent Reorganization Energy and Free Energy Change for Donor/Acceptor Electron Transfer at Micelle Surfaces:  Theory and Experiment

Abstract

Theories are presented for calculating the solvent reorganization energy and the free energy change which occur in photoinduced donor/acceptor electron transfer at the surface of micelles. The theories are based on the Marcus theory for spherical reactants in a dielectric continuum. The micelle is modeled with regions of differing dielectric properties, representing the micelle core, the headgroup region, and the surrounding water. The free energy change accompanying electron transfer can be calculated from redox measurements made in bulk liquids. The theories are applied to previously published photoinduced intermolecular electron-transfer data between octadecylrhodamine B (ODRB) and N,N-dimethylaniline (DMA) molecules.1 The ODRB and DMA molecules are located in the surface region of three different types of surfactant micelles: dodecyl-, tetradecyl-, and cetyl-trimethylammonium bromide (DTAB, TTAB, and CTAB, respectively). The data show an increased rate of electron transfer with increasing micelle radius. Application of the new theory to the electron-transfer data along with information provided by neutron scattering experiments show that the headgroup regions of the three micelles have different dielectric constants because water penetration into the headgroup regions decreases as the surfactant length increases.

Photoinduced Excited State Electron Transfer at Liquid/Liquid Interfaces

“…This can be estimated using the Rehm-Weller equation, which requires excitation energy and redox potentials and assumes spherical ions in a continuum electrostatic model. 127 (As an example for using this approach see 59 ). As will be demonstrated below, the assumption of spherical ions in a continuum electrostatic 28 solvent is quite poor here.…”

“…The terms u PS and u RS are the total interaction energies between all the solvent molecules (water and DMA molecules, excluding the one DMA molecule selected to be the electron donnor) and the product (P) molecules and reactant (R) molecules, respectively; u IP is the interaction between the ion pairs DMA + /C314 -held at a fixed separation R (this quantity is estimated to be −1/εR, with ε being the dielectric constant of the medium in the Rhem-Weller expression); and δE 0 is the gas phase energy difference equal to the difference between the ionization potential of the donor and the electron affinity of the acceptor, minus the energy corresponding to the wavelength where the emission and absorption spectra cross. 59,127 From Eq. 10 and 11 we obtain:…”

“…[57][58] Tavernier et al used a continuum electrostatic model to calculate the reorganization free 4 energy and the reaction free energy for a redox pair at the surface of model spherical micelles. 59 Recently, a phenomenological thermodynamic approach based on partial desolvation of ions at interfaces has been used to estimate the activation free energy for two different reactions, assuming either a sharp boundary model 60 or a diffuse model for the interface structure. 61 We used molecular dynamics simulations and the umbrella biasing technique developed by Warshel 62 to calculate the reorganization free energy for ET at a model L/L interface 63 and at the water/DCE interface 64 in order to assess the accuracy of the continuum electrostatic model.…”

Photoinduced Intermolecular Electron Transfer in Micelles: Dielectric and Structural Properties of Micelle Headgroup Regions

“…Similarly, the third term is the contribution from the surrounding water, minus the contribution from the shell dielectric over that region. Analytical solutions to the integrals have been presented previously 8,68 and can be found in Appendix A. The Marcus expression for λ o in a continuum solvent can be obtained by taking the first term in eq 4 and removing the Kharkats corrections 69 for donor and acceptor volumes.…”

“…8,15,20,[40][41][42][43][44][45] The difference between the donor and acceptor standard potentials (∆E°), standard free energy of transfer (∆G), and reorganization energy (λ), shown in Figure 2, determine the energetics of the reaction. These quantities are determined by solute energy levels, local dielectric properties, and molecular sizes and charges.…”