Dynamic Light Scattering

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Dynamic light scattering is a powerful technique that can be used to determine the size distribution profile of small particles in solution.

When light hits small particles the light scatters in all directions (Rayleigh scattering) so long as the particles are small (<250 nm). If the light source is a laser, and thus is monochromatic and coherent, then one observes a time-dependent fluctuation in the scattering intensity. These fluctuations are due to the fact that the small molecules in solutions are undergoing Brownian motion and so the distance between the scatterers in the solution is constantly changing with time. This scattered light then undergoes either constructive or destructive interference by the surrounding particles and within this intensity fluctuation information is contained about the time scale of movement of the scatterers.

If one analyzes the time dependence of this fluctuation one can obtain the diffusion coefficient of the particles, and by using the Stokes-Einstein equation the hydrodynamic radius can be calculated. The time-dependent intensity fluctuation is analyzed using a digital correlator. This device takes the ensemble average of the number of photons counted in a sampling interval multiplied by a time delayed version of that signal as a function of the time delay.

$C(\tau)= \langle I_{1}(t)*I_{2}(t+\tau) \rangle$

At short time delays the correlation is high because the particles do not have a chance to move to a great extent from the initial state that they were in. The two signals are thus essentially unchanged when compared after only a very short time interval. As the time delays become longer, the correlation starts to exponentially fall off to zero, meaning that there is no correlation between the intensity of scattering of the initial state with the final state after a long time period has elapsed (relative to the motion of the particles). This exponential decay is obviously then related to the motion of the particles specifically, the diffusion coefficient. To fit the decay (i.e. the autocorrelation function), numerical methods are used based on calculations of assumed distributions. If the sample was monodisperse the decay would simply be a single exponential.