scholarly journals Molecular Modeling to Estimate the Diffusion Coefficients of Drugs and Other Small Molecules

Molecules ◽  
2020 ◽  
Vol 25 (22) ◽  
pp. 5340
Author(s):  
Shuichi Miyamoto ◽  
Kazumi Shimono
Keyword(s):  
Diffusion Coefficient ◽  
Molecular Modeling ◽  
Small Molecules ◽  
Einstein Equation ◽  
Diffusion Coefficients ◽  
Small Deviation ◽  
Molecular Transport ◽  
Diffusion Rates ◽  
Van Der Waals Radii ◽  
Potential Use

Diffusion is a spontaneous process and one of the physicochemical phenomena responsible for molecular transport, the rate of which is governed mainly by the diffusion coefficient; however, few coefficients are available because the measurement of diffusion rates is not straightforward. The translational diffusion coefficient is related by the Stokes–Einstein equation to the approximate radius of the diffusing molecule. Therefore, the stable conformations of small molecules were first calculated by molecular modeling. A simple radius rs and an effective radius re were then proposed and estimated using the stable conformers with the van der Waals radii of atoms. The diffusion coefficients were finally calculated with the Stokes–Einstein equation. The results showed that, for the molecules with strong hydration ability, the diffusion coefficients are best given by re and for other compounds, rs provided the best coefficients, with a reasonably small deviation of ~0.3 × 10−6 cm2/s from the experimental data. This demonstrates the effectiveness of the theoretical estimation approach, suggesting that diffusion coefficients have potential use as an additional molecular property in drug screening.

scholarly journals Viscosities, diffusion coefficients, and mixing times of intrinsic fluorescent organic molecules in brown limonene secondary organic aerosol and tests of the Stokes–Einstein equation

2019 ◽  
Vol 19 (3) ◽  
pp. 1491-1503 ◽  
Author(s):  
Dagny A. Ullmann ◽  
Mallory L. Hinks ◽  
Adrian M. Maclean ◽  
Christopher L. Butenhoff ◽  
James W. Grayson ◽  
...  
Keyword(s):  
Einstein Equation ◽  
Diffusion Coefficients ◽  
Organic Molecules ◽  
Secondary Organic Aerosol ◽  
Organic Aerosol ◽  
High Mass ◽  
Einstein Relation ◽  
Mixing Times ◽  
Diffusion Rates ◽  
And Diffusion

Abstract. Viscosities and diffusion rates of organics within secondary organic aerosol (SOA) remain uncertain. Using the bead-mobility technique, we measured viscosities as a function of water activity (aw) of SOA generated by the ozonolysis of limonene followed by browning by exposure to NH3 (referred to as brown limonene SOA or brown LSOA). These measurements together with viscosity measurements reported in the literature show that the viscosity of brown LSOA increases by 3–5 orders of magnitude as the aw decreases from 0.9 to approximately 0.05. In addition, we measured diffusion coefficients of intrinsic fluorescent organic molecules within brown LSOA matrices using rectangular area fluorescence recovery after photobleaching. Based on the diffusion measurements, as the aw decreases from 0.9 to 0.33, the average diffusion coefficient of the intrinsic fluorescent organic molecules decreases from 5.5×10-9 to 7.1×10-13 cm2 s−1 and the mixing times of intrinsic fluorescent organic molecules within 200 nm brown LSOA particles increases from 0.002 to 14 s. These results suggest that the mixing times of large organics in the brown LSOA studied here are short (<1 h) for aw and temperatures often found in the planetary boundary layer (PBL). Since the diffusion coefficients and mixing times reported here correspond to SOA generated using a high mass loading (∼1000 µg m−3), biogenic SOA particles found in the atmosphere with mass loadings ≤10 µg m−3 are likely to have higher viscosities and longer mixing times (possibly 3 orders of magnitude longer). These new measurements of viscosity and diffusion were used to test the accuracy of the Stokes–Einstein relation for predicting diffusion rates of organics within brown LSOA matrices. The results show that the Stokes–Einstein equation gives accurate predictions of diffusion coefficients of large organics within brown LSOA matrices when the viscosity of the matrix is as high as 102 to 104 Pa s. These results have important implications for predicting diffusion and mixing within SOA particles in the atmosphere.

scholarly journals The diffusion coefficients of dye solutions and their interpretation

1935 ◽  
Vol 148 (865) ◽  
pp. 681-695 ◽  
Keyword(s):  
Particle Size ◽  
Diffusion Coefficient ◽  
Einstein Equation ◽  
Diffusion Coefficients ◽  
Complex Ions ◽  
Nernst Equation ◽  
Theoretical Paper ◽  
Qualitative Measure ◽  
Dye Solutions

