Langmuir 1995,11, 3327-3332
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Thermodynamic Study of the Temperature-Concentration Dependence along the Krafft Boundary. Differential Scanning Calorimetry Measurements and Modeling for the N-Dodecanoyl-N-methylglucamine-Water System N. A. Smirnova” and T. G. Churjusova Department of Chemistry, St. Petersburg University, 2 Universitetsky pr., 198904 St. Petersburg, Russia Received November 9, 1994. In Final Form: March 22, 1995@ The dependenceof the surfactant solubilitytemperature on the micellar solution concentration is analyzed on the basis of strict thermodynamic relationships and using the ideal monodispersed micellar solution model. The approach is illustrated in applicationto the N-dodecanoyl-N-methylglucamine-watersystem. Experimental measurements of the surfactant dissolution temperatures and heats have been performed for the system under study by the differential scanning calorimetry (DSC) method. The calculated temperature change along the Kraf€t boundary is in reasonable agreement with the experiment. Problems of the DSC data treatment for the phase transition of interest are discussed. By definition the Kraf€t boundary on the temperaturecomposition phase diagram a t constant pressure corresponds to the equilibrium between the liquid solution and the pure crystal surfactant, the latter being often hydrated. In Figure 1 representing a fragment of the phase diagram for surfactant (1)-water (2) system the KrafTt boundary is the part ABC of the solubility curve. In the diagram (and later on) T i s the temperature, X I is the surfactant concentration in mole fractions, and L and S denote the liquid isotropic solution and the solid surfactant, respectively. At point B (the KrafTt point) the solubility curve intersects with the critical micelle concentration (cmc) curve, part AB of the solubility curve corresponds to the equilibrium “molecular solution-solid surfactant”. Point C stands for the micellar solution in the equilibrium both with the solid and with the liquid crystalline (E)phases. The branch BC relating to the “micellar solution-crystal surfactant” equilibrium represents the lower temperature boundary for the micellar region. The surfactant solubility curve is not the only encountered type of the lower temperature boundary for this region. In some systems the micellar state persists on cooling until the ice starts to crystallize at the temperature a bit below 0 “C. So in this case it is the ice crystallization curve which presents the lower temperature boundary for the micellar region, such a behavior being typical for systems with easily melted surfactants. In some cases the cooling of micellar solutions results in gel formation, but when such a transition is observed, the problem of attaining equilibrium state needs special attenti0n.l Only systems where micellar solution-crystal surfactant equilibrium takes place will be considered in the paper. The surfactant solubility curve lies at temperatures above 0 “C and has a distinctive shape. It starts from a very low surfactant concentration (the curve of the ice crystallization is not practically revealed in the diagram) and goes up steeply at the beginning. The slope of the curve varies drastically near the Kr& point, so a “knee” and a ”plateau” above the knee are visible. In many systems the plateau is nearly horizontal, that is, the surfactant solubility increases very rapidly with a small temperature increase above the Krafft point. Such behavior is observed for zwitterionic and some nonionic Abstract published in Advance ACS Abstracts, J u l y 15, 1995. (1)Laughlin, R. G.The Aqueous Phase Behavior of Surfactants; Academic F’ress: London, San Diego, New York, 1994. @
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L+s
s ? -T
I . x1
Figure 1. A fragment of the phase diagram for surfactantwater system. L, E, and S denote liquid solution, liquid
crystalline, and solid phases, respectively; the dotted line is the cmc curve. surfactants. A relatively steeper slope of the Krafft plateau is typical for ionic surfactants where the temperature rise along the branch BC is often 15-20 “C.l For the interpretation ofthe Krafft point and the KrafTt boundary, different approaches are proposed starting from those based on the pseudophase separation model and considering dissolution as the hydrated crystal surfactant melting.2i3 Critical analysis of main approaches can be found in ref 4. Though at present a general thermodynamic treatment seems clear, much remains to be done for the quantitative description and the molecular modeling of the micellar solution-solid surfactant phase transition in systems of various chemical nature. Here both systematic experimental studies and theoretical elaborations are needed. The published data on the temperature-composition dependence along the KrafTt boundary are not numerous and relate mainly to systems with ionic surfactants. Only for a few systems are the heats of the L S L phase transition available in the literature. Though considerable advances have been made during the last years in molecular modeling of micellar solutions, nevertheless, even the possibilities given by the simplest models have not yet been used for the treatment of the micellar solution-crystal surfactant equilibrium. In the present work we shall consider general thermodynamic relationships describing temperature vs composition along the surfactant solubility curve and the results following from an ideal micellar solution model.
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(2) Shinoda, K; Hutchinson, E. J. Phys. Chem. 1962,66, 577.
(3)Shinoda, K.;Yamaguchi, N.; Carlsson, A. J. Phys. Chem. 1989, 93, 7216. (4) Rusanov, A. I. Micelloobrazovanie v rastvorach poverchnostnoactivnich veschestv (in Russian); Chimia: St. Petersburg, 1992.
