A Direct NMR Method To Measure Self‐Diffusion Coefficients in Liquids by Monitoring Diffusing Molecules through One‐Dimensional Imaging

ChemPhysChem ◽  
2021 ◽  
Author(s):  
Behdad Aghelnejad ◽  
Geoffrey Bodenhausen ◽  
Philippe Pelupessy
Keyword(s):  
Diffusion Coefficients ◽  
One Dimensional ◽  
Self Diffusion ◽  
Nmr Method

scholarly journals Revisiting Anisotropic Diffusion of Carbon Dioxide in the Metal-Organic Framework Zn2(dobpdc)

2018 ◽  
Author(s):  
Alexander C. Forse ◽  
Stephen A. Altobelli ◽  
Stefan Benders ◽  
Mark S. Conradi ◽  
Jeffrey A. Reimer
Keyword(s):  
Diffusion Coefficients ◽  
Metal Organic Framework ◽  
Chemical Shift Anisotropy ◽  
Structural Defects ◽  
Gradient Field ◽  
Line Broadening ◽  
One Dimensional ◽  
Self Diffusion ◽  
Metal Organic ◽  
D Values

The diffusion of gases confined in nanoporous materials underpins membrane and adsorption-based gas separations, yet relatively few measurements of diffusion coefficients in the promising class of materials, metal-organic frameworks (MOFs), have been reported to date. Recently we reported self-diffusion coefficients for <sup>13</sup>CO<sub>2</sub> in the MOF, Zn<sub>2</sub>(dobpdc), (dobpdc<sup>4–</sup> = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) that has one-dimensional channels with a diameter of approximately 2 nm. By analyzing the evolution of the residual <sup>13</sup>C chemical shift anisotropy lineshape at different gradient strengths, we obtained self-diffusion coefficients both along (D<sub>||</sub>) and between (D<sub>⊥</sub>) the one-dimensional MOF channels. The observation of non-zero D⊥ was unexpected based on the single crystal X-ray diffraction structure and flexible lattice molecular dynamics simulations, and we proposed that structural defects may be responsible for self-diffusion between the MOF channels. Here we revisit this analysis and show that homogeneous line broadening must be taken into account to obtain accurate values for D⊥. In the presence of homogeneous line broadening, intensity at a particular NMR frequency represents signal from crystals with a range of orientations relative to the applied magnetic field and magnetic gradient field. To quantify these effects, we perform spectral simulations that take into account homogeneous broadening and allow improved D⊥ values to be obtained. Our new analysis best supports non-zero D⊥ at all studied dosing pressures and shows that our previous analysis overestimated D⊥.

scholarly journals Revisiting Anisotropic Diffusion of Carbon Dioxide in the Metal-Organic Framework Zn2(dobpdc)

2018 ◽  
Author(s):  
Alexander C. Forse ◽  
Stephen A. Altobelli ◽  
Stefan Benders ◽  
Mark S. Conradi ◽  
Jeffrey A. Reimer
Keyword(s):  
Diffusion Coefficients ◽  
Metal Organic Framework ◽  
Chemical Shift Anisotropy ◽  
Structural Defects ◽  
Gradient Field ◽  
Line Broadening ◽  
One Dimensional ◽  
Self Diffusion ◽  
Metal Organic ◽  
D Values

The diffusion of gases confined in nanoporous materials underpins membrane and adsorption-based gas separations, yet relatively few measurements of diffusion coefficients in the promising class of materials, metal-organic frameworks (MOFs), have been reported to date. Recently we reported self-diffusion coefficients for <sup>13</sup>CO<sub>2</sub> in the MOF, Zn<sub>2</sub>(dobpdc), (dobpdc<sup>4–</sup> = 4,4′-dioxidobiphenyl-3,3′-dicarboxylate) that has one-dimensional channels with a diameter of approximately 2 nm. By analyzing the evolution of the residual <sup>13</sup>C chemical shift anisotropy lineshape at different gradient strengths, we obtained self-diffusion coefficients both along (D<sub>||</sub>) and between (D<sub>⊥</sub>) the one-dimensional MOF channels. The observation of non-zero D⊥ was unexpected based on the single crystal X-ray diffraction structure and flexible lattice molecular dynamics simulations, and we proposed that structural defects may be responsible for self-diffusion between the MOF channels. Here we revisit this analysis and show that homogeneous line broadening must be taken into account to obtain accurate values for D⊥. In the presence of homogeneous line broadening, intensity at a particular NMR frequency represents signal from crystals with a range of orientations relative to the applied magnetic field and magnetic gradient field. To quantify these effects, we perform spectral simulations that take into account homogeneous broadening and allow improved D⊥ values to be obtained. Our new analysis best supports non-zero D⊥ at all studied dosing pressures and shows that our previous analysis overestimated D⊥.

scholarly journals Theoretical Modelling of Ion Exchange Processes in Glass: Advances and Challenges

2021 ◽  
Vol 11 (11) ◽  
pp. 5070
Author(s):  
Xesús Prieto-Blanco ◽  
Carlos Montero-Orille
Keyword(s):  
Ion Exchange ◽  
Diffusion Coefficients ◽  
Molten Salts ◽  
Theoretical Modelling ◽  
Copper Films ◽  
Theoretical Frameworks ◽  
Self Diffusion ◽  
Exchange Processes ◽  
The One ◽  
Made In

