Lecture 1 Notes: The Poisson Equation
Last time we showed that whenever D L the electrolyte has
a quasi-neutral bulk (or outer) region the geometrical scale L,
at
where
there is very little mean charg
Lecture 3 Notes: Diffuse charge at electrodes
We have talked about the electric double structures and corresponding models describing the ion
and potential distribution in the double layer. Now we sta
Lecture 5 Notes: Electrokinetics
1
Linear Electrokinetic Resonse of a Nanochannel
We start with the system in equilibrium
Q = 0
I=0
2 = ()
pE = eq
Where pe is the electrostatic pressure.
Now, c
Lecture 4 Notes: Electrostatic Correlations
1. Mean-Field Theory
Continuum models like the Poisson-Nernst-Planck equations are mean-field approximations which
describe how discrete ions are affected b
Lecture 6 Notes: Electrokinetic Energy Conversion
1
Principles
1.1
General Theory
We have the following equation for the linear electrokinetic response of a nanochannel:
"!
"
!
" !
P
Q
KP KEO
=
I
KEO
Lecture 2 Notes: Double Layer Capacitance
1
1.1
Double-layer Capacitance
Stern Layer
As was discussed in the previous lecture, the Gouy-Chapman model predicts unphysically large counter-ion concentrat
Lecture 10 Notes: Porous Electrodes
1. Effective Equations for Thin Double Layers
For supercapacitor electrodes, convection is usually negligible, and we drop out convection
terms here. Lets focus on
Lecture 9 Notes: Transport in Porous Media
1. Conduction
In the previous lecture, we considered conduction of electricity (or heat conduction or mass
diffusion) in a composite medium, where each compo
Lecture 7 Notes: Percolation
In electrochemical energy systems, porous electrodes are generally used to maximize interfacial
area to facilitate Faradaic reactions between the electron-conducting elect
Lecture 8 Notes: Macroscopic Conductivity of Composites
1. Conductivity of Composite Media
We consider a volume of a composite material subjected to a 1-D applied electric field, and
giving rise to a