Gibbs–Donnan effect

The Donnan equilibrium describes in physical chemistry, the unequal distribution of dissolved charged particles (ions), which arises when a semipermeable membrane for the solvent and some, but not all ions present in the solution is conducting. In this case, the passing ions are distributed on both sides of the membrane at different concentrations. This uneven distribution leads to a potential difference ( Donnan potential or better Donnan voltage) and a difference in the osmotic pressure ( Donnan pressure). The extent of the deviation is indicated by the Donnan coefficient.

Named this effect after the chemist Frederick George Donnan, who in 1911 proposed a theory to explain such membrane equilibria. The concentration distribution is referred to as the Donnan equilibrium ( Gibbs - Donnan equilibrium), the underlying process as Gibbs Donnan effect or Donnan law.

The Donnan effect is particularly important for living cells as well as for technical systems of meaning.

Basics

Condition for the occurrence of the Gibbs - Donnan effect is the presence of an ion species that is not transmitted through the semipermeable membrane. This is generally for macromolecules such as soluble proteins or nucleic acids in biological cells of the case. With appropriate membrane composition but this can be true for one type of ion a low molecular weight salt. As dissolved in sodium chloride (common salt) the diameter of the hydrated Cl - ion considerably greater than the smaller of the Na ion. To the Donnan effect occurs even if ions can not diffuse freely through anchor at an interface, as in membrane proteins or charged polymer molecules ( see ion exchange ) of the case.

The osmotic system is in equilibrium when the chemical potentials of the solvent and the other transmitted on both sides of the membrane materials are the same. In the presence of charge carriers must also be on both sides in the volume ( off the double layer ) represent the sum of the equivalent concentrations to be balanced, because the interior of a conductor is (in equilibrium ) field-free and thus free of net charge. Is now on one side of the membrane a non- permeating ion species more concentrated, which must be compensated by permeating ions. The concentration is, therefore, different in equilibrium on both sides. This inequality is a potential difference of a few millivolts ( mV) is connected. Runs the uneven distribution to a difference in the activity of the water, creates an osmotic pressure.

Donnan coefficient

The ( Gibbs ) Donnan coefficient rD, a dimensionless number that indicates the permeant ions, such as change the concentration ratios due to the potential difference. Are, for example, on both sides of the membrane ( indices a, i is the outside, inside ) the permeable monovalent ions K ( potassium) and Cl - (chloride ) are present, as well as inside a macromolecule z charges Pz , then Cl after pulled in and pushed K outward:

Wherein the equality holds, because the potential difference affects equally but in an opposite direction to the two ions.

RD can be taking advantage of the neutrality conditions

Specify as a function of the concentration of the charged macromolecule:

Where the approximation is valid for dilute solutions. The permeant ions are therefore distributed more dissimilar, the higher the concentration and the charge number of the macromolecule. The latter is often dependent on the degree of dissociation of the pH value.

Donnan potential

The connection between the membrane potential and Donnan coefficient obtained from the Nernst equation:

ΔΦ is the difference of the electrical potential in mV, R is the universal gas constant, T is the absolute temperature in K, and F is the Faraday constant, C · mol -1.

The following table of examples shows that the presence of a non-permeable ion can lead to large differences in concentration in the transmitted ions. At the same time considerable Donnan potentials can occur cited by:

(all concentrations given in mol · l-1, temperature: 298 K). The height of the membrane potential depends on the mobile ions on the ratio of the charged macromolecule. Such ions are present in a high concentration, the presence of the fixed ion affects only slightly.

Osmotic pressure

At equilibrium, the osmotic pressure ratio of the activities of the solvent gives on both sides of the membrane:

Where: the molar volume of the solvent, R is the universal gas constant and T is the absolute temperature in K.