J. Phys. Chem. 1983, 87, 4520-4524
4520
Distribution of Polydisperse Nonionic Surfactants between Oil and Water 0. 0. Warr, F. Grleser,f and t. W. Healy' Depaflmnt of Chemistry, Unlverslty of Melbowne. V k . 3052, Australia (Receivd: September 28, 1982; In Final F m : December 1, 1982)
Theoretical and experimentalstudies of the process of partition between an oil (hexane)and water for nonylphenol ethoxylate nonionic surfactants are reported. For a polydistributed nonionic with a mean ethoxylate chain length of 9 it is demonstrated that aggregates are not present in the oil phase at surfactant concentrations in the range of interest of this study. Total partition at concentrations below the critical micelle concentration (cmc) is preferentially into the oil. The statistical mean composition below the cmc is independent of the total concentration in both phases. Above the cmc there is a marked change in the composition of both phases. The experimental partition and compositiondata are well described by the ideal mixing-phaseseparation model of nonionic Surfactants in oil-water systems.
Introduction The distribution of amphipathic molecules between immiscible liquids (oil and water, for example) is used as the basis of the definition of the hydrophilic/lipophilic nature or balance of the ~urfactant.'-~For nonionic surfactants like alkyl or alkyl-aryl ethoxylates, it is known that the ratio of the hydrocarbon to the ethoxy chain length controls the partition as well as controlling the interfacial tension, micellization,4fisurface adsorption>' and emulsion f~rmation.~ In a recent paper, Harusawa and Tanakas considered the oil-water partitioning behavior of binary and polydisperse mixed nonionic surfactant systems of the nonylphenol ethoxylate type. They confirmed the general observation that, for mixed surfactants above the critical micelle concentration (cmc) of the mixture, the partition into the oil phase is much more pronounced than is observed for single-component surfactants. We present here an alternative treatment of partitioning of mixtures to that of Harusawa and Tanakaa with the specific aim of predicting the distribution ratiogfor any mixed system as well as the distribution of each of the component species between the oil, micelle, and aqueous environments. Consideration of the partitioning behavior of any amphiphilic species requires first a knowledge of their solution chemistry in both solvents. To this end the behavior of polydisperse nonylphenol ethoxylate surfactants in various organic solvents was studied by 'H NMR to determine the surfactant aggregation in the oil phase. The aqueous chemistry of these nonionics has been reported previous19 and is included explicitly in the present model of the partitioning system. In this work, the distribution of polydisperse nonylphenol ethoxylates with mean ethoxy chain lengths of 5 and 9 (denoted by N5 and N9) between hexane and water have been studied to determine their partition between all states in both phases. Theory The present analysis is based on the assumptions as used previously@JO that nonionic surfactants can be treated as ideal mixtures in all states and that the mixed micelles are described in terms of a phase-separation model. For oil-water partitioning, a further restriction is made, and verified subsequently, that no aggregates are present in the oil phase. The mole fraction of species in micelles is given by 'Queen Elizabeth I1 Fellow. 0022-3654/83/2087-452Q~0~ .50/0
where CT is the total (analytical) concentration of surfactant, ai is the mole fraction of species i in the total mixed solute, Omon is the concentration of monomeric i in aqueous solution, and Coilis the concentration of i in the immiscible liquid (oil) phase. If we assume that only monomeric surfactants can cross the liquid-liquid interface, then for each i
Ki = Cioil/Cimon where Ki is an equilibrium constant, or distribution ratio, for the distribution of the species i between liquid phases. Treating micelles as a phase, and the cmc as a point, we have the additional condition below the cmc, assuming that no aggregates are present in the oil phase, viz. (3)
This allows us to define an effective equilibrium constant for the mixture, Keff(Kdx in ref 81,for submicellar solutions
Below the cmc, calculation of the distribution of all species between phases is straightforward and the distribution is concentration independent. However, in the presence of micelles, eq 4 no longer applies. In order to (1)Schott, H. J . Pharm. Sci. 1971, 60,648. (2) Lin, I. J.; M a " , L. Prog. Colloid Polym. Sci. 1978, 63,99. (3) Harusawa, F.; Saito, T.;Nakajima, H.; Fukushima, S. J. Colloid. Interface Sci. 1980, 74, 435. (4) Warr, G. G.; Grieser, F.; Healy, T. W. J . Phys. Chem. 1983, 87, 1
nnl\
ILIW.
(5) Hsiao, Lun; Dunning, H. N.; Lorenz, P. B. J. Phys. Chem. 1956, 60,657. (6) Furlong, D. N.; Aston, J. R. Colloids Surf. 1982, 4 , 121. (7).Ueno, M.; Takasawa, Y.; Miyashige, H.; Tabata, Y.; Meguro, K. Colloid Polym. Sci. 1981, 259, 761. (8) Harusawa, F.; Tanaka, M. J. Phys. Chem. 1981,85, 882. (9)Greenwald, H. L.; Kice, E. B.; Kenly, M.; Kelly, J. A d . Chem. 1961, 33,465. (10)Clint, J. H. J . Chem. SOC.,Faraday Trans. I 1975, 71, 1327.
