Lengthscale dependence of critical exponents determined by vibration-corrected two-particle microrheology

The gelation behaviour of fibrillar aggregates of the milk protein beta-lactoglobulin (BLG) is studied using two-particle (2-P) microrheology. This technique offers several advantages over traditional 1-P microrheology, including insensitivity to probe-medium interactions. A novel vibration-removal technique is developed, illustrating that the static error disappears in 2-P microrheology, thus increasing the upper limit to the elastic modulus measurable using particle tracking microrheology. The principle of time-cure superposition has previously been applied to 1-particle microrheological data to calculate the critical gelation exponents for a number of systems, including gels of fibrillar protein aggregates. In this work, the 2-particle Mean Square Displacements (MSDs) around the gel-point of fibrillar BLG gels were found to similarly superpose, but yielded significantly different exponents to 1-P data, suggesting that the network is not self-similar at all lengthscales, even around the gel-point.