Surface Freezing and Molecular Miscibility of Binary Alkane–Alkane

Jan 21, 2014 - Department of Visual Communication Design, Faculty of Design, Kyushu University, Fukuoka 815-8540, Japan. ABSTRACT: The surface ...
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Surface Freezing and Molecular Miscibility of Binary Alkane−Alkane and Fluoroalkane−Alkane Liquid Mixtures Takanori Takiue,*,† Mayuko Shimasaki,† Miyako Tsuura,† Hiroyasu Sakamoto,‡ Hiroki Matsubara,† and Makoto Aratono† †

Department of Chemistry, Faculty of Sciences, Kyushu University, Hakozaki 6-10-1, Higashi-ku, Fukuoka 812-8581, Japan Department of Visual Communication Design, Faculty of Design, Kyushu University, Fukuoka 815-8540, Japan

‡

ABSTRACT: The surface freezing (SF) of liquid n-heptadecane (C17)−n-octadecane (C18) and 1-perfluorooctyl decane (F8H10)−C18 mixtures were studied by surface tension and external reflection absorption FTIR (ERA-FTIR) measurements. The surface tension versus temperature curves of all pure liquids show a sharp break point at Ts corresponding to a surface liquid (SL)−SF transition. The entropy of surface formation is very negative, indicating a well-ordered structure of the SF layer. The ERA-FTIR spectra in the SF state suggested that the C18 molecules are densely packed in the solid state, while the packing of the hydrocarbon (HC) part of F8H10 is a little looser than the fluorocarbon (FC) part because of the difference in the cross-sectional area. In the C17−C18 mixture, the SL−SF transition was found at all bulk compositions. The estimation of the surface composition suggested that two components are miscible both in SL and SF states. The excess entropy of the surface is almost zero in both states, and thus, it was concluded that the two components are mixed almost ideally at the surface. In the case of the F8H10−C18 system, on the other hand, the SL layer is enriched in F8H10 with lower surface tension than C18 compared to bulk liquid. The surface composition in the SF state is almost zero or unity, indicating that F8H10 and C18 molecules are practically immiscible mainly due to the weak interaction between different components. Furthermore, the negative excess entropy in the SL layer suggests domain formation of F8H10 molecules at the surface.

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INTRODUCTION The characteristics of soft interfaces such as gas/liquid and liquid/liquid interfaces affect appreciably a lot of phenomena including foaming, emulsification, wetting, lubrication, and so on. Thus, the study on the states of interfacial films is of great importance for understanding the basic science underlying these phenomena as well as developing new functional materials in technology. In particular, the mixed component systems exhibit a wide variety of molecular organization not only in the bulk solution but at interfaces, and the miscibility of molecules strongly depends on the mutual interaction between the adsorbed molecules.1 It is generally known that the interaction between a hydrocarbon (HC) and fluorocarbon (FC) is weak compared with those between the same species.2,3 In our previous studies on the adsorbed film of 1-icosanol (C20OH) and a 1H,1H,2H,2H-perfluorodecanol (FC10OH) mixture at the hexane solution/water interface, the miscibility of molecules in the adsorbed film was investigated by constructing the phase diagram of adsorption (PDA) and evaluating the excess thermodynamic quantities of adsorption.4,5 The PDA shows that the C20OH and FC10OH molecules are miscible at all proportions in the expanded state, while they are practically immiscible in the condensed state. The mixing of C20OH and FC10OH in the expanded film accompanies a positive excess Gibbs energy and volume of adsorption. These results are attributable to weaker interaction between C20OH and © 2014 American Chemical Society

