S1: Hardware considerations

DStat relies on three op-amps: the control and buffer amplifiers in the potentiostat (U1 and U2 in Fig. 2(c) in the main text) and the transimpedance amplifier in the current measurement circuit (U3 in Fig. 3(b) in the main text). In DStat, these amplifiers are the LMP7702 (Texas Instruments, Dallas TX, USA) for control and buffer and LMP7721 (Texas Instruments) for transimpedance, respectively. These models were carefully selected on the basis of a number of criteria. To keep polarization error small, the buffer was chosen to have a minuscule input bias current (~200 fA; a function of its CMOS input stage), allowing it to maintain a negligible reference electrode current. To avoid problems with potential inaccuracies, control and buffer amplifiers with large open loop gains and small voltage noise densities and input voltage offsets were selected, as a closed loop gain error exists that is the reciprocal of the open loop gain (for an inverting amplifier with gain of -1), and potential accuracy is also affected by the amplifiers’ voltage noise densities and input voltage offsets. Additionally, the control and buffer amplifiers’ bandwidths should be sufficiently high to accommodate the potential roles of the potentiostat—a bandwidth of a few hundred kilohertz may be ample for typical experiments at macroelectrodes, but several megahertz may be required for fast scanning experiments or electrochemical impedance spectroscopy. In DStat, the LMP7702 fulfils the requirements for both amplifiers while reducing design complexity by containing two amplifiers in the same physical package. Further, the LMP7702 has an open loop gain of approximately 106, an input bias voltage of±32 μV, and an input referred voltage noise density of 9 nV/ √ Hz (at 1 kHz), allowing potential accuracy to tens of microvolts, and with a unity gain bandwidth of 2.5 MHz, potential control can be maintained at high enough frequencies for DStat’s intended uses. In the transimpedance measurement circuit, the input bias current of the op-amp is summed with the current at the working electrode input and can cause a large offset error, especially at high gain. For example, a simple op-amp such as the Texas Instruments LM741 can have an input bias current as high as 500 nA, a non-trivial error for low-current voltammetry; if this amplifier were used, the measurement circuit would cause output saturation at gains over 3 MΩ (for a ±1.5 V output range) without an applied current, making measurements impossible. Further, input bias current can vary significantly between opamps of the same model, which complicates calibration, and electronic compensation requires manual tuning, increases noise, and may not be able to fully remove input bias current. To overcome these challenges, we chose the internally-compensated LMP7721, which has an extremely small input bias current of 3 fA ( ~1 electron every 53 μs), effectively eliminating bias current error.