High frequency microrheology with optical tweezers

This thesis presents a method to measure the linear viscoelastic response of fluids by tracking and analyzing the thermal, Brownian motion of suspended tracer particles, known as passive microrheology. The particle is confined in a harmonic optical trap and its one dimensional trajectory is obtained by a home-built split beam detection system, which works similar but responds faster than position detection with commercial quadrant photodiodes. The theory which is necessary to convert the particle trajectory into the complex shear modulus is derived in detail, pointing out that the commonly used Mason-Weitz method needs to be modified in order to obtain correct results at high frequencies due to hydrodynamic effects of the fluid. It follows a detailed explanation of the data analysis procedure which is verified for water up to angular frequencies of 10⁷ rad/s in very good agreement with the theory. Finally, there is an outlook how to apply the method to actual complex fluids.