Determine complex viscosity using DLS microrheology

Abstract

Dynamic Light Scattering (DLS) based microrheology can be used to accurately measure the complex viscosity of protein solutions. The viscosity of bovine serum albumin BSA in phosphate buffered saline was determined with carboxylated melamine microspheres. The method uses the Generalized Stokes-Einstein Relation to find the mean square displacement MSD and complex viscosity.

Introduction

In recent years there has been significant interest in the determination of the flow properties of high concentration protein formulations. In this work we present an application of Dynamic Light Scattering (DLS) based microrheology to measure the complex viscosity of a model protein system.

Particles embedded/dispersed in a medium undergo Brownian motion and are thus displaced from their original positions over time. The mean square displacement (MSD) of the particles is determined by the viscoelasticity of the medium. Consequently, measuring the MSD allows information about the viscoelasticity of the sample to be extracted, so long as the size of the dispersed particles are known. In a dynamic light scattering experiment the autocorrelation function (g) of the scattered light can be written as a function of the MSD of the scatterers (Δr2) with time, where q is the scattering vector:

We can then calculate the MSD of probe particles embedded in the system of interest by performing a DLS experiment, and then use the Generalized Stokes- Einstein Relation (GSER) to obtain the complex modulus of the medium as a function of angular frequency:

Finally the complex viscosity can be obtained from the viscoelastic modulus using the, relationship below:

For simple polymeric solutions and liquids the complex viscosity as a function of angular frequency can be equivocated to the dynamic shear viscosity as a function of shear rate according to the Cox-Merz relationship:

Hence it is possible to determine the dynamic viscosity as a function of shear rate from a DLS microrheology test providing this relationship holds.