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Related Concept Videos

Factors Affecting Activity Coefficient01:17

Factors Affecting Activity Coefficient

The extended Debye-Hückel equation indicates that the activity coefficient of an ion in an aqueous solution at 25°C depends on three partially interdependent properties: the ionic strength of the solution, the charge of the ion, and the ion size. 
The activity coefficient value for an ion is close to one when the solution has almost zero ionic strength, i.e., when the solution shows close to ideal behavior. As the ionic strength of the solution increases from 0 to 0.1 mol/L, a decrease in the...
Debye–Huckel–Onsager Conductance Equation01:28

Debye–Huckel–Onsager Conductance Equation

The Debye-Hückel-Onsager equation is a cornerstone of physical chemistry, providing a method to determine the molar conductance (Λm) and molar conductance at infinite dilution (Λ°m) for uni-univalent electrolytes.Uni-univalent electrolytes are electrolytes that dissociate in solution to produce one cation with a +1 charge and one anion with a –1 charge per formula unit.This equation addresses two crucial phenomena: the asymmetry effect and the electrophoretic effect. According to this equation,...
Passive Diffusion: Overview and Kinetics01:17

Passive Diffusion: Overview and Kinetics

Passive diffusion is a critical process that allows small lipophilic drugs to cross the cell membrane along a concentration gradient. This mechanism's efficiency depends on four primary factors: the membrane's surface area, the drug's lipid-water partition coefficient, the concentration gradient, and the membrane's thickness.
When administered orally, drugs establish a substantial concentration gradient between the gastrointestinal (GI) lumen and the bloodstream, expediting their diffusion into...
Ionic Strength: Effects on Chemical Equilibria01:19

Ionic Strength: Effects on Chemical Equilibria

The addition of an inert ionic compound increases the solubility of a sparingly soluble salt. For example, adding potassium nitrate to a saturated solution of calcium sulfate significantly enhances the solubility of calcium sulfate. Le Châtelier's principle cannot predict this shift in the equilibrium. Instead, this could be explained in terms of changes in the effective concentration of the ions in solution in the presence of added inert salt.
In this solution, the primary cation—the calcium...
Ostwald’s Dilution Law01:25

Ostwald’s Dilution Law

Consider a binary electrolyte AB with a concentration ‘c’ that reversibly dissociates into its constituent ions. The degree of this dissociation is represented by ⍺. This means that the equilibrium concentration of each ionic species can be expressed as ⍺c. As well as this, the fraction of the electrolyte that remains undissociated at equilibrium is given by (1−⍺). The corresponding equilibrium concentration for this undissociated portion is then calculated as (1−⍺)c. For such solutions,...
Theory of Strong Electrolytes01:23

Theory of Strong Electrolytes

The interionic forces of the strong electrolytes depend on the solvent's dielectric constant, which is the ability of a solvent to store electrical energy, based on its polarizability. and the solution's concentration. In high-dielectric solvents and in dilute solutions, weak electrostatic forces keep ions apart. However, in low-dielectric solvents or concentrated solutions, stronger interionic forces may cause ions to pair up as ionic doublets despite being fully ionized. The theory of strong...

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Updated: Jun 9, 2026

The Diffusion of Passive Tracers in Laminar Shear Flow
08:01

The Diffusion of Passive Tracers in Laminar Shear Flow

Published on: May 1, 2018

Particle size dependence of the ionic diffusivity.

Rahul Malik1, Damian Burch, Martin Bazant

  • 1Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Nano Letters
|August 28, 2010
PubMed
Summary
This summary is machine-generated.

Particle size significantly impacts diffusion in certain materials. Nanoparticles exhibit faster diffusion than bulk, explaining the nanoscale function of materials like lithium iron phosphate in batteries.

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Last Updated: Jun 9, 2026

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Adapting Taylor Dispersion to Measure the Dispersion Coefficient of Electrolyte Solutions via an Accessible Microfluidic Setup
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Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy
09:16

Measurement of Particle Size Distribution in Turbid Solutions by Dynamic Light Scattering Microscopy

Published on: January 9, 2017

Area of Science:

  • Materials Science
  • Electrochemistry
  • Solid-State Chemistry

Background:

  • Traditional models assume diffusion constants are independent of particle size.
  • The benefits of nanosizing materials are attributed solely to reduced transport path lengths.
  • Conflicting experimental data exists for key battery materials like LiFePO(4).

Purpose of the Study:

  • To investigate the particle size dependence of diffusion constants in materials with anisotropic diffusion.
  • To develop a model explaining the observed performance of nanoscale materials.
  • To reconcile conflicting data regarding LiFePO(4) properties.

Main Methods:

  • Theoretical modeling of diffusion in materials with one-dimensional atomic migration channels.
  • Analysis of diffusion constants as a function of particle size.
  • Application of the model to explain the behavior of LiFePO(4).

Main Results:

  • Demonstrated that diffusion constants are dependent on particle size for materials with 1D migration channels.
  • Observed significantly slower diffusion in bulk materials compared to nanoparticles.
  • The model successfully explains the exclusive nanoscale functionality of LiFePO(4).

Conclusions:

  • Diffusion is not always independent of particle size, particularly in materials with specific atomic structures.
  • Nanoscale materials can exhibit enhanced diffusion properties due to intrinsic size effects, not just shorter paths.
  • This finding provides a fundamental understanding for designing advanced battery materials.