Measurement of Ternary Mutual Diffusion Coefficients from Ill-Conditioned Taylor Dispersion Profiles in Cases of Identical or Nearly Identical Eigenvalues of the Diffusion Coefficient Matrix
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Bibliographic record
Abstract
Taylor dispersion has gained popularity for the measurement of mutual diffusion coefficients ( D ik ) for multicomponent solutions. In practice, however, the analysis of dispersion profiles, like the analysis of free-diffusion boundaries measured by optical interferometry, becomes ill-conditioned for solutes of similar diffusivities if the eigenvalues of the D ik matrix differ by less than about (5 to 10) %. These numerical difficulties, well-known in studies of multiexponential decays with nearly identical decay constants, can produce large errors in measured D ik coefficients and even rule out studies of important systems, including solutions of isomers, oligomers, polydisperse polymers, strongly associated solutes, and mixed electrolytes composed of ions of similar mobility. To investigate diffusion in these systems, equations are derived for the Taylor dispersion profiles produced by ternary mutual diffusion with equal eigenvalues. Using these equations, a simple least-squares procedure is developed to evaluate D ik coefficients from equal-eigenvalue profiles. D ik coefficients are reported from the analysis of severely ill-conditioned refractive-index profiles measured for aqueous solutions of 1-propanol + 2-propanol, 1-propanol + glycine, and mannitol + tetra(ethyleneglycol). In cases where the eigenvalues are not identical, but differ by several percent, the resulting errors in the D ik coefficients are estimated to be small and similar in magnitude to the accuracy of the Taylor measurements.
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| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.005 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
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