Modification of the Stokes–Einstein Equation with a Semiempirical Microfriction Factor for Correlation of Tracer Diffusivities in Organic Solvents

Chen, Shaw H.; Wei, Simon K.-H.

doi:10.1021/ie201438h

Cited by 11 publications

(9 citation statements)

References 39 publications

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“… Diffusion coefficients were referenced to the diffusivity of a spherical, noninteracting molecule (TMS), which functioned as an internal viscosity standard. Here, D i and D st are diffusion coefficients of the species of interest and the standard, respectively, k B is Boltzmann’s constant, T is the absolute temperature, η is the solvent viscosity, R i and R st are the hydrodynamic radii of the species of interest and the standard, respectively, and c is a shape correction factor to account for nonspherical sample molecules and is calculated empirically (eq ). …”

Section: Resultsmentioning

confidence: 99%

Ionic Liquid Aggregation Mechanism for Nanoparticle Synthesis

2020

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Nanoparticle synthesis with silylamine reversible ionic liquids (RevILs) has been previously demonstrated to offer unique alternatives to traditional nanoparticle syntheses, allowing for size control and facile deposition onto support surfaces via the switchable nature of the IL. However, the mechanism of nanoparticle synthesis remains uncharacterized. The use of RevILs facilitates the synthesis of size-controlled nanoparticles without the use of additional stabilizing agents (i.e., surfactants, ligands, and polymers) that passivate the nanoparticle surface, which are traditionally required to control the nanoparticle size. Traditional techniques often require harsh activation steps that ultimately impact nanoparticle size and morphology. While RevIL syntheses offer an excellent alternative, as they do not require additional activation steps, the mechanism through which nanoparticles are synthesized in these systems has not been studied previously. Preceding work hypothesized nanoparticles prepared with RevILs are formed via a reverse micelle mechanism, in which nanoparticles are stabilized and templated within the aqueous core of the organized micelle structures. In this work, DOSY-NMR is used to demonstrate that nanoparticles synthesized with 3-aminopropyltriethylsilane RevIL are not formed through a reverse micelle mechanism but rather a switchable aggregation mechanism that affords control over the nanoparticle size via manipulation of the RevIL structure and concentration. Furthermore, it is shown that the addition of water to RevIL systems has detrimental effects on the aggregation behavior of the ionic liquid molecules in solution, causing disassembly of the ion pairs. However, because nanoparticle reduction likely occurs faster than the disassembly of the ion pairs, nanoparticle size is unaffected by the addition of water during nanoparticle reduction.

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Section: Resultsmentioning

confidence: 99%

Ionic Liquid Aggregation Mechanism for Nanoparticle Synthesis

2020

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“… where D i and D st are the diffusivities of the sample and the standard, respectively; k B is Boltzmann’s contant; T is temperature; c i is the shape factor; η is the viscosity of the solvent; and R i is the hydrodynamic radius. The size factors were determined empirically with eq …”

Section: Resultsmentioning

confidence: 99%

Precursor Ion–Ion Aggregation in the Brust–Schiffrin Synthesis of Alkanethiol Nanoparticles

et al. 2016

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Tetraoctylammonium bromide is used in the Brust–Schiffrin nanoparticle synthesis to phase-transfer chloroaurate ions from the aqueous phase to the organic phase. While it is established that the quaternary ammonium complex self-associates in the organic phase, the actual self-assembled structure is poorly understood. We have confirmed the presence of ion–ion aggregates through quantitative 1H nuclear magnetic resonance spectroscopy (NMR), pulsed field gradient, diffusion-ordered NMR (DOSY-NMR), and density functional theory (DFT) based NMR chemical shift calculations. Tetraoctylammonium complexes (TOA-X, where X = Br, Cl, AuCl4–x Br x , AuBr4/Br, and AuBr4/Cl/Br) were investigated to measure the extraction of water into deuterated chloroform. 1H NMR- and DFT-based NMR shielding calculations indicated that deshielding of water is due to hydration of the anion and not the formation of the aqueous core of a reverse micelle. DOSY-NMR results were consistent with the formation of small aggregates at typical Brust–Schiffrin synthesis concentrations. The extent of aggregation correlated with the electronegativity of the anion and was analyzed with a modified, isodesmic, indefinite aggregation model. The substitution of bromoauric acid for chlororoauric acid at conditions emulating the Brust–Schiffrin synthesis in chloroform increased the aggregation of the quaternary ammonium complex. The increase in aggregation corresponded with an increase in the size of the produced nanoparticles from 4.3 to 4.6 nm. Understanding the self-assembly and supramolecular structure of precursors in the Brust–Schiffrin synthesis will enable further refinement of models describing the growth of noble metal nanoparticles.

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“…Due to the constant need for reliable estimation of diffusivities, modeling and correlation of diffusion data have long been a subject of immense research interest. Currently, publications found in this area of study are considerable in the literature. − There is clearly still a strong demand for good models and general equations that can be applied to accurately correlate or predict diffusivities of solute compounds in solutions, especially those that are applicable for a broad range of solvents and temperatures.…”

Section: Introductionmentioning

confidence: 99%

Diffusivities of Aromatic Compounds: A New Molecular-Hydrodynamic Model for Nonassociated Pseudoplanar Solutes at Infinite Dilution

Chan

Chang

et al. 2019

Ind. Eng. Chem. Res.

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Diffusivities of nonassociated aromatic compounds at infinite dilution in methanol and in cyclohexane were measured by the Taylor dispersion method. At constant temperatures, the diffusivity reciprocals of the pseudoplanar solutes in either solvent showed a linear dependence on the molecular volumes of the solutes. The activation energies of solute diffusion were determined, and the results for each solvent indicated that such energies are fairly insensitive to the size and mass of the disc-shaped solutes ranging from benzene to hexamethylbenzene. The effects of temperature, solute size, and solvent properties on diffusivity were further found to be accurately described by a new molecular-modified fractional Stokes–Einstein relation. Employing additional literature diffusivities for the same type of solutes, a general fractional molecular-hydrodynamic equation with only two constants has been established to predict 326 limiting mutual diffusivities that cover a broad range of solutes, solvents, and temperatures to an average absolute deviation of 2.61% only.

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Modification of the Stokes–Einstein Equation with a Semiempirical Microfriction Factor for Correlation of Tracer Diffusivities in Organic Solvents

Cited by 11 publications

References 39 publications

Ionic Liquid Aggregation Mechanism for Nanoparticle Synthesis

Ionic Liquid Aggregation Mechanism for Nanoparticle Synthesis

Precursor Ion–Ion Aggregation in the Brust–Schiffrin Synthesis of Alkanethiol Nanoparticles

Diffusivities of Aromatic Compounds: A New Molecular-Hydrodynamic Model for Nonassociated Pseudoplanar Solutes at Infinite Dilution

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