Soft Matter Characterization From Ultrasonic Microrheology and Fractional Calculus

Understanding soft matter mechanical behavior is of great interest as multiphasic combinations of their composition induce new properties which can be exploited for innovative applications. However, the final features optimization requires a tight multiscale control of the structure, even during the elaboration early stages. This paper presents a multifrequency technique to investigate this evolution at mesoscopic scale and its bonds with other scales. A TMS resonator is used as a discrete spectral ultrasonic microrheometer from 5MHz to 50MHz. Then, soft matter can be described as an elastic structure, due to macromolecular interactions, immersed in an effective viscous fluid. An original model of the measured mechanical impedance is proposed and enables the simultaneous monitoring of the effective viscosity and the internal structure. It is based on fractional calculus. In addition to complex shear modulus, the evolution of a fractional parameter, ranging from zero for solids to one for Newtonian fluids, can be studied. The model and the experimental set-up are validated with various complex materials: Newtonian glycerol mixtures, cosmetic emulsions, and silica gels. Effective viscosity accuracy is demonstrated (less than 5% of error for Newtonian fluids). Structural values of complex fluids range from 0.6 (gels) to 1 (liquids). The extracted structural parameter can be linked to the fractal dimension. Hence, this technique is relevant to describe soft matter structure. Moreover, the structural parameter on-line monitoring can be useful to optimize the elaboration process of new products. Indeed, a microscopic characteristic time can be extracted and correlated to the macroscopic gelation time.