J. Phys. Chem. 1993,97, 13820-13823
13820
Thermodynamic Consideration on Phase Behavior of the Ternary Two-Phase System of Water, Nonane, and Ethylene Glycol Monobutyl Ether Makoto Aratono,’ Fujiharu Nagoya, Takanori Takiue, and Norihiro Ikeda Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki. Higashiku, Fukuoka 81 2, Japan Received: May 24. 1993; In Final Form: September 9, 1993”
The phase behavior of a ternary two-phase system composed of water, nonane, and ethylene glycol monobutyl ether (C4E1)was investigated thermodynamically. The compositions of the water and nonane phases were measured precisely as a function of the total concentration of C4E1 and temperature under atmospheric pressure by gas liquid chromatography. A new kind of criterion of ideality for the two-phase equilibrium was proposed and examined by using the composition data obtained. The composition region of ideal dilute solution behavior was determined for the two phases as a function of temperature. It was suggested that the formation of the aggregate of C4E1 in the water phase is enhanced at lower temperatures and that in the nonane phase at higher temperatures, respectively. Furthermore the entropy and enthalpy of transfer of ether molecules from the water to the nonane phase were evaluated not by calorimetry but by applying the thermodynamics to the composition data. The transfer was found to accompany the positive entropy and be endothermic.
Introduction A large number of studieshave been made on the phase behavior of multicomponent systems containing water, oil, and a nonionic amphiphileto understand microemul~ion,l-~ multicritical points,4Ss wetting behavior of the amphiphile phase between oil and water phases,G8and other general problem^.^ The equilibrium compositions of phases and the thermodynamic analysis of them are expected to give thermodynamic quantities of transfer of component molecules and to afford a better understandingof interface formation between two phases, as reported in our previous studies on the phase and interfacial behavior of binary two-phase systems.I0 Although phase boundaries have been usually determined by visual or optical methods for three-component systems, the compositions of phases at a given condition cannot be determined by these methods because the tie lines are not necessarily parallel to the base of a Gibbs triangle even for a simple three-componentsystem. In these respects, it is useful to develop the experimental method to determine the compositions of phases and the thermodynamicequationsto analyze the results. Further, by applying the theory on fluctuation and phase diagrams” to the composition relations, it may be possible to get information on structure of aggregate. In this study, we chose the three-component system composed of water, nonane, and ethylene glycol monobutyl ether (C4E1) and determined precisely the compositions of phases as a function of temperature by using gas liquid chromatography.I2 Thermodynamic equations were developed to examine the ideality of solution, aggregate formation, and thermodynamic quantities of transfer of molecules between phases.
Experimental Section Materials. Water was triply distilled, the second and third stages being done from alkaline permanganate solution. GRgrade nonane and ethylene glycol monobutyl ether (C4E1) purchased from Tokyo Kasei Kogyo (Japan) were distilled under atmospheric pressure and under low pressure (354.4 K at 29 mmHg), respectively. Their purities were checked by a gas chromatography and were more than 99.9%. Measurements. The equilibriumcompositionswere determined by using a gas chromatographwith a thermal conductivity detector e
Abstract published in Advance ACS Absrracrs, December 1, 1993.
0022-365419312097-13820$04.00/0
(HITACHI 263-70). The threecomponent mixture having equal weights of water and nonane with a given amount of C4E1 was stirred vigorously for 1 h and then allowed to stand for 1-30 h to obtain complete phase separation. Then small amounts of the respective phases were introduced to the gas chromatograph and separated in a stainless steel column of 3-m length and 2-mm inner diameter packed with Unisole 400 (Gaskuro Kogyo Inc.). The area of the chromatogram was estimated by the chromatograph integrator (HITACHI D-2500) and then converted to the composition values by using calibration results based on the peak areas of samples having known compositions in the one-phase region. The experimental error of the determination of compositions was about 6 X l e 3 , 1 X 10-4, and 3 X 10-4 in mole fraction for water, nonane, and C4E1, respectively.
