Development of humidity correction algorithm for surface acoustic wave sensors. Part 2. Mathematical model for water and nitrobenzene co-adsorption on aminopropyltriethoxysilane coated surface acoustic wave sensors

Abstract

Nitrobenzene and water adsorption isotherms were obtained on an aminopropyltriethoxysilane coated surface acoustic wave sensor (SAWS) at < 5, 17, 33 and 47% relative humidity ( RH) at 6, 13, 25 and 47 °C. The nitrobenzene isotherms were BDDT type 1 (Langmuir) and water isotherms BDDT type 3. The nitrobenzene isotherms were fitted to a series of algorithms based on Langmuir theory and the coefficients of the algorithms derived from the experimental data. The derived model was then used to predict the original isotherms, achieving a good match (better than the ± 12% predicted by error analysis) in the mid-ranges, increasing to as much as minus 35% at 6 °C, 47% RH approaching the saturation vapour pressure of nitrobenzene, and minus 20% at 47 °C, 47% RH approaching the isotherm plateau region. The theoretical model indicates that the nett heat of adsorption of nitrobenzene (isosteric heat of adsorption minus enthalpy of condensation) is the critical parameter affected by RH and temperature. The effect of this on the heat of adsorption is however not readily quantifiable and the corrections needed to model the isotherms had to be derived empirically, rather than based on those two thermodynamic quantities. The results of the work underline the necessity to compensate for changes in RH and temperature, and indicate important selection criteria for coatings to be used with not only an SAWS, but any other sensor which relies on vapour adsorption as part of its response mechanism.