Donnan equilibrium -how is the potential difference caused?

[Urmi Roy]

So I was watching a video about Gibbs-Donnan equilibrium ()

On one side of the semipermeable membrane, there is a solution of potassium ions and impermeable protein ion (negative 1 charge). On the other side there is potassium chloride.

It said that after the electrical and chemical gradients are satisfied and the system reaches equilibrium, there is no net charge on either side, since the no. of moles of negatively charged ions on each side is equal to the no. of moles of positively charged ions.

Then how is there are potential difference across the membrane? I'm thinking that it might be because the protein ions adsorb on to the membrane surface, imparting a charge to it. Is that true?

 

[DrDu]

It said that after the electrical and chemical gradients are satisfied and the system reaches equilibrium, there is no net charge on either side, since the no. of moles of negatively charged ions on each side is equal to the no. of moles of positively charged ions.

Yes, you are right. There are surface charges (a double layer) at the membrane which cause the potential difference. Only the bulk of the solutions are net charge free.

The situation is analogous to a pn junction of semiconductors.

 

[Urmi Roy]

Yes, you are right. There are surface charges (a double layer) at the membrane which cause the potential difference. Only the bulk of the solutions are net charge free.

The situation is analogous to a pn junction of semiconductors.

I know that electrical double layers are associated with zeta potential and stern potential. They form due to surface adsorption (on membrane) of certain ions. However, isn't donnan potential different?
I had an impression (from the video) that donnan potential is potential difference between the solutions on either side...they say that donnan potential is because some of the ions are not permeable in the membrane...I'm quite confused at this stage.

From the definition of donnan potential from wikipedia,
"Donnan potential appears as a result of Donnan equilibrium, which refers to the distribution of ion species between two ionic solutions separated by a semipermeable membrane or boundary. The boundary layer maintains an unequal distribution of ionic solute concentration by acting as a selective barrier to ionic diffusion. Some species of ions may pass through the barrier while others may not."

 

[DrDu]

In the Donnan equilibrium, the surface charges are not due to adsorption. It is simply that the charges which can diffuse through the membrane will be missing on one side near the surface and accumulate on the other side of the surface. The width of the region where charge balance is disturbed is of the order of the Debye length,
http://en.wikipedia.org/wiki/Debye_length
.
And, as I said, it is completely analogous to the situation in a pn junction:
http://en.wikipedia.org/wiki/P–n_junction

 

[Urmi Roy]

Sorry for the trouble, but I'm still a little confused...

In a p-n junction, the n side, (after the hole/electron movement takes place) acquires a net positive charge (and the p side acquires a net negative charge).

It is simply that the charges which can diffuse through the membrane will be missing on one side near the surface and accumulate on the other side of the surface.
http://en.wikipedia.org/wiki/P–n_junction

Yes, but the net charge on each side (including the thin layer sticking to the membrane) is zero.

(Even in the video, they explain that the net charge on either side of the membrane is zero, including the layer coating the membrane...however, they still say there is a net negative charge on one side of the membrane..doesn't make sense to me)

 

[DrDu]

Even in the video, they explain that the net charge on either side of the membrane is zero, including the layer coating the membrane...

Ok, I have no chance to argue against something as authoritative as a youtube video, but methinks they didn't even mention the formation of a boundary layer.

 

[Urmi Roy]

I'm just trying to put together and relate the different sources of information I'm getting.

Forgetting about the video, could you please explain what you meant in saying "It is simply that the charges which can diffuse through the membrane will be missing on one side near the surface and accumulate on the other side of the surface."

Here's an example:
If we have KCl on one side (side 1)and KBr (side 2) on the other side (membrane is impermeable to Br- but permeable to K+ and Cl-), Cl- will move to side 2 of the membrane, and accumulate to form a negative layer next to the membrane?

But wouldn't more K+ from side 1 to neutralize the negative charge due to Cl-?

 

[DrDu]

Have a look at this presentation, namely the graphics on page 14:

http://physics.berkeley.edu/research/yildiz/Teaching/PHYS177/Lecture%20PDFs/Lecture14.pdf

 

[Urmi Roy]

Thanks, this was really helpful :-)

 

[Urmi Roy]

Btw, since the establishment of donnan equilibrium involves formation of a double layer, is it correct to say that after this double layer is formed, we can measure the zeta potential of the layer? Or is zeta potential totally unrelated?

(My main concern is concentration polarization...I'm just wondering if the double layer formed due to donnan equilibrium contributes to concentration polarization)

 

[DrDu]

Btw, since the establishment of donnan equilibrium involves formation of a double layer, is it correct to say that after this double layer is formed, we can measure the zeta potential of the layer? Or is zeta potential totally unrelated?

(My main concern is concentration polarization...I'm just wondering if the double layer formed due to donnan equilibrium contributes to concentration polarization)

I am not very familiar with the term "zeta potential" as far as I understand, it is measured for particles in motion relative to an electric field. Maybe you can measure something alike for a moving semipermeable membrane.