In the last few years, some advances have been made in the theoretical modelling of ion exchange processes in glass. On the one hand, the equations that describe the evolution of the cation concentration were rewritten in a more rigorous manner. This was made into two theoretical frameworks. In the first one, the self-diffusion coefficients were assumed to be constant, whereas, in the second one, a more realistic cation behaviour was considered by taking into account the so-called mixed ion effect. Along with these equations, the boundary conditions for the usual ion exchange processes from molten salts, silver and copper films and metallic cathodes were accordingly established. On the other hand, the modelling of some ion exchange processes that have attracted a great deal of attention in recent years, including glass poling, electro-diffusion of multivalent metals and the formation/dissolution of silver nanoparticles, has been addressed. In such processes, the usual approximations that are made in ion exchange modelling are not always valid. An overview of the progress made and the remaining challenges in the modelling of these unique processes is provided at the end of this review.

scholarly journals Self-Diffusion Coefficients, Aggregation Numbers and the Range of Existence of Spherical Micelles of Oxyethylated Alkylphenols

2021 ◽  
Author(s):  
Victor P. Arkhipov ◽  
Natalia A. Kuzina ◽  
Andrei Filippov
Keyword(s):  
Aqueous Solutions ◽  
Diffusion Coefficients ◽  
The Self ◽  
Self Diffusion ◽  
Aggregation Numbers ◽  
Temperature Ranges ◽  
Spherical Micelles ◽  
Limiting Values

AbstractAggregation numbers were calculated based on measurements of the self-diffusion coefficients, the effective hydrodynamic radii of micelles and aggregates of oxyethylated alkylphenols in aqueous solutions. On the assumption that the radii of spherical micelles are equal to the lengths of fully extended neonol molecules, the limiting values of aggregation numbers corresponding to spherically shaped neonol micelles were calculated. The concentration and temperature ranges under which spherical micelles of neonols are formed were determined.

scholarly journals Effect of Modification on the Fluid Diffusion Coefficient in Silica Nanochannels

Molecules ◽  
2021 ◽  
Vol 26 (13) ◽  
pp. 4030
Author(s):  
Gengbiao Chen ◽  
Zhiwen Liu
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Surface Effect ◽  
Bulk Water ◽  
Self Diffusion ◽  
Average Diffusion Coefficient ◽  
Average Diffusion ◽  
Chain Lengths ◽  
Fluid Diffusion ◽  
Self Diffusion Coefficient

The diffusion behavior of fluid water in nanochannels with hydroxylation of silica gel and silanization of different modified chain lengths was simulated by the equilibrium molecular dynamics method. The diffusion coefficient of fluid water was calculated by the Einstein method and the Green–Kubo method, so as to analyze the change rule between the modification degree of nanochannels and the diffusion coefficient of fluid water. The results showed that the diffusion coefficient of fluid water increased with the length of the modified chain. The average diffusion coefficient of fluid water in the hydroxylated nanochannels was 8.01% of the bulk water diffusion coefficient, and the diffusion coefficients of fluid water in the –(CH2)3CH3, –(CH2)7CH3, and –(CH2)11CH3 nanochannels were 44.10%, 49.72%, and 53.80% of the diffusion coefficients of bulk water, respectively. In the above four wall characteristic models, the diffusion coefficients in the z direction were smaller than those in the other directions. However, with an increase in the silylation degree, the increased self-diffusion coefficient due to the surface effect could basically offset the decreased self-diffusion coefficient owing to the scale effect. In the four nanochannels, when the local diffusion coefficient of fluid water was in the range of 8 Å close to the wall, Dz was greater than Dxy, and beyond the range of 8 Å of the wall, the Dz was smaller than Dxy.

Self-diffusion of bimodal suspensions of hydrodynamically interacting spherical particles in shearing flow

1994 ◽  
Vol 281 ◽  
pp. 51-80 ◽  
Author(s):  
Chingyi Chang ◽  
Robert L. Powell
Keyword(s):  
Diffusion Coefficients ◽  
Cluster Size ◽  
Near Field ◽  
Spherical Particles ◽  
Random Structure ◽  
Shearing Flow ◽  
Self Diffusion ◽  
Long Time ◽  
Mobility Matrix ◽  
Many Body Interactions

We study the average mobilities and long-time self-diffusion coefficients of a suspension of bimodally distributed spherical particles. Stokesian dynamics is used to calculate the particle trajectories for a monolayer of bimodal-sized spheres. Hydrodynamic forces only are considered and they are calculated using the inverse of the grand mobility matrix for far-field many-body interactions and lubrication formulae for near-field effects. We determine both the detailed microstructure (e.g. the pair-connectedness function and cluster formation) and the macroscopic properties (e.g. viscosity and self-diffusion coefficients). The flow of an ‘infinite’ suspension is simulated by considering 25, 49, 64 and 100 particles to be one ‘cell’ of a periodic array. Effects of both the size ratio and the relative fractions of the different-sized particles are examined. For the microstructures, the pair-connectedness function shows that the particles form clusters in simple shearing flow due to lubrication forces. The nearly symmetric angular structures imply the absence of normal stress differences for a suspension with purely hydrodynamic interactions between spheres. For average mobilities at infinite Péclet number, Ds0, our simulation results suggest that the reduction of Ds0 as concentration increases is directly linked to the influence of particle size distribution on the average cluster size. For long-time self-diffusion coefficients, Ds∞, we found good agreement between simulation and experiment (Leighton & Acrovos 1987 a; Phan and Leighton 1993) for monodispersed suspensions. For bimodal suspensions, the magnitude of Ds∞, and the time to reach the asymptotic diffusive behaviour depend on the cluster size formed in the system, or the viscosity of the suspension. We also consider the effect of the initial configuration by letting the spheres be both organized (size segregated) and randomly placed. We find that it takes a longer time for a suspension with an initially organized structure to achieve steady state than one with a random structure.

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