Formulation of Stokes’ Radii in DMF, DMSO and Propylene Carbonate with Solvent Structure Cavity Size as Parameter

Abstract

Conductance of univalent ions in DMSO (dimethyl sulfoxide), DMF (dimethylformamide) and PC (propylene carbonate) was determined by use of tetrabutylammonium-tetrabutylborate as standard electrolyte of equal cationic and anionic conductance. Empirical formulation of Stokes’ radius was attempted on the assumption of a structure-cavity affecting the ionic transport in a medium of aprotic and polar solvent as well as water. By application of classical fluid dynamics Stokes’ radius rs is given in terms of −(2⁄3)rc+(1⁄σs) (rc–ro)2, where rc is crystal ionic radius, ro and σs are parameters characteristic of the cavity and molecular sizes, respectively, with respect the solvent.

Pulsed-Field Gradient NMR Self Diffusion and Ionic Conductivity Measurements for Liquid Electrolytes Containing LiBF4 and Propylene Carbonate

“…where r is the effective radius of an ion, k B is Boltzmann's constant, T is temperature, D is the self diffusion coefficient of the relevant ion, η is the bulk viscosity and 6c SE is a factor that is usually between 4 and 6 for a perfect slip boundary and stick boundary, respectively [65]. If c SE takes the value of 1, then equation 19 becomes the classical Stokes-Einstein equation which assumes that the translating object is perfectly spherical; therefore a deviance of c SE away from can indicate a non spherical structure.…”

Class of Solid-like Electrolytes for Rechargeable Batteries Based on Metal–Organic Frameworks Infiltrated with Liquid Electrolytes

“…The different trends in ionic conductivity between M-MOF-2 (M = Li, Na, K, and Cs) from the 1st group and the M-MOF (M = Na, Mg, and Al) from the 3rd period could be interpreted by the different trends in the solvation size and strength of cations. For cations from the same group (Li + , Na + , K + , and Cs + ), the cations show increasing (ionic) radii but with same charge, leading to mildly decreasing charge density and solvation size . For cations from the same period (Na + , Mg 2+ , and Al 3+ ), the cations show decreasing (ionic) radii ions but with increasing charge, leading to dramatically increasing charge density and solvation size …”

“…With increasing the ionic radii and decreasing the charge density, Li + , Na + , K + , and Cs + ions in DMSO were reported with decreasing solvated sizes of 0.318, 0.303, 0.291, and 0.246 nm, respectively. 4,39 Consistently, Li-DMSO, Na- DMSO, K-DMSO, and Cs-DMSO show increasing ionic conductivities of 4.6, 5.7, 6.1, and 6.5 mS cm −1 , respectively. 40 Figure 5a,b presents the Nyquist plots and temperaturedependent conductivity of the corresponding solid-like electrolytes (denoted similarly as M-MOF-2, M = Li, Na, K, and Cs), respectively.…”

“…For cations from the same group (Li + , Na + , K + , and Cs + ), the cations show increasing (ionic) radii but with same charge, leading to mildly decreasing charge density and solvation size. 39 For cations from the same period (Na + , Mg 2+ , and Al 3+ ), the cations show decreasing (ionic) radii ions but with increasing charge, leading to dramatically increasing charge density and solvation size. 41 Table S3 presents ionic and Stokes' (solvation) radii of cations in several solvents, where Li + /Na + from the same group and Na + /Mg 2+ from the same period share similar ionic radii but dramatic differences in solvation sizes.…”

“…Infused with such electrolytes in MOF yields similar trends of ion conduction behaviors like their liquid counterparts. 155 PC rs (nm) 155 PC rs (nm) 80 H2O rs (nm) 159 H2O rs (nm) 160 The lithium-ion transference number (tLi + ) and sodium-ion transference number (tNa + ) were measured using the potentiostatic polarization method. 86 The anion-immobilizing MOF particles notably improves the cation-transference numbers higher than 0.5 (Figure 4.19a-b, tLi + ≈ 0.7， tNa + ≈ 0.5) relative to a typical value of 0.3 from the liquid electrolytes, [161][162] confirming the role of OMSs on selectively tuning ion transport behaviors.…”