LS Instruments | DWS particle sizing

DWS particle sizing

Besides the measurement of the microrheological properties of a sample, Diffusing Wave Spectroscopy (DWS) can also accurately determine the mean diameter of particles in dispersions of known viscosity $\eta$ at a very well-defined temperature $T$ . In particular, this clever approach enables particle sizing in samples with turbidity exceeding the turbidity limit accessible by the most advanced Dynamic Light Scattering (DLS) technologies.

The DWS RheoLab^TM from LS Instruments is the only instrument that offers this novel light scattering technology for particle sizing. In particular, the DWS RheoLab^TM performs accurate and reliable measurements in a matter of minutes over a broad range of sizes, concentrations, and materials

During a sizing measurement, the mean square displacement (MSD) of the suspended particles is measured using DWS in backscattering geometry. Each sizing measurement automatically performs a measurement in backscattering VH (horizontally polarized light) geometry and a measurement in backscattering VV (vertically polarized light) geometry and calculates the corresponding particle diameters $d_{VH}$ and $d_{HH}$ via the fit of the measured MSD's using the Stokes-Einstein relation:

$(\Delta r_{VH, VV}^{2}) = 6D_{VH, VV}\tau$

where the diffusion coefficient $D$ of the particles is

$D_{VH, VV} = \frac{k_{B}T}{3\pi \eta d_{VV, VH}}$

and $k_{B}$ is the Boltzmann constant. From the obtained diameters $d_{VH}$ and $d_{VV}$ the average particle diameter is estimated [1].

$d = \frac{4}{({\frac{1}{\sqrt{d_{VV}}}+\frac{1}{\sqrt{d_{VH}}}})^2}$

The principle of particle sizing using DWS is similar to that used by dynamic light scattering (DLS) except that multiply scattered light is considered instead of single scattered light. To ensure the detection of multiply scattered light, the samples must be turbid. As an example, for polystyrene particles dispersed in water, the best results are obtained for particle diameter $d$ in the range of 80 nm to 2000 nm and volume fractions $\Phi \geq 1 %$ .

Note that the approach described above yields only the real particle size for freely diffusing particles. For samples at high particle concentrations (i.e. volume fraction $\Phi \geq 10 %$ ) or strongly interacting particles (e.g. highly charged particles at very low ionic strength) the individual particles "see or feel each other", and consequently exhibit different dynamics.

In general, this leads to a measured apparent particle size that is larger than the real particle size. For hard spheres, the following relation can be used to correct these effects [2].

$d_{corrected} = d(1-1.83\Phi +0.88\Phi^{2} )$

DWS particle sizing can also be applied for the sizing of polydisperse samples, however, in this case, the obtained particle size is an effective size averaged over all particles weighted by their scattering strength. Note that it is not possible to determine the size distribution of the particles, as it is possible by dynamic light scattering (DLS).

For optimal results in DWS-sizing experiments, one should consider that the mathematical model for the intensity autocorrelation function (ACF) is based on the assumption of an optically very thick sample (semi-infinite medium), that is L/l* > 50 and a wide cell in the absence of absorption. In practice, one often encounters limited container sizes, L/l* < 30 as well as some absorption. In these cases, the intensity correlation function shows deviations from the idealized case at short correlation times. While the software corrects for these, the sizing results are gradually affected and become less accurate until for L/l* < 10 (or correspondingly strong absorption) DWS sizing becomes unreliable.

For a more detailed discussion on particle sizing with DWS, please refer to the work of Scheffold F. (2002) [1]

DWS can be used to perform particle sizing from 100 nm to 1 micron. For monodisperse particles of particles with a gaussian size distribution, the accuracy is better than 5%.

Fig. 9: A) Accuracy of DWS sizing measurements as a function of turbidity, characterized by the inverse of the transport mean free path, l*. Measurements were carried out on aqueous suspensions of spherical polystyrene particles with radii of (◼) 111 nm, (∙) 220 nm, (▴) 280 nm, (▾) 385 nm, and (⧫) 960 nm, and on melamine particles with radii of (◻) 296 nm, and (∘) 516 nm, at different mass fractions (indicated by the colored numbers in the bottom right-hand corner). Within the size range [100 nm, 1 μm] and the turbidity range shown, an accuracy of ± 5 % is achieved. B) Examples of inappropriate (left) and appropriate (right) samples for DWS sizing measurements. However, we note that the left sample can be measured using Modulated 3D Cross-Correlation DLS.

References:

[1] Scheffold F., Particle Sizing with Diffusing Wave Spectroscopy. Journal of Dispersion Science and Technology, 23(5):5941, 2002.

[2] Beenakker C.W.J and Mazur P. Diffusing of spheres in a concentrated suspension. Physica, 126(A):347-370, 1984

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