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J. Phys. Chem. 1996, 100, 20122-20125
Thermodynamic Study on Phase Transition in Adsorbed Film of Fluoroalkanol at the Hexane/Water Interface. 2. Pressure Effect on the Adsorption of 1,1,2,2-Tetrahydrohenicosafluorododecanol Takanori Takiue,* Atsuro Yanata, Norihiro Ikeda,† Yoshiteru Hayami,‡ Kinsi Motomura, and Makoto Aratono Department of Chemistry, Faculty of Science, Kyushu UniVersity 33, Fukuoka 812-81, Japan ReceiVed: August 5, 1996; In Final Form: October 7, 1996X
The adsorption behavior of 1,1,2,2-tetrahydrohenicosafluorododecanol, CF3(CF2)9(CH2)2OH (FC12OH), at the hexane/water interface was investigated in both the absence and presence of the deposit by measuring the interfacial tension γ of its hexane solution against water as a function of pressure p and molality m1 at 298.15 K. It was concluded that a breakpoint on the γ vs p and γ vs m1 curves in a very low concentration region shows a first-order phase transition from the gaseous to the condensed state in the adsorbed film. It was found that the volume change of adsorption per mole of FC12OH is larger than that of 1,1,2,2tetrahydroheptadecafluorodecanol, CF3(CF2)7(CH2)2OH (FC10OH). Then it was suggested that the increase in the partial molar volume of alcohol with increasing fluorocarbon chain length is larger in the solution than in the interface because of the weak mutual interaction of the fluorocarbon chain with hexane molecules. Furthermore, another breakpoint due to the solubility of FC12OH in hexane was observed on the γ vs p and γ vs m1 curves in a high concentration and pressure region. A small value of partial molar volume change accompanied by the adsorption from the solid substantiates our view that the condensed state of the adsorbed film resembles the solid state.
Introduction We have shown that the pressure dependence of interfacial tension gives quite useful information about the structure of the interface and the molecular interaction in the adsorbed film from the viewpoint of the volume.1-6 In our previous paper,7 we studied the adsorption behavior of 1,1,2,2-tetrahydroheptadecafluorodecanol, CF3(CF2)7(CH2)2OH (FC10OH), at the hexane/water interface by measuring the interfacial tension as a function of pressure and evaluating the volume change of adsorption. It was found that two types of first-order phase transitions take place from the gaseous to the expanded state and from the expanded to the condensed state in the adsorbed film of FC10OH. Furthermore, it was suggested that the difference in microscopic circumstances, such as the gaseous, expanded, and condensed state and the presence of hexane molecules, in the adsorbed film appreciably affects the volumetric behavior at the interface. Now it is quite useful to elucidate the influence of the fluorocarbon chain length on the adsorption behavior of fluoroalkanol from the viewpoint of volume. So we employed 1,1,2,2-tetrahydrohenicosafluorododecanol, CF3(CF2)9(CH2)2OH (FC12OH), because the adsorption behavior of FC12OH at the hexane/water interface was already studied from the viewpoints of entropy and energy.8 In the course of measuring the interfacial tension as a function of pressure and molality at 298.15 K, we noticed that a deposit of FC12OH appeared in the hexane solution. Therefore the adsorption behavior of FC12* To whom correspondence should be addressed: Department of Chemistry, Faculty of Science, Kyushu University 33, Hakozaki, Higashiku, Fukuoka 812-81, Japan. E-mail;
[email protected]. † Present address: Department of Environmental Science, Faculty of Human Environmental Science, Fukuoka Women’s University, Fukuoka 813, Japan. ‡ Present address: Department of Home Economics, Chikushi Jogakuen Junior College, Dazaifu, Fukuoka 818-01, Japan. X Abstract published in AdVance ACS Abstracts, November 15, 1996.
