Polydisperse diffusion coefficient

The translational diffusion coefficient in Eq. 11 can in principle be measured from boimdary spreading as manifested for example in the width of the g (s) profiles although for monodisperse proteins this works well, for polysaccharides interpretation is seriously complicated by broadening through polydispersity. Instead special cells can be used which allow for the formation of an artificial boundary whose diffusion can be recorded with time at low speed ( 3000 rev/min). This procedure has been successfully employed for example in a recent study on heparin fractions [5]. Dynamic fight scattering has been used as a popular alternative, and a good demonstra-... 

Here, S0 is the signal when G = 0, D is the self-diffusion coefficient, yG is the gyromagnetic ratio and am are roots of the Bessel function equation amaf3 2(ama) — (l/2)J3/2(a ma) = 0. If the system is polydisperse, the signal decay is due to contributions from droplets of different sizes. Then, the signal attenuation is given by the volume average over all sizes as... 

In a sedimentation equilibrium run, the stationary radial concentration profile, which is established after a few hours for a 1-mm column, is analyzed according to Equation (72) or, in case of polydisperse samples, Equations (74) or (75). Contrary to the sedimentation velocity experiment, the diffusion coefficient D is not required. 

If one does not use the short gradient pulse (SGP) approximation, the term A has to be substituted with (A 8/3). In the case of a mono-disperse system, the plot of ln(E) versus y2g282A is a straight line having the absolute value of the slope equal to the self-diffusion coefficient. For polydisperse sample, the signal intensity decay can be interpreted in terms of a distribution of diffusing species ... 

Among the many industrial applications, one can recall the analyses on carbon black, where FIFFF and SdFFF were used in synergy, and on carbon nanotube, for which a frit inlet AsFlFFF channel was used. Water-soluble polydisperse polymers were fractionated, with a very high selectivity, according to differences in the diffusion coefficient, yielding a diffusion coefficient spectrum which was then converted into a molecular weight (M) distribution curve based on the relationship between D and molecular weight [36]. 

In this contribution, the experimental concept and a phenomenological description of signal generation in TDFRS will first be developed. Then, some experiments on simple liquids will be discussed. After the extension of the model to polydisperse solutes, TDFRS will be applied to polymer analysis, where the quantities of interest are diffusion coefficients, molar mass distributions and molar mass averages. In the last chapter of this article, it will be shown how pseudostochastic noise-like excitation patterns can be employed in TDFRS for the direct measurement of the linear response function and for the selective excitation of certain frequency ranges of interest by means of tailored pseudostochastic binary sequences. 

K represents the following constant parameters n is the index of refraction of the liquid, X is the laser wavelength in air, and 0 is the angle at which the scattering intensity is measured. For polydisperse samples, the autocorrelation function plot is the sum of exponentials for each size range. Once the average translational diffusion coefficient of the sample is determined, the equivalent spherical diameter can be determined by using the Stokes-Einstein... 

Lead, J. R., Wilkinson, K. J., Balnois, E., Cutak, B. J., Larive, C. K., Assemi, S., and Beckett, R. (2000). Diffusion coefficients and polydispersities of the Suwannee River Fulvic Acid Comparison of fluorescence correlation spectroscopy, pulsed-field gradient nuclear magnetic resonance, and flow field-flow fractionation. Environ. Sci. Technol. 34(16), 3508-3513. 

Third, a serious need exists for a data base containing transport properties of complex fluids, analogous to thermodynamic data for nonideal molecular systems. Most measurements of viscosities, pressure drops, etc. have little value beyond the specific conditions of the experiment because of inadequate characterization at the microscopic level. In fact, for many polydisperse or multicomponent systems sufficient characterization is not presently possible. Hence, the effort probably should begin with model materials, akin to the measurement of viscometric functions [27] and diffusion coefficients [28] for polymers of precisely tailored molecular structure. Then correlations between the transport and thermodynamic properties and key microstructural parameters, e.g., size, shape, concentration, and characteristics of interactions, could be developed through enlightened dimensional analysis or asymptotic solutions. These data would facilitate systematic... 

The relative second moment, K2 jF, a dimensionless quantity, is a measure of polydispersity. It is the intensity-weighted variance divided by the square of the intensity-weighted average of the diffusion coefficient distribution. The relative second moment is also called the polydispersity... 

For S v Si, we observed variations of I with the scattering wave-vector but this was not the case for the diffusion coefficient. Furthermore, the autocorrelation function of the scattered intensity showed significant deviations from an exponential form. This indicates an increasing polydispersity of the droplets when S increases. 

In polydisperse solutions, the decay of the autocorrelation function is not a single exponential and it is challenging to extract the distributions of diffusion coefficients and sizes from the non-exponential decay of the intensity correlations. In the case of a bidisperse distribution with diffusion coefficients that differ by at least a factor of 2, it is possible to fit the decay of the intensity correlations by a sum of two exponentials and obtain the corresponding sizes and relative concentrations of the two components -----------------------------------------------------------... 

Most ultracentrifuge studies of humic substances have used the sedimentation-velocity method. Flaig et al. (1975) have reviewed this work. In general, the results of this work indicated that all the solutions studied were polydisperse as we have discussed previously, in a polydisperse system, the ordinary sedimentation-velocity equation cannot be applied because each different particle size has a different diffusion coefficient and different sedimentation constant. 

In the presence of size polydispersity, there is an additional incoherent contribution to C(, t) decaying through the self-diffusion coefficient Ds((/)) [42,43,91]. The latter can also be measured for monodisperse hard sphere suspensions at finite concentrations at qR corresponding to the first minimum of S( ), i.e., when the interactions can be ignored [91]. These three different diffusion coefficients exhibit distinctly different dependence on q and 0. From these three transport quantities, Z>cou( ) is absent in monodisperse homopolymers, whereas Ds can hardly be measured in polydisperse homopolymers due to the vanishingly small contrast. 

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