In a previous theoretical paper Hartley and Robinson have pointed out what very misleading results are obtained in calculating the particle size of a dye from the diffusion coefficient if the Stokes-Einstein equation is used and the electrical forces are neglected. The complicating effect of the electrical forces on the diffusion coefficient has, of course, been realized in researches on other colloidal electrolytes. Thus Svedberg, Tizelius, Northrop, McBain and others have taken them into account in the case of proteins, while McBain and Liu pointed out that the diffusion coefficient of soaps is given by an extension of the Nernst equation. But in experiments with dyes, although many diffusion measurements were reported, this aspect of the matter had been entirely overlooked. An investigation of the diffusion coefficients of dyes is, therefore, of particular interest and also because of the light it throws on the more general problem of determination of the particle size of a colloidal electrolyte, where the particle (unlike that of the protein, which appears to be a simple molecule) consists of a number of ions in association. Many dyes are colloidal electrolytes containing multivalent complex ions. Their diffusion coefficient is consequently largely determined by the mobilities of the ions. It was shown that a minimum value for the diffusion coefficient can be calculated from the conductivity. It follows that all dyes that have high conductivities—this seems to include most, if not all, substantive dyes—must have high diffusion coefficients. Consequently, as was shown, it is not possible to obtain even a qualitative measure of the particle size from the diffusion coefficient and the Stokes-Einstein equation.

Ansiotropy of the Diffusion Coefficient in Nematic Liquid Solutions Measured by NMR Techniques

1973 ◽  
Vol 28 (6) ◽  
pp. 964-967
Author(s):  
G. J. Krüger ◽  
H. Spiesecke
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Small Molecules ◽  
Diffusion Coefficients ◽  
Nematic Phase ◽  
Nematic Liquid Crystals ◽  
Gradient Coil ◽  
Liquid Solutions ◽  
Nmr Techniques ◽  
Relative Measurements

A gradient coil has been constructed for exact relative measurements of the longitudinal (Dʟ) and transverse (Dᴛ) diffusion coefficients of nematic liquid crystals and of small molecules dissolved therein. Some small molecules dissolved in the nematic phase of Licristal IV showed a Dʟ/Dᴛ ratio varying from about 1.1 to 1.25, depending on the concentration. In contrast, tetramethylsilane dis­solved in p-methoxy-benzylidene-p'-n-butyl-aniline showed no anisotropy in the nematic phase.

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.

scholarly journals Time-Dependent Diffusion Coefficients for Chaotic Advection due to Fluctuations of Convective Rolls

Fluids ◽  
2018 ◽  
Vol 3 (4) ◽  
pp. 99 ◽  
Author(s):  
Kazuma Yamanaka ◽  
Takayuki Narumi ◽  
Megumi Hashiguchi ◽  
Hirotaka Okabe ◽  
Kazuhiro Hara ◽  
...  
Keyword(s):  
Diffusion Coefficient ◽  
Liquid Crystals ◽  
Diffusion Coefficients ◽  
Coarse Graining ◽  
Chaotic Advection ◽  
Time Dependent ◽  
Local Order ◽  
Weak Turbulence ◽  
Normal Diffusion ◽  
Convective Rolls

The properties of chaotic advection arising from defect turbulence, that is, weak turbulence in the electroconvection of nematic liquid crystals, were experimentally investigated. Defect turbulence is a phenomenon in which fluctuations of convective rolls arise and are globally disturbed while maintaining convective rolls locally. The time-dependent diffusion coefficient, as measured from the motion of a tagged particle driven by the turbulence, was used to clarify the dependence of the type of diffusion on coarse-graining time. The results showed that, as coarse-graining time increases, the type of diffusion changes from superdiffusion → subdiffusion → normal diffusion. The change in diffusive properties over the observed timescale reflects the coexistence of local order and global disorder in the defect turbulence.

Diffusion of Zinc in Two-Phase Mg-Al Alloy

2007 ◽  
Vol 263 ◽  
pp. 189-194
Author(s):  
Ivo Stloukal ◽  
Jiří Čermák
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Effective Diffusion ◽  
Residual Activity ◽  
Diffusion Path ◽  
Al Alloy ◽  
Serial Sectioning ◽  
Two Phase ◽  
Interphase Boundaries ◽  
The Mean

Coefficient of 65Zn heterodiffusion in Mg17Al12 intermetallic and in eutectic alloy Mg - 33.4 wt. % Al was measured in the temperature region 598 – 698 K using serial sectioning and residual activity methods. Diffusion coefficient of 65Zn in the intermetallic can be written as DI = 1.7 × 10-2 m2 s-1 exp (-155.0 kJ mol-1 / RT). At temperatures T ≥ 648 K, where the mean diffusion path was greater than the mean interlamellar distance in the eutectic, the effective diffusion coefficient Def = 2.7 × 10-2 m2 s-1 exp (-155.1 kJ mol-1 / RT) was evaluated. At two lower temperatures, the diffusion coefficients 65Zn in interphase boundaries were estimated: Db (623 K) = 1.6 × 10-12 m2 s-1 and Db (598 K) = 4.4 × 10-13 m2 s-1.