S0022-3654(96)02355-6 CCC: $12.00
OH from the deposit at the hexane/water interface was also studied closely from the viewpoint of the volume by measuring the pressure dependence of γ in the presence of the deposit. Experimental Section 1,1,2,2-Tetrahydrohenicosafluorododecanol (FC12OH) purchased from PCR Inc. was recrystallized once from its chloroform solution. The purity was checked by gas-liquid chromatography. The method of purification of water and hexane was described in our previous paper.7 The equilibrium interfacial tension was measured by the pendant drop method 9 within an experimental error of 0.05 mN m-1 up to a concentration of ca. 2.0 mmol kg-1. The densities of pure water and hexane10,11 were used for the calculation of the interfacial tension. Results and Discussion The interfacial tension γ of the hexane solution of FC12OH against water is shown as a function of pressure p at 298.15 K in Figure 1. The γ value increases slightly with increasing pressure at a very low concentration and decreases steeply at a high concentration. It is seen that the γ vs p curves in a low concentration region have a breakpoint at which the slope changes abruptly. The γ values in Figure 1 at a given pressure were plotted against molality m1 in Figure 2. There is a breakpoint on the γ vs m1 curve at a very low concentration. The γ value of the breakpoint increases and the corresponding m1 value decreases with increasing pressure, as shown by the broken lines in Figures 1 and 2. It should be noted that the slopes of the γ vs p and γ vs m1 curves of FC12OH change more drastically at the breakpoints than those of 1,1,2,2tetrahydroheptadecafluorodecanol (FC10OH).7 This suggests that the adsorbed film of FC12OH exhibits a different type of phase transition from that of FC10OH.8 Furthermore, it should be noted that other breakpoints were observed on these curves © 1996 American Chemical Society
Phase Transition in Adsorbed Fluoroalkanol Film
J. Phys. Chem., Vol. 100, No. 51, 1996 20123
Figure 1. Interfacial tension vs pressure curves at constant molality (m1, mmol kg-1) as follows: (1) 0, (2) 0.099, (3) 0.148, (4) 0.201, (5) 0.301, (6) 0.404, (7) 0.498, (8) 0.598, (9) 0.699, (10) 0.805, (11) 0.996, (12) 1.198, (13) 1.397, (14) 1.599, (15) 1.802, (16) 2.310.
Figure 2. Interfacial tension vs molality curves at constant pressure (p, MPa) as follows: (1) 0.1, (2) 20, (3) 40, (4) 60, (5) 80, (6) 100, (7) 120.
at high concentration and pressure, above which the γ value is independent of m1. We will look closely at this finding in the latter part of this paper. Now we analyze the experimental results by using the thermodynamic relations. The fundamental equation describing the interfacial tension is given by
dγ ) -sH dT + νH dp - ΓH1 dµ1
(1)
where sH, νH, and ΓH1 are the interfacial excess entropy, the volume, and the number of moles of solute per unit area defined with respect to the two dividing planes making the excess number of moles of water and hexane zero,12 respectively. Assuming an ideal dilute solution and substituting the chemical potential of the solute into eq 1, we have
dγ ) -∆s dT + ∆ν dp - ΓH1 (RT/m1) dm1
(2)
Here ∆s and ∆ν are the entropy and volume changes associated with the adsorption of the solute from the hexane solution to the interface
∆y ) yH - ΓH1 yO1 , y ) s, ν
(3)
where yO1 is the partial molar thermodynamic quantity of the solute in the hexane solution. Then first the interfacial density ΓH1 was evaluated by applying the equation
ΓH1 ) -(m1/RT)(∂γ/∂m1)T,p
(4)
to the γ vs m1 curves shown in Figure 2. The results are shown as the ΓH1 vs m1 curves together with that of FC10OH at 80 MPa7 in Figure 3. It is seen that the ΓH1 value of FC12OH changes discontinuously from a very small value to a relatively
Figure 3. Interfacial density vs molality curves at constant pressure: (p, MPa) as follows: (1) 0.1, (2) 20, (3) 40, (4) 60, (5) 80, (6) 100, (7) 120, (8) FC10OH at 80 MPa; (•) ΓH1 at mS1 .
large one. By comparing the ΓH1 vs m1 curves at 80 MPa, we note that an intermediate region on curve 8 is not observed on curve 5 of the FC12OH system. Next, to make clear the state of the adsorbed film of FC12OH, we calculated the values of interfacial pressure π and mean area per adsorbed molecule A by the following equations:
π ) γ0 - γ
(5)
A ) 1/NAΓH1
(6)
and
and then drew the π vs A curves in Figure 4, where the curve of FC10OH at 80 MPa7 was also shown for comparison. It is seen that each curve of FC12OH consists of two portions: the area does not change appreciably in one portion and does change considerably in another. We have concluded previously that the two types of phase transitions take place from the gaseous
20124 J. Phys. Chem., Vol. 100, No. 51, 1996
Takiue et al.
