Analysis of Macromolecular Polydispersity in Intensity Correlation Spectroscopy: The Method of Cumulants
01 Dec 1972-Journal of Chemical Physics (American Institute of Physics)-Vol. 57, Iss: 11, pp 4814-4820
TL;DR: The first order electric field correlation function of laser light scattered by polydisperse solutions of macromolecules can be written as a sum or distribution of exponentials, with decay rates proportional to the diffusion coefficients of the solute molecules as discussed by the authors.
Abstract: The first order electric field correlation function of laser light scattered by polydisperse solutions of macromolecules can be written as a sum or distribution of exponentials, with decay rates proportional to the diffusion coefficients of the solute molecules. It is shown that the logarithm of this correlation function is formally equivalent to a cumulant generating function. A method is described by which the distribution function of the decay rates (and thus the extent of polydispersity) can be characterized, in a light scattering experiment, by calculation of the moments or cumulants. The systematic and random statistical errors in the calculated cumulants are discussed.
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Cites methods from "Analysis of Macromolecular Polydisp..."
...The cumulant analysis method was introduced by Koppel (1972) which became widely popular due to its ease and reliability, and was considered as the method of choice by the International Standards Organisation (ISO) in 1996 and again in 2008 (ISO 2008)....
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...Therefore, the high-order cumulants are not recommended to be used (Koppel 1972)....
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...Koppel (1972) derived the cumulat ivegenerating function K(−τ, Γ) that is related to the logarithm of g1(τ) and the m th cumulant of distribution function km(Γ): km Γð Þ ¼ d mK −τ ;Γð Þm d −τð Þ −τ ¼ 0 where; K −τ ;Γð Þ ¼ lng1 τð Þ ð15Þ The km(Γ) can be rewritten to derive moments about the mean…...
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TL;DR: The present review highlights the difficulties in validating the data from biodistribution studies without accurate particle size determination.
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TL;DR: In this paper, a framework for interpreting experiments on Doppler shifts in light scattering from pure liquids and polymer solutions is presented, where the spectral density of the light scattered into a given frequency range and angle by a liquid composed of identical, isotropic particles much smaller than the wavelength of the incident light is expressed in terms of the Fourier transform of the two-body space.
Abstract: A framework for interpreting experiments on Doppler shifts in light scattering from pure liquids and polymer solutions is presented. The spectral density of the light scattered into a given frequency range and angle by a liquid composed of identical, isotropic particles much smaller than the wavelength of the incident light is expressed in terms of the Fourier transform of the two‐body space—time correlation function. The formalism is then applied to the problem of light scattering from dilute polymer solutions. The Doppler shifts are evaluated for a polymer molecule undergoing translational Brownian motion, and for a rigid rod‐shaped molecule undergoing Brownian motion about its center of mass. It is concluded that for a pure liquid more accurate experiments are needed to determine the form of the long‐range part of the space—time correlation function. For polymer solutions, for which Doppler shift measurements have never been done, Doppler shift measurements should yield information about the shape of t...
329 citations
TL;DR: In this article, a mathematical approach based on the inversion of the Laplace integral equation by a method of Fourier transforms was proposed to estimate the physically significant parameters Ni and λi. The results of the analysis appeared in the form of a frequency spectrum.
Abstract: A frequently encountered problem in many branches of science involves the resolution of experimental data into a sum of independent exponential curves of the form f(t)= ∑ i=1nNiexp(−λit), in order to estimate the physically significant parameters Ni and λi. Such problems arise, for example, in the analysis of multicomponent radioactive decay curves, and in the study of the dielectric properties of certain compounds. This paper is concerned with the numerical evaluation of a mathematical approach to the problem. The approach is based on the inversion of the Laplace integral equation by a method of Fourier transforms. The results of the analysis appear in the form of a frequency spectrum. Each true peak in the spectrum indicates a component, the abscissa value at the center of the peak is the decay constant λi, while the height of the peak is directly proportional to Ni/λi. Results obtained on an IBM 650 computer indicate that the method may possess certain advantages over previous methods of analysis.
245 citations