Results and Discussion Compositions of Phases at Constant Temperature under Atmospheric Pressure. We use the superscriptsW and 0 to denote the water and nonane phases and the subscripts 1, 2, and 3 to denote water, nonane, and C4E1, respectively. The equilibrium compositions were determined as a function of temperature and total mole fraction of C4E1 x3 in the whole system having equal weights of water and nonane under atmospheric pressure. The results are plotted against x3 in Figure 1 and shown in the form of the ~3~ vs x3O plot in Figure 2, where the filled circle on the end of the respective curves shows the concentration at which the third phase appears. In the followings, the mole fraction of C4E1 at this concentration in the water phase is denoted by xjWJand that in the nonane phase by x ~ O J ,respectively. It is seen that the rise in temperature increases the concentration of C4E1 in the nonane phase and decreases it in the water phase, respectively. This indicates that the upper critical solution behavior of the binary oil-nonionic amphiphile mixture and the lower one of the binary water-nonionic amphiphile mixture greatly influence the phase behavior of three component systems.13 It is probable that the abrupt increase of solubility of nonane at a concentration in the water phase in Figure 1b is related to aggregate formation because the concentration is similar to the one around which it takes place in the water phase in the absence of n0nane.~~J4JSAlso in the nonane phase, therefore, aggregate formation may start around the concentration where water becomes detectable. In connection with the aggregate formation, we point out the following: first, the almost constant value of X3O Q 1993 American Chemical Society
Phase Behavior of a Ternary Two-Phase System
The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13821
op 20 N
z
*-
0-
E
IO
0
0.051 0 1 290
I I 295
300
305
TlK
Figure 3. Mole fraction of C4E1 vs temperature curves: (1) xjWvn, (2) xjwJ,(3) and (4)xjoJ. xjOsn,
0
1
2
3
4
5
6
1O2X3
Figure 1. Mole fraction of component vs total mole fraction of C4E1 curvesat constant temperatures: (a) in thewater phase, (b) in thenonane phase; T = (1) 293.15,(2)295.65,(3) 298.15,(4)300.65,(5) 303.15, and (6) 305.65 K.
where
is the thermodynamic quantity of transfer of component r from the water to the nonane phase and
4
respectively. When the nonane phase is the ideal dilute solution, the right hand side of eq 2 is written in terms of mole fractions as
3
:p 2
z
1
102x3"
Figure 2 Mole fraction of C4E1 in the water phase vs mole fraction of C4E1 in the nonane phase curves at constant temperatures: T = (1) 293.15,(2) 295.65,(3) 298.15,(4)300.65,(5) 303.15,and (6)305.65 K.
Since both sides of eq 5 can be evaluated separately from the experiments, the equation is utilized for examining whether the solution of nonane phase is the ideal dilute one. By using the analogue of eq 5 for the water phase, the ideality of the aqueous solutioncan be examined independently. Here it should be noted that the In xjw vs In xjo line having a slope of unity has been used as a criterion of ideal solution behavior for a two-phase eq~i1ibrium.l~ This is equivalentto using the next simple relation, instead of eq 5 , obtained from eq 1:
We point out, however, that the ideality of the solutionsof water and nonane phases cannot be determined independently by applyingeq6to theexperimentalresults. In this respect, therefore, eq 5 is more useful than eq 6. The left hand side (LHS) of eq 5 was evaluated from the xlo vs x3O curves, and the right hand side (RHS) was calculated from the results in Figure la. It was observed that the value of LHS deviates from that of the RHS at a mole fraction which we denote xj0vn. By using the analogue of eq 5 for the water phase, the valuesof ~ 3were~ also. determined. ~ They are shown as a function of temperature in Figure 3 together with the mole fractions