Thermodynamics of organic electrochemical transistors

Abstract

Despite their increasing usefulness in a wide variety of applications, organic electrochemical transistors still lack a comprehensive and unifying physical framework able to describe the current-voltage characteristics and the polymer/electrolyte interactions simultaneously. Building upon thermodynamic axioms, we present a quantitative analysis of the operation of organic electrochemical transistors. We reveal that the entropy of mixing is the main driving force behind the redox mechanism that rules the transfer properties of such devices in electrolytic environments. In the light of these findings, we show that traditional models used for organic electrochemical transistors, based on the theory of field-effect transistors, fall short as they treat the active material as a simple capacitor while ignoring the material properties and energetic interactions. Finally, by analyzing a large spectrum of solvents and device regimes, we quantify the entropic and enthalpic contributions and put forward an approach for targeted material design and device applications.

Fig. 1. Thermodynamic vs classic model of the OECT capacitance.

a Typical setup for the IV measurement of an OECT using a non-polarizable Ag/AgCl pellet as a gate electrode. Such setup is used throughout this work too. b Redox reaction driving the operation of OECTs. The amount of oxidized and reduced PEDOT leads to the transfer curve sketched below. c Key difference between the FET-based model for OECTs and our thermodynamic model: the nonlinear charge accumulation resulting from the Gibbs free energy, in strong contrast with a linear accumulation typical of a capacitor.

Fig. 2. Thermodynamics of OMIECs.

a Temperature and ϕ dependence of the Gibbs free energy (with H_mix = 0, using ${\mu }^{p^{+}}=-60\mathrm{meV/mol}$ and ${\mu }^{p^0}=0$). Higher temperatures shift the minimum towards ϕ₀ = 0.5 and to lower energies. b Measurement of the current flowing in a PEDOT:PSS thin-film at a different temperatures, in deionized water (DIW) and saltwater DIW:NaCl 100 mM (circles). Curves are fitted with a linear regression (solid lines). The experiment in DIW (see Methods for details) is used to estimate the contribution of the temperature-dependent mobility, which is then subtracted, leading to the blue dashed line. The same contribution is subtracted from the current measured in DIW:NaCl. The negative slope shows that, besides the increased mobility, the doping density is lowered. Note that at room temperature, the current drops by 8% with respect to when it is in distilled water (DIW), hence ϕ₀(T = 300 K) = 0.08. c Calculated concentration of reduced PEDOT⁰ and doped/oxidized PEDOT⁺ in the film at different temperatures.

Fig. 3. Thermodynamic model and fits.

a Step-by-step workflow of our thermodynamic analysis. Starting with the Gibbs energy G, the chemical potential μ can be obtained. These properties are material-specific and by measuring the resistance of the PEDOT/electrolyte system only the equilibrium can be probed. By applying an external field, the equilibrium is perturbed (yellow box), and the current-voltage characteristics can be obtained as explained in the main text and in Supplementary Note 2. The pink and blue spheres indicated a fully oxidized and fully reduced PEDOT phase, respectively. b Transfer characteristics of a PEDOT:PSS OECT with a channel of 100 mM aqueous NaCl solution at V_ds = −0.6 V and −0.3 V. The experimental curves (red circles) have been fitted (solid lines) with b the FET-based model (Bernards model), c with the thermodynamic model in the assumption of H_mix = 0, and d with the thermodynamic model including the enthalpy of mixing. The device features W = 50 μm, L = 200 μm, t = 200 nm. The parameters for the fits are: V_p = 0.57 V and Λ_hC = 40 F/cm/s/V for the FET model. For the scenario with H_mix = 0: ${\mu }^{p^{+}}+{\mu }^{p^0}=1\cdot 10^{-21}J$, Λ_h[PSS⁻] = 1.06 × 10²² C/cm²/s/V, T = 300K, and α = 0.2 (see Eq. Supplementary Eq. 14). When adding the enthalpy: h₁ = 0.20, h₂ = 0.18, h₃ = 0.20.

Fig. 4. Quantification of enthalpy.

Investigation of the chemical potential and free energy underlying the transfer characteristics of an OECT immersed in a 100 mM NaCl aqueous solution, b 100 mM KCl aqueous solution, c ionic liquid, d 100 mM LiClO₄ in butanol, and e 100 mM LiClO₄ in water. Experimentally determined curves with V_ds = 5 mV (circles) are fitted with the blue solid curves. The histograms on the right display the parameters used for the fits. In Supplementary Table 1 the values and the errors of the parameters used for the fits are reported, together with the fitting procedure. All energies are in k_BT units.