Optimised determination of viscoelastic properties using compliant measurement systems

An analysis of a novel indentation model has been implemented to obtain master curves describing the optimal experimental parameters necessary to achieve the highest possible accuracy in the determination of viscoelastic properties of soft materials. The indentation model is a rigid indenter driven by a compliant measurement system, such as an atomic force microscope or optical tweezers, into a viscoelastic half space. The viscoelastic material is described as a multiple relaxation Prony series. The results have been extended via an application of a viscoelastic equivalence principle to other physical models such as poroelasticity. Optimisation of the indentation parameters has been conducted over many orders of magnitude of the velocity, viscoelastic moduli, spring stiffness, relaxation times and the duration of indentation resulting in a characteristic master curve. It is shown that using sub-optimal conditions gives the appearance of a more elastic material than is actually the case. For a two term Prony series the ideal ramp duration was found to be approximately one eighth of the relaxation. Also the ideal ramp duration for a three term Prony series was determined and shown to guarantee distinct relaxation times under specific conditions.