The Effect of Salts on the Critical Concentration, Size, and Stability of

EFFECT OF SALTS ON SOAP MICELLES

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(8) HARKINS A N D JURA:J . Am. Chem. SOC.66, 1366 (1944).

(6) HUNT, BLAINE,A N D ROWAS:J. Research N:rtl. Bur. Standards 43, 547 (1949). (7) LAMBERT AND CLARK: Proc. Roy. SOC.(Londoni Al22, 505 (1929). (8) LAMBERT AND F O S T E R : h o c . IlOy. S O C . (London) A138, 368 (1932). (9) PIERCE, WILEY,ASII SMITH: J . Phys. & Colloid Chem. 63, W9 (1949).

T H E EFFECT OF SALTS ON THE CRITICAL CONCENTRATION, SIZE, AYD STABILITY OF SOAP MICELLES MARCUS E. IIOBBS Department of Chemistry, Duke University, Durham, North Carolina

Received June 6 , 1960 I . INTRODUCTION

‘The theory of the soap micelle outlined recently by Debye (5) considers the micelle, in the light of work by McBain (9) and Harkins and coworkers (7), its being composed of a double layer of electrolyte molecules with approximately cylindrical symmetry. The charged polar heads of the soap ions form the ends and the oriented hydrocarbon chains the body of the cylinder. When salt effects are not considered, Debye shows that the electrostatic work of forming an electrified disc with a radius equal to that of the micelle cylinder is proportional to n3’*and, by assuming that the cohesive work of formation is proportional to n, the number of molecules in the micelle, a stable micelle is predicted when the total energy of formation is a t a minimum. The present work considers the influence of the ions in solution on the electrostatic work of forming the charged micelle discs and estimates how much the interaction of the two end discs of a micelle increases the work of formation of the unit. 11. THE SIZE OF MICELLES FORMED I N SALT SOLUTIONS

The problem of obtaining the potential function for a disc of electricity of surface density u which is immersed in an electrolyte solution appears to be soluble, at present, only by approximation. I n an attempt to deal with this problem we shall msume that the disc has a low charge density, so that the potentials in its vicinity will be calculable in terms of the Debye-Huckel (6) potential function: namely, e-“’/r. Here K is the reciprocal of the “ion atmosphere” thickness and T is the distance between the point at which the potential is sought and the charge location. The assumption implicit in the use of the above potential function is the condition that

kT