0743-746319512411-3327$09.00/00 1995 American Chemical Society
Smirnova and Churjusova
3328 Langmuir, Vol. 11, No.9, 1995
The aim ofthe discussion is to estimate the role of different factors effecting the temperature slope of the KrafR boundary in surfactant-water systems. The consideration of relationships for binary systems seems interesting not only in itself but also as a step to modeling of the third Here xk stands for the surfactant mole fraction in the component effects on the surfactant dissolution tempersolution and AH1 is the differential molar heat of the ature which is a practically important p r ~ b l e m .The ~ crystal hydrate dissolution. In the case of an unhydrated approximations used are applicable to nonionic systems, crystal surfactant ( m = 0) eq 3 is simplified as and the system N-dodecanoyl-N-methylglucamine -water has been chosen for the experimental study. (4) The chemical formula of the surfactant under investigation is CH~(CH~)&(O)N(CH~)CH~(CHOH)&HZOH; the common abbreviation is MEGA-12. The study of Due to the great difference in the surfactant and water N-dodecanoyl-N-methylglucamines(MEGA-n surfactants) molar masses the inequality xk 0 (due to the numbers at different temperatures, and thermodynamic stability criterion), it follows from eq 4 that (dT/axk)p > parameters of micellization have been detem~ined.~ For 0, which is in accord with experimental observations. N-dodecanoyl-N-methylglucamine the phase diagram over Equation 4 is a general and strict thermodynamic the whole range of concentration is published in the relation for the equilibrium between the solution and the literatures1 In our work temperatures and enthalpies of solid phase of constant composition, the dependence being the L S L phase transition have been measured by valid both for micellar and for nonaggregated molecular the differential scanning calorimetry method. Thermoor ionic systems. The values in the right-hand side of eq dynamic treatment of the DSC data is presented. 4,particularly the magnitude of the (aplttxb~l)~,~ derivative in its dependence on the concentration, may vary greatly Thermodynamic Equations for L S L Phase for different systems. Molecular aggregation in micellar Transition Temperature and Their Application systems results in a small value for the derivative and to Ideal Micellar Solutions hence in a small slope of the KrafR plateau. Micellar Thermodynamic relationships will be given below for solutions in some aspects are similar to those nonideal the system where the surfactant is a crystal hydrate molecular solutions which, being homogeneous, are close containing m water molecules per a surfactant molecule. to the liquid-liquid phase separation: the stability Denoting surfactant and water molecules by X and W, criterion (8,pJ&xl),,~ > 0 is still valid but the magnitude respectively, we represent the crystal hydrate as XW,; m of the derivative is small. For such systems, where = 0 corresponds to a particular case of an unhydrated molecular aggregation is highly pronounced (though the surfactant. According to the equilibrium conditions it structure of aggregates is much more uncertain and follows flexible than the micellar structure), the shape of the solubility curve is similar to that for micellar systems, the plateau being observed here too. For solutions with a true miscibility gap one has (ap1/kl),,~= 0 in the range of immiscibility and the precipitation curve relating to or more simply the liquid-liquid-solid equilibrium is strictly horizontal. But if the solution is homogeneous, the slope of the precipitation curve has to be nonzero and this is just the case for the micellar solution-solid phase equilibrium. Considering the specificity of micellar solutions, one whereps is the chemical potential of the surfactant crystal can conclude that the (~,ullaxl),,~value for them should be hydrate, pk and pk denote the surfactant and water greatly affected by the average aggregation number (n). chemical potentials in the solution. For equilibrium The hypothetical limiting case of the infinite n corresponds changes in the temperature and the saturated solution to the pseudophase separation model representing the composition atp = constant (p is the pressure)the following micellar solution like a two phase system consisting of equation is valid aqueous and micellar pseudophases; the model states that d($) L +md($) L = d k ) (apl/&l),,~= 0 and the slope of the KrafR plateau is zero, which evidently does not agree with the reality. The simplest model permitting consideration ofthe dependence of the (apllttxl),,~value on the aggregation number is the ideal monodispersed micellar solution model. The results From (2) and the Gibbs-Duhem and Gibbs-Helmholtz following from the model will be discussed below. equations, we obtain As surfactant monomers and aggregates are in equilibrium, their chemical potentials p11 and pln obey the (5) Smirnova, N. A. In 13th ZUPAC conference on Chemical Thercondition modynamics. Abstracts; Clermont- Ferrand, 1994;p 147.(Paper is submitted to Fluid Phase Equilib.) 1 (6)Hildreth, J. E.K. Biochem. J . 1982,207, 363. (7)Hanatani, M.; Nishifuji, K.; Futai, M.; Tsuchiya, T. J. Biochem. P l = P l l = , P.l-n 1984,95,1349. where plnrelates to micelles with the aggregation number ( 8 ) Yu,F.; McCarty, R. E. Arch. Biochem. Biophys. 1986,61, 238. (9)Okawauchi, M. Bull. Chem. Soc. Jpn. 1987,60, 2718. n.
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Temperature-Concentration Dependence Study
Langmuir, Vol. 11, No. 9, 1995 3329
The following equation stemming from eqs 4 and 5 is valid along the whole ABC solubility curve
x11 and f l l being respectively the monomer mole fraction and activity coefficient. For the BC branch we can write also
where the values with the subscript I n relate to micelles composed of n molecules. Expression 6 is helpful for the qualitative discussion of the specific shape of the surfactant solubility curve.4 It can be used also for quantitative estimations if the monomer concentration in dependence on the gross compositionxll(xl) is known from the experiment or from model calculations. For very diluted solutions (XI
