JOURNAL OF COLLOID AND INTERFACE SCIENCE 189, 189–198 (1997) ARTICLE NO. CS974808 Equilibrium and Transport Properties of Aqueous Pentaethyleneglycol- 1-hexyl Ether and Sodium Hexanesulfonate at 25°C L. Paduano, R. Sartorio, V. Vitagliano, 1 and L. Costantino Chemistry Department of Naples University Federico II, Via Mezzocannone 4, 80134 Naples, Italy Received April 1, 1996; accepted February 3, 1997 K Å [ S 0 n M / q ] [ S 0 ] n [ M / ] q Densities, viscosities, and diffusion coefficients were measured for two aqueous surfactants, pentaethyleneglycol-1-hexyl ether (C 6 E 5 ) and the sodium salt of 1-hexanesulfonic acid (C 6 SO 3 Na), Å 1 0 a n a n {[ q ( a 0 1) / n ]/ n ]} q C n/q01 . [4] through the critical micelle concentration range, and the results were briefly discussed. The micellization process was treated as an equilibrium. The diffusion data could be well fitted using a If n is sufficiently large, the equilibrium model also pre- quite narrow range of association numbers, n , and equilibrium dicts the onset of micellization in a very narrow range of constants, K .  1997 Academic Press Key Words: surfactants; diffusion; density; viscosity. concentration. However, the monomer concentration does not become constant at higher concentrations. The CMC is somewhat arbitrarity, and various choices INTRODUCTION have been proposed, related to the extrema of the free-energy derivatives which are related to the curvature of various The micellization process of a surfactant can be described solution properties through the transition region ( 1 ) . Almost either as a phase-separation, so that the concentration of the identical calculated values of a can be obtained for any n monomer species becomes constant and equal to the critical value, provided an appropriate K value is chosen (1). An micelle concentration ( CMC ) at higher concentrations, or approximate relation between n and K , valid for large n as a chemical equilibrium. values, is given by the expression For a nonionic surfactant log K Å0n log[CMC] [5] nS Å S n [1] for nonionic surfactants, and with equilibrium constant log K Å0 ( n / q 0 1)log[CMC] [6] K Å C n C n 1 Å 1 0 a n a n C n01 , [2] for ionic surfactants like C 6 SO 3 Na. Both micellization models can be used to discuss experi- where C is the stoichiometric concentration of surfactant mental data for surfactant solutions. Both are simplified ( S ), C 1 and C n the concentration of monomer and that of models that do not account, for instance, for the polydisper- micelles, and a is the fraction of S in the monomeric state. sity or for the activity coefficients of the solute species. For ionic surfactants, like C 6 SO 3 Na, the presence of coun- However, the models are good enough to allow reasonable terions modifies Eqs. [1] and [2] insight into the behavior of surfactant solutions through the micellization process ( 2 ) , although more sophisticated mod- nS 0 / qM / Å S n M q0n q , [3] els are described in the literature (3–4). According to the phase-transition model, sharp changes where q is the number of counterions bound to each micelle. in the solution properties appear at the CMC, if such changes are not found, a treatment in terms of equilibrium [1] or [3] is preferable. For low molecular weight surfactants this 1 To whom correspondence should be addressed. Fax: /3981 5527771. E-mail: vita@chemna.dichi.unina.it. model was found to be more appropriate (5, 6). 189 0021-9797/97 $25.00 Copyright  1997 by Academic Press All rights of reproduction in any form reserved.