1979
DOI: 10.1002/macp.1979.021800119
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Inverse problems in polymer characterization: Direct analysis of polydispersity with photon correlation spectroscopy

Abstract: Dedicated to Prof. Dr. Leo De Maeyer on the occasion of his 501h birthday SUMMARY:A method is presented for inverting the Fredholm integral equations of the first kind that arise in many experimental determinations of molecular weight distributions of high polymers. The well known problems of instability and nonuniqueness are minimized by constraining the distribution to be the smoothest nonnegative one that is consistent with the data. Analyses of simulated photon correlation spectroscopy data show that good … Show more

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Cited by 803 publications
(478 citation statements)
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“…The particle size distribution from DLS measurement was derived by deconvolution of the measured intensity autocorrelation function of the sample. 40 Generally, deconvolution was accomplished using a non-negatively constrained least squares (NNLS) 41,42 fitting algorithm, common examples being CONTIN, 43 Regularization, and the General Purpose and Multiple Narrow Mode algorithms 44,45 included in the Zetasizer Nano software. The distribution was obtained by the NNLS method using an alpha value, which is a function parameter of the fitting sensitivity of the raw data.…”
Section: Calculation Of the Distribution Of Various Proteins From Dlsmentioning
confidence: 99%
“…The particle size distribution from DLS measurement was derived by deconvolution of the measured intensity autocorrelation function of the sample. 40 Generally, deconvolution was accomplished using a non-negatively constrained least squares (NNLS) 41,42 fitting algorithm, common examples being CONTIN, 43 Regularization, and the General Purpose and Multiple Narrow Mode algorithms 44,45 included in the Zetasizer Nano software. The distribution was obtained by the NNLS method using an alpha value, which is a function parameter of the fitting sensitivity of the raw data.…”
Section: Calculation Of the Distribution Of Various Proteins From Dlsmentioning
confidence: 99%
“…To obtain a distribution of relaxation rates in the studied system, spectra were analyzed by the line shape analysis 22 on the level of g (1) (q, t) instead of relying on an Inverse Laplace Transform of S(q, t) (e.g. CONTIN algorithm 32 ). The nonlinear-least-squares simplex-based minimization procedure fitted each g (1) (q, t) repeatedly to sums of stretched exponentials with different initial parameters and/or number of modes, checking for RMS error and numerical stability of the fits.…”
Section: Methodsmentioning
confidence: 99%
“…In order to characterize the hydrodynamic behavior of the suspended particles the multisampling time autocorrelation functions were analyzed by oneexponential fit (Microcal Origin  6.0) and by inverse Laplace transformation using the CONTIN 31 program.…”
Section: Methodsmentioning
confidence: 99%
“…31 This program determines G(Γ) by performing an inverse Laplace transform on equation (7). 8,33,34 Figure 3 shows time correlation functions well fitted through a single exponential for microemulsions containing either isoamyl or amyl alcohol as co-surfactant.…”
Section: Dynamic Light Scatteringmentioning
confidence: 99%