FC10OH molecules than those between the same species, which is more enhanced in the condensed film in which the molecules are closely packed with each other. Furthermore, the structure analysis of the adsorbed film by X-ray reflectivity (XR) measurement demonstrated that in the expanded state, FC10OH molecules form condensed phase domain coexisting with low-density gaseous phase around the phase transition temperature.6 On the other hand, C20OH molecules do not show the domain formation. Such an inhomogeneous film structure of FC10OH is induced partly by unfavorable mixing of FC chains with hexane molecules at the interface, and thus, the interfacial state and structure are affected not only by the solute−solute interaction but also by solute−solvent one. In 1992, Earnshaw et al. studied the liquid surface of pure n-heptadecane (C17) by surface tension measurement and found that the surface tension γ versus temperature T curve shows a distinct break at Ts, which is a few degrees above the bulk freezing temperature Tb. This phenomenon corresponds to the condensed film formation at the surface even when the bulk is in the liquid state and thus is called surface freezing (SF).7 SF phenomena have been reported at the surfaces of liquid alkanes,8 alcohols,9 alkenes,10 and semifuorinated alkanes.11,12 Received: June 29, 2013 Revised: January 20, 2014 Published: January 21, 2014 1519

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Surface Tensiometry. The surface tensions γ of C17−C18 and F8H10−C18 liquid mixtures were measured as a function of temperature T and the mole fraction x2 of C18 in the mixture under atmospheric pressure by the pendant drop method based on the shape analysis of pendant drops.23 The experimental error in the γ value was estimated within ±0.05 mN m−1. Differential Scanning Calorimetry (DSC). The bulk freezing temperatures Tb of the liquid mixture as well as individual pure liquids were determined by a differential scanning calorimeter (DSC: Perkin-Elmer Pyris1) with an intercooler cooling device. DSC was operated at a heating and cooling rate of 0.5 K min−1 between 263.15 and 333.15 K. The samples that weighed 1−2 mg were sealed in aluminum pans, and empty pans were used as a reference. Purge nitrogen gas was kept to 0.15 MPa during the measurement. The heating and cooling cycle was repeated five times. External Reflection Absorption FTIR spectroscopy (ERA-FTIR). ERA-FTIR spectra were collected with a Perkin− Elmer Fourier transform infrared spectrometer (Spectrum One) equipped with an external reflection attachment (Specac). The mercury−cadmium−telluride (MCT) detector was used by cooling it with liquid nitrogen. The incident angle of 40° was used. All spectra were collected at 4 cm−1 resolution by using 1024 scans. The temperature of the liquid substances was controlled within ±0.05 K by circulating thermostatted water through a brass cell jacket. ERA-FTIR data were reported as absorbance A = −log R/R0, where R0 and R are the reflectivity of the liquid surface at high temperature (at 313.15 K for C18 and 316.65 K for F8H10 system) as a reference and at desired temperatures for the measurement, respectively. The baseline was selected at 2800 and 3000 cm−1 for C−H stretching and at 1500 and 900 cm−1 for C−F stretching.

Among others, in the systematic studies on SF of n-alkanes (Cn; CH3(CH2)n−2CH3) by Deutsch et al., it was found that the SF phenomena are observed for alkanes with carbon numbers of 15 ≤ n ≤ 50. Furthermore, the structural analyses by XR and grazing incidence X-ray diffraction (GIXD) have revealed that the SF layer of n-alkanes has monolayer thickness with hexagonal molecular packing corresponding to the rotator phase of bulk solid alkane (n ≤ 30) and that the molecules are tilted toward nearest neighbors for 30 < n < 44 and next-nearest neighbors for 44 ≤ n.8 In addition to the above findings, the studies by other techniques such as simulation,13 ellipsometry,14 sum frequency spectroscopy,15 and light scattering16,17 have shown that the molecules in the SF layer fluctuate perpendicularly to the surface, and some molecules have already oriented at the surface above the SL− SF transition temperature Ts. Also, in the theoretical work by Tkachenko et al.,18,19 they claimed that entropic contributions due to molecular fluctuations in the SF layer, end and internal mismatch, should be taken into account to explain the appearance of SF phenomena from the view of the entropic mechanism. Because the SF is the condensed film formation at the liquid surface, the structure and properties of the SF layer are expected to be determined by the mutual interaction between the film-forming molecules. Therefore, the study on SF at the surface of binary liquid mixtures is highly advantageous to clarifying the miscibility of molecules at the surface mainly from the viewpoint of the mutual interaction between them without taking account of the solute−solvent interaction. In this study, we aim at clarifying the effect of molecular interaction on the mixing of molecules at liquid surfaces of binary HC−HC and FC−HC mixtures. We employed nheptadecane (C17) and n-octadecane (C18) as HC substances and 1-perfluorooctyl decane (F8H10) as the FC substance because their Tb’s are around room temperature, and therefore, the surface tension measurement is rather easier and provides sufficient accuracy for finding T s and thermodynamic analysis. According to earlier extensive studies,20−22 it is highly expected that the C17−C18 mixture shows ideal mixing at the surface. Thus, the comparison of the results by thermodynamic analysis between two mixtures enables us to understand more accurately the effect of molecular interaction on the SF phenomena and miscibility of molecules at the surface of the F8H10−C18 mixture. The surface tensions of the C17−C18 and F8H10−C18 mixtures were measured as a function of the temperature and composition of C18 in the liquid mixture under atmospheric pressure. The surface mole fraction of C18 was evaluated, and the excess entropy and energy of the surface were estimated thermodynamically and compared between both mixtures in order to discuss the relation between the miscibility of the molecules and molecular interaction at the surface.

