�
IV. Transport Phenomena ±
Lecture 23: Ion Concentration Polarization±
MIT Student (and MZB)
Ion concentration polarization in electrolytes refers to the additional voltage drop (or “internal
resistance
�
) across the electrolyte associated with ion concentration gradients, which exists in
addition to the Ohmic voltage drop associated with the mean conductivity. We focus on consider
quasineutral “bulk” electrolytes.
1. NernstPlank equations
Assume there is no convective transport (
General NernstPlank equations:
).
, where
,
(Einstein relation)
For dilute solution (with neglecting electrostatic correlations):±
Then, NernstPlank equation goes to ±
To determine
, we can use electroneutrality/charge conservation.
(Condition of “quasielectroneutrallity”)
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Lecture 23: Ion concentration polarization
10.626 (2011) Bazant
2. Dilute Binary Electrolyte
From quasielectroneutrality, for a binary salt, we can define salt concentration
C
via
which satisfies a simple diffusion equation with a certain average or
“ambipolar” diffusivity, as derived in the last lecture:
For dilute binary electrolyte,
, the effective diffusivity goes to harmonic mean of the ion
diffusivities, weighted by the charge of the opposite species( < > denotes the harmonic mean).
Generally, the effective diffusivity for ambipolar electrolyte
is an average of
and
giving more weight to smaller diffusivity
D
and smaller charge
z
. The diffusion is dominated by
the smaller mobility. As an analogy, consider “teacher” with a small “student” traversing a room.
Even though the student has the tendency to move much faster than his/her accompanying
teacher, he/she is limited in the extent of this mobility by the teacher’s speed and position. That
is, highly mobile “student” ions could not stray far from its less mobile “teacher” ion to be
maintained electroneutrality of bulk electrolyte. It is the reason why the equation of effective
diffusivity expresses the coupling of the positive and negative species. It is noted that this
equation is only effective at describing bulk solution, which satisfy electroneutrality assumption.
The equation no longer valid when the electroneutrality assumption breaks down, such as near
charged surfaces.
Fig 1. Interpretation of the effective ambipolar diffusivity of a dilute binary electrolyte where the anions are the
“students” (or children) and the cations are the “teachers”, who strive to maintain a fixed “teacherstudent ratio”
consistent with electroneutrality. The ambipolar diffusivity gives more weight to the slower/larger ion with smaller
charge (the teacher) since other ion (the student) responds more quickly to electric fields, not only the applied
external electric field (which attracts students to different boundaries, as below), but also the internal “diffusion
field” which helps the ions to maintain electroeutrality when their diffusivities are different.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '03
 RogerD.Kamm
 Electrochemistry, pH, Electric charge, Ion, Cathode, Bazant, ion concentration polarization

Click to edit the document details