Hole-limited electrochemical doping in conjugated polymers

Simultaneous transport and coupling of ionic and electronic charges is fundamental to electrochemical devices used in energy storage and conversion, neuromorphic computing and bioelectronics. While the mixed conductors enabling these technologies are widely used, the dynamic relationship between ionic and electronic transport is generally poorly understood, hindering the rational design of new materials. In semiconducting electrodes, electrochemical doping is assumed to be limited by motion of ions due to their large mass compared to electrons and/or holes. Here, we show that this basic assumption does not hold for conjugated polymer electrodes. Using operando optical microscopy, we reveal that electrochemical doping speeds in a state-of-the-art polythiophene can be limited by poor hole transport at low doping levels, leading to substantially slower switching speeds than expected. We show that the timescale of hole-limited doping can be controlled by the degree of microstructural heterogeneity, enabling the design of conjugated polymers with improved electrochemical performance.

Simulations were performed using a finite difference method.The potential was initialised as a linear drop at the polymer/electrolyte interface to simulate the depletion region.The motion of ions over each time increment was calculated using the following 1D drift-diffusion equation for cation flux.Where Jcat is the cation flux at each position x, µcat is the cation mobility in PEDOT:PSS, [Cat] is the cation concentration at each position x, dV/dx is the electric field at each position x, and Dcat is the diffusion coefficient of cations in PEDOT:PSS which was approximated using the Einstein relation (Dcat = 0.0259 V x µcat).The change in [Cat] at each space increment (x) along the length (L) was calculated using Equation S2 as follows.The relative change in transmission (∆T/T0) of PEDOT:PSS is on the order of 20%, thus the linear approximation (Beer's Law) can be made (the visible light absorption is linearly proportional to the concentration of neutral PEDOT chains).Thus, the relative change in transmission (∆T/T0) was estimated using the concentration of absorbing neutral chains, which is inversely proportional to p as described in Equation S5.
Finally, the transmission was rescaled to set the minimum ∆T/T0 to 0 and maximum ∆T/T0 to 1 for comparison with the experimental results.
A summary of the physical constants used in the simulation is summarised in Table S1.
Supplementary Note 2: Estimation of carrier density change during hole-limited doping.
During the Type I doping front, the transmission intensity ∆T/T0 of the doped region reaches approximately 10%, and ∆T/T0 in the fully doped state is approximately 44 %.To estimate the final doping level, we can integrate the voltage-dependent volumetric capacitance from the initial voltage (VWE,i = -0.4V vs. Ag/AgCl) to the final voltage (VWE,f = 0.6 V vs. Ag/AgCl) giving a differential charge density of 146 C cm -3 , or hole concentration of approximately 9.1×10 20 cm -3 .If we use a single absorption cross section to model the broadband transmission in this system, we expect the differential transmission to scale according to the following Equation S6.
Where ∆p is the differential charge carrier density and  is the absorption cross section of the neutral CP chains, and L is the path length through the film which remains fixed.Thus, we can estimate that the Type I doping front corresponds to doping to approximately 2.4×10 20 cm -3 .Using this value of charge density in Poisson's equation, the maximum length of film which could be doped to this level without compensating anionic charges is approximately 1.7×10 -7 cm, 5 orders of magnitude smaller than the length of the device (L = 5×10 -2 cm).Thus, we can assume that the induced holes measured optically in the Type I doping front are compensated with equal and opposite ionic charge.

