Introduction
Diffusing Wave Spectroscopy (DWS) is an advanced light scattering technique based on the measurement of multiple light scattering. It is primarily used to perform contact-free rheology, as well as particle sizing on a wide range of samples, such as suspensions, emulsions, pastes, or gels. DWS offers a powerful alternative to mechanical rheology, as the measurements are non-destructive, conducted on a sample in a sealable cuvette, and as fast as 30 seconds. This enables a wide range of applications such as rapid formulation screening, gelation monitoring, or long-term stability studies.
Principle of DWS
In a DWS experiment, a laser beam is shone onto a highly turbid sample in which the light is scattered multiple times, as it propagates randomly through the sample. Scatterers are typically particles in a suspension or droplets in an emulsion. The resulting intensity fluctuations are analyzed using a photon detector coupled to a correlator.
Two different detection geometries can be distinguished in DWS:
- In transmission mode, the scattered light is detected after having passed through a sample. In backscattering mode, one collects the light that is scattered back toward the incident beam.
Using the backscattering geometry, one can characterize samples that are too opaque to work comfortably in transmission mode – this is however relatively uncommon. We note that in transmission mode, when measuring opaque samples one can use very thin with an optical path as low as 1 mm.
- The backscattering geometry may also be used to conduct DWS sizing – please refer to the corresponding section for more information.
Fig. 1: Basic set-up of a DWS experiment in transmission geometry on a sample containing particles performing Brownian motion.
In a viscoelastic sample, the Brownian motion of the particles is affected by the microstructure of the sample: the resulting scattered light thus fluctuates over time. Particles in a matrix of low viscoelasticity will exhibit relatively fast dynamics, while particles in a highly viscoelastic sample will diffuse more slowly. For solid viscoelastic samples, Brownian motion will be constrained to finite volumes dictated by the permanent mesh size. The analysis of the dynamics of these intensity fluctuations thus provides information on the viscoelastic and structural properties of the sample.
A detailed description of the principle of DWS with the corresponding equations can be found in the document “Opening the black box - Equations of Microrheology.pdf”
Fig. 2: Principle of DWS, DWS Microrheology, and DWS particle sizing.
Based on the intensity fluctuations, the intensity correlation function is computed, in a similar way as in Dynamic Light Scattering (DLS). The Mean-Square Displacement (MSD) is then extracted: this data provides a wealth of information relevant to the sample microstructure, viscoelasticity, and stability, without requiring knowledge of additional parameters such as particle size. More information is provided in the section “Mean-Square Displacement”.
From here, one can perform DWS microrheology – provided that the size of the particles is known and that some conditions are met- or DWS particle sizing, in the case of a purely viscous sample.
This technology is implemented in our DWS RheoLabTM.
[1] Weitz, D. A.; Pine, D.J. Diffusing-wave Spectroscopy. In Dynamic Light Scattering; Brown, W., Ed.; Oxford University Press: New York, 652-720 (1993).
For what kind of samples is it?
DWS can be applied to systems as varied as liquids, polymer solutions, gels, emulsions, or foams. The range of applicability is only limited by the optical properties of the material in question.
DWS is unique in the fact that it is a multiple-scattering technique, thus samples usually have to be opaque. The majority of samples screened via DWS are white, although colored samples can also be analyzed, provided that the light absorption is not too strong. DWS relies on multiply scattered photons and is thus perfectly suitable for strongly scattering samples that are not amenable to DLS, such as dairy products, opaque cosmetics, or dermaceutics, as well as inks, paints, and other concentrated opaque formulations. Note that when working with transparent samples, one might also add tracer particles to increase the turbidity and thus make such samples suitable for DWS.
Since the DWS is a contact-free technique, samples whose fragile microstructure would be otherwise destroyed by a mechanical measurement can then be characterized without any applied force, in sealed conditions. This is especially advantageous for long-term stability measurements.