X ~ O , ~ and X ~ ~ ItJ is . seen that the value of ~ 3 ~ decreases 9 " and that of xjoJ increases with increasing temperature. This suggests that theaggregate formation isenhanced, and, as a result, the solubility of C4El increases at higher temperature in the oil-rich phase. In the water-rich phase, the value of increases slightly and that of xjWJdecreases with increasing temperature; aggregate formation is diminished, and the solubility of C4E1 decreases at higher temperature. Furthermore it is seen that the aggregates -A",, d T + Agv, d p prI0 dxlo + pljo dx,O - 1 4 2 dxzW ~ exist both in the water and nonane phases at the lower two p,3w dxjW= 0, r = 1,2, 3 (1) temperatures. Phase Prism. To show the temperature dependence of the the composition relation is written for the nonane phase as phase behavior of three-component systems, the phase prism was (axp/axjo), = - - ( X , ~ P , , ~+ x ~ + ~ ~~ ~ N ~ ~ 3~ 0 )~constructed / ~ by stacking a Gibbs triangleat different temperatures and drawn in Figure 4, where the three-phase region is also given (XlWPI + x,wP,p + XjWCL3P), r = 192 (2) by the central triangle. It is easily seen that the composition of
at the lowest temperature and that of xjW at the highest temperature, as is shown in Figure 2, is one piece of evidence that aggregate formation takes place in the water and nonane phases, respectively.I6 Second, the experimental finding that the xl0/ xgoand x2w/xjwratiosdo not appreciably depend on temperature implies that the increase of the mutual solubility of water and nonane is promoted mainly by the presence of the aggregate of C4E1 molecules and not by a change of the mutual solubility of the binary water and nonane system with temperature. Now we look at the results from the thermodynamic point of view. The properties of solution are changed by aggregate formation and then deviate from those of the ideal dilute solution. Although the colligative properties of solution are available to examine this point, we show that the composition relations can bea kind of criterionof ideal dilutesolution of a two-phasesystem. By solving the three simultaneous equations of the equilibrium condition of ternary two-phase system given by
+
p
~
3
~
9
~
Aratono et al.
13822 The Journal of Physical Chemistry, Vol. 97, No. 51, 1993
11
10 9 8 7
8 5 4
3
2 1
n 290
300
295
305
T /K
Figure 5. Mole fraction of C4E1 in the water phase vs temperature curves a t constant mole fraction of C4E1 in the nonanc phase: 1 0 * ~ 1 ~ = (1) 0.5, (2) 1, (3) 2, (4) 3, ( 5 ) 4, (6) 5, (7) 6, (8) 7, ( 9 ) 8, (10) 9, (1 1) 10, (12) 11, (13) 12, and (14) 14; (15) X ~ ~ T. ~ ~ V S
.
I
Y -J
ur0.04
0 2
4
0
0.2
0.4
0.6
0.8
-
0
1
I I I I
I
water XZ nonane Figure 4. Phase prism constructed a t different temperatures: T = (1) 293.15, (2) 295.65, (3) 298.15, (4) 300.65, (5) 303.15, and (6) 305.65
K.
the middle phase rotates clockwise and the tie line connecting the equilibrium compositions of the two phases rotates counterclockwise with increasing temperature, respectively. This means that the hydrophilicity of C4E1 is diminished with increasing temperature. By reference to the solution behavior of binary systems in the vicinity of the lower or upper critical solution temperature,'0J8 we say that C4El molecules are rather energetically stable through the hydration in the water phase and rather entropically stable in the nonane phase, respectively. ThermodynamicQuantitiesof Transfer. The entropy of transfer of C4E1 is obtained from eq 1 and given by
where xmDlrefers to the one of four mole fractions appearing in eq 1, and then the corresponding enthalpy is
Therefore it should be noted that the entropy and enthalpy of transfer are obtained not only by calorimetry but by measuring the compositions of the two phases as a function of temperature a t constant pressure. Within the concentration range of ideal dilute solution behavior, eq 7 is reduced to
