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 charge density =
i zi eci compared to the total charge densi
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 start to investigate the effect of double
layer on the rea
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, consider applyig a small perturbation P, V and calculate
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 by the mean concentrations c i and potential . Each ion
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 KE
V
The basic idea1 is to apply P and to try to harves
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 concentrations at large potentials. As
an example, at 2.5 V, whic
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 effective equations governing the transports and electr
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 component has a nonzero conductivity. In a
porous medium, we
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 electrode matrix and the
ion-conducting electrolyte. In batt
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 potential difference, :
Figure 1: Macroscopic composite