Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles |
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Authors: | Rachel Callendar Derek G Leaist |
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Institution: | (1) Department of Chemistry, University of Western Ontario, London, Ontario, N6A 5B7, Canada |
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Abstract: | Binary mutual diffusion coefficients D can be estimated from the width at half height W
1/2 of Taylor dispersion profiles using D=(ln 2)r
2
t
R/(3W
2
h) and values of the retention time t
R and dispersion tube radius r. The generalized expression D
h=−(ln h)r
2
t
R/(3W
2
h
) is derived to evaluate diffusion coefficients from peak widths W
h
measured at other fractional heights (e.g., (h = 0.1, 0.2,…,0.9). Tests show that averaging the D
h
values from binary profiles gives mutual diffusion coefficients that are as accurate and precise as those obtained by more
elaborate nonlinear least-squares analysis. Dispersion profiles for ternary solutions usually consist of two superimposed
pseudo-binary profiles. Consequently, D
h
values for ternary profiles generally vary with the fractional peak height h. Ternary profiles with constant D
h
values can however be constructed by taking appropriate linear combinations of profiles generated using different initial
concentration differences. The invariant D
h
values and corresponding initial concentration differences give the eigenvalues and eigenvectors for the evaluation of the
ternary diffusion coefficient matrix. Dispersion profiles for polymer samples of N i-mers consist of N superimposed pseudo-binary profiles. The edges of these profiles are enriched in the heavier polymers owing to the decrease
in polymer diffusion coefficients with increasing polymer molecular weight. The resulting drop in D
h
with decreasing fractional peak height provides a signature of the polymer molecular weight distribution. These features
are illustrated by measuring the dispersion of mixed polyethylene glycols. |
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Keywords: | Diffusion mutual diffusion polydispersity Taylor dispersion Ternary diffusion |
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