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If they are polydisperse, can beĮxpressed as an integral over a distribution of decay rates, from which the distribution of sizesįigure 2. Hydrodynamic radius of the particles being examined. If the scattering particles are not spherical, DLS measurements provide the apparent Here is the Boltzmann constant, is the absolute temperature, and is the viscosity of the Is the quantity of interest in the present work, from D using the Stokes-Einstein relation, One can find the hydrodynamic radius, which
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Where D is the translational diffusion coefficient. The autocorrelation function of electric field,, decays exponentially with delay time: If the particles are spherical, monodisperse, and undergo Brownian motion, Where is a constant that depends on the size of the detector and the details of the optics of theĮxperimental set up. If the scattering is a Gaussian process, is related to the autocorrelation function of theĮlectric field,, by the Siegert relation The normalizedĬorrelation function of the scattered intensity is referred to as and is given by
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Normalized by the value of the correlation function at long times. Which is proportional to, and then computes the correlation function. In our experiment, a digital correlator takes the digitized photo-count measured by the detector, Intensities and the above equation becomes Sampling time interval is very large, there is no correlation between the pairs of sample Since the particles have not moved from their initial position and the correlation is high. Here, the angle bracket represents an average over time. One denotes the scattered intensity at an arbitrary time by and that at a later time by Good statistics, this comparison is normally made at many different values of t and averaged. The intensity autocorrelation function shows theĬorrelation between scattered intensity at a given time t and a later time. We can get quantitative information out of these fluctuations by examining the decay In the number of particles in the scattering volume, but from changes in the position of the It should be emphasized that the fluctuations in the scattered intensity do not result from changes 1: Left: A schematic illustration of the fluctuations in scattered intensity observed for scattering from large and small size particles, Right: Correlation functions for large and small size particles. Figure 2.1 shows a schematic example of an intensity-time plot for small and largeįigure 2. Small particles diffuse more quickly, and so cause a rapidlyįluctuating signal, whereas larger particles diffuse more slowly, resulting in more slowly varyingįluctuations. Size of the diffusing particles, so they can be analysed to calculate the average size of a The time scale of these fluctuations depends on the DLS involves measuring the fluctuations in the intensity of the scattered light andĪnalyzing them to the extract information. These fluctuations in the scattered intensity are the key concept of DLSĮxperiments. This in turn causesįluctuations in the intensity, which is defined as Time, and E(t), the total scattered electric field at the detector, also fluctuates. Particles vary in time, so the phase of each scattered wave arriving at the detector fluctuates in In the scattering volume, which is the volume that isīoth illuminated by the incident beam and observed by the detector, the positions of the Scattered fields due to all of the particles. The total scattered electric field at the detector is the superposition of the In a colloidal suspension, the motion of the particles is random and is due toīrownian motion. Intensity of scattered light is measured at a particular angle with a photomultiplier detector In dynamic light scattering, laser light is scattered by a collection of suspended particles, and the