Study On Dynamic Light Scattering Measurement Of Ultra-low Concentration Particle Systems

Dynamic light scattering(DLS)technique is an effective method widely used in nanometer and submicron particle measurements,whose accuracy is restricted by concentration.For the ultra-low concentration particle system,the particle number fluctuation in and out from scattering volume caused by Brownian motion cannot be ignored,resulting in the distorted intensity autocorrelation function(ACF),which leads to an inaccurate particle size distribution(PSD)by the usual method.Based on the DLS characteristics,the influence of number fluctuation on DLS measurement at ultra-low concentration is investigated by analyzing the recovery results in this paper.The main work includes:1.The mechanism of DLS measurements restricted by ultra-low concentrations was analyzed based on DLS theory.At conventional concentration,the field ACFs and intensity ACFs satisfy the Siegert relation from which calculate the field ACFs and obtain PSDs by the usual method.At ultra-low concentrations,the field ACFs and intensity ACFs no longer satisfy the Siegert relation due to the effect of particle number fluctuation on ACFs.The usual method based on Siegert relation mistakes the change of scattered light caused by the number fluctuation as the change of scattered light caused by the Brownian motion,resulting in inaccurate PSDs.2.The kernel function matrix of the inversion equation is reconstructed to remove the effect of particle number fluctuation.Using the quantitative relationship of the Siegert relation,the equivalent field ACFs are constructed from the intensity ACFs at ultra-low concentrations,and the relationship between the equivalent field ACF and particle size is directly established by kernel function reconstruction.Accurate PSDs are obtained from the simulation,but there is a certain degree of deviation in the experiment.This is because the measured intensity ACFs contain more noise than the simulated ACFs,especially in the tail of the long delay time of the ACFs.The baseline noise overwhelms the number fluctuation term.3.The baseline of intensity ACF at ultra-low concentration is reset to adapt to the usual method.Based on the first-order difference characteristics analyses of intensity ACFs at ultra-low concentrations,truncated points are found between Brownian motion attenuation ranges and number fluctuation attenuation ranges.At these points,the baselines are reset and the intensity ACFs are truncated,which removed the number fluctuation terms.The truncated intensity ACFs and field ACFs meet the Siegert relation,which means accurate PSDs can be obtained by the usual method.The simulations and experimental results show the accuracy of this method.4.The scattered light signals at ultra-low concentrations are simulated by the Autoregressive(AR)model to investigate the variation of number fluctuation terms under the small sample size of the scattered light signals.The insufficient samples of scattered light signals lead to deviations of intensity ACFs.At ultra-low concentrations,sufficient sample size is required to accurately estimate the number fluctuation term in the intensity ACF,while the samples of scattered light signals collected in experiments are often not enough to obtain the complete number fluctuation terms.Simulations and experiments show that,due to insufficient sample size,the amplitude of the number fluctuation term increases and the fitted characteristic time of number fluctuation is less than the actual value.With the development of the DLS technique application field,the measurement of ultra-low concentration particle systems has become an unavoidable problem in the application of submicron and nano particles.Through the analysis of the influence of particle number fluctuation term in intensity ACF on particle size inversion and the research on weakening the role of particle number fluctuation term in the inversion,this paper is benefital to expand the lower limit of concentration in DLS measurement and promotes the progress of DLS technique.