Continuous particle size distribution analysis with dynamic light scattering. MAXAMPER: a regularization method using the maximum amplitude for the average error and the Lagrange's multipliers method.
This work deals with a new method to evaluate the scattered light intensity distributions with particle size by means of photon correlation spectroscopy. Basically, the data analysis consists in: 1) To find the least squares solution (L2 norm), and 2) To find the solution that is not significantly different from the least squares solution (within a certain significance level) that simultaneously minimizes the sum of the modulus of the residuals (L1 norm). A simple procedure is achieved by using the Lagrange's multipliers method. The two aspects that debilitate CONTIN (a rather empirical regularization based on the continuity of the distributions and the non-suitable use of the Fisher's F test) are prevented in this work, granting more meaningful results. The method was applied to simulated curves, in several typical situations (mono-modal and bi-modal, narrow and broad distributions). The quality of the results is better for narrower mono-modal distributions and bi-modal distributions having well separated peaks, as expected. Latex beads (nanospheres) having 114 nm in diameter were used to test the method in experimental conditions. MAXAMPER better reproduces monodispersed distribution profiles than CONTIN and the first moments of the distributions are in agreement with the expected value in most of the analysis.
Departamento de Química e Bioquímica, Faculdade de Ciências da Universidade de Lisboa, Portugal.
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MX
Fernandes
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NC
Santos
M A
MA
Castanho
D000465:Algorithms; D008863:Microspheres; D010316:Particle Size; D012542:Scattering, Radiation; D013057:Spectrum Analysis / Q000379:methods; D013223:Statistics as Topic