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RESULTS AND DISCUSSIONS Pure Component Systems. Figure 1 shows the equilibrium surface tension γ versus temperature T curves of

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Figure 1. Surface tension versus temperature curves of pure systems: (1) C17, (2) C18, (3) F8H10. The error in the γ value is equivalent to the size of the data point.

EXPERIMENTAL SECTION Materials. n-Heptadecane (C17) and n-octadecane (C18) purchased from Aldrich Co. Ltd. were purified by distillation under reduced pressure. 1-Perfluorooctyl decane (F8H10) purchased from AZmax Co. Ltd. was purified by recrystallization once from hexane solution. Their purities were estimated above 99.5% by gas−liquid chromatography and checked by observing no time dependence of the surface tension of the pure liquid for 60 min (less than 0.1 mN m−1).

pure systems. All of the γ versus T curves have a distinct break point at temperature Ts (C17: 296.85 K; C18: 302.25 K; and F8H10: 311.15 K), a few degrees above Tb (C17: 295.65 K; C18: 301.15 K; and F8H10: 307.45 K), corresponding to the SF. The γ value increases gradually above and decreases very 1520

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steeply below Ts with decreasing T. In what follows, we call the surface state above Ts the surface liquid (SL) state. By adopting the two dividing planes that make the surface excess numbers of moles of air and oil zero simultaneously, the total differential of γ for the two-phase and twocomponent system is expressed by24 dγ = −Δs dT + Δυ dp

the SF layer, and it eventually induces larger entropy at the surface for F8H10 than that for alkanes. Another is an up and down staggering of F8H10 molecules at the surface to reduce the repulsive force between the dipoles produced at the FC− HC chain linkage. The XR analysis of the SF layer of F12H8 confirmed such arrangement by a larger surface roughness compared to that predicted by a capillary wave.11,12 ERA-FTIR was applied to the surface of the pure C18 and F8H10 liquids in order to know the conformation of molecules at the surface. The temperature dependence of the ERA-FTIR absorption spectra at the liquid C18 surface (No. 1−5) is shown together with the spectrum observed at the surface of solid C18 (No. 6) in Figure 2a. In our previous study, we

(1)

where Δy (y = s, υ) is the thermodynamic quantity of surface formation given by Δy = Γ oIΔyo + Γ aIΔya = Γ oI(yoI − yoO ) + Γ aI(yaI − yaA ) (2)

ΓIi

Here, (i = o, a) is the number of moles inherent in the surface, and Δyi is the mean partial molar quantity change of component i by the adsorption. Thus, the entropy of surface formation per unit surface area Δs is evaluated by applying ⎛ ∂γ ⎞ Δs = −⎜ ⎟ ⎝ ∂T ⎠ p

