More commonly referred to as a quartz crystal microbalance (QCM), thickness-shear mode (TSM) quartz resonator devices utilize an acoustic wave to establish a bulk-detection mechanism prompting their utilization as gravimetric sensors with nanogram mass sensitivity and capability to measure various film property dynamics, due to variations in the system environment, of thin-films that are uniformly distributed across the resonator surface. The development of an absolute TSM-based nanobalance and an experimental technique using conventional TSM resonators for the real-time measurement of the change in the viscoelastic shear modulus and fractional free-hole volume of a poly(isobutylene) film due to the sorption of various organic vapors are presented in this thesis work. Development of an electrode-modified TSM quartz resonator that is responsive to nanogram mass loadings, while exhibiting a mass sensitivity profile that is independent of material placement on the sensor platform, is detailed in this thesis work. The resulting nanogram balance would greatly enhance the field of mass measurement and become useful in applications such as droplet gravimetry, the study of non-volatile residue (NVR) contamination in solvents. A ring electrode design predicted by an analytical theory for sensitivity distribution to achieve the desired uniform mass sensitivity distribution is presented in this work. Using a microvalve capable of depositing nanogram droplets of a polymer solution, and a linear stepping stage for radial positioning of these droplets across the sensor platform, measurements of the mass sensitivity distributions were conducted and are presented. The measurements agree well with theory. Further improvements are possible and are identified to achieve better uniformity and to reduce the instability in the resonant frequency of these devices. Additionally, droplet gravimetric results for NVR in methanol droplets using the modified TSM devices are presented, which compare well with determinations made by evaporation of larger volumes of the stock solutions. Storage modulus, G', loss modulus, G", and, consequently, the shear modulus, G (G=G'+jG"), of polymer and polymer/solvent systems were measured in this work using a TSM quartz resonator. The polymer poly(isobutylene) was spin-coated as a film of a few microns thickness on the surface of the TSM device and, upon inducing oscillation of the device at its resonance frequency (several mega-Hertz), the impedance characteristics were measured. In addition, the poly(isobutylene) film was exposed to known weight concentrations, up to 20%, of benzene, chloroform, n-hexane, and dichloromethane vapors diluted in nitrogen gas, and the impedance characteristics were measured. Data collected from the impedance analyzer were examined by modeling the polymer and polymer/solvent loaded TSM device with an electrical equivalent circuit and a mechanical perturbation model to reliably yield the shear modulus. Using a superposition theory and the shear modulus, the fractional free volume of the polymer/solvent systems were determined. These results correlate well with values found using the Vrentas-Duda free-volume (FV) theory. A novel experimental technique for measuring fractional free-hole volumes of polymer/solvent mixtures is established in this thesis work.