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Free keywords:
photon-correlation spectroscopy; size distributions; normalization errors; regularization method; submicron particles; colloidal particles; integral-equations; posed problems; human lymph; l-curve
Abstract:
Laser drifts, dust, and impurities in a sample are physical reasons for offsets in both field and intensity autocorrelation functions. In this paper, a method is described by which the two offsets are determined by a variation method. Data were analyzed with the size distribution algorithm CONTIN, using the selection method of L-curves for getting the offsets and a combination of the methods of F-test, stability plot, and L- curve for getting the final solution from the corrected data. This solution was selected according to the parsimony principle, under which the preferred solution is that with the simplest size distribution. Consistency was checked by means of two additional tools. The first is the difference between the field autocorrelation function of a regularized solution and the least-squares solution, called the difference in g1, which is compared with the residuals of the least-squares solution. The second is the relative increase in variance or the discrepancy from the best fit solution. The procedure for the determination of the offsets is described by means of experimental data of high statistical accuracy from a semidilute aqueous solution of the surfactant octaethylene glycol dodecyl monoether (C12E8). The method was tested with data containing different contributions of dust and with data from different poly(ethylene glycol) n-alkyl monoethers (C12E8, C14E8, and C16E8). After correction of the data for the two offsets, the Size distributions obtained from data analysis were free of elements of unstable solutions such as side peaks at the integration limits. It is shown that differences in the size characteristics of narrow monomodal distributions of about 0.3-0.4 nm can be distinguished and that two peaks of a bimodal size distribution with a size ratio of 2:1 can be resolved.
