Number fluctuations are defined as variations in the number of particles within the scattering volume during the course of a dynamic light scattering (DLS) measurement. As a consequence of Brownian motion, particles within the scattering volume are moving, leading to constructive and destructive interference effects at the detector. In DLS instruments, these intensity fluctuations are correlated across very small time scales and then transformed to give the diffusion coefficient and the hydrodynamic size. The obvious assumption in the technique, is that these intensity fluctuations are due solely to Brownian motion. However, the scattering intensity is proportional to the sample concentration. So the corollary to this assumption is that the number of particles within the scattering volume during the course of the measurement must be constant. Number fluctuations are generally easy to spot, and are typically manifested as elevated baselines and/or discontinuities in the correlation curve, examples of which are shown in Figure 1.
Figure 1: Example correlograms showing manifestation of number fluctuations.
Number fluctuations are particularly problematic with dynamic light scattering instruments that utilize highly focused optics to increase sensitivity. In order to produce a high power density in the scattering volume, the laser and detector optics in these types of systems are focused to very narrow diameters, e.g. 16 um. While the increased power density increases the sensitivity of the instrument to sample concentration, the smaller scattering volume also significantly increases the likelihood of number fluctuations if larger particles are present (see Figure 2). As a direct consequence of the smaller scattering volume, the upper size limit for reliable measurements with these systems is significantly lower than the Zetasizer Nano system which uses patented optics that don't require extreme focusing to achieve its high specifications..
Figure 2: Schematics detailing the introduction of number fluctuation problems with DLS instruments using highly focused optics.
Factors that can lead to number fluctuations are the presence of small amounts of dust, the presence of sample particles that are outside the range of the instrument, or very low concentrations. The latter is a factor that can only be addressed by increasing the sample concentration. With regard to dust and very large particles however, many times one can either spin the sample in a bench top centrifuge for about 5 minutes or let the sample set undisturbed in the cell chamber for 5-10 minutes to allow settling of the larger particles, and ultimately achieve reasonable measurement conditions.
In the automatic mode of the DTS software for the Malvern Zetasizer Nano system, random number fluctuations are automatically filtered (digitally) from the measured average correlation curve, in that the data is taken as a series of pieces of data, each of which is assessed for number fluctuations, and rejected if it fails the q test and is deemed to be an outlier. Note however, the emphasis on the word random. If each of the sub-sets of data is contaminated by the effect of number fluctuations, then any data will be treated as real and the size distribution results will reflect the presence of very large particles.
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