(3)

to the γ versus T curves in Figure 1. The Δs values in SF states of C17, C18, and F8H10 are −0.84, −0.95, and −0.41 J K−1 m−2, respectively. The negative Δs in the SF state is primarily due to the orientation of molecules at the surface. The structure analysis of the SF layer of n-alkane (Cn ; 16 ≤ n ≤ 50) as well as that of FmHn (m/n ; 12/8, 12/14, and 8/8) by XR and GIXD8,11,12 indicated that the SF layers are monolayers with the electron density close to those of the solid rotator phase of Cn and FmHn. Moreover, taking account of the fact that the electron density profile in the SF layer of F12H8 manifested that the FC and HC chains point toward the air and liquid phases, respectively, it is likely that the FC part of F8H10 molecules is in the upper side of the monolayer at the surface. Because the contribution of air to Δs is negligibly small in both the SL and SF states, let us describe Δs by Δs = Γ oI(soI − soO) + Γ aI(saI − saA ) = Γ σ(soσ − soO)

(4)

σ

where Γ is the total surface density of oil and air almost equal to that of the closely packed monolayer of oil molecules and sσo is the corresponding entropy. Then, the entropy change associated with the SL−SF transition given by Figure 2. ERA-FTIR spectra at constant temperature: (a) C18 surface at T = (1) 308.15, (2) 305.65, (3) 303.15, (4) 302.15, and (5) 301.65 K; (6) surface of solid C18 at 298.15 K; (b) F8H10 surface (CH2 stretching region) at T = (1) 313.15, (2) 312.15, (3) 311.15, (4) 309.15, and (5) 308.65 K; (c) F8H10 surface (CF2 stretching region) at T = (1) 313.15, (2) 312.15, (3) 311.15, (4) 309.15, and (5) 308.65 K. The dashed lines in (b) correspond to 2915 and 2918 cm−1.

(ΔsSF − ΔsSL) = soσ ,SF − soσ ,SL (5) Γσ σ was estimated by assuming the Γ values to be 8 μmol m−2 for C17 and C18 and 6 μmol m−2 for F8H10, which are, respectively, the saturated surface density of HC and FC compounds with perpendicular orientation at the surface. The value is larger for F8H10 (−0.08 kJ K−1 mol−1) than that for C17 (−0.12 kJ K−1 mol−1) and C18 (−0.13 kJ K−1 mol−1). The values of C17 and C18 almost coincide with those of the earlier work (−0.118 for C17 and −0.125 kJ K−1 mol−1 for C18).8 Because the Δs value in the SL state is almost the same for the three systems, it is suggested that the surface entropy in the SF state is larger for the former than that for the latter. One of the responsible origins for this is the difference in the cross-sectional area between FC and HC chains. Because the cross-sectional area is larger for the FC chain (0.28 nm2) than that for the HC one (0.18 nm2), it is expected that there is a space for HC chains to fluctuate just underneath of the FC layer, even though FC chains of F8H10 are densely packed in

found that the wavenumber of the antisymmetric CH2 stretching shifts from ∼2923 to ∼2915 cm−1 with surface phase transition, and the former was assigned to the expanded and the latter to the condensed phase at the air/water interface.25 The spectra measured at the liquid C18 surface have both bands below and above Ts, positive absorbance at 2930 cm−1 and negative at 2915 cm−1. Because the absorbance A is given by A = −log(R/R0), the positive absorbance is attributable to lower absorption at the desired temperature than that at the reference one, and the negative one is attributable to the larger absorption than that at the 1521