@ 1983 American Chemical Society
The Journal of Physical Chemistry, Voi. 87, No. 22, 1983 4521
Distribution of Polydisperse Nonionic Surfactants
determine the behavior of the mixture in the presence of micelles, we must first determine the point at which micelles begin to occur in the system. In the same way as for an aqueous solution, we can deduce the cmc of the two-phase system, i.e., the total concentration (C',) required in the two-phase system to form micelles in the aqueous phase. (Details of this derivation are given in the Appendix.) Thus, Ch, is given by
c0 E
5L L
(5) where CMjis the cmc of the jth species. At the cmc, the total concentration in the aqueous phase is C h / ( l + K,ff). In order to calculate the behavior of the mixed system above this concentration, we define the dimensionless variable z, which is identifed with the fraction of all species present which are not in micelles.
g
C’, we define two dimensionless parameters z = (1/cT)zcjmon(1 J
+ Kj)
(6)
c,/cl,
(AB) The parameter c is used as a convenience in computing, thereby ensuring that the variables used are of order 1. Using eq 1 and A5 we obtain c =
Qmon
aiCMi
=
1- z
For a mixture with n components it is clear that eq A10 yields an nth-order polynomial. As it is written we may solve this numerically by a fourth-order Runge-Kutta computer program.” We form the derivative of z with respect to the scaled concentration, c, viz.
where
(A9)
CMi + -(1 + Ki) cc’,
from which we form z in terms of known parameters
Using this relation, together with the initial conditions z = 1, c = 1, we can calculate z as described above and
hence determine Cimonand Ciog using eq A9 and 2, respectively. Registry No. a-(Nonylphenyl)-w-hydroxypoly(oxy-1,2ethanediyl),9016-45-9; hexane, 110-54-3.
Light Scattering Study of Solutions of Sodium Octanoate Mlcelles 1.Zemb, M. Drlfford,’ M. Hayoun, and A. Jehanno Department de Physicochimie, Cen Saclay, 91 191 Qif-sur-YvetteCedex, France (Received October 19, 1982; In Final Farm: January 3 1. 1983)
Sodium octanoate micelles have been studied by light scattering at surfactant concentrations up to 1.8 M. The micellar weight as determined by intensity measurements shows an increase in the aggregation number from 11at the cmc to 26 at 1.8 M. Dynamic light scattering reveals a “reactive”diffusionwhich is a purely translational effect due to the chemical exchange between the micelles and free monomers. Introduction Aqueous micelles of sodium octanoate (cmc N 0.4 M) have been extensively studied.’2 Because this is a limiting case of micelle formation with a large cmc and a very low aggregation number, the determination of aggregation numbers by different experimental methods3p4and numerical evaluations5 is difficult. In this system at large volume fractions (4 I 0.4), the intermicellar correlations resulting from repulsive interactions between the charged particles are important. A recent neutron scattering study6 shows a strong contribution from the intermicellar structure factor S(q). The application of modern liquid theory to colloidal systems7+ now allows an analysis of the scattering data from solutions ~~~
~
(1) B. Wennerstrom and B. Lindman, Phys. Rep., 52, 1 (1979). (2) F. Eriksson,J. C. Erikeson, and P. Stenius in ‘Solution Chemistry of Surfactants”, Vol. 11, K. Mittal, Ed., 1979, p 297. (3) B. Lindman and B. Brun, J.Colloid Interface Sci., 42,388 (1973). (4) P. 0. Persson, T. Drakenberg, and B. Lindman, J. Phys. Chem., 83, 3011 (1979). (5) G. Gunarrson and H. Wennerstrom, to be submitted for publication. (6) J. B. Hayter and T. Zemb, Chem. Phys. Lett., 93, 91 (1982). (7) W. Agterof, J. Van Zomeron, and A. Vrij, Chem. Phys. Lett., 43, 363 (1976). (8) J. B. Hayter and J. Penfold, Mol. Phys., 42, 109 (1981). (9) L. Belloni, Thbse 3bme cycle, Paris, 1982, Note CEA-N-2292. 0022-365416312087-4524$01.50/0
of charged micelles at any concentration and gives some fundamental information on the interaction between the micelleslO or microemuhion aggregates.” The calculation of the analytic structure factor S(q) using the mean spherical approximation (MSA) with a repulsive electrostatic potential between interacting charged micellesa has been used to analyze neutron scattering experiments. Another approach has been proposed to study the interparticle interaction from quasielastic light scattering.I2 When one uses the generalized Stokes-Einstein equation developed to first order in volume fraction (including thermodynamic and hydrodynamic factors), with a pair interaction potential from DLVO theory, a qualitative fit is obtained from measurements performed with SDS micelles (diffusivity and intensity). This theory has been applied to cationic micelles13 as a function of surfactant and salt concentrations. An excellent agreement with diffusivity data is shown at low surfactant concentration and in a range of salt concen(IO) J. B. Hayter and J. Penfold, J. Chem. SOC., Faraday Trans. f,77, 1851 (1981). (11) D. J. Cebula, D. Y. Myers, and R. H. Ottewill, Colloid, Polym. Sci., 107, 96 (1982). (12) M. Corti and V. Degiorgio, J. Phys. Chem., 85, 711 (1981). (13) R. Dorshow, J. Briggs, G. A. Bunton, and D. F. Nicoli, J.Phys. Chem., 86, 2388 (1982). 0 1983 American Chemical Society
