Study On The Inversion Algorithms Of Bimodal Particle Size Distribution With Dynamic Light Scattering

Dynamic light scattering(DLS)is a widely used technique for estimating the particle size distribution(PSD)with particles in the submicrometer range,through the inversion of intensity autocorrelation function(ACF).However,the recovery of the PSD is an inherentely difficult problem for the Fredholm integral of the first kind.In order to get a more accurate PSD,we often use Tikhonov constrained regularization method(Tikhonov-CR).And the performance of this method would be usually affected by the random noise in ACF data and the measurement information hidden in the ACF data.The effect will be more serious in the measurement of the bimodal particle size distributon.In order to restrain the effect from the random noise in the ACF data and make the best use of the measurement information,realizing the recovery of the bimodal PSDs accurately,this paper porposed three modified methods based on the Tikhonov constrained regularization method,after analysing the distribution characteristic of the measurement information and the random no ise.Three methods are the characteristic weighted constrained regularization method(CW-CR method),the noise weighted constrained regularization method(NW-CR method),and the regional noise weighted constrained regularization method(NSW-CR method).By applying these methods in single-angle and multi-angle DLS,this paper studied the recovery performance of each methods.And the main work of this paper consists of,1.It was studied the intrinsic reasons of the poor results in the measurement of the bimodal PSDs,analyzing the distribution characteristic of the intensity ACF data.In this paper,the different bimodal PSDs and unimodal PSDs were measured with the DLS,and recovered by Tikhonov CR method.After the analysis of the ACF data and the recovery PSDs,the author found the reason of the poor result for bimodal particle systems.In the measurement of bimodal PSDs,the information of the particle size distribution will be decreased with the reduction of the the peak ratio of the PSDs.When the measurement information is not enough to achieve the inversion,the results will be bad,even causeing a large error.And Tikhonov-CR method used the same weight for the different ACF data,losing the information of the bimodal PSDs and making the results so poor.2.The CW-CR method was studied.In DLS,the information distribution in ACF data of bimode particle systems has the characteristic,growing to a maximum and then decressing.In order to make the best use of the information,the paper proposed CW-CR method based on the information distribution.By using different weight coefficients for the ACF data at different delay times,CW-CR method can improve the accuracy of the inversion of bimodal PSDs.3.The NW-CR method was studied.This paper mainly studied the internal mechanism of the influence of the random noise on the inversion of PSDs and the working principle of the NW-CR method.In DLS,the effect of the random noise would be different for different ACF data,and it would be more serious at the long delay time.In order to restrain this effect,this paper proposed the NW-CR method,based on the Tikhonov-CR method.This method restrained the effect of the random noise by using different weight coefficients for the ACF data with different noise,improving the recovery PSDs.And the multi-angle DLS data can provide more particle size information.So this paper achieved the recory of the bimodal PSDs with a peak position ratio of less than 2:1 and containing large particle(350nm),using the multi-angle DLS and the NW-CR method.4.The NSW-CR method was studed.This paper mainly studied the distribution characteristic of the random noise in ACF data and the measurement information.Base on this,this paper proposed the NSW-CR method.At different sections of the delay time in DLS,the measurement information would be different,and the effect of the noise is also different.By using different segment weighted adjustment parameters for the date in different section of delay time,the NSW-CR method can further restrain the effect of the random noise especially in the long delay time.Besides it can also make the measurement information more maximally adjusted and balanced,making the best use of the measurement information for a more accurate revovery of PSDs.So this method can realize the accurate inversion of bimodal PSDs,improved the accuracy and and ability of the results.The measurement of bimodal PSD is a difficult problem in the field of particle size measurement with dynamic light scattering.And it also is the research focus in this field.With the development of the submicron and nano materials,the demand of the bimodal particle system,especially with a small ratio of peak position,is increasing.The inversion of the bimodal PSDs was studied in this work and seeks to obtain more accurate PSD to meet the increasingly social requirements of complicated PSDs.