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reference temperature. Below Ts, the intensity of the band at 2915 cm−1 increases with decreasing T in the negative direction, indicating that the condensed film of C18 increases below Ts. The intensity of the band at 2930 cm−1, on the other hand, increases positively below Ts. This suggests that the fraction of gauche conformation decreases with decreasing T, although some C18 molecules have gauche defects in the SF layer. Furthermore, the shape of the spectrum at the solid surface is very similar to that at the liquid surface. The peak heights are much higher both in the positive and negative directions, and the corresponding wavenumbers are lower at the solid surface than those at the liquid surface. Thus, it is suggested that the C18 molecules in the SF state are not so closely packed like those in the solid state; this is not inconsistent with the experimental finding by XR measurement that the electron density in the SF layer of the alkane is close to that of the rotator phase. In the case of the liquid F8H10 surface, the ERA-FTIR spectra in the C−H stretching vibration (3000−2800 cm−1) and the C−F stretching vibration (1500−900 cm−1) regions are shown in Figure 2b and c, respectively. Although the spectra in the former region show a small absorbance and large scatter probably due to the fact that the total number of C−H’s is very small compared with C18 and the HC chain of F8H10 lying beneath the FC chain, it may be said that they have peaks due to the antisymmetric CH2 stretching at 2918 cm−1, which is a little larger than that observed at the liquid C18 surface as well as at the solid surface. In the latter region, the peaks at 1280−1120 and 1350−1120 cm −1 are respectively identified as the CF 2 stretching and CF 3 stretching bands. The intensities of the bands at 1257, 1203, and 1150 cm−1 increase negatively, and those at 1231 and 1160 cm−1 increase positively with decreasing T. Furthermore, the wavenumbers of the peaks are very close to those observed at the solid F8H10 surface. These results suggest that FC chains are densely packed while HC ones are a little loosely packed in the SF layer of F8H10. Binary C17−C18 Mixture. The surface tension γ of the C17−C18 mixture was measured as a function of temperature T at a fixed mole fraction x2 of C18 in bulk liquid under atmospheric pressure. The results are shown as the γ versus T curves in Figure 3a. All of the curves show a distinct break at Ts a few degrees above the bulk freezing temperature Tb due to the SL−SF transition. The γ value increases gradually above and decreases rapidly below Ts with decreasing T. In Figure 3b are the γ values plotted against x2 at constant T. The γ value increases monotonically with increasing x2 at high T. On the other hand, the γ versus x2 curve at low T has a sharp break at x2 depending on T; the γ value increases slightly below (SL state) and decreases almost linearly above the break point (SF state) with increasing x2. The SF temperature Ts of the C17−C18 mixture is plotted against x2 in Figure 4 (curve 1). The value increases almost linearly with increasing x2. In the case of a binary liquid mixture, the total differential of γ is expressed as ⎛ RT ⎞ dγ = −Δs dT + Δυ dp − Γ 2H⎜ ⎟ dx 2 ⎝ x1x 2 ⎠

Figure 3. (a) Surface tension versus temperature curves of a C17− C18 mixture at constant bulk composition: x2 = (1) 0 (C17), (2) 0.0500, (3) 0.1008, (4) 0.1747, (5) 0.2500, (6) 0.3002, (7) 0.4020, (8) 0.5005, (9) 0.6003, (10) 0.6999, (11) 0.7518, (12) 0.8036, (13) 0.9048, (14) 1 (C18). (b) Surface tension versus bulk composition curves of a C17−C18 mixture at constant temperature: T = (1) 308.15, (2) 303.15, (3) 300.65, (4) 299.15, (5) 298.15, (6) 297.15, (7) 296.15, and (8) 295.15 K. The error in the γ value is equivalent to the size of the data point.

Figure 4. SF temperature versus bulk composition curve: (1) C17− C18 mixture, (2) F8H10−C18 mixture: (○) Ts, (▲) Tb.

neously26 and by assuming the solution to be ideal. Here, ΓHi is the excess number of moles of component i per unit surface area, and Δs and Δυ are respectively the entropy and volume of surface formation per unit surface area, defined by Δy = y H − Γ1Hy1 − Γ 2Hy2

(6)

by employing two dividing planes satisfying the conditions that both the surface excess number of moles of air and the summation of those two components are zero simulta-

y = s, υ

(7)

In order to discuss the miscibility of molecules at the surface, the surface excess density ΓH2 of C18 was evaluated by applying the equation 1522

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T ,p

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entropy of surface formation Δs was evaluated by using the equation (8)

⎛ ∂γ ⎞ Δs = −⎜ ⎟ ⎝ ∂T ⎠ p , x

to the γ versus x2 curves in Figure 3b. Then, the mole fraction xσ2 of C18 at the surface was calculated by using the equation x 2σ =

(13)

and is plotted against x2 in Figure 6. The Δs value decreases slightly with increasing x2 and changes discontinuously from

(x 2 + Γ 2Ha1σ ) [1 + Γ 2H(a1σ − a 2σ )]

