An Algebraic Approach for Determining Viscoelastic Moduli From Creep Compliance Through Application of the Generalised Stokes-Einstein Relation and Burgers Model

Abstract

DLS Microrheology involves tracking the time dependent motion or mean square displacement of dispersed tracer particles of known size using Dynamic Light Scattering (DLS) in order to determine viscoelastic properties of the dispersion medium. The viscoelastic moduli are calculated using a generalised form of the Stokes-Einstein equation which requires Fourier Transformation of the MSD. An alternative approach for estimating the viscoelastic moduli uses a modified algebraic form of the generalized Stokes-Einstein equation, which employs a power law expression to describe the local change in MSD with time. Since the mean square displacement is linearly related to the creep compliance, it can be shown that the same algebraic approach can also be applied to creep measurements made on a rotational rheometer, giving access to the low frequency moduli in a fraction of the time required for oscillatory testing. Furthermore, the quality of the conversion process can be improved by fitting a Burgers model to the time domain data prior to conversion thus minimising errors associated with local differentiation, which is fundamental to the conversion approach.

Keywords

• burgers model
• creep compliance
• microrheology
• viscoelastic modulus
• low frequency
• interconversion