Gibbs–Donnan effect

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Donnan equilibrium across a cell membrane (schematic)

The Gibbs–Donnan effect (also known as the Donnan's effect, Donnan law, Donnan equilibrium, or Gibbs–Donnan equilibrium) is a name for the behavior of charged particles near a semi-permeable membrane that sometimes fail to distribute evenly across the two sides of the membrane.[1] The usual cause is the presence of a different charged substance that is unable to pass through the membrane and thus creates an uneven electrical charge.[2] For example, the large anionic proteins in blood plasma are not permeable to capillary walls. Because small cations are attracted, but are not bound to the proteins, small anions will cross capillary walls away from the anionic proteins more readily than small cations.

Some ionic species can pass through the barrier while others cannot. The solutions may be gels or colloids as well as solutions of electrolytes, and as such the phase boundary between gels, or a gel and a liquid, can also act as a selective barrier. The electric potential arising between two such solutions is called the Donnan potential.

The effect is named after the American physicist Josiah Willard Gibbs and the British chemist Frederick G. Donnan.[3]

The Donnan equilibrium is prominent in the triphasic model for articular cartilage proposed by Mow and Lai, as well as in electrochemical fuel cells and dialysis.

The Donnan effect is extra osmotic pressure attributable to cations (Na+ and K+) attached to dissolved plasma proteins.


The presence of a charged impermeant ion (for example, a protein) on one side of a membrane will result in an asymmetric distribution of permeant charged ions. The Gibbs–Donnan equation at equilibrium states (assuming permeant ions are Na+ and Cl):

[NaSide 1] × [ClSide 1] = [NaSide 2] × [ClSide 2]


Start Equilibrium Osmolarity
Side 1: 9 Na, 9 Cl
Side 2: 9 Na, 9 Protein
Side 1: 6 Na, 6 Cl
Side 2: 12 Na, 3 Cl, 9 Protein
Side 1: 12

Side 2: 24

Double Donnan[edit]

Note that Sides 1 and 2 are no longer in osmotic equilibrium (i.e. the total osmolytes on each side are not the same)

In vivo, ion balance does not equilibriate at the proportions that would be predicted by the Gibbs-Donnan model, because the cell cannot tolerate the attendant large influx of water. This is balanced by instating a functionally impermeant cation extracellularly to counter the anionic protein, Na+. Na+ does cross the membrane via leak channels (the permeability is approximately 1/10 that of K+, the most permeant ion) but, as per the pump-leak model, it is extruded by the Na+/K+-ATPase.

See also[edit]


  1. ^, retrieved 28 August 2006
  2. ^ The Gibbs–Donnan Equilibrium..., D.C. Mikulecky, retrieved 28 August 2006
  3. ^ F.G. Donnan (1911) "Theorie der Membrangleichgewichte und Membranpotentiale bei Vorhandensein von nicht dialysierenden Elektrolyten. Ein Beitrag zur physikalisch-chemischen Physiologie" (The theory of membrane equilibrium and membrane potential in the presence of a non-dialyzable electrolyte. A contribution to physical-chemical physiology), Zeitschrift für Elektrochemie und angewandte physikalische Chemie, 17 (10) : 572-581.
  • IUPAC Compendium of Chemical Terminology 2nd Edition (1997)
  • Van C. Mow Basic orthopaedic biomechanics and mechano-biology, 2nd Ed. Lippincott Williams & Wilkins, Philadelphia, 2005

External links[edit]