Chapter

The Quartz Crystal Microbalance in Soft Matter Research

Part of the series Soft and Biological Matter pp 143-168

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The Small Load Approximation Revisited

  • Diethelm JohannsmannAffiliated withInstitute of Physical Chemistry, Clausthal University of Technology Email author 

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Abstract

The chapter contains two extensions of the SLA. The first (Sect. 6.1) generalizes the SLA to arbitrary resonator shapes and modes of vibration. The load impedance in this formulation is a 3rd-rank tensor. The formalism shows that the statistical weight in area-averaging is the square of the local amplitude. The second extension (Sect. 6.2) is a perturbation analysis, applied to the model of the parallel plate. The perturbation is carried to 3rd order. The 3rd-order result fixes an inconsistency obtained when treating viscoelastic thin films in air with the conventional SLA.