The getter effect in the Langmuir regime

The concentration of an analyte in a closed test chamber containing a chemical sensor is affected by the adsorption-desorption processes acting on the sensor surface. This phenomenon is called the "getter" whose effect has been known for many decades to occur in, e.g., vacuum tubes even if its mathematical expression has not been elaborated upon so far for affinity based chemical sensors. In this paper, we describe the "getter" equation and its consequences for affinity based chemical sensors in both the gas phase and the liquid phase with the starting point in the standard kinetic equation leading to Langmuir-like adsorption isotherms. More specifically, we calculate the "getter" isotherm and compare it with the Langmuir isotherm. The getter phenomenon is shown to be important at sufficiently small analyte concentrations (partial pressure in the gas phase or molecular concentration in the liquid phase) and in test chambers or sample cells of small volumes. A simple rule of thumb is given when the "getter" effect may be important. As an example, for a sample cell with a volume of 1 ml and a sensor surface area of 1 cm2 without a constant flow of analyte through it, the "getter" phenomenon may occur around parts per million levels for a gas sensor and around submicromolar concentrations for a sensor in a liquid. Experimental examples from the literature where the "getter" effect is observed will be given. We also show a more general electric equivalent circuit which accounts also for the getter effect by using a coverage dependent series resistance in the equivalent circuit previously suggested for Langmuir adsorption under constant partial pressure/concentration in the test chamber.