We describe a quantitative method for using the quartz crystal microbalance (QCM) to characterize the high frequency viscoelastic response of glassy polymer coatings with thicknesses in the 5-10 μm regime. By measuring the frequency and dissipation at the fundamental resonant frequency (5 MHz) and at the third harmonic (15 MHz), we obtain three independent quantities. For coatings with a predominantly elastic response, characterized by relatively low phase angles, these quantities are the mass per unit area of the coating, the density-shear modulus product, and the phase angle itself. The approach was demonstrated with a model polyurethane coating, where the evolution of these properties as a function of cure time was investigated. For fully cured films, data obtained from the QCM are in good agreement with results obtained from traditional dynamic mechanical analysis.

Abstract. We introduce a natural extension of collapsible pushdown systems called annotated pushdown systems that replaces collapse links with stack annotations. We believe this new model has many advantages. We present a saturation method for global backwards reachability analysis of these models that can also be used to analyse collapsible pushdown systems. Beginning with an automaton representing a set of configurations, we build an automaton accepting all configurations that can reach this set. We also improve upon previous saturation techniques for higher-order pushdown systems by significantly reducing the size of the automaton constructed and simplifying the algorithm and proofs.

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