Supplementary Note 3: Internal electric fields during Type I and Type II doping.
During doping and dedoping front experiments, the internal electric fields across the material will evolve with time due to the different charge carrying species.In this section, we discuss how the optical data can be used to infer the internal fields.
First, we discuss the assumptions made for this analysis.The first assumption we make is that ionic carriers can cross the polymer-electrolyte interface (left side) freely and cannot cross the polymer-ITO interface (right side).Conversely, electronic carriers can freely cross the polymer-ITO interface and cannot cross the polymer-electrolyte interface.Second, we assume that changes in ∆T/T0 are electroneutral at the length scale probed by our optical measurements as discussed in Supplementary Note 2. Thus, wherever the derivative dT/dt peaks is where the ion and hole currents converge in space.This assumption also results in a constant current density along the length of the polymer.Finally, we assume that charge neutrality can be broken at the Debye length which will result in nonlinear potential drops along the length of the film according to the electrostatic 1D Poisson's equation (Equation S7).
2 () V and x are the potential and distance along the length of the polymer, respectively, Canion, Ccation, and p are the concentrations of anions, cations, and holes along the length of the polymer, respectively, e is the elementary charge, and  0 and   are the permittivity of free space and relative dielectric constant, respectively.
When the potential is initially applied to the ITO contact and before charges move, from Equation S7 we would expect a linear potential drop along the length of the polymer since the  2 ()  2 must be 0.Then, as charges drift, the electric field will evolve such that most of the potential drop is across the highest resistance element in the circuit following Ohm's law.For doping and dedoping of PEDOT:PSS, holes are highly mobile and thus the conductivity of holes is higher than that of ions, so the potential drop occurs primarily across the ionic part of the circuit resulting in an initial peak in the derivative at that interface (Fig. 2b).The potential of the electrolyte is fixed so the potential flattens over time resulting in diffuse doping/dedoping characteristics (Fig. 2a) Unlike doping/dedoping in PEDOT:PSS, during doping of p(g1T2-g5T2), dT/dt initially peaks near the ITO contact.Thus, we can infer that the initial ion drift current must exceed the initial hole drift current.Rather than broadening with time, the peak originating near the ITO contact moves across the length of the film linearly and the intensity remains nearly constant.This result indicates that, with time, the convergence point and of Jion and Jh moves towards the electrolyte as doping proceeds, but the doping rate (dT/dt) is invariant with time and as the length of the moderately doped (poorly doped) region increases (decreases).That is, Jion is equal to Jh and both remain constant with time.If the rate of doping were limited by transport of ions from the electrolyte to the region of doping, the rate of doping would accelerate as the distance ions must travel decreases.Similarly, if the doping rate were limited by hole transport through the moderately doped region, the doping rate to slow down as the distance holes must travel increases.Thus, we can conclude that the process limiting the speed of doping occurs at the boundary between the moderately doped and the poorly doped parts of the film, and the drop in potential should be largest at this rate-limiting boundary.
From our characterization of µh as a function of potential (and therefore doping level), we know there is a sharp transition in µh between carrier concentrations of approximately 1×10 20 cm -3 (-0.2 V vs. Ag/AgCl) and 2.4×10 20 cm -3 (0.0 V vs. Ag/AgCl).The doping level reached during Type I doping is within this sharp µh transition.Therefore, we attribute the transport of holes from the doped (conductive) region of the film into the poorly doped (nonconductive region) as the rate limiting step.We also note that once the entire polymer film is moderately doped (when the Type I doping front reaches the polymer-electrolyte interface), the rate of doping increases substantially as observed by the peak in dT/dt at approximately 3 s (Fig. 2f).
The results from turning on of OECTs are also consistent with the explanation above (Fig. 4).During the hole-limited doping regime, the gate-source current is constant with time, consistent with doping being limited at the interface between the moderately doped and poorly doped regions of the polymer (Fig. 4f).Additionally, the doping front moves away from the source and drain towards the centre of the channel linearly with time (Fig. 4d).The measured potential drops along an OECT channel confirm a delay in the rise of the potential measured further away from the source electrode (Extended Data Fig. 8), indicating that the region of largest potential drop follows the propagation of the doping front from the source electrode towards the drain electrode (Fig. 4c and Fig. 4d).
To better understand the driving forces for ion and hole motion during doping front experiments, we measured the internal potential drops along the length of p(g1T2-g5T2) channel (L = 2.5 mm, W = 0.4 mm) using inserted voltage probes (0.5 mm spacing) along the channel as schematically depicted in Extended Data Fig. 3a (note that the gate is not drawn to scale).Briefly, the sample was prepared by making OECTs with inserted voltage probes (30 µm width) using the same methodology described in the methods section followed by spin coating of polystyrene from a 20 mg/mL solution in toluene.Then, a sharp tweezer was used to scratch a trench for exposing the film to the electrolyte at the position of the 5 th voltage probe, approximately 2.5 mm from the gold contact.Potentials were measured at each probe (V1-4) using a 4-channel oscilloscope (Keysight DSOX1204G) while a source-measure unit (Keysight B2902A) was used to apply a pulse between the Ag/AgCl gate and the gold contact.We note that the voltage probes measure the electrochemical potential of holes with respect to the grounded gold contact at the end of the channel, which includes contributions due to the local electric potential as well as shifts in the Fermi level resulting from doping.The resulting internal potential profiles in the hole-limited doping regime show that initially, the entire channel rapidly reaches the potential of the electrolyte, indicating a voltage drop primarily between the hole injecting gold contact (which is grounded) and the polymer (Extended Data Fig. 3b).As the Type I doping front proceeds, the potential at each probe increases starting with the probe nearest the hole injecting gold contact (V4) to the probe nearest the electrolyte (V1), indicating that the region of largest potential drop moves from the grounded gold contact and propagates towards the electrolyte.This result is highlighted by the darker colour traces.In contrast, during Type II doping (VG from -0.3 V to -0.6 V), the internal potential of the entire channel drops rapidly to the change in electrolyte potential (-0.3 V) (Extended Data Fig. 3c).Then, the potential at all of the probes increases simultaneously while maintaining a linear profile, leaving the largest potential drop between the electrolyte and channel.This is also observed in the time dependent voltage measurements at each probe (Extended Data Fig. 3dg) (time = 0 ms denotes the time when a potential is applied), where the onset of potential increase is delayed from the time of applied voltage only in the hole-limited doping regime (Extended Data Fig. 3f).The timescales of this experiment vary from the optical experiments, likely due to substantial differences in sample preparation.

∆
[]()( +   ) =   (   ( − ) −   ())/ (Equation S2)Where tstep is the length of the time increments and dx is the length of the space increments.The change in concentration of holes (∆p) was calculated by conserving local charge neutrality according to Equation S3. was recalculated using the volumetric capacitance C * of PEDOT:PSS which was held constant for the simulation (C * = 40 F cm -3 ) using Equation S4.