This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: IV Transport Phenomena Lecture 21: Solids and Concentrated Solutions MIT Student (and MZB) March 28, 2011 1 Transport in Solids 1.1 Diffusion The general model of chemical reactions can also be used for thermally activated diffusion. Figure 1: Particle diffusion by thermally activated transitions Here the excess chemical potential acts like the potential energy of par ticle state. Thermally activated transition without drift or bias implies a random walk phenomena where the diffusivity is a function of meanaverage time between steps and is given by: 1 Lecture 21: Transport in solids and concentrated solutions 10.626 (2011) Bazant E ∴ TS E min γ e k T k T TS = B and γ = e B Δ x 2 E = = Δ A ⇒ D e k T 2 B (4) τ whereΔ E A = E TS E min is the activation energy barrier. 1.1.2 Ideal solid solution (Lattice gas) Model: Consider a lattice gas model where the transition state requires two vacan cies. Then we have, Diffusivity Δ x 2 D = (1) 2 τ τ =mean time between transitions The mean average transition time is a function of the potential energy gap between the transition state and stable original state. ex ex k B T τ = τ e ( µ TS µ ) = τ γ TS (2) γ 1 ∝ T = attempt frequency for transitions, and recall, µ ex = k B T ln γ . τ Finally, we can now write diffusivity of solids in terms of activity coeffi cients....
View
Full
Document
This note was uploaded on 11/27/2011 for the course CHEMICAL E 20.410j taught by Professor Rogerd.kamm during the Spring '03 term at MIT.
 Spring '03
 RogerD.Kamm
 pH, Reaction

Click to edit the document details