Abstract
Provencher's constrained regularization method of inverting the Laplace transform was tested on 7 decades wide simulated quasielastic light scattering (QELS) data. The standard method with integration and logarithmic grid was shown to undersmooth seriously theG(Γ) distribution in the region of largeΓ (small relaxation timeτ). The regularization can be considerably improved by switching the integration off. Then, smooth distributions of relaxation timeτ of the generalized exponential type are reproduced essentially correctly with a tendency to replace asymmetric peaks by more symmetric ones with shoulders (in the Gaussian distribution ofτ) or side peaks (in the Gaussian distribution of 1/τ) on the slow decrease sides. In distributions with singularities such as edges of histogram bins or delta functions, the coarse shape of the distribution is recovered essentially correctly, but smoothing of singularities causes a distortion of wide regions of the relaxation spectrum usually in the form of sinusoidal waves. The bias introduced by taking the square root of theg 2 function was shown to worsen sometimes the CONTIN results considerably. Thus, the use of Provencher's CONTIN program with logarithmic grid and integration switched off is recommended for the analysis of very wide QELS autocorrelation curves.
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References
Štěpánek P., Koňák Č., Jakeš J.: Polym. Bull.16 (1986) 67.
Provencher S. W.: Comput. Phys. Commun.27 (1982) 213.
Stock R. S., Ray W. H.: J. Polym. Sci., Polym. Phys. Ed.23 (1985) 1393.
Provencher S. W.: Makromol. Chem.180 (1979) 201.
Kubín M.: Collect. Czech. Chem. Commun.32 (1967) 1505.
Provencher S. W.: Comput. Phys. Commun.27 (1982) 229.
McWhirter J. G., Pike E. R.: J. Phys. A: Math. Nucl. Gen.11 (1978) 1729.
Ray C., Smith W. T., Grandy J. R.: Maximum Entropy and Bayesian Methods in Inverse Problems. D. Reidel Publishing Company, München, 1985.
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The author is very indebted to Dr. P. Štěpanek for attracting his attention to the fact that the peak at greatestτ is usually much more smoothed than the other peaks in the standard CONTIN calculations, for making the installation of the standard CONTIN program on the computer Siemens 7536 available to him, for reading the manuscript, and for valuable comments.
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Jakeš, J. Testing of the constrained regularization method of inverting Laplace transform on simulated very wide quasielastic light scattering autocorrelation functions. Czech J Phys 38, 1305–1316 (1988). https://doi.org/10.1007/BF01597611
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DOI: https://doi.org/10.1007/BF01597611