The values of Ags, were calculated by applying eq 9 to the xgW vs T curves at constant x3O shown in Figure 5 . The results and the corresponding values of A g h , are plotted against xjo a t 298.15 K in Figure 6 . We can say that the transfer of C4E1 molecules from the water to the nonane phase accompanies an increase in entropy and is endothermic. These findings indicate
that the attractive interaction between molecules restricts more strongly the motion and orientation of molecules in the water phase than in the nonane phase. Furthermore, thesesubstantiate our statement given above that C4E1 molecules are rather energeticallystable through the hydration in the water phase and rather entropically stable in the nonane phase, respectively. In our next paper, the adsorption behavior of C4E1 molecules a t the nonane/water interface will be discussed by using the thermodynamic analysis of the interfacial tension and the results obtained in this paper.20
Acknowledgment. The present paper was supported in part by Grant-in-Aid for Scientific Research No. 04453010 from the Ministry of Education, Science and Culture and by the Cosmetology Research Foundation (Grant 5-91-10). References and Notes (1) (a) Kahlweit, M.; Strey, R. Angew. Chem., Int. Ed. Engl. 1985,21, 654-668. (b) Kahlweit, M.; Strey, R.; Haase, D.; Kunieda, H.; Schmeling, T.; Faulhaber, B.; Borkovec, M.; Eicke, H.-F.; Busse, G.; Eggerrs, F.; Funck, T.; Richmann, H.; Magid, L.; Soderman, 0.; Stilbs, P.; WinLler, J.; Dittrich, A.; Jahn, W. J. Colloid Interface Sci. 1987,118,436-453. (c) Kahlweit, M.; Strey. R.; Haase, D.; Firman, P. Lungmuir 1988,4785-790. (d) Kahlweit, M.; Strey, R.; Busse, G. J . Phys. Chem. 1990, 94, 3881-3894. (2) Shinoda, K.; Lindman, B. Lungmuir 1987, 3, 135-149. (3) Kunieda, H.J . Colloid Interface Sci. 1989, 133, 237-243. (4) (a) Widom, B. J. Chem. Phys. 1975, 62, 1332-1336. (b) Widom. B. Lungmuir 1987, 3, 12-17. (5) Lovellette, M. J . Phys. Chem. 1981, 85, 1266-1270. (6) (a) Kahlweit, M.; Strey, R.; Firman, P.; Haase, D. Langmuir 1985, I, 281-288. (b) Kahlweit, M.; Strey, R.; Firman, P. J. Phys. Chem. 1986, 90,671-677. (c) Kahlwcit, M.; Strey, R.; Aratono, M.; Jen, J.; Schubert, K. V.J. Chem. Phys. 1991, 95, 2842-2853. (7) Chcn, L.4.; Jeng, J.; Robert, M.; Shukla, K. P. Phys. Rev. A 1990, 42,4716-4723. (8) Aratono, M.; Kahlweit, M.J . Chem. Phys. 1991, 95, 8578-8583.
Phase Behavior of a Ternary Two-Phase System (9) Degiorgio, V.;Corti, M.Physicsof Amphiphiles: Micelles, Vecicles and Microcmulsions; North-Holland Physics Publishing: Amaterdam; 1985, and references cited therein. (10) (a) Aratono, M.; Motomura, K, Bull. Chem. Soc. Jpn. 1985, 58, 3205-3209. (b) Aratono, M.;Motomura, K. J. Colloid Interface Sci. 1987, 117, 159-164. (c) Aratono, M.;Nakayama, S.;Ikeda, N.; Motomura, K. Colloid Polym. Sci. 1990, 268, 877-882. (11) Teubner. M.J. Chem. Phys. 1992.96. 3811-3813. (12) (a) Kilpatrick, P. K.; Gonnan, C. A.; Davis, H.T.; Scriven, L. E.; Miller, W.G. J. Phys. Chem. 1986,90, 5292-S299. (b) Kiptrick, P. K.; Davis, H.T.; Scriven, L. E.;Miller, W.G. J. Colloid Interface Sci. 1987,118,
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(13) Kahlweit, M.; L e " , 5040.
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The Journal of Physical Chemistry, Vol. 97, No. 51, 1993 13823 (14) Quirion, F.;Magid, L.J.; Drifford, M. Longmuir 1990,6,244-249. (15) Elizalde, F.;Gracia, J.; Costas, M. J . Phys. Chem. 19w), 92, 35653568. (16) Harusawa, F.;Saito, T.; Nakajima, H.; Fukushima, S . J. Colloid Interface Sci. 1980, 74, 435440. (17) Manabe. M.; Koda, M.:Shirahama, K. Bull. Chem.Soc.Jpn. 1975, 48,3553-3556. (18) Prigogine, I.; Defay. R. Chemical Thermodynamics;Everett, D. H., Trans.: Longmans: London, 1954; p 393. (19) Sassen, C. L.; Filemon, L.M.; de Loos, T. W.:de Swaan Arom, J. J. Phys. Chem. 1989,93, 6511-6516. (20) Aratono, M.; Nagoya, F.;Takiue, T.; Ikcda. N.; Motomura, K. To
be published.
