Diffusion coefficients for binary, ternary, and polydisperse solutions from peak-width analysis of taylor dispersion profiles

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(h)(2)) 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(h) (2)) 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.