2

(9)

aσi

where is the partial molar area of component i and assumed to be 0.18 nm2, which is the cross-sectional area of the HC chain. The results are shown as the xσ2 versus x2 curves at constant temperatures in Figure 5. In this figure, the

Figure 6. Entropy of surface formation versus bulk composition curves of a C17−C18 mixture at constant temperature: T = (1) 301.15, (2) 300.15, (3) 299.15, (4) 298.15, and (5) 297.15 K.

slightly positive in the SL state to largely negative in the SF state at the SL−SF transition. In order to estimate the deviation from ideal mixing of molecules at the surface, the excess entropy of the surface sσ,E, defined by29

Figure 5. Surface composition versus bulk composition curves of a C17−C18 mixture at constant temperature: T = (1) 300.65 and (2) 296.65 K; black and blue solid lines correspond, respectively, to the SL and SF states, and the red dotted line represents the ideal mixing at the surface.

(14) s σ ,E = s σ ,M − s σ ,M,I where sσ,M,I is the entropy of ideal mixing at the surface, was calculated and is shown as the sσ,E versus x2 curves in Figure 7. The value is slightly negative in the SL and positive in the

red dotted line represents the criterion for ideal mixing of molecules at the surface, given by x 2σ x1σ

⎡ a σ (γ1 − γ ) ⎤ exp⎢⎣ 1 RT ⎥⎦ x = 2 σ x1 exp⎡ a2 (γ2 − γ ) ⎤ ⎢⎣ RT ⎥⎦

(10)

which is derived from the equilibrium condition between the surface and bulk liquid mixture, μσi = μi Here, μσi and μi are respectively the chemical potential of component i in the ideal mixture at the surface μi σ = μi σ , θ (T , p) + RT ln xiσ − γaiσ

(11)

and that in the perfect solution μi = μi0 (T , p) + RT ln xi

Figure 7. Excess entropy of surface versus surface composition curves of a C17−C18 mixture at constant temperature: T = (1) 303.15, (2) 300.65, and (3) 296.65 K.

(12)

where μσ,θ is the standard chemical potential at the surface i and is regarded as the chemical potential of pure component i when the surface layer is assumed to be likened as a perfect solution and μ0i is the chemical potential of the pure component.27,28 In the SL state, the xσ2 versus x2 curve almost coincides with the ideal mixing line, and thus, C17 and C18 molecules mix ideally in the SL state. Furthermore, in the SF state, the xσ2 versus x2 curve slightly deviates but is very close to the ideal mixing line, suggesting that the mixing of C17 and C18 molecules with a chain length difference of only 1 are almost ideal even in the SF state. The miscibility of molecules at the surface is further examined from the viewpoint of the entropy. First, the

SF state, but their absolute values are much smaller than that obtained for the water−ethanol mixture (sσ,E ≈ −8 J K−1 mol−1 at the minimum), which shows definite deviation from ideal mixing, in our previous study.29 Furthermore, the excess energy of the surface uσ,E was calculated by using the equation u σ ,E = u σ ,M − u σ ,M,I = u σ ,M

(15)

where we take account of the fact that the energy of ideal mixing at the surface is zero; uσ,M,I = 0. Within the error bars, uσ,E = 0 for all xσ2. The results of excess entropy and energy 1523

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manifest the ideal mixing of C17 and C18 molecules in both the SL and SF states mainly due to small energy loss by the mixing of homologous molecules with a chain length difference of only 1. This is consistent with the previous findings that the alkane mixture with a small reduced chain length mismatch (Δn/n)̅ 2 (0.0033 for C17−C18 mixture) exhibits ideal mixing at the surface.20−22 Binary F8H10−C18 Mixture. The γ versus T curves at constant x2 of the F8H10−C18 mixture are shown in Figure 8.

Figure 8. Surface tension versus temperature curves of a F8H10−C18 mixture at constant bulk composition: x2 = (1) 0 (F8H10), (2) 0.0310, (3) 0.0598, (4) 0.0980, (5) 0.1498, (6) 0.1975, (7) 0.9000, (8) 0.9246, (9) 0.9485, (10) 0.9692, (11) 0.9796, (12) 0.9853, (13) 0.9892, (14) 0.9950, and (15) 1 (C18). The error in the γ value is equivalent to the size of the data point.

