Regime de arrasto sublinear em escalas mesoscópicas de materiais viscoelásticos

Abstract

Soft materials usually present exponential or power-law viscoelastic relaxations when stressed. Although the mechanical responses are relevant to determine possible applications and design new materials, the origins of these macroscopic behaviors in terms of their small-scale interactions and compositions are still unclear. Here, we propose a model of macromolecules arranged in a lattice immersed in a viscous fluid, similar to colloidal and polymeric solutions. The macromolecules interact with their neighbors in the network (with a spring interaction $k$) and fluid through a non-linear drag regime. More specifically, the dissipative force is given by $\gamma v^{\alpha}$, where $\gamma$ is a constant coefficient, $v$ is the speed of the macromolecule, and $\alpha$ an exponent. Using molecular dynamics simulations, we perform numerical indentation assays and reproduce viscoelastic signatures in the force curves of the sample as those obtained in atomic force microscopy. We apply statistical and data analyses with machine learning techniques to classify each viscoelastic material (represented by the set of parameters $k$, $\gamma$, $\alpha$) as exponential or power-law behavior. We find that, for materials not so soft, not purely elastic, the exponent $\alpha$ completely describes the type of macroscopic relaxation. Our results show that the linear drag regime ($\alpha\approx 1$) recovers exponential relaxation materials, which can be described by the so-called linear standard solid model. However, the network response presents power-law relaxations in sublinear drag regimes ($\alpha\approx 0.5$). Physically, the sublinear regime of the drag forces is related to micro-deformations of the macromolecules, while $\alpha=1$ represents the rigid case. Therefore, our results suggest that mesoscopic-scale deformations are responsible for the material rheological responses, namely, the exponential and power-law relaxations.