System and method for self-calibrating of ion selective electrodes based on differential voltage measurement

A system of temperature self-calibrating ion-selective electrodes (ISEs) for determining one or more field parameters, comprising:

• at least two ISEs and a reference electrode (RE);
• one electronic buffer coupled to each of the at least two ISEs and adapted to generate a voltage associated with each of the at least two ISEs and with respect to voltage of the RE;
• an analog to digital converter (ADC) coupled to each of the electronic buffers and configured to convert analog signals to digital signals;
• a processing unit executing software held in a non-transitory memory and coupled to the ADC and configured to receive the digital signals from the ADC and further configured to:
• calibrate the at least two ISEs and the RE, wherein the calibration includes placement of the at least two ISEs in a calibration solution with a predetermined concentration of target ions as a temperature of the calibration solution varies according to a known schedule, wherein the calibration of the at least two ISEs includes determining calibration parameters of each of the at least two ISEs with respect to the RE;
• determine the one or more field parameters by:
• placement of the at least two calibrated ISEs and the RE into a field solution;
• determine voltage across a first ISE of the at least two calibrated ISEs and the RE (VFi);
• determine voltage across a second ISE of the at least two calibrated ISEs and the RE (VF(i+1);
• and
• determine difference of VFi and VF(i+1);
• to thereby determine the one or more field parameters,
• wherein the calibration of the at least two ISEs by the processing unit includes:
• measure voltage across each of the at least two ISEs and the RE after placing each of the at least two ISEs with the RE separately or together in the calibration solution;
• establish at least two predetermined temperatures for the calibration solution;
• curve fit the measured voltage against temperature into a linear function;
• and
• determine slope and intercept of the linear function to thereby establish the calibration parameters of each of the at least two ISEs with respect to the RE,
• wherein the calibration parameters of each of the at least two ISEs with respect to the RE include mi−mref and Ci−Cref, wherein mi and Ci are parameters that depend on physical and chemical properties of the at least two ISEs, and mref and Cref are parameters that depend on physical and chemical properties of the RE, and
• wherein the slope and the intercept of the linear function is determined based on
• V=(kB/zcq ln(nc)+mi−mref·Tc+(Ci−Cref),
• where kB is the Boltzmann's constant with a value of 1.3807×10−23 joules per kelvin,
• q is the elementary charge with a value of 1.60217663×10−19 coulombs,
• Tc is the temperature of the calibration solution in Kelvin according to the known schedule,
• Zc is a charge number of the calibration solution, and
• nc is the predetermined concentration of target ions in the calibration solution in moles per volume, where the slope of the linear function represents (kB/zcq ln(nc)+mi−mref) as a quantity to be determined for each of the at least two ISEs, the intercept of the linear function represents (Ci−Cref) as a quantity to be determined for each of the at least two ISEs, and i represents an index associated with the at least two ISEs.