A mathematical model of OECTs with variable internal geometry

Organic Electrochemical Transistor (OECTs) are devices that can measure the ionic content of liquid samples and biological systems. The response of an OECT can provide information on the physiological conditions and characteristics of a biological system. In a typical OECT configuration, the system or sample is connected to a reference electrode (the gate) and to a semiconducting material, typically PEDOT:PSS, with two other terminals (the drain and the source) for connection to an external circuit. The transistor architecture of OECTs enables signal control and amplification. Upon application of an external electromagnetic field at the electrodes, ions are driven from the liquid sample towards the PEDOT:PSS channel, where they modify the conductivity of the channel and generate a continuous current as a function of time. The intensity of that current and the time to the steady state can be correlated to the characteristics of the ions in solution. In most of the existing theories that model the behavior of OECTs, the internal configuration and geometrical parameters of the device are assumed to be constant over time. This simplifying assumption breaks down in living systems and in all those soft devices with elevated value of compliance and absorption (such as devices on paper, textile or polymeric sponges). Similar simplified models may fail to predict the behavior of real systems within acceptable bounds. Here, we present a mathematical model that describes the behavior of OECTs in which the geometry of the internal fluidic circuits of the system can change over time. These circuits represent the network of chambers and channels through which the liquid solution flows from the gate to the drain-source electrodes, enabling the transport of ions. At a certain time, the liquid solution shall be spread throughout a fraction only of the entire network available for liquid transport, i.e. the wet fraction p. The mathematical model that we have developed in this work uses the data generated by OECTs to determine the wet fraction p and the concentration C of ions of a system. The model enables quantification of a system without calibration of the device, which may be of interest for those working in the fields of bioengineering, biomedical sensors, wearable electronics, flexible electronics. In experiments where the variables of system were varied over large intervals, the model achieved an excellent performance and a precision up to 92%.