Figure 9. (a) Surface tension versus bulk composition curves of a F8H10−C18 mixture at constant temperature (low x2 region): T = (1) 313.15, (2) 311.15, (3) 310.15, (4) 308.15, and (5) 306.15 K. (b) Surface tension versus bulk composition curves of a F8H10−C18 mixture at constant temperature (high x2 region): T = (1) 310.15, (2) 308.15, (3) 303.15, (4) 301.15, and (5) 300.15 K. The error in the γ value is equivalent to the size of the data point.

The liquid mixture exhibits a miscibility gap between x2 = 0.2 and 0.9 at temperatures employed in this study. The curves have a distinct break point due to the SL−SF transition below x2 = 0.2 and above 0.98. The γ value increases gently above and decreases steeply below the break point with decreasing T. On the other hand, the γ value between x2 = 0.90−0.97 increases slightly and monotonically with decreasing T. In Figure 9 are shown the γ versus x2 curves at constant T in low (Figure 9a) and high x2 regions (Figure 9b). The γ values at low x2 increase slightly above (SL state) and largely below the break point (SF state) with increasing x2. The values at high x2, on the other hand, increase monotonically below (SL state) but decrease slightly above the break point (SF state) with increasing x2. The SF temperature Ts versus x2 plot is shown in Figure 4 together with the bulk freezing temperature Tb determined by DSC. The Ts value decreases by the addition of one component into the other. It is noted that Ts is lower than Tb in 0.98 ≤ x2 ≤ 0.985, and thus, the SF phenomenon takes place under metastable condition. The miscibility of F8H10 and C18 at the surface was examined by evaluating the surface composition of C18 xσ2 in a similar procedure as that mentioned above. Although it is generally known that FC and HC mix nonideally in the liquid state, the activity coefficients of F8H10 and C18 in their liquid mixture were not found in the literature. Instead of this, the effect of them on the estimation of xσ2 was examined by using the activity coefficients in the perfluorohexane−hexane mixture.30 In the experimental x2 region (x2 = 0−0.1 and 0.8−1), the xσ2 value was almost equal to that obtained by eq 9 under the assumption of an ideal solution within the error bars. Here, therefore, we assumed that the liquid mixture is

regarded to be ideal in this study. The aσ1 and aσ2 values were assumed, respectively, to be 0.28 and 0.18 nm2, corresponding to the cross-sectional area of FC and HC chains. The results are shown as the xσ2 versus x2 curve at a given T in low (Figure 10a) and high x2 regions (Figure 10b). The red dotted line represents the ideal mixing in the SL state at 313.15 K given by eq 10. In the SL state, the surface is enriched in F8H10, which shows lower surface tension compared to C18 in the bulk liquids, and the mixing of F8H10 and C18 molecules deviates from ideal mixing because of weaker mutual interaction between F8 H 10 and C 18 molecules than those between the same ones. The xσ2 value in the SF state, on the other hand, is close to zero at low and unity at high x2, suggesting that F8H10 and C18 molecules are much less miscible in the SF state. The effect of molecular interaction on the miscibility of molecules is strongly dependent on the surface state. The nonideal mixing of molecules at the surface was further examined by evaluating the excess entropy of the surface sσ,E. Figure 11a shows the sσ,E versus xσ2 curve at constant T. The sσ,E value is positive except in the SL state at high xσ2. Taking account of the finding that the mixing of HC and FC compounds in the bulk liquid is generally accompanied by positive excess entropy (∼2.7 J K−1 mol−1 for the hexane− perfluorohexane mixture),31 the positive sσ,E is primarily due to the weak interaction between F8H10 and C18 molecules at 1524

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Figure 10. (a) Surface composition versus bulk composition curves of a F8H10−C18 mixture at constant temperature (low x2 region): T = (1) 313.15 and (2) 308.15 K. (b) Surface composition versus bulk composition curves of a F8H10−C18 mixture at constant temperature (high x2 region): T = (1) 300.15 and (2) 308.15 K; black and blue solid lines correspond, respectively, to the SL and SF states, and the red dotted line represents the ideal mixing at the surface.

