### Abstract

The formation of tactoids from thixotropic sols, of Schiller layers from iron‐oxide sols, the separation of tobacco virus solutions and bentonite sols into two liquid layers and the crystallization of proteins are regarded as examples of unipolar coacervation (micelles having like charges) which must involve attractive forces.

Kallmann, Willstätter, Freundlich, De Boer, Hamaker, Houwink and others have assumed that the attraction is due to van der Waals forces. They have also analyzed the stability of colloidsystems by diagrams giving the potential energy as a function of the distance between micelles. It is now shown that the Coulomb attraction between the micelles and the oppositely charged ions in the solution gives an excess of attractive force which must be balanced by the dispersive action of thermal agitation and another *repulsive* force. Thus there is no need to assume long range van der Waals forces. The past use of energy diagrams is criticized because it has ignored the effect of the thermal agitation and the attraction of the ``gegenions'' in solution. Instead of potential energy it is proposed that osmotic pressure *p* be used, which includes these previously neglected factors. A maximum in *p* as the colloid concentration increases is the condition for the separation into two phases (coacervation).

The Debye‐Hückel theory (1st approximation) for the osmotic pressure of electrolytes takes into account both these factors and permits a rough calculation of the conditions under which coacervation occurs. The 2nd approximation, which considers particle size, does not agree as well with experiment as the first approximation. The reasons for this lack of agreement are discussed.

The micelles in unipolar coacervates are not in contact, but are separated by relatively large distances (10–5000A). Either a specific repulsive force or a decrease in the Coulomb attraction as the concentration increases (due to decreased charges on micelles) can account for stable coacervates. The assumption of a definite ζ‐potential, rather than a definite charge on the micelles, gives automatically just such a decrease in attraction.

The general mathematical theory of coacervation presents great difficulties because the approximations of the Debye‐Hückel theory cannot be used. However, the one‐dimensional problem of the forces acting between parallel colloidal platelets can be solved rigorously in terms of elliptic integrals. For highly charged particles in sufficiently dilute solutions of electrolytes, the pressure *p* in the liquid between the two plates is given by *p* = (π/2)*D*(*kT/eb*)^{2} = 8.9×10^{—7}/*b* ^{2} dynes/cm^{2} where *b* is the distance in cm between the plates and *D* is the dielectric constant (81 for water at *T* = 293°K). This pressure which tends to force the plates apart is independent of the charge on the plates and on the electrolyte concentration (univalent ions only). Polyvalent ions decrease the force. This force is of the right magnitude to account for the stability of unipolar coacervates. It also furnishes a quantitative explanation of the Jones‐Ray effect, by which low salt concentrations decrease the capillary rise in surface tension experiments with water.

Experimental determinations were made of the relaxation times τ for the decay of birefringence in bentonite and vanadium pentoxide sols, after stirring was stopped. In one sample of bentonite, τ varied with the 22nd power of the concentration, while in V_{2}O_{5}sols the exponent was 1.8. The temperature coefficients of τ were also measured and the activation energies were calculated.

A theory of the relaxation of birefringence was developed, according to which the micelles in dilute thixotropic bentonite sols are arranged normally in a cubic lattice (isotropic). Temporary shear in the liquid orients the micelles and produces birefringence although the lattice remains cubic. The experimental data confirm the theory and indicate that the energy barrier opposing reorientation of micelles in a particular bentonite sol varied with the inverse 20th power of the distance between the micelles. With V_{2}O_{5} this exponent was about 4. Further support for the theory was obtained by experiments which gave ``angles of isocline'' for bentonite particles in a flowing sol that varied from 65° to 78°.

In bipolar coacervates (which contain micelles of unlike polarities) the electric fields and the charges on the micelles*increase* as the micellar concentration increases. When a certain concentration is reached, the field rises to a value so high as to cause increased hydration which holds the micelles apart and gives stability to the coacervate.

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