Light Scattering Probes of Viscoelastic Fluids and Solids

Abstract

In this article, we discuss recent advances in static and dynamic light scattering applied to soft materials. Special emphasis is given to light scattering methods that allow access to turbid and solid‐like systems, such as colloidal suspensions, emulsions, glasses, or gels. Based on a combination of single‐ and multispeckle detection schemes, it is now possible to cover an extended range of relaxation times from a few nanoseconds to minutes or hours and length scales below 1 nm up to several microns. The corresponding elastic properties of viscoelastic fluids or solid materials range roughly from below 1 Pa to several 100 kPa. Different applications are discussed such as light scattering from suspensions of highly charged colloidal particles, colloid and protein gels, as well as dense surfactant solutions.

Keywords:

• Dynamic light scattering
• Photon correlation spectroscopy
• Diffusing wave spectroscopy
• Microrheolgy
• Colloids
• Biopolymers
• Micelles

Acknowledgements

We would like to thank our colleagues and collaborators for their contributions to the different projects reviewed in this article, namely Claus Urban, Sara Romer, Sergey Skipetrov, Luis Rojas, Fréderic Cardinaux, Luca Cipelletti, Taco Nicolai and Ronny Vavrin. We gratefully acknowledge financial support from the Swiss National Science foundation.

Notes

^aThis approximation for weak scattering is equivalent to the first Born approximation. Within the frame of the Raleigh Gans Debeye (RGD) formalism, it can easily be expanded to scatterers of any size aand shape, as long as the scattering contrast is weak (ka|n ₁/n ₂ − 1| ≪ 1, where n ₁/n ₂denotes the index contrast).16&17

^bAbsorption can be taken into account by substituting 2k ₀ ² α(t) ([β·S]/[S]) (s/l ^*)→2k ₀ ² α(t) ([β·S]/[S]) (s/l ^*) + (s/3l _a ), where l _a is the microscopic absorption length along the multiple scattering paths. For nonabsorbing scatterers, l _a is the absorption length of the pure solvent.

^cWe note that it seems feasible, though tedious, to manually adjust the cell position in order to have the same signal count rate on both detectors. Under that premise, we assume that the Pusey–van Megen method can also be applied to 3DDLS, though the details of such an approach have not yet been worked out.

^dIf colloidal particles with ka > 1 are used, typical values L ₂ ≅ (1 − 2)l ^*are sufficient to suppress transmission of unscattered light (because l ^* ≫ l).

^eRecently, a rigorous theoretical derivation (albeit certain constraints) for this generalized Stokes–Einstein relation was reported in Refs. 83&84.

^fDWS can detect particle displacements in the subnanometer range with visible light. For (the limting case of) L/l ^* = 150, a displacement of leads to a detectable decay of g ₂(t) − 1 ≈ 0.99. For a purely elastic solid material, we find from Eq. 34, G = kT/(πaδ ²) (with ⟨Δ_r ²(s)⟩ = δ ²and ). Hence, a 1 µm tracer particle and a still detectable 0.1 nm displacement corresponds to a measureable elastic modulus of ca. 1 MPa.