Figure 4. Interfacial pressure vs mean area per molecule curves at constant pressure (p, MPa) as follows: (1) 0.1, (2) 20, (3) 40, (4) 60, (5) 80, (6) 100, (7) 120, (8) FC10OH at 80 MPa.
Figure 5. Volume change associated with the adsorption vs molality curves at constant pressure (p, MPa) as follows: (1) 0.1, (2) 20, (3) 40, (4) 60, (5) 80, (6) 100, (7) 120; (s) ∆ν vs p, (‚ ‚ ‚) ∆ν(S) vs p.
to the expanded state and from the expanded to the condensed state in the adsorbed film of FC10OH. It is obvious in Figure 4 that the π vs A curves of the FC10OH and FC12OH systems at 80 MPa (curves 5 and 8) almost coincide at very small and at very high A values. Therefore we can say that the adsorbed film of FC12OH exhibits a phase transition from the gaseous to the condensed state. The absence of an expanded state presumably results from the stronger cohesive force between FC12OH molecules compared with that between FC10OH molecules. Now let us consider the adsorption behavior of FC12OH from the viewpoint of the volume. The volume change associated with the adsorption of FC12OH, ∆ν, was evaluated by applying the following equation,
∆ν ) (∂γ/∂p)T,m
(7)
1
to the γ vs p curves shown in Figure 1 and plotted against m1 at various pressures in Figure 5 (solid line). It is seen that the ∆ν value is positive and almost equal to that of the pure hexane/ water interface because of the low values of ΓH1 in the gaseous state. On the other hand, it is largely negative and strongly depends on pressure in the condensed state. The decrease of ∆ν accompanied by the adsorption of FC12OH suggests the smaller volume of FC12OH molecules at the interface than in the bulk solution.
Figure 6. Volume change of adsorption per mole of alcohol vs molality curves at 0.1 and 80 MPa: (1) FC12OH, (2) FC10OH at 0.1 MPa; (3) FC12OH, (4) FC10OH at 80 MPa.
The influence of fluorocarbon chain length on the volumetric behavior of fluoroalkanol at the hexane/water interface is clarified by calculating the volume change of adsorption per mole of FC12OH, ∆ν/ΓH1 , and comparing it with that of FC10OH. In Figure 6 are shown the ∆ν/ΓH1 vs m1 curves at 0.1 and 80 MPa. It is seen that the ∆ν/ΓH1 value of the condensed state is more negative for the longer fluorocarbon chain at a given pressure. This result may be explained in terms of the partial molar volumes of the fluoroalkanols as follows; since it is reasonably presumed that the contribution of solvent molecules to the ∆ν value is negligibly small in the condensed state,7 ∆ν/ ΓH1 is the difference in values between the mean partial molar volume inherent in the interface νjH1 and the partial molar volume in the hexane solution νO1 , νjH1 - νO1 . It is likely that the increase in νO1 caused by the increase in fluorocarbon chain length is larger than the corresponding increase in νjH1 because fluorinated molecules are mixed with hydrocarbon molecules in the bulk solution;13 the value of νjH1 - νO1 of FC12OH is expected to be smaller than that of FC10OH. Furthermore, it is noted that the ∆ν/ΓH1 value at a high pressure is larger than that at a low pressure. This may arise mainly from the larger decrease of νO1 with rising pressure compared with the corresponding decrease of νjH1 . Here, we mention the phase transition found in this study. Assuming that the two states R and β coexist in the interface, the equilibrium interfacial tension is given by H,β H,R R H,R dγeq ) -{(∆sβ/ΓH,β 1 - ∆s /Γ1 )/(1/Γ1 - 1/Γ1 )} dT + H,β H,R R H,R {(∆νβ/ΓH,β 1 - ∆ν /Γ1 )/(1/Γ1 - 1/Γ1 )} dp (8)
where ∆ν is the entropy change associated with adsorption. It is also written as a function of temperature and pressure by
dγeq ) (∂γeq/∂T)p dT + (∂γeq/∂p)T dp
(9)
The coefficients of dp of eqs 8 and 9 were evaluated separately7 and compared in Figure 7; the agreement is good enough to consider the order of phase transition to be first. Now let us examine the adsorption at a concentration above mS1 which designates the concentration of the breakpoint at the low γ value on a γ vs m1 curve. Since the γ value does not depend on m1 above mS1 in Figure 2, the appearance of either a macroscopic phase such as a solid or a pseudomacroscopic phase such as a reverse micelle was suggested. By observing closely
Phase Transition in Adsorbed Fluoroalkanol Film
J. Phys. Chem., Vol. 100, No. 51, 1996 20125
∆y(S) ) yH - ΓH1 yS1 , y ) s, ν
(12)
yS1
Figure 7. Values of coefficient of dp of eqs 8 and 9 vs pressure curve: (O) eq 8, (s) eq 9.
