Normal and inverted regimes of charge transfer controlled by density of states at polymer electrodes

Abstract

Conductive polymer electrodes have exceptional promise for next-generation bioelectronics and energy conversion devices due to inherent mechanical flexibility, printability, biocompatibility, and low cost. Conductive polymers uniquely exhibit hybrid electronic-ionic transport properties that enable novel electrochemical device architectures, an advantage over inorganic counterparts. Yet critical structure-property relationships to control the potential-dependent rates of charge transfer at polymer/electrolyte interfaces remain poorly understood. Herein, we evaluate the kinetics of charge transfer between electrodeposited poly-(3-hexylthiophene) films and a model redox-active molecule, ferrocenedimethanol. We show that the kinetics directly follow the potential-dependent occupancy of electronic states in the polymer. The rate increases then decreases with potential (both normal and inverted kinetic regimes), a phenomenon distinct from inorganic semiconductors. This insight can be invoked to design polymer electrodes with kinetic selectivity toward redox active species and help guide synthetic approaches for the design of alternative device architectures and approaches.

Fig. 1

Redox reaction coupled with hybrid electronic–ionic transport at a polymer electrode. a Oxidation of the redox species at the polymer/electrolyte interface is enabled by potential-dependent oxidation of the polymer film coupled with intercalation of counter ions (A⁻) from the electrolyte and changes in polymer morphology (center circles). b Molecular structure of P3HT. c Cyclic voltammograms (scan rate of 50 mV s^-1) of an e-P3HT film in the deposition bath (solid black line) and in a solution of 1 mM FcDM and 0.1 M TBAHFP in acetonitrile (dashed red line)

Fig. 2

Distribution of unoccupied and occupied states in polymer and electrolyte. The DOS of an e-P3HT film derived from the experimental oxidation current in cyclic voltammetry (purple curve, bottom axis) is shown next to simulated distributions of occupied (Red) and unoccupied (Ox) states in the electrolyte according to Eq. (3) and an analogous expression for unoccupied states, assuming equal concentrations of red and ox (green curves, top axis). Simulation parameters were E ⁰(FcDM^0/+) ≈ E _1/2(FcDM^0/+) = +0.07 V vs. Ag/Ag⁺, λ = 0.5 eV, and T = 298 K. Occupancy of the P3HT DOS and hole transfer from polymer to the electrolyte are illustrated for the example of a Fermi level E _f at −5.5 eV at the surface of the polymer electrode

Fig. 3

Typical Nyquist plot of the impedance of e-P3HT in 1 mM FcDM solution at a bias voltage of 0.35 V. Labels indicate the angular frequencies ω at select points

Fig. 4

Charge-transfer resistance of e-P3HT in contact with ferrocenedimethanol solution. Experimental potential-dependent charge-transfer resistance obtained from fits of the impedance spectra (black symbols and line, with error bars indicating the fitting uncertainty), and simulation based on the Marcus–Gerischer model using the experimental DOS from cyclic voltammetry (red line). Simulation parameters (origins described in main text): A = 0.4 cm², k ^t = 1.6 × 10⁻²² cm⁴ s⁻¹, c ^red = 6 × 10¹⁷ cm⁻³, λ = 0.6 eV, E ⁰(FcDM^0/+) = +0.07 V vs. Ag/Ag⁺ or −4.94 eV vs. vacuum (indicated by dashed gray line), T = 298 K

Fig. 5

Effect of the distributions of electronic states in electrolyte and polymer on the charge-transfer resistance according to the Marcus–Gerischer model. a Experimental charge-transfer resistance (black symbols, with error bars showing the fitting uncertainty) and simulated charge-transfer resistances (colored lines) for varied reorganization energy λ of the electrolyte at fixed width σ = 0.18 eV of the Gaussian polymer DOS. b Experimental (black symbols with fitting uncertainty as error bars) and simulated (colored lines) R _ct for varied σ at fixed λ of 0.6 eV. Other simulation parameters were N = 10²¹ cm⁻³ (number of states per unit volume), E _ct = −5.45 eV (center of the Gaussian distribution), A = 0.4 cm², k ^t = 1.6 × 10⁻²² cm⁴ s⁻¹, c ^red = 6 × 10¹⁷ cm⁻³, E ⁰(FcDM^0/+) = +0.07 V vs. Ag/Ag⁺ (or −4.94 eV), and T = 298 K. The red curves correspond to a simulation using the reorganization energy of the best fit shown in Fig. 4 (λ = 0.6 eV) together with the Gaussian DOS width that best describes the experimental DOS of the polymer (σ = 0.18 eV)