J. Phys. Chem. 1993,97, 5141-5143
5141
Thermodynamic Study on Phase Transition at the Water/Undecyl Alcohol Interface Makoto Aratono,' Takanori Takiue, Norihiro Ikeda, Akira Nakamura, and Kinsi Motomura Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki, Higashiku, Fukuoka 81 2, Japan Received: December 8, 1992; In Final Form: February 18, I993
The interfacial tension of the water/undecyl alcohol (UNA) system was measured as a function of pressure at various temperatures. The interfacial tension vs pressure and temperature curves were found to have a break point. It was shown that the volume, entropy, and energy of interface formation evaluated have negative values and change discontinuously at the pressure and temperature of the break point. The equations describing the phase transition at the interface of a binary two-phase system were developed and applied to the present system. It was proved thermodynamically that the phase transition takes place at the break point. Further, it was suggested that the transition was the one between expanded and condensed states of the interface.
IntrOdUCtiOtl
From the systematic thermodynamic studies of adsorption of long-chain alcohols at oil/water interfaces, we have concluded that the interface is transformed abruptly from an expanded state to a condensed one at a certain temperature, pressure, or concentration.' Furthermore, with respect to the water/undecyl alcohol (UNA) system which is free from an oil such as hydrocarbons, we have suggested that the break point on the interfacial tension vs temperature and pressure curves is caused by the phase transition at the interface2 However, this suggestion remains unproved. The present paper lays emphasis on its thermodynamic proof. First, we measure the interfacial tension as a function of pressure and temperature in much more detail and then evaluate the thermodynamic quantities of interface formation. Next, we develop the thermodynamic equations describing the phase transition at the interface of a binary twophase system and apply them to the water/UNA system.
5 ' 0
I 20
40
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100
p / MPa
Figure 1. Interfacial tension vs pressure curves at constant temperatures: (1) T = 293.15, (2) 295.15, (3) 298.15, (4) 300.65, (5) 303.15, (6) 305.65, (7) 308.15 K; (8) yq v s p .
Experimental Section The methods of purification of UNA and water were described in our previous paper.* The density value at atmosphericpressure was measured by a digital density meter (Anton Paar 60/602) and that at high pressure was calculated from the compression measured by using pyezometer at high pressure. The interfacial tension was measured by the pendant drop method. The error of interfacial tension value was within 0.05 mN m-'. The procedures of density and interfacial tension measurements were described in our previous paper^.^,^
Results and Discussion Since the number of degrees of freedom is 2 for this system, we choose temperature T and pressure p as the thermodynamic independent variables. The interfacial tension y was measured as a function of pressure at constant temperature and plotted against pressure in Figure 1. It is noted that the interfacial tension is low and depends considerably on pressure and temperature. The y value decreases with increasing pressure, and the y vs p curves, except the one at the lowest temperature, are constituted of the two lines having different slopes. To visualize the temperature dependence of interfacial tension, the y values at a given pressure were read and plotted against temperature in Figure 2. It is seen that the interfacial tension increases with increasing temperature, and they vs Tcurves, except the one at the highest pressure, have a break point. It should be noted that the dependence of interfacial tension on pressure and temperature is similar to those of the water/hydrocarbon solution of long-chain 0022-3654/93/2097-5 141$04.00/0
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Figure 2. Interfacial tension vs temperature curves at constant pressures: (1) p = 0.1, (2) 10, (3) 20, (4) 30, (5) 40,(6) 50, (7) 60, ( 8 ) 70 MPa; (9) yq vs 7'Y
alcohol system at a high concentration' but forms a striking contrast to that of the water/hydrocarbon systems.3~~ From Figures 1 and 2, we determined graphically the break point characterizedby the values of interfacialtension 79,pressure p,and temperature 7 9 The 9v s p and D curves are shown in Figures 1 and 2, respectively, and play an important role in examining what takes place at the point as we shall see later. It is seen that the value of'y increases with increasing pressure and temperature. 0 1993 American Chemical Society
Aratono et al.
5142 The Journal of Physical Chemistry, Vol. 97, No. 19, 1993
b
-0.1
.
