Characterization of porous thin films using quartz crystal shear resonators

A new model for the characterization of porous materials using quartz cryst al impedance analysis is proposed. The model describes the equivalent elect rical and/or mechanical impedance of the quartz crystal in contact with a f inite layer of a rigid porous material which is immersed in a semi-infinite liquid. The characteristic porosity length (xi), layer thickness (d), liqu id density (rho), and viscosity (eta) are taken into account. For films thi ck compared with the characteristic porosity length (d much greater than xi ), the model predicts a net increase of the area which is translated into a linear relationship between the quartz equivalent impedance Z = R + XL (XL = i omega L, omega = 2 pi f, f being the oscillation frequency of the quar tz resonator) and the ratio d/xi. For low-viscosity Newtonian liquids, for which the velocity decay length d = (2 omega eta/rho)(1/2) is much smaller than xi, Z corresponds to the impedance of a semi-infinite liquid in contac t with an increased effective quartz area which scales with the ratio d/xi. In this case, R = XL in agreement with Kanazawa equation. For liquids of h igher viscosity, the effect of the fluid trapped by the porous matrix is ap parent and is reflected in the impedance, which has an imaginary part (XL) higher than its real part (R). In the limit of a very viscous liquid, the m ovement of the porous film is completely transferred to the liquid and all the mass moves in-phase with the quartz crystal electrode. In this limiting case the model predicts a purely inductive impedance, which corresponds to a resonant frequency in agreement with the Sauerbrey equation. The model a llows us, for the first time, to explain the almost linear behavior of R vs XL along the growth process of conducting polymers, which present a well-k nown open fibrous structure. Films of polyaniline-polystyrenesulfonate were deposited on the quartz crystal under several conditions to test the model , and a very good agreement was found.