Characterization of porous thin films using quartz crystal shear resonators

A new model for the characterization of porous materials using quartz crystal impedance analysis is proposed. The model describes the equivalent electrical and/or mechanical impedance of the quartz crystal in contact with a finite layer of a rigid porous material which is immersed in a semi-infinite liquid. The characteristic porosity length (xi), layer thickness (d), liquid density (rho), and viscosity (eta) are taken into account. For films thick 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 quartz 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 contact 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 higher viscosity, the effect of the fluid trapped by the porous matrix is apparent 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 movement 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 allows 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-known 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.