An Overview of the Interdiffusion Studies in Mo-Si and W-Si Systems

2014 ◽  
Vol 354 ◽  
pp. 79-83
Author(s):  
Soumitra Roy ◽  
Soma Prasad ◽  
Aloke Paul
Keyword(s):  
Crystal Structures ◽  
Atomic Number ◽  
Diffusion Coefficients ◽  
Relative Increase ◽  
The Other ◽  
Reactive Diffusion ◽  
Refractory Elements ◽  
Other Hand ◽  
Two Systems ◽  
Diffusion Rates

The growth of phases by reactive diffusion in Mo-Si and W-Si systems are compared. The crystal structures of MSi2 and M5Si3 phases (M = Mo, W) are similar in these two systems. However, the diffusion rates of the components change systematically with a change in the atomic number. Integrated diffusion coefficients in both phases increase with an increasing atomic number of refractory elements i.e. from Mo to W. On the other hand, the ratio of diffusivities of the components decreases. This indicates a relative increase in the diffusion rates of the metal components with increasing atomic number and a difference in defects concentrations in these two systems.

Molten Slag Structure and Diffusion Coefficients of Cr3+ and Si4+ during Micro-Carbon Cr-Fe Alloy Production

2011 ◽  
Vol 79 ◽  
pp. 77-82
Author(s):  
Yi Min ◽  
Jian Huang ◽  
Cheng Jun Liu ◽  
Mao Fa Jiang
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Coefficients ◽  
Molten Slag ◽  
Optimization Method ◽  
Structure Theory ◽  
Average Diffusion Coefficient ◽  
Slag Structure ◽  
Initial Stage ◽  
Silicate Structure ◽  
Average Diffusion

Based on the silicate structure theory, the molten slag structure and the existential state of and during micro-carbon Cr-Fe alloy production process were analysised, and then their diffusion coefficients were calculated. The results showed that, during the initial stage, the average diffusion coeffecient of and is close to the , the reaction process is controlled by the diffusion of () and corporately, during the later stage, the diffusion coefficient of is less than average diffusion coefficient of and , the controlling step is the diffusion of . According to the evolution of diffusion coefficient, molten slag composition optimization method was advised to increase the diffusion ability of and for enhancing the reaction efficiency and the recovery rate of chromium.

Induced polarization and pore radius — A discussion

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. D519-D526 ◽  
Author(s):  
Andreas Weller ◽  
Zeyu Zhang ◽  
Lee Slater ◽  
Sabine Kruschwitz ◽  
Matthias Halisch
Keyword(s):  
Diffusion Coefficient ◽  
Relaxation Time ◽  
Diffusion Coefficients ◽  
Pore Radius ◽  
Mercury Porosimetry ◽  
Induced Polarization ◽  
Reliable Estimate ◽  
Characteristic Relaxation Time ◽  
A Value ◽  
Apparent Diffusion

Permeability estimation from induced polarization (IP) measurements is based on a fundamental premise that the characteristic relaxation time [Formula: see text] is related to the effective hydraulic radius [Formula: see text] controlling fluid flow. The approach requires a reliable estimate of the diffusion coefficient of the ions in the electrical double layer. Others have assumed a value for the diffusion coefficient, or postulated different values for clay versus clay-free rocks. We have examined the link between a widely used single estimate of [Formula: see text] and [Formula: see text] for an extensive database of sandstone samples, in which mercury porosimetry data confirm that [Formula: see text] is reliably determined from a modification of the Hagen-Poiseuille equation assuming that the electrical tortuosity is equal to the hydraulic tortuosity. Our database does not support the existence of one or two distinct representative diffusion coefficients but instead demonstrates strong evidence for six orders of magnitude of variation in an apparent diffusion coefficient that is well-correlated with [Formula: see text] and the specific surface area per unit pore volume [Formula: see text]. Two scenarios can explain our findings: (1) the length scale defined by [Formula: see text] is not equal to [Formula: see text] and is likely much longer due to the control of pore-surface roughness or (2) the range of diffusion coefficients is large and likely determined by the relative proportions of the different minerals (e.g., silica and clays) making up the rock. In either case, the estimation of [Formula: see text] (and hence permeability) is inherently uncertain from a single characteristic IP relaxation time as considered in this study.

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