Donnan equilibrium -how is the potential difference caused?

In summary, the Gibbs-Donnan equilibrium describes the distribution of ion species between two ionic solutions separated by a semipermeable membrane. This equilibrium results in a net zero charge on both sides of the membrane, but there is still a potential difference due to surface charges at the membrane. This potential difference is similar to a pn junction in semiconductors. The Donnan potential is a result of this equilibrium and is caused by the presence of ions that are not permeable through the membrane. The formation of a double layer is involved in this equilibrium and can contribute to concentration polarization, but its relation to zeta potential is unclear.
  • #1
Urmi Roy
753
1
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?
 
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  • #2
Urmi Roy said:
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.
 
  • #3
DrDu said:
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."
 
  • #4
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
 
  • #5
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).

DrDu said:
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)
 
  • #6
Urmi Roy said:
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.
 
  • #7
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-?
 
  • #8
Have a look at this presentation, namely the graphics on page 14:

http://physics.berkeley.edu/research/yildiz/Teaching/PHYS177/Lecture%20PDFs/Lecture14.pdf [Broken]
 
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  • #9
Thanks, this was really helpful :-)
 
  • #10
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)
 
  • #11
Urmi Roy said:
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.
 

1. What is Donnan equilibrium?

Donnan equilibrium is a principle that describes the distribution of ions across a semipermeable membrane. It states that when a semipermeable membrane separates two solutions with different concentrations of charged particles, the ions will distribute themselves in a way that balances the osmotic pressure on both sides of the membrane.

2. How is Donnan equilibrium achieved?

Donnan equilibrium is achieved through the diffusion of ions across a semipermeable membrane. This diffusion is driven by the difference in concentration of ions on either side of the membrane. As ions move from an area of high concentration to an area of low concentration, they create a potential difference across the membrane.

3. What causes the potential difference in Donnan equilibrium?

The potential difference in Donnan equilibrium is caused by the unequal distribution of ions across the semipermeable membrane. This difference in ion concentration creates an electrical potential, which is known as the Donnan potential. The Donnan potential can be measured as a voltage or electric potential difference across the membrane.

4. What factors affect Donnan equilibrium?

The factors that affect Donnan equilibrium include the concentration and charge of the ions on either side of the membrane, the permeability of the membrane to different ions, and the presence of any other molecules or ions that may interact with the charged particles. Temperature and pressure can also have an impact on Donnan equilibrium.

5. How is Donnan equilibrium relevant in biological systems?

Donnan equilibrium plays a critical role in maintaining the balance of ions and osmotic pressure in biological systems. It is essential for processes such as cell osmoregulation, nerve conduction, and nutrient uptake. Without Donnan equilibrium, cells would not be able to function properly and maintain their internal environment.

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