Figure 11. (a) Excess entropy of surface versus surface composition curves of a F8H10−C18 mixture at constant temperature: T = (1) 313.15, (2) 308.15, (3) and 300.15 K. (b) Excess energy of surface versus surface composition curves of a F8H10−C18 mixture at constant temperature: T = (1) 313.15 and (2) 308.15 K.

the surface. The positive sσ,E in the SF state seems to rely on an additional factor such as the disorder of the lattice structure when FC compounds with a large cross section mix with HC compounds with a small one. Furthermore, it should be noted that the sσ,E value in the SL state at high xσ2 is very negative. The negative sσ,E suggests the formation of more ordered structure at the surface compared to the ideal mixing. In our previous study on the adsorbed film of FC alcohol at the hexane/water interface by XR measurement,6 it was found that FC alcohol forms a condensed-phase domain in the expanded state close to the expanded−condensed phase transition point. Therefore, it is probable that F8H10 molecules can form a domain at the liquid C18/air surface. The positive sσ,E in the SL state at low xσ2, on the other hand, suggests that the domain formation of C18 molecules at the liquid F8H10/air surface is not likely. The above difference may rely on a stronger dispersion interaction between F8H10 molecules than C18 ones due to the rigidity and larger molecular mass of the FC chain compared to the HC chain. The excess energy of the surface uσ,E supports the above idea on the nonideal mixing of F8H10 and C18 in the SL state. Figure 11b shows the uσ,E versus xσ2 curve at a given T. It is seen that the uσ,E value is positive at low and largely negative at high xσ2. The positive value indicates that the mixing of C18 with F8H10 is energetically unfavorable because of a weak interaction between F8H10 and C18 molecules. On the other hand, the negative value at high xσ2 is mainly due to the

energy gain by the domain formation of F8H10 at the surface, which overcomes the disadvantage caused by a decrease in entropy. Finally, let us compare the two-dimensional phase diagrams in the two systems. In Figure 12 are shown the Ts versus xσ2 diagrams at the SL−SF transition point. Black and red lines represent Ts versus x2σ,SL and Ts versus x2σ,SF curves, respectively. It is clearly seen that the diagram of the C17−

Figure 12. SF temperature versus surface composition curves: (1) C17−C18 mixture, (2) F8H10−C18 mixture; black and red lines and Ts versus xσ,SF represent Ts versus xσ,SL 2 2 , respectively. 1525

dx.doi.org/10.1021/jp406431m | J. Phys. Chem. B 2014, 118, 1519−1526

The Journal of Physical Chemistry B

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C18 mixture is a thin cigar shape, which is a typical diagram obtained for ideal mixing of molecules at the surface. The diagram of the F8H10−C18 mixture, on the other hand, looks like a eutectic type, which indicates that both components are less miscible in the SF state than in the SL state.

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SUMMARY n-Heptadecane (C17), n-octadecane (C18), and 1-perfluorooctyl decane (F8H10) show a surface freezing (SF) phenomenon at their liquid surfaces. ERA-FTIR spectra in the SF state suggested that C18 molecules are densely packed like the solid state, while the HC part of F8H10 shows a little loose packing even when the FC part is closely packed. The mixing of C17 and C18 molecules at the surface is almost ideal in both the SF and SL states because of small energy loss by mixing different molecules. On the other hand, F8H10 and C18 molecules mix nonideally in the SL state and are practically immiscible in the SF state due to weak interaction between FC and HC chains. Negative excess entropy in the SL state suggests the domain formation of F8H10 at the surface.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +81 92 642 2578. Fax: +81 92 642 2607. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported in part by the Grant-in-Aid for Scientific Research (C) of the Ministry of Education, Culture, Sports, Science and Technology of Japan (No. 22550017).

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REFERENCES

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dx.doi.org/10.1021/jp406431m | J. Phys. Chem. B 2014, 118, 1519−1526