General Approach to Model the Surface Charge Induced by Multiple Surface Chemical Reactions in Potentiometric FET Sensors

Abstract

We propose a general methodology to calculate the individual sensitivity and the cross-sensitivities of potentiometric sensor devices (e.g. ISFETs, CHEMFETs) with an arbitrary number of non-interacting receptors binding to ionic species or analytes in the electrolyte. The surface charge generated at the (bare or functionalized) interface with the electrolyte is described by Poisson equation coupled to a linear system of equations for each type of receptor, where the unknowns are the fractions of sites binding with a given ion/analyte. Our general model encompasses in a unique framework a few simple special cases so far separately reported in the literature and provides for them closed-form expressions of the average site occupation probability. Detailed procedural description of the usage and benefits of the model is shown for specific cases with concurring surface chemical reactions.

General Model and Equivalent Circuit for the Chemical Noise Spectrum Associated to Surface Charge Fluctuation in Potentiometric Sensors

“…1. Note that, differently from our previous work on steady state analysis [35], here it is possible to have loops in the transition diagram representation.…”

“…We assign the occupation probabilities f L and f LA as well as the net signed number of elementary charges z L and z LA , respectively, to the unbound (L) and bound (LA) states of the ligands, which are the only two possible configurations [35]. Obviously f L = 1 − f LA , so that only one occupation probability has to be computed.…”

“…Other extensions of this models are possible. For example, the generalization to different clusters of identical sites each responding to a different surface reaction set can be addressed as done in [35]. Conversely, the further extension to nonidentical sites responding to the same surface reaction set, but with different reaction rates (situation that gives non-Lorentzian spectral profiles [21]) would require defining a discrete set of reaction constants, i.e.…”

“…Similarly to the previous case of one chemical reaction, the following study of the noise requires solving a set of rate equations (called master equation), coupled by the kinetics of the chemical reactions. As pointed out in [33], [35] if each site has N possible states, N −1 chemical reactions can be identified among them. Let us denote f i the occupation probability of a generic state and r ij the reaction connecting state i with j, as illustrated in Fig.…”

“…The out-of-equilibrium state probabilities f i are timedependent. The contribution to the master equation of the reaction r ij can be expressed as: 1 "States" are defined as a particular complexation form of a site [35].…”