The Quartz Crystal Microbalance in Soft Matter Research

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


The Small Load Approximation Revisited

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

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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.