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Understanding the microscopic origin of the rheological behavior of soft matter is a long-lasting endeavour. While early efforts concentrated mainly on the relationship between rheology and structure, current research focuses on the role of microscopic dynamics. We present in two companion papers a thorough discussion of how Fourier space-based methods may be coupled to rheology to shed light on the relationship between the microscopic dynamics and the mechanical response of soft systems. In this first companion paper, we report a theoretical, numerical and experimental investigation of dynamic light scattering coupled to rheology. While in ideal solids and simple viscous fluids the displacement field under a shear deformation is purely affine, additional non-affine displacements arise in many situations of great interest, for example in elastically heterogeneous materials or due to plastic rearrangements. We show how affine and non-affine displacements can be separately resolved by dynamic light scattering, and discuss in detail the effect of several non-idealities in typical experiments., 13 pages, 7 figures. First paper of a series of two companion papers. The second companion paper will be posted shortly

We discuss in two companion papers (arXiv:1802.03737 and the present manuscript) how Fourier-space measurements may be coupled to rheological tests in order to elucidate the relationship between mechanical properties and microscopic dynamics in soft matter. In this second companion paper, we focus on Differential Dynamic Microscopy (DDM) under shear. We highlight the analogies and the differences with Dynamic Light Scattering coupled to rheology, providing a theoretical approach and practical guidelines to separate the contributions to DDM arising from the affine and the non-affine part of the microscopic displacement field. We show that in DDM under shear the coherence of the illuminating source plays a key role, determining the effective sample thickness that is probed. Our theoretical analysis is validated by experiments on 2D samples and 3D gels., This is a companion paper to the manuscript arXiv:1802.03737

Power law rheology is of widespread occurrence in complex materials that are characterized by the presence of a very broad range of microstructural length and time scales. Although phenomenological models able to reproduce the observed rheological features exist, in general a well-established connection with the microscopic origin of this mechanical behavior is still missing. As a model system, this work focuses on a fractal colloidal gel. We thoroughly characterize the linear power law rheology of the sample and its age dependence. We show that at all sample ages and for a variety of rheological tests, the gel linear viscoelasticity is very accurately described by a fractional Maxwell (FM) model, characterized by a power law behavior. Thanks to a unique setup that couples small-angle static and dynamic light scattering to rheological measurements, we show that in the linear regime, shear induces reversible nonaffine rearrangements which might be at the origin of the power law rheology and we discuss the possible relationship between the FM model and the microscopic structure of the gel.Power law rheology is of widespread occurrence in complex materials that are characterized by the presence of a very broad range of microstructural length and time scales. Although phenomenological models able to reproduce the observed rheological features exist, in general a well-established connection with the microscopic origin of this mechanical behavior is still missing. As a model system, this work focuses on a fractal colloidal gel. We thoroughly characterize the linear power law rheology of the sample and its age dependence. We show that at all sample ages and for a variety of rheological tests, the gel linear viscoelasticity is very accurately described by a fractional Maxwell (FM) model, characterized by a power law behavior. Thanks to a unique setup that couples small-angle static and dynamic light scattering to rheological measurements, we show that in the linear regime, shear induces reversible nonaffine rearrangements which might be at the origin of the power law rheology and we discuss the ...

We develop and thoroughly test a stress-controlled, parallel plates shear cell that can be coupled to an optical microscope or a small angle light scattering setup, for simultaneous investigation of the rheological properties and the microscopic structure of soft materials under an imposed shear stress. In order to minimize friction, the cell is based on an air bearing linear stage, the stress is applied through a contactless magnetic actuator, and the strain is measured through optical sensors. We discuss the contributions of inertia and of the small residual friction to the measured signal and demonstrate the performance of our device in both oscillating and step stress experiments on a variety of viscoelastic materials., 14 pages, 10 figures