where is the molar thermodynamic quantity of FC12OH in the solid. We evaluated ∆ν(S) from the slope of the γ vs p curves at a concentration above mS1 and showed it by the dotted line in Figure 5 together with the ∆ν vs m1 curves. It is seen that the ∆ν(S) value is slightly positive and independent of pressure. Furthermore the ∆ν(S)/ΓH1 value, which is approximately considered as the difference in values between νjH1 and νS1 as mentioned above, was calculated and plotted against p in Figure 8. Here the ΓH1 values above mS1 were assumed to be equal to the one at mS1 (solid circles in Figure 3). We note that the magnitude of ∆ν(S)/ΓH1 seems to be negligibly small compared with the molar volume of FC12OH (ca. 300 cm3 mol-1), although the value is certainly positive. Therefore it is probable that the partial molar volume in the interface is very close to that in the solid, and the former is slightly larger than the latter. This is in accord with the finding that the value of A is very close to the cross sectional area of the fluorocarbon chain in the condensed state. Also we note that the ∆ν(S)/ΓH1 value hardly depends on pressure. This fact substantiates that the condensed state of the adsorbed film resembles the solid state from the viewpoint of volume; that is, the compressibility is negligibly small.14 Acknowledgment. This work was supported in part by Grant-in-Aid for Scientific Reasearch (B) No. 06453057 from the Ministry of Education, Science, and Culture, Japan. References and Notes
Figure 8. Volume change of adsorption per mole of FC12OH from the solid state vs pressure curve.
the hexane solution, we found a tiny deposit and therefore referred mS1 to the solubility of FC12OH in hexane solution at a given pressure. Assuming the deposit to be a pure crystal of FC12OH and substituting its chemical potential
dµ1 ) -sS1 dT + νS1 dp
(10)
into eq 1, the total differential of γ is expressed as
dγ ) -∆s(S) dT + ∆ν(S) dp
(11)
Here we introduced the thermodynamic quantity change associated with the adsorption from the solid state ∆y(S) defined by
(1) Matubayasi, N.; Motomura, K.; Aratono, M.; Matuura, R. Bull. Chem. Soc. Jpn. 1978, 51, 2800. (2) Aratono, M.; Yamanaka, M.; Motomura, K.; Matuura, R. Colloid Polym. Sci. 1982, 260, 632. (3) Aratono, M.; Yamanaka, M.; Matubayasi, N.; Motomura, K.; Matuura, R. J. Colloid Interface Sci. 1980, 74, 489. (4) Motomura, K.; Iyota, H.; Aratono, M.; Yamanaka, M.; Matuura, R. J. Colloid Interface Sci. 1983, 93, 264. (5) Iyota, H.; Aratono, M.; Yamanaka, M.; Motomura, K.; Matuuua, R. Bull. Chem. Soc. Jpn. 1983, 65, 2402. (6) Lin, M.; Firpo, J. L.; Mansoura, P.; Baret, J. F. J. Chem. Phys. 1979, 30, 2202. (7) Takiue, T.; Yanata, A.; Ikeda, N.; Motomura, K.; Aratono, M. J. Phys. Chem. 1996, 100, 13743. (8) Hayami, Y.; Uemura, A.; Ikeda, N.; Aratono, M., Motomura, K. J. Colloid Interface Sci. 1995, 172, 142. (9) Matubayasi, N.; Motomura, K.; Kaneshina, S.; Nakamura, M. Bull. Chem. Soc. Jpn. 1977, 50, 523. (10) Eduljee, H. E.; Newitt, D. M.; Weale, K. E. J. Chem. Soc. 1951, 3086. (11) Fine, R. A.; Millero, F. J. J. Phys. Chem. 1973, 59, 5529. (12) Motomura, K. J. Colloid Interface Sci. 1978, 64, 348. (13) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.; Butterworth: London, 1982; Chapter 5. (14) Prigogine, I.; Defay, R. Chemical Thermodynamics; Everett, D. H., Translator; Longmans: London, 1954; Chapter 12.
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