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Free keywords:
Dynamic light scattering; Size distributions; Regularized inversion; Noise; Normalization errors; Resolution
Abstract:
The noise levels and the decay characteristics in experimental data from dynamic light scattering measurements determine the number of details of continuous size distributions that can be resolved. Here, a procedure is described that allows one to obtain resolution limits empirically from experimental data on hand. This is done by comparing differences of autocorrelation functions associated with size distributions of different complexity with noise in the experimental data. Size distributions of rather different complexity but related to autocorrelation functions that describe the experimental data nearly equally well are obtained from series of regularized inversions carried out by the size distribution algorithm CONTIN. The procedure is demonstrated with two data sets of different noise content. It is shown that a monomodal size distribution with a relative width (standard deviation/average radius) of about 0.2 can be determined with a high accuracy, when the residuals in data of the first order autocorrelation function are of the order of 10−4. A bimodal size distribution with narrow peaks of relative widths of about 0.05 and a size ratio of about 3:2, the autocorrelation function of which describes these data equally well, cannot be resolved from this level of noise. If data accuracy is increased about ten fold, it should be possible to distinguish between these two quite different size distributions and to make a decision on whether the underlying size distribution is actually a monomodal or a bimodal one. To obtain data of such high statistical accuracy would imply a rather long measurement duration yet.
