## Dynamic light scattering Dynamic light scattering, as the name suggested, is a scattering technique. It can give the diffusivity of particles in certain solution, and from The instruments will record the (overall) light intensity $I$ with time, then compute the autocorrelation function of the intensity, $g^{2}(\tau)$. The exponential decays of the $g^{1}(\tau)$, for autocorrelation function with electric field, is related to the diffusivity of the particles. Also, dispersity can also be computed by some fitting or inversion or extraction algorithm. >[!Notice] >Dynamic light scattering is indeed an **inelastic scattering** process, but since the energy transfer is small, it is designated as [quasi-elastic scattering](https://en.wikipedia.org/wiki/Quasielastic_scattering). The word was initial used for [quasielastic neutron scattering](https://en.wikipedia.org/wiki/Quasielastic_neutron_scattering). >DLS is somethings called quasielastic scattering, also. ### Description We use a polarized laser beam to shot into a sample, and capture the scattered light through another polarizer. This will generate a speckle pattern. By analyzing the intensity speckle, we can get a profile of intensity distribution changing with time, $I(t)$. Since this is the reciprocal pattern of the particles, and the particles are having random Brownian motion, one may expect the speckle being random as well, and autocorrelation function of this intensity $g^{2}(\tau)$ decays with time, depending on a Brownian motion term. For 1st order correlation, i.e., $E$, the relation would be $g^{1}(\tau;q)=g^{1}(0;q)e^{-\Gamma \tau} = e^{-\Gamma \tau}$ since at $\tau=0$, $g^{1}(0;q) =1$. Here the decay rate is $\Gamma =q^{2} D_{t}$, $q = \frac{4\pi n_{0}}{\lambda} \sin\left( \frac{\theta}{2} \right)$. $D_{t}$ is translational diffusivity, $q$ is wave vector, $\lambda$ is the incident light wavelength, $n_{0}$ is the solvent refractive index, $\theta$ is an angle between the detector and the sample. This first order autocorrelation function can then be turned into the second order form, since the intensity is easier to be measured, i.e., $g^{2}(\tau;q) = 1+\beta[g^{1}(\tau;q)]$ The $\beta$ here is a correlation factor depends on the instrument setup. >[!Notice] >We do this in a second order autocorrelation form is because we measure $I$ but the directly response is $E$, and $I=|E|^{2}$. With the recorded intensity, by computing the autocorrelation function, we can have $g^{2}$ obtained as $g^{2}(q;\tau) = \frac{\braket{ I(t) I(t+\tau) }}{\braket{ I(t) }^{2} } $ Then fit the decay curve with all known variables like viscosity $\eta$ and temperature $T$, we may get multiple $\Gamma$, and therefore $D_{t}$, which corresponds to different hydrodynamic radius of particles, based on [[Einstein relation]], i.e., $D=\frac{k_{B}T}{6\pi \eta r}$. This fitting could be done by different algorithms, like Cumulant method, non-negative least squares method, CONTIN method, etc., depending on the system being measured. After the data analysis, we may obtain the information on particles size and their distribution, also dispersity. >[!Info] >See more: https://en.wikipedia.org/wiki/Dynamic_light_scattering >and the paper (literally the same contents): [[Dynamic light scattering a practical guide and applications in biomedical sciences]]