Dynamic light scattering
Dynamic light scattering (DLS) is a technique in physics that can be used to determine the size distribution profile of small particles in suspension or polymers in solution.
It has been shown that the intensity ACF is the Fourier transform of the power spectrum, and therefore the DLS measurements can be equally well performed in the spectral domain.
The scattered light then goes through a second polarizer where it is collected by a photomultiplier and the resulting image is projected onto a screen.
Even if the light source is a laser, and thus is monochromatic and coherent, the scattering intensity fluctuates over time.
This fluctuation is due to small particles in suspension undergoing Brownian motion, and so the distance between the scatterers in the solution is constantly changing with time.
The dynamic information of the particles is derived from the autocorrelation of the intensity trace recorded during the experiment.
To fit the decay (i.e., the autocorrelation function), numerical methods are used, based on calculations of assumed distributions.
The Siegert equation relates the second-order autocorrelation function with the first-order autocorrelation function g1(q;τ) as follows: where the first term of the sum is related to the baseline value (≈1) and the parameter β is a correction factor that depends on the geometry and alignment of the laser beam in the light scattering setup.
[5] Back scattering detection (e.g., 173° or 175°) is particularly interesting for turbid and highly concentrated samples, which contain large particles.
Some DLS instruments in the market also allow automatic angle selection based on a continuous transmittance measurement.
As opposed to conventional DLS instruments, this method is angle independent as it probes samples isotropically from all directions.
Even though the DLS measurement using a single-angle detection has been the most diffuse technique, the application to many systems of scientific and industrial relevance has been limited due to often-encountered multiple scattering, wherein photons are scattered multiple times by the sample before being detected.
Particle-particle collisions can be suppressed by dilution, and charge effects are reduced by the use of salts to collapse the electrical double layer.
The refractive index of the solvent plays a crucial role in light scattering and is important to calculate the Stokes radius from the Stokes-Einstein equation.
[11][12][13] Therefore, previous refractive index data from the scattering medium should be evaluated with dedicated instruments, known as refractometers.
In these cases, prior knowledge of the refractive index and absorbance of the material is required in order to apply the Mie scattering.
[16] An important feature of the NNLS optimization is the regularization term used to identify specific solutions and minimize the deviation between the measure data and the fit.
The shape of this term can determine if the solution will represent a general broad distribution with small number of peaks or if narrow and discrete populations will be fit.
An alternative method for analyzing the autocorrelation function can be achieved through an inverse Laplace transform known as CONTIN developed by Steven Provencher.
[23][24] The CONTIN analysis is ideal for heterodisperse, polydisperse, and multimodal systems that cannot be resolved with the cumulant method.
If the particle in question is not spherical, the rotational motion must be considered as well because the scattering of the light will be different depending on orientation.
According to Pecora, rotational Brownian motion will affect the scattering when a particle fulfills two conditions; they must be both optically and geometrically anisotropic.
In 2007, Peter R. Lang and his team decided to use dynamic light scattering to determine the particle length and aspect ratio of short gold nanorods.
Both relaxation states were observed in VV geometry and the diffusion coefficients of both motions were used to calculate the aspect ratios of the gold nanoparticles.
DLS software of commercial instruments typically displays the particle population at different diameters.
