Research ArticleELECTROCHEMISTRY

Chemical potential–electric double layer coupling in conjugated polymer–polyelectrolyte blends

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Science Advances  15 Dec 2017:
Vol. 3, no. 12, eaao3659
DOI: 10.1126/sciadv.aao3659
  • Fig. 1 Charging of CP-PE blends.

    (A) PEDOT:PSS comprises two phases—the PEDOT phase with electronic charge carriers in the form of (bi)polarons (holes) and the PSS phase with ionic charge carriers. The polarons are electrostatically stabilized by the negative sulfonate groups, with the spatial separation of the electronic and ionic charge carriers creating an EDL. (B) Energy diagram of a PEDOT:PSS electrode immersed in an electrolyte (PBS) with a Ag/AgCl reference electrode. VB, valence band; q, particle charge. The work function of pristine PEDOT is lower than that of gold, giving rise to an interface potential difference and heavy doping at Vapp = 0 V. The charging of the PEDOT-PSS interface creates an EDL, where the potential difference is approximately proportional to the hole concentration. (C) For Vapp = −0.9 V, the PEDOT is essentially de-doped, which increases the potential at the gold-PEDOT interface while the EDL is discharged. (D) The drift-diffusion–Poisson’s equations and boundary conditions for the system. A quasi-electric field term is included for the holes due to the shift in chemical potential. The Au-PEDOT boundary conditions are obtained by equating the Fermi level and setting the space charge to 0. The electrolyte boundary conditions are the bulk concentration (c0) and Vc = 0 V. (E) To measure the hole concentration dependence on the applied potential, Vapp was stepped from 0.3 V (blue circles) to −0.85 V (yellow circles) in 50-mV steps. The nonfaradaic charge of each step was obtained by subtracting the linear faradaic contribution. (F) The applied potential versus the measured hole concentration (○). Equation 12, which includes both the capacitive contribution of the EDL and the change in chemical potential, fits well (gray line). The previously reported purely capacitive model (16, 17) (red dashed line) deviates significantly at lower concentrations.

  • Fig. 2 Modeling of OECT characteristics.

    (A) The OECT comprises a PEDOT:PSS channel, gold source and drain terminals, and a Ag/AgCl gate electrode. (B) The model (line) was fitted to the measurement data (○) for a low drain voltage (−20 mV) to minimize the nonlinearity of the channel. The obtained mobility (inset) shows the expected dependency on hole concentration. (C) With the model parameters set, the measured transfer curves for VD = −0.3 V (○) and VD = −0.5 V (pentagons) could be accurately reproduced (lines). The curves show ideal organic field-effect transistor characteristics for VG in [−0.1, 0.3] V. (D) Hole concentration in the channel for VD = −0.5 V and VG = −0.3 V (blue line) to 0.7 V (yellow). The hole concentration is depleted at the drain contact for higher gate voltages. (E) Effective potential (Veff = Vp + μp/e) in the channel for VD = −0.5 V and VG = −0.3 V (blue line) to 0.7 V (yellow line). For higher gate voltages, most of the potential is dropped within the last micrometer of the channel next to the drain contact. (F) The output characteristics (○) are accurately reproduced (lines) with the same parameter set as for the transfer curves.

  • Fig. 3 Modeling of PEDOT:PSS electrode-electrolyte systems.

    (A) The PEDOT:PSS electrode is electrically connected through a gold contact, and the electrolyte is grounded with a Ag/AgCl reference electrode. (B) Potentials and concentrations for Vapp = 0 V (solid lines) and −0.7 V (dashed lines). The hole concentration (blue lines) markedly changes with the applied voltage, whereas relative changes in the cation (red lines) and anion (yellow lines) concentrations are small due to the high concentration of fixed charges (black line). The electrostatic potential in the PEDOT phase (blue lines) changes a lot, whereas the potential in the PSS and electrolyte phases (red lines) is nearly constant. (C) The model predicts the expected proportional relationship between stored charge and film thickness [50 nm (yellow line) to 500 nm (blue line)]. (D) The main features of the measured cyclic voltammograms (○, 1.0 V/s; ◊, 0.5 V/s; and Δ, 0.2 V/s) are predicted by the model. (E) By reducing the hole mobility, the commonly observed peaks in the forward scan direction can be reproduced. (F) The calculated EIS modulus and phase angles (lines) agree well with the measured data (○).

  • Fig. 4 Moving reduction fronts.

    (A) The encapsulated PEDOT:PSS film is electronically contacted to the left and ionically contacted to the right. At t = 0, the applied potential to the left is set to −2 V, which initiates the reduction of the film in contact with the electrolyte. The reduction front moves to the left with time and can be monitored optically. (B) The calculated hole concentration versus time. (C) The electrostatic potential in the PEDOT phase [Vp, 0 s (blue line) to 45 s (yellow line)] is quite flat due to the high mobility of the holes. The electrostatic potential in the PSS/electrolyte phase [Vc, 0 s (black line) to 45 s (green line)] varies more due to the slower ions. Most of the potential drop occurs in the electrolyte next to the film due to concentration polarization. (D) Comparison of the calculated and experimental [data from Rivnay et al. (13)] change in transmission. a.u., arbitrary unit.

  • Table 1 Variables, parameters, and constants.
    jiFlux of species iCvVolumetric capacitance
    pHole concentrationcfixPE fixed charge concentration
    c±Cation/anion concentrationVDDonnan potential
    VappApplied potentialeElementary charge
    VpCP electrostatic potentialεDielectric constant
    VcPE/electrolyte electrostatic potentialkBBoltzmann constant
    DpHole diffusion coefficientfF/RT
    D±Cation/anion diffusion coefficientFFaraday’s constant
    μpHole chemical potentialRMolar constant
    BParameter, see Eq. 1TTemperature, 300 K

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/12/eaao3659/DC1

    fig. S1. Chemical potential approximation.

    fig. S2. Charge measurements.

    fig. S3. OECT equations.

    fig. S4. Transport in OECTs.

    fig. S5. Example of the simulation of EIS data.

    fig. S6. Square-wave response.

    fig. S7. Concentration polarization at the electrolyte interface in moving front simulation [0 s (blue line) to 45 s (yellow line)].

    fig. S8. PEDOT:PSS transmittance at the 600-nm peak for varied potentials [adopted from Sonmez et al. (33)].

    fig. S9. CVs of 600-nm-thick PEDOT:PSS films.

    fig. S10. OECT fabrication scheme.

    table S1. Simulation parameter values.

  • Supplementary Materials

    This PDF file includes:

    • fig. S1. Chemical potential approximation.
    • fig. S2. Charge measurements.
    • fig. S3. OECT equations.
    • fig. S4. Transport in OECTs.
    • fig. S5. Example of the simulation of EIS data.
    • fig. S6. Square-wave response.
    • fig. S7. Concentration polarization at the electrolyte interface in moving front simulation 0 s (blue line) to 45 s (yellow line).
    • fig. S8. PEDOT:PSS transmittance at the 600-nm peak for varied potentials adopted from Sonmez et al. (33).
    • fig. S9. CVs of 600-nm-thick PEDOT:PSS films.
    • fig. S10. OECT fabrication scheme.
    • table S1. Simulation parameter values.

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