-
v
E -0.2-
'ic
. a -0.37
1
-0.08
E
I
-0.10 1
0
I
I
1
20
60
40
I
80
I
100 -0.4-
p I MPa Figure 3. Volume of interface formation vs pressure at constant temperatures: (1) T = 293.15, (2) 295.15, (3) 298.15, (4) 300.65, ( 5 ) 303.15, (6) 305.65, (7) 308.15 K.
To shed light on the interface formation, let us consider this from the thermodynamic standpoint. The interfacial tension of the two-componentand two-phase system is written as a function of temperature and pressure b F 7
-0.5
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31 0
300 TI K
Figure 4. Entropy of interface formation vs temperature at constant pressures: ( 1 ) p = 0.1, (2) 10, (3) 20, (4) 30, ( 5 ) 40, (6) 50, (7) 60,(8) 70 MPa.
+
d r = -AS d T Avdp (1) Here As and Av are respectively the entropy and volume of interface formation per unit interfacial area and defined with respect to the two dividing planes making the excess numbers of moles of water and alcohol zero:
rwH =o
-20
-
-40
I
I
I
I
I
I
; .
(2)
v
-60-
and
roH =o
a
(3) Then Av and As are evaluated by using the slope of the y vs p and y vs T curves through the equations (aY/aP), =
a -80-100-
(4)
2ol
and (aY/ar), = -As (5) respectively. Further, the energy of interface formation Au is calculated by
+
AU = y TAs-PAv (6) The value of Av was obtained by applying eq 4 to the curves given in Figure 1 and plotted against pressure in Figure 3. It is seen that the value is negative and depends appreciably on temperature. It should be noted that the value changes abruptly to the more negative one at pq with increasing pressure at a given temperature. The As values obtained by using eq 5 and Figure 2 are plotted against temperature in Figure 4; the values are negative and change discontinuously to the less negative one at P with increasing temperature at a given pressure. Further, the energy was evaluated by substituting the values of 7,As,and Av into eq 6 and plotted against temperature at constant pressure in Figure 5. It is seen that the contact of water and alcohol molecules at the interface diminishes the energy. Therefore, we can say that theinterface formationis accompanied bythenegative changes of volume, entropy, and energy; that is, the alcohol molecules are enforced to restrict their orientation and motion in the interfacial region because of the energetically favorable interaction of their hydroxide groups with water molecules. Since the thermodynamic properties in the bulk phase change continuously evenat the breakpointson theinterfacial tensionvspressure and temperature curves, it is reasonable to say that the property of the interfacial region changes abruptly at the break point.
- 1 8
-l -1401
290
300 T I K
310
Figure 5. Energy of interface formation vs temperature at constant pressures: (1) p = 0.1, (2) 10, (3) 20, (4) 30, ( 5 ) 40, (6) 50, (7) 60, (8) 70 MPa.
We shall now prove our view that the break point on a curve results from the transition between interfacial states. If two states coexist at a break point, two simultaneous equations hold: dyq = -Asa d T 4
+ Ava dpq
(7)
and
+
dyq = -As@ d P A/ dpq (8) where a and /3 denote the two different states. This means that the number of degrees of freedom is reduced to 1 when the two states coexist at the interface.* Therefore, the break point is determined only by specifying the temperature or pressure. Eliminating d P or d p from eqs 7 and 8, we obtain the equation drq/dpq = (Ava/Asa- A#/As@)/(l/Asa- l/&) or
(9)
(10) d y q / d P = -(Asa/Ava - As@/A/)/(l/Ava - 1/A/) respectively. The left-hand side (LHS) and the right (RHS)can be evaluated separately and will be coincident with each other when a phase transition occurs at the break point.
The Journal of Physical Chemistry, Vol. 97, No. 19, I993 5143
Thermodynamic Study on Phase Transition
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p I MPa
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TI K
Figure 8. Values of the LHS and RHS of eq 11 vs temperature curve. E 7 y
0.10
.
