J . Phys. Chem. 1994,98, 274-278
274
Surface Potential Measurements in Mixed Micelle Systems Rachel A. Hobson, Franz Crieser,. and Thomas W. Healy Advanced Mineral Products Research Centre, School of Chemistry, University of Melbourne, Parkville 3052, Australia Received: July 30, 1993; In Final Form: October 7, 1993@
The relationship between the measured electrostatic surface potential of two mixed surfactant systems, n-dodecyl octaoxyethylene glycol monoether (C1ZES)/sodium dodecyl sulfate (SDS) and C12E8/n-dodecyltrimethylammonium chloride (DTAC), and the free ionic surfactant concentration in these mixtures has been examined. The surface potential measurements were based on the well established technique of using micelle-solubilized acid-base indicators. Free monomer concentrations were determined from results obtained using the mixed micelle critical micelle concentrations and then processing this information using a nonideal mixed micelle theory. For the systems studied it has been found that a change in the modulus of the surface potential per unit change in log(ionic surfactant concentration) is approximately 59 mV. This is in accordance with the Nernstian relationship put forward by Healy et a1.I linking the electrostatic surface potential of a charged micelle to the equilibrium monomer concentration.
Introduction
then for a single charged system studied at 25 "C it follows that
Healy et al.1 proposed that a Nernstian relationship existed between the electrostatic surface potential of an ionic micelle and its critical micelle concentration, cmc. That is, a change in the modulus of the surface potential per unit change in log(cmc) is 59 mV at 25 OC. The micellar system was viewed thermodynamically, assuming that a surfactant monomer can be added to the micelle without changing the micelle properties, therefore implying that the micellar phase is behaving as a macroscopic phase and the surfactant monomer ion becomes the potentialdetermining ion. For micellar systems, with micelles of mean aggregation number ( m ) ,the chemical potential of a surfactant in a micelle can be expressed as
dl\kd/d log aaq= 59.16 mV (4) The objective of this study was to examine eqs 3 and 4 in detail using both nonionic/anionic and nonionic/cationic mixed surfactant systems. The monomer concentrations of the charged species weredetermined from mixed surfactant cmcmeasurements in conjunction with the corresponding electrostatic surface potentials of their mixed micelles. These combined measurements meant that the relationship between the potential and the free monomer concentration could be established.
where pomic,(,,,) is the standard chemical potential of a surfactant in a micellar state, I the valency of the charged surfactant monomer, e the elementary electrostatic charge, 90the mean electrostatic potential at the plane of the surfactant headgroups in a micelle, and Pdipolc the chemical potential due to surface dipoles. The chemical potential of a surfactant monomer in aqueous solution is given by where b o q is the standard chemical potential of surfactant monomer in aqueous solution, k the Boltzmann constant, T the absolute temperature, and aaqthe activity of the surfactant monomer in aqueous solution. As there is an equilibrium between the surfactant monomer inaqueoussolutionandin themicellar state, the following equation can be generated by equating the above two equations,
This gives the relation between the surface potential and the surfactant monomer concentration in equilibriumwith the micelle. If the set of terms following the first term in eq 3 remains constant with a change in free ionic monomer concentration,
* Author for correspondence.
I
Abstract published in Advance ACS Akrracts, December 1, 1993.
0022-3654/94/2098-0274%04.50/0
Experimental Section The mixed ionic/nonionic systems studied were n-dodecyl octaoxyethylene glycol monoether, C H , ( C H ~ ) I I ( O C H ~ C H ~ ) ~ OH, (C12E8)/sodium dodecyl sulfate, C H ~ ( C H ~ ) I I O SNa+ O~(SDS), and C 12E8/n-dodecyltrimethylammonium chloride,CH3( C H ~ ) ~ I N ( C H C1~ ) ~(DTAC), + with a constant electrolyte background of 5 mM NaCl. The electrolyte was present to maintain constant ionic strength during the pH titrations of the indications. The DTAC was obtained from Tokyo Kasei Kogyo Co. When measuring the cmc of DTAC, it was found that a minimum occurred in the plot of surface tension against the surfactant concentration,implying that surface active impuritieswere present in the DTAC. The 'dip" could be due to small amounts (less than 1%) of either an alcohol of similar chain length or a longer chained trimethylammonium chloride.2 After recrystallizing three times from methanol/diethyl ether? the minimum was no longer observed and a cmc of 11.9 mM was obtained. This value compares well with published data.4 C12E8 and SDS (specially purified) were obtained from the Nikko Chemical Co. and B.D.H. Chemicals Ltd., respectively; neither surfactant showed dips in its surface tension results, and hence they were used as received. NaCl was obtained from AJAX Chemicals (Analytical grade). Millipore filtered water was used to prepare the aqueous solutions (conductivity
