Diffusing-wave spectroscopy

Diffusing-wave spectroscopy (DWS) is an optical technique derived from dynamic light scattering (DLS) that studies the dynamics of scattered light in the limit of strong multiple scattering. ^{[1] [2]} It has been widely used in the past to study colloidal suspensions, emulsions, foams, gels, biological media and other forms of soft matter. If carefully calibrated, DWS allows the quantitative measurement of microscopic motion in a soft material, from which the rheological properties of the complex medium can be extracted via the microrheology approach.

One-speckle diffusing-wave spectroscopy

Laser light is sent to the sample and the outcoming transmitted or backscattered light is detected by an optoelectric sensor. The light intensity detected is the result of the interference of all the optical waves coming from the different light paths.

• 
  Typical setup of diffusing-wave spectroscopy

The signal is analysed by calculating the intensity autocorrelation function called g₂. ${\displaystyle g_{2}(\tau )={\frac {\langle I(t)I(t+\tau )\rangle _{t}}{\langle I(t)\rangle _{t}^{2}}}}$

For the case of non-interacting particles suspended in a (complex) fluid a direct relation between g₂-1 and the mean squared displacement of the particles <Δr²> can be established. Let us note P(s) the probability density function (PDF) of the photon path length s. The relation can be written as follows: ^[3]

${\displaystyle g_{2}(\tau )-1=[\int {dsP(s)\exp(-(s/l*)k_{0}^{2}\langle \Delta r^{2}(\tau )\rangle )}]^{2}}$

with ${\displaystyle k_{0}={\frac {2\pi n}{\lambda }}}$ and ${\displaystyle l*}$ is the transport mean free path of scattered light.

For simple cell geometries, it is thus possible to calculate the mean squared displacement of the particles <Δr²> from the measured g₂-1 values analytically. For example, for the backscattering geometry, an infinitely thick cell, large laser spot illumination and detection of photons coming from the center of the spot, the relationship between g₂-1 and <Δr²> is:

${\displaystyle g_{2}(\tau )-1=\exp \left(-2\gamma {\sqrt {\langle \Delta r^{2}(\tau )\rangle k_{0}^{2}}}\right)}$, γ value is around 2.

For less thick cells and in transmission, the relationship depends also on l* (the transport length). ^[4]

For quasi-transparent cells, an angle-independent variant method called cavity amplified scattering spectroscopy ^[5] makes use of an integrating sphere to isotropically probe samples from all directions, elongating photon paths through the sample in the process, allowing for the study of low turbidity samples under the DWS formalism.

Multispeckle diffusing-wave spectroscopy (MSDWS)

This technique either uses a camera to detect many speckle grains (see speckle pattern) or a ground glass to create a large number of speckle realizations (Echo-DWS ^[6] ). In both cases an average over a large number of statistically independent intensity values is obtained, allowing a much faster data acquisition time.

• 
  Typical setup of Multispeckle Diffusing-wave spectroscopy

${\displaystyle g_{2}(\tau )={\frac {\langle I(t)I(t+\tau )\rangle _{p}}{\langle I(t)\rangle _{p}^{2}}}}$

MSDWS is particularly adapted for the study of slow dynamics and non ergodic media. Echo-DWS allows seamless integration of MSDWS in a traditional DWS-scheme with superior temporal resolution down to 12 ns. ^[7] Camera based adaptive image processing allows online measurement of particle dynamics for example during drying. ^[8]

References

1. G. Maret; P. E. Wolf (1987). "Multiple light scattering from disordered media. The effect of brownian motion of scatterers". Zeitschrift für Physik B . 65 (4): 409. Bibcode:1987ZPhyB..65..409M. doi:10.1007/BF01303762. S2CID   121962976.
2. D. J. Pine; D. A. Weitz; P. M. Chaikin; E. Herbolzheimer (1988). "Diffusing wave spectroscopy". Physical Review Letters . 60 (12): 1134–1137. Bibcode:1988PhRvL..60.1134P. doi:10.1103/PhysRevLett.60.1134. PMID   10037950.
3. F. Scheffold; et al. (2004). "New trends in optical microrheology of complex fluids and gels" (PDF). Progress in Colloid and Polymer Science . 123: 141–146. doi:10.1007/b11748. ISBN   978-3-540-00553-7. Archived from the original (PDF) on 2011-07-21.
4. D. A. Weitz; D. J. Pine (1993). "Diffusing-wave spectroscopy". In W. Brown (ed.). Dynamic Light scattering. Clarendon Press. pp. 652–720. ISBN   978-0-19-853942-1.
5. Graciani, Guillaume; King, John T.; Amblard, François (2022-08-30). "Cavity-Amplified Scattering Spectroscopy Reveals the Dynamics of Proteins and Nanoparticles in Quasi-transparent and Miniature Samples". ACS Nano. 16 (10): 16796–16805. arXiv: 2111.09616 . doi:10.1021/acsnano.2c06471. ISSN   1936-0851. PMID   36039927. S2CID   244345602.
6. "Light scattering technique reveals properties of soft solids".
7. P. Zakharov; F. Cardinaux; F. Scheffold (2006). "Multispeckle diffusing-wave spectroscopy with a single-mode detection scheme". Physical Review E . 73 (1): 011413. arXiv: cond-mat/0509637 . Bibcode:2006PhRvE..73a1413Z. doi:10.1103/PhysRevE.73.011413. PMID   16486146. S2CID   6251182.
8. L. Brunel; A. Brun; P. Snabre; L. Cipelletti (2007). "Adaptive Speckle Imaging Interferometry: a new technique for the analysis of microstructure dynamics, drying processes and coating formation". Optics Express . 15 (23): 15250–15259. arXiv: 0711.1219 . Bibcode:2007OExpr..1515250B. doi:10.1364/OE.15.015250. PMID   19550809. S2CID   5753232.

External links

• Diffusing Wave Spectroscopy Overview with video
• Diffusing Wave Spectroscopy Overview with Animations
• Particle Sizing using Diffusing Wave Spectroscopy