7
E
the one of the RHS from the values of Av and As shown in Figures 3 and 4. They are respectively given by the full line and circles in Figure 8. It is realized that the coincidence is also satisfactory in this case. Therefore, our view on the break points given above was further substantiated. In our previous studies on the adsorption of long-chain alcohol at oil/water interfaces,' we concluded that the phase transition takes place at the break point on the curve of interfacial tension against temperature, pressure, or concentration of the alcohol in the oil. Furthermore, comparison of the interfacial pressure vs mean area per alcohol molecule curves with the corresponding ones of insoluble monolayers at the air/water interface led us to the conclusion that the transition occurs between the expanded and condensed states.' Comparing these results with the present one of the water/UNA interface and taking into account the interfacial tension vs pressure curves reported by Lin et al.? we cansuggest that the transitionofthewater/UNAsystemissimilar in kind to the one of long-chain alcohol at oil/water interfaces. With respect to this point, it is worth pointing out, although the interface may consist of alcohol and water, that eq 11 is analogous to the Clapeyron equation for three-dimensionalphase transition of the one-component systemloand that the magnitude of d p / dTcs is very close to that of the liquid-solid phase transition of an organic alcohol or acid and fairly different from that of the vapor-liquid phase transition.''
G G
3
-0.05 290
295
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310
T I K
Figure 6. (a) Values of the LHS and RHS of eq 9 vs pressure curve. (b) Values of the LHS and R H S of eq 10 vs temperature curve.
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Acknowledgment. This work was supported in part by a grant from the Cosmetology Research Foundation (5-91-10). 300 TeqlK
310
Figure 7. Pressure vs temperature curve at break points.
The value of the LHS of eq 9 was estimated from the curve given in Figure 1 and shown by the full line in Figure 6a. The one of the RHS was calculated from the values of Au and As at the discontinuous points given in Figures 3 and 4 and depicted by circles in Figure 6a. A similar procedure was applied to eq 10 by using the curve in Figures 2,3, and 4, and the results are shown in Figure 6b. It is noted that the coincidence of LHS and RHS is satisfactory within the errors in experiment and calculation. Therefore, we can draw the conclusion that the phase transition takes place at the break points on the interfacial tension vs pressure and temperature curves. From eqs 7 and 8, another equation is derived by eliminating dy as d p q / d P = (Asa - A#)/(Au" - A/) (11) The variation of the phase transition pressure'p with the phase transition temperature Tcs is shown in Figure 7: the p"9 value increases almost linearly with increasingtemperature. Thevalue of the LHS was estimated from the curve given in Figure 7 and
References and Notes (1) (a) Matubayasi, N.; Motomura, K.; Aratono, M.; Matuura, R. Bull. Chem. SOC.Jpn. 1978,51,2800. (b) Ikenaga, T.; Matubayasi, N.; Aratono, M.; Motomura, K.; Matuura, R. Bull. Chem. SOC.Jpn. 1980, 53, 653. (2) Aratono, M.; Takiue, T.; Ikeda, N.; Nakamura, A.; Motomura, K. J. Phys. Chem. 1992,96,9422. (3) Matubayasi, N.; Motomura, K.; Kaneshina, S.; Nakamura, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1977, 50, 523. (4) Motomura, K.; Iyota,H.; Aratono, M.; Yamanaka, M.; Matuura, R. J. Colloid Interface Sci. 1983, 93, 264. ( 5 ) (a) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348. (b) Motomura, K.; Aratono, M. fungmuir 1987, 3, 304. (c) Aratono, M.; Motomura, K. Bull. Chem. SOC.Jpn. 1985, 58, 3205. (d) Aratono, M.; Motomura, K. J. Colloid Interface Sci. 1987, 117 , 159. (6) Hansen. R. S. J . Phys. Chem. 1962, 66,410. ( 7 ) Turkevich, L. A.; Mann, J. A. Longmuir 1990, 6, 445. (8) Prigogine, I.; Defay, R. In Surface Tension and Adsorption; Everett, D. H., Translator; Longmans: London, 1966; Chapter 6. (9) Lin, M.; Firpo, J. L.; Mansoura, P.; Baret, J. F. J. Chem. Phys. 1979, 71, 2202. (10) Prigogine, I.; Defay, R. In Chemical Thermodynamics; Everett, D. H.,Translator; Longmans: London, 1954; Chapter 14. (1 1) Timmermans, J. Physico-Chemical Constants of Pure Organic Compounds; Elsevier: New York, 1950.
