Role of a finite exposure time on measuring an elastic modulus using microrheology

The role of a finite exposure time sigma on measuring rheological properties using microrheology techniques is theoretically investigated. We concentrate on studying fluid models displaying a plateau in the mean-squared displacement (MSD) of the embedded probe particle. A model is developed to compare the resulting experimentally measured MSD of the particle to its expected value in the fluid model. A plateau MSD is greatly modified in a measurement when sigma is greater than the plateau onset time. Moreover, apparent dynamics drastically differ from the true dynamics at frequencies omega less than or approximately equal sigma(-1) . These results quantify when and how a finite exposure time effects the measured MSD of a probe particle which can then alter the extracted rheological properties and physical interpretations.