The Fractional Free Volume of the Sorbed Vapor in Modeling the Viscoelastic Contribution to Polymer-Coated Surface Acoustic Wave Vapor Sensor Responses

Surface acoustic wave (SAW) vapor sensors with polymeric sorbent layers can respond to vapors on the basis of mass loading and modulus decreases of the polymer film. The modulus changes are associated with volume changes that occur as vapor is sorbed by the film. A factor based on the fractional free volume of the vapor as a liquid has been incorporated into a model for the contribution of swelling-induced modulus changes to observed SAW vapor sensor responses. In this model, it is not the entire volume added to the film by the vapor that contributes to the modulus effect; it is the fractional free volume associated with the vapor molecules that causes the modulus to decrease in a manner that is equivalent to free volume changes from thermal expansion. The amplification of the SAW vapor sensor response due to modulus effects that are predicted by this model has been compared to amplification factors determined by comparing the responses of polymer-coated SAW vapor sensors with the responses of similarly coated thickness shear mode (TSM) vapor sensors, the latter being gravimetric. Results for six to eight vapors on each of two polymers, poly(isobutylene) and poly(epichlorohydrin), were examined. The model predicts amplification factors of the order of about 1.5−3, and vapor-dependent variations in the amplification factors are related to the specific volume of the vapor as a liquid. The fractional free volume factor provides a physically meaningful addition to the model and is consistent with conventional polymer physics treatments of the effects of temperature and plasticization on polymer modulus.