Description
When light hits small particles, the light scatters in all directions (Rayleigh scattering) as long as the particles are small compared to the wavelength (below 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. This fluctuation is 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. Sample preparation either by filtration or centrifugation is critical to remove dust and artifacts from the solution.
The dynamic information of the particles is derived from an autocorrelation of the intensity trace recorded during the experiment. The second order autocorrelation curve is generated from the intensity trace as follows:
where is the autocorrelation function at a particular wave vector, and delay time, and is the intensity. 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 decays exponentially, meaning that, after a long time period has elapsed, there is no correlation between the scattered intensity of the initial and final states. This exponential decay is related to the motion of the particles, specifically to 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 is monodisperse then the decay is simply a single exponential. The Siegert equation relates the second-order autocorrelation function with the first-order autocorrelation function as follows:
where the parameter β is a correction factor that depends on the geometry and alignment of the laser beam in the light scattering setup. It is roughly equal to the inverse of the number of speckle (see Speckle pattern) from which light is collected. The most important use of the autocorrelation function is its use for size determination.
Read more about this topic: Dynamic Light Scattering
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