Diffusion Coefficients for Binary, Ternary, and Polydisperse Solutions from Peak-Width Analysis of Taylor Dispersion Profiles

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.