The Donnan Membrane Equilibrium


THE famous theorem of Gibbs concerning the equality of the chemical potential µ of an independent component throughout a system of co-existent phases in equilibrium at constant temperature and pressure is widely known. It is perhaps not so well known that, if external fields of force or electrically charged components (ions or electrons, for example) are present, an extension of the foregoing theorem is required, though Gibbs himself dealt with this matter in the case of a gravitational field. The subject was very well discussed in an important paper by Milne1 in 1925. If the system of phases be under the action of an external field of potential O per unit of mass, then, corresponding to each independent component, an equation of the type µ + O= constant holds throughout the system. This corresponds to Gibbs' result for a gravitational field. A similar state of affairs holds good for a centrifugal field. A very interesting type of this sort was dealt with on Gibbsian lines by Kai O. Pedersen2 in 1934. Let us now suppose that certain components have associated with them electric charges of amount et- per unit mass (where the subscript refers to such a component i). The presence of the charges will give rise to an electrostatic field, and there may be also present an external electrostatic field. Denote the total electrostatic potential by?. Then, instead of the condition µ = constant, throughout the system of phases, we have the condition µ; + = constant, and if a gravitational field of potential O per unit of mass is also present, the condition becomes µ+ O + e,*Y = constant. If we are dealing with the distribution of ions in ordinary laboratory apparatus (say in experiments on membrane equilibria of ions across a semi-permeable membrane) the term O practically cancels out. Not so, however, the electrical term, which may now be written in the form zi, where Zi F? is the electrovalency of the ionic component i (positive for a cation and negative for an anion) and F is the Faraday constant. Both µ; and the term ZiF refer now to a gram molecule of the ion,i. The expression µ; -l- Zi F has been called the 'electrochemical potential' by Guggenheim3, to whom we are indebted for its introduction and practical use in modern physical chemistry.

The Donnan Membrane Equilibrium

By Dr. S. G. Chaudhury. Pp. viii + 112 + xv. (Howrah: A. P. Bhattacharya, 1945.) 10 rupees.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1

    Proc. Camb. Phil. Soc, 22, Pt. 4, 493 (1925).

  2. 2

    Z. phys. Chemie, 170, A, 41 (1934).

  3. 3

    J. Phys. Chem., 33, 842 (1929).

  4. 4

    Donnan, F. G., and Guggenheim, E. A., Z. phys. Chem., 162, A, 346 (1932); Donnan, F. G., Z. phys. Chem., 168, A, 369 (1934).

  5. 5

    See equation 27 of the second paper mentioned in ref. 4.

Download references

Rights and permissions

Reprints and Permissions

About this article

Cite this article

DONNAS, F. The Donnan Membrane Equilibrium. Nature 157, 495–496 (1946) doi:10.1038/157495a0

Download citation


By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.