Dynamic Light Scattering

A dynamic light scattering apparatus was built with a HeNe laser; the beam incident on a sample of particles(microspheres of one or multiple diameters or casein undigested and digested) suspended in water scatters into a random pattern product of the coherent superposition of the outgoing waves scattered from the spheres. Because the spheres are in constant Brownian motion, the pattern randomly changes in time. A phomultiplier tube was placed in the pattern and the random fluctuations in the light intensity were measured and analyzed. The signal’s autocorrelation functions were computed to verify the spheres’ diameter. The results show that the apparatus is able to measure the diameter of single sized particles but not on a mixture with two different size microspheres. Further analysis needs to be done in order to determine the size of protein digested fragments. Introduction When monochromatic, coherent beam of light is incident on a dilute solution of macromolecules such as proteins or suspension of colloidal particles such as polystyrene or latex microspheres and the solvent refractive index is different from that of the solute (proteins or microspheres) the incident light is scattered by each illuminated particle in all directions [1]. The scattered light waves from different macromolecules or particles mutually interfere or combine, at a distant fast photomultiplier tube (PMT) and produce a scattered intensity I(t) that is not uniform on the scattering or detection plane. If all the particles are stationary, the scattered light intensity at each direction would be a constant (independent of time). However in reality all the scatters in solution are undergoing constant Brownian motions [2], and this fact leads to fluctuations of the scattered intensity pattern on the detection plane and the fluctuations in I(t)) if the detection area is sufficiently small. Dynamic or quasi-elastic light scattering measures the intensity fluctuations instead of the average light intensity as in static light scattering. When incident light is scattered by a moving macromolecule or particle, the detected frequency of the scattered light will be slightly higher or lower than that of the original incident light owing to Doppler Effect, depending on whether the particle moves towards or away from the detector [1]. Thus, the frequency distribution of the scattered light is slightly broader than that of the incident light. This is why dynamic light scattering is called quasi elastic. This frequency broadening is so small (~10-10 Hz) in comparison to the light frequency (~10 Hz) that it is very difficult to detect in the frequency domain, but it can be recorded in the time domain via a time autocorrelation function (eq 1). At time t, the scattered light intensity is I(t) and at a very small time later (t+ the diffusing particles will have new positions and the intensity at the PMT will have a value I(t+t) which correlates with I(t), the closer the measurement is to time zero, the more similar I(t+t) is to I(t) since the particles have not had much time to move. As time goes on there is no more similarity between the starting state and the current state; the measured intensities do no correlate anymore to the beginning one. At time there is a 100% autocorrelation; as time progresses, the autocorrelation diminishes reaching zero as there is no more similarity between starting and ending states. The decay of the autocorrelation is described by an exponential decay function (eq 2) which relates the autocorrelation to the diffusion coefficient D and the measurement vector K, where n is the refraction index of the solvent and  is the beam frequency (eq 3), then using stokes equation the hydrodynamic diameter can be calculated, where KB is Boltzman’s constant, T is temperature,  is viscosity of the solvent and d is the hydrodynamic radius (eq 4).