Realizing microrheological response of configurable viscoelastic media with a dynamic optical trap

The local viscoelastic (VE) environment governs the motion of an embedded microsphere and consequently, pertinent dynamical phenomena. However, studying such phenomena with varying VE properties remains challenging for various reasons, including the strong coupling among the VE parameters and their dependence on experimental conditions, such as temperature. Here, we demonstrate the experimental realization of configurable VE media with broad variations, wherein the VE properties can be systematically and independently tuned, employing a dynamic optical trap. Specifically, the dynamics of a particle in a slowly diffusing optical trap provides the linear microrheological response of single-relaxation VE fluids, namely Jeffreys or Maxwell-Voigt (MV) fluids, where the trap strength and its diffusion coefficient regulate the elastic response and the low-frequency viscosity, respectively. The characteristic features in the mean square displacement (MSD) of the trapped particle match those of a probe particle in real MV fluids, and the simulation results follow the harmonically bound Brownian particle with long-time diffusion model describing single-relaxation complex fluids. Our scheme is further validated by demonstrating excellent quantitative agreement between the experimentally observed MSDs of the trapped bead and those from the corresponding analytical predictions. We extend the applicability of this scheme for realizing the microrheological response of double-relaxation VE media by incorporating appropriately correlated noise in the trap trajectory, signifying its validity for any linear VE media with multiple relaxations. Our scheme can be further extended to realize probe particle dynamics in an active VE environment, e.g., an entangled network of active polymers, by translating the trap along an active Brownian trajectory. Therefore, our scheme enables systematic microrheological studies in VE regimes that are otherwise challenging to realize or not readily accessible with real materials.