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 $92\%$.

有机电化学晶体管（OECT）是可以测量液体样品和生物系统中离子含量的设备。OECT的响应可以提供有关生理状况和生物系统特征的信息。在典型的OECT配置中，系统或样品连接到参考电极（栅极）和半导电材料（通常为PEDOT：PSS），另外两个端子（漏极和源极）用于连接到外部电路。OECT的晶体管架构可实现信号控制和放大。在电极上施加外部电磁场后，离子会从液体样品中流向PEDOT：PSS通道，在此离子会修改通道的电导率并根据时间生成连续电流。该电流的强度和达到稳态的时间可以与溶液中离子的特性相关。在对OECT行为进行建模的大多数现有理论中，都假定设备的内部配置和几何参数随时间是恒定的。这种简化的假设破坏了生命系统以及所有这些系统具有较高柔顺性和吸收性的柔软设备（例如纸上，纺织品或聚合物海绵上的设备）。类似的简化模型可能无法在可接受的范围内预测实际系统的行为。在这里，我们提供了一个数学模型，该模型描述了OECT的行为，其中系统内部流体回路的几何形状会随时间变化。这些电路代表腔室和通道的网络，液体溶液通过这些腔室和通道从栅极流到漏源电极，从而实现了离子的传输。在一定时间，液体溶液应仅散布在整个可用于液体运输的网络中的一部分，即湿部分$p$。我们在这项工作中开发的数学模型使用OECTs生成的数据来确定湿分数$p$ 和浓度 $C$离子的数量。该模型无需对设备进行校准就可以对系统进行量化，这对于从事生物工程，生物医学传感器，可穿戴电子设备，柔性电子设备领域的人们可能是感兴趣的。在系统变量在较大间隔内变化的实验中，该模型具有出色的性能和高达$92％$。