Modified Stokes–Einstein Equation for Molecular Self-Diffusion Based on Entropy Scaling

Abstract

The Stokes–Einstein (SE) equation is often applied as an approximation of self-diffusion coefficients D of molecular species based on the shear viscosity of fluids. The SE relation gives rough estimates of self-diffusion coefficients in liquid states and (divergently) high deviations for the gaseous phase. Inspired by Rosenfeld’s entropy scaling approach, we find a universal function of residual entropy f(s res) to describe the ratio between experimental and calculated D from SE equation for all investigated substances. The so-obtained modified SE equation, containing 5 universal parameters adjusted to experimental data of 61 substances of 11 different chemical families, can be used for predicting D in the entire fluid region, with averaged absolute deviations of 12.3% compared to experimental data (5407 data points). The application of the proposed model to diffusion coefficients at infinite dilution shows average deviations of 20.8% for widely different systems (412 data points).

Photocatalytic degradation activity of goji berry extract synthesized silver-loaded mesoporous zinc oxide (Ag@ZnO) nanocomposites under simulated solar light irradiation

“…Mainly, DLS provides larger values because of the hydrodynamic shell, which is dependent on the structure, shape, and roughness of the particles 56 . According to Stokes–Einstein (SE) equation, the measured diffusion coefficients are related to the hydrodynamic radius as D = k B T/6πηR h , where k B is Boltzmann’s constant (1.38 × 10 –23 J/K), T is the temperature, η is the viscosity of the suspension medium, and R h is the hydrodynamic radius 57 . There was an increase in the size of nanocomposites with the addition of silver to ZnO (Fig.…”

Mechanistic Formulation Design of Spray-Dried Powders

“…In the absence of any experimental data for the diffusion coefficients of the solutes in the solvent of interest, which is usually the case for newly discovered drugs or biologics, the Stokes-Einstein equation can be used as an approximation, as shown below (Bird et al, 2006;Zmpitas and Gross, 2021)…”

“…where D i,j is the diffusion coefficient of solute i in solvent j at infinite dilution, . Here, V i is the molecular volume in m 3 that can be obtained via different methods (Bird et al, 2006;Edward, 1970;Kooijman, 2002;Zmpitas and Gross, 2021), for example, by using the Van der Waals volumes obtained from the atomic and group incremental volumes (Blokhina et al, 2017;Bondi, 1964;Edward, 1970). The hydrodynamic diameters of some of the excipients and APIs used in the formulation of pharmaceutical solid particles were calculated based on their Van der Waals volumes (Edward, 1970) and are presented in Table 1.…”

Modeling Subsurface Hydrogen Storage With Transport Properties From Entropy Scaling Using the PC‐SAFT Equation of State

“…We note the ideal gas contribution $${s}^{\text{ig}}\left(\left\{{\rho }_{i}\right\},T\right)$$ is different from $${s}^{\text{ig}}\left(p,T,\left\{{x}_{i}\right\}\right)$$ (with p as pressure) by a factor of $$\mathrm{ln}\left(p/\left({\sum }_{i}{\rho }_{i}{k}_{B}T\right)\right)$$ and consequently the corresponding residual quantities are different. The entropy scaling principle, as of now, has no convincing statistical mechanical basis, yet it is proven to be an effective and robust method to calculate transport coefficients of pure components and mixtures (Hopp et al., 2018; Loetgering‐Lin & Gross, 2015; Loetgering‐Lin et al., 2018; Zmpitas & Gross, 2021). In this work, we use nonlinear relations from the literature for the transport coefficients of water and the diffusion coefficient of hydrogen.…”