Theoretical interpretations of diffusion coefficients

Tyrrell, H. J. V.

doi:10.1016/b978-0-408-17591-3.50010-1

Cited by 60 publications

(96 citation statements)

References 189 publications

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“…52,53 The term intradiffusion was probably first introduced by Albright and Mills. 68,69 Following these authors, in the book by Tyrrell and Harris, 70 self-diffusion is considered as a special case of intradiffusion in a system which contains only two distinguishable (by isotopic labeling, for example) forms of the same chemical species. Self-diffusion can be measured at low concentrations when the interaction between particles is negligible.…”

Section: Cross-diffusion Without Reactionmentioning

confidence: 99%

“…70 Three approaches, the optical interferometry technique, 59 the diaphragm-cell technique, 61 and the Taylor dispersion technique [64][65][66] have been adapted for measuring cross-diffusion coefficients. Such powerful methods as dynamic light scattering (DLS) and pulsed NMR have not thus far been utilized to determine cross-diffusion coefficients.…”

Section: Cross-diffusion Without Reactionmentioning

confidence: 99%

“…Cross diffusion for charged particles at very low concentrations (infinitely dilute solutions) can be described with the NernstHartley equations, 70,[95][96][97] valid when the off-diagonal Onsager coefficients are zero. These equations are often used, even at large concentrations of charged species, to provide at least a qualitative description of diffusion processes.…”

Section: Cross-diffusion Without Reactionmentioning

confidence: 99%

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Cross-diffusion and pattern formation in reaction–diffusion systems

Vanag

Epstein

2009

Phys. Chem. Chem. Phys.

272

199

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Cross-diffusion, the phenomenon in which a gradient in the concentration of one species induces a flux of another chemical species, has generally been neglected in the study of reaction-diffusion systems.We summarize experiments that demonstrate that cross-diffusion coefficients can be quite significant, even exceeding ''normal,'' diagonal diffusion coefficients in magnitude in systems that involve ions, micelles, complex formation, excluded volume effects (e.g., surface or polymer reactions) and other phenomena commonly encountered in situations of interest to chemists. We then demonstrate with a series of model calculations that cross-diffusion can lead to spatial and spatiotemporal pattern formation, even in relatively simple systems. We also show that, in the absence of cross-diffusion among the reacting species, introduction of a nonreactive species that induces appropriate cross-diffusive fluxes with reactive species can lead to pattern formation.

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Section: Cross-diffusion Without Reactionmentioning

confidence: 99%

Section: Cross-diffusion Without Reactionmentioning

confidence: 99%

Section: Cross-diffusion Without Reactionmentioning

confidence: 99%

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Cross-diffusion and pattern formation in reaction–diffusion systems

Vanag

Epstein

2009

Phys. Chem. Chem. Phys.

272

199

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“…The experimental methods that were used to measure mutual differential diffusion coefficients are: conductimetric (uncertainty ± 0.2%) [18][19][20][21][22][23][24][25][26][27][28]; Gouy and Rayleigh interferometry (uncertainty b0.1%) [21]; and Taylor dispersion (uncertainty ± 1-2%) [21]. The experimental diffusion coefficients, D, in aqueous solutions of electrolytes, at 25°C, were collected from Refs.…”

Section: Estimation Of a From Experimental Mean Ionic Activity Coeffimentioning

confidence: 99%

“…The experimental diffusion coefficients, D, in aqueous solutions of electrolytes, at 25°C, were collected from Refs. [4,[21][22][23][24][25][26][27][28] and, for two cases (NaClO 4 and NaClO 3 ), measured recently with our technique [19,20]. They were used to calculate the values of a shown in Table 1, assuming the Onsager-Fuoss model Eq.…”

Section: Estimation Of a From Experimental Mean Ionic Activity Coeffimentioning

confidence: 99%

Mean distance of closest approach of ions: Sodium salts in aqueous solutions

Ribeiro

Esteso

Lobo

et al. 2006

Journal of Molecular Liquids

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Synthesis, Crystal Structures, and Ion Pairing of κ⁶N Complexes with Rare‐Earth Elements in the Solid State and in Solution

Wingering,

Hohnstein,

Krämer

et al. 2023

Chemistry A European J

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The rare earth element complexes (Ln=Y, La, Sm, Lu, Ce) of several podant k 6 N-coordinating ligands have been synthetized and thoroughly characterized. The structural properties of the complexes have been investigated by X-ray diffraction in the solid state and by advanced NMR methods in solution. To estimate the donor capabilities of the presented ligands, an experimental comparison study has been conducted by cyclic voltammetry as well as absorption experiments using the cerium complexes and by analyzing 89 Y NMR chemical shifts of the different yttrium complexes. In order to obtain a complete and detailed picture, all experiments were corroborated by state-of-the-art quantum chemical calculations. Finally, coordination competition studies have been carried out by means of 1 H and 31 P NMR spectroscopy to investigate the correlation with donor properties and selectivity.

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Theoretical interpretations of diffusion coefficients

Cited by 60 publications

References 189 publications

Cross-diffusion and pattern formation in reaction–diffusion systems

Cross-diffusion and pattern formation in reaction–diffusion systems

Mean distance of closest approach of ions: Sodium salts in aqueous solutions

Synthesis, Crystal Structures, and Ion Pairing of κ⁶N Complexes with Rare‐Earth Elements in the Solid State and in Solution

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Theoretical interpretations of diffusion coefficients

Cited by 60 publications

References 189 publications

Cross-diffusion and pattern formation in reaction–diffusion systems

Cross-diffusion and pattern formation in reaction–diffusion systems

Mean distance of closest approach of ions: Sodium salts in aqueous solutions

Synthesis, Crystal Structures, and Ion Pairing of κ6N Complexes with Rare‐Earth Elements in the Solid State and in Solution

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Product

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Synthesis, Crystal Structures, and Ion Pairing of κ⁶N Complexes with Rare‐Earth Elements in the Solid State and in Solution