Molecular Orientation and Multilayer Formation in the Adsorbed Film

Oct 9, 2009 - of Visual Communication Design, Faculty of Design, Kyushu UniVersity, Fukuoka 815-8540, Japan. ReceiVed: June 16, 2009; ReVised ...
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J. Phys. Chem. B 2009, 113, 14667–14673

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Molecular Orientation and Multilayer Formation in the Adsorbed Film of 1H,1H,10H,10H-Perfluorodecane-1,10-diol at the Hexane/Water Interface; Pressure Effect on the Adsorption of Fluoroalkane-diol Takanori Takiue,*,† Tsubasa Fukuda,† Daiki Murakami,† Hiroyasu Sakamoto,‡ Hiroki Matsubara,† and Makoto Aratono† Department of Chemistry, Faculty of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan, and Department of Visual Communication Design, Faculty of Design, Kyushu UniVersity, Fukuoka 815-8540, Japan ReceiVed: June 16, 2009; ReVised Manuscript ReceiVed: August 17, 2009

The adsorption of 1H,1H,10H,10H-perfluorodecane-1,10-diol (FC10diol) at the hexane solution/water interface was investigated by the measurement of interfacial tension γ as a function of pressure p and concentration m1 and the thermodynamic data analysis. The results obtained were compared with those of 1H,1H,2H,2Hperfluorodecanol (TFC10OH) in order to clarify the effect of molecular orientation on the structure and property of the adsorbed film from the viewpoint of volume change of adsorption. The interfacial pressure π versus mean area per adsorbed molecule A curve revealed two types of phase transitions among expanded, parallel condensed, and multilayer states. The A value in the condensed state and the transition pressure between the expanded and condensed states were larger for FC10diol than for TFC10OH, which manifests the different molecular orientation that the dispersion interaction between hydrophobic chains is weaker in the parallel orientation of FC10diol than in the perpendicular orientation of TFC10OH. The partial molar volume of FC10diol in the condensed state VjH.C is slightly larger than that of TFC10OH, 1 although the partial molar volume in the hexane solution is much smaller for FC10diol than for TFC10OH. This supports the view that the fluorocarbon chains of FC10diol remain in their contact with hexane even in the condensed film because of the parallel molecular orientation. The partial molar volume in the multilayer VjH,M was very close to the molar volume of solid FC10diol VS1 and smaller than that of VjH.C at the 1 1 condensed-multilayer phase transition, and increased gradually with molecular piling. This substantiates that FC10diol molecules are densely packed in a first few layers just above the phase transition and a little loosely packed in the upper layers of the multilayer with increasing molecular piling. Furthermore, the volume change associated with adsorption from the solid FC10diol ∆V(S) evaluated from the γ versus p curve under the existence of solid deposit was positive and showed a minimum against concentration for the multilayer state. This is primarily due to the minimum in interfacial density at the solubility limit ΓH,S and thus due to 1 the minimum in VjH,M 1 . Introduction The study on the structure and property of soft interfaces such as liquid/liquid interfaces at high pressures is valuable, for example, in order to understand the correlation between the structure and the function of biological membranes of living cell under high pressure in deep sea.1–4 Thus far, we have investigated the adsorption of various surface active substances at oil/water interfaces by the interfacial tension measurement and thermodynamic data analysis.5–7 In particular, the pressure dependence of interfacial tension gives the volume change of adsorption that provides quite useful information about the structure of and the molecular interaction in the adsorbed film.8–11 The pressure effect on the adsorbed films of fluorocarbon (FC) alcohols, 1H,1H,2H,2H-perfluorodecanol (TFC10OH), and its analogue 1H,1H,2H,2H-perfluorododecanol (TFC12OH), at the hexane/water interface,12,13 revealed that the adsorbed film exhibits two types of phase transitions among gaseous, ex* To whom correspondence should be addressed. Phone: +81 92 642 2578. Fax: +81 92 642 2607. E-mail: [email protected]. † Department of Chemistry, Faculty of Sciences, Kyushu University. ‡ Department of Visual Communication Design, Faculty of Design, Kyushu University.

panded, and condensed states for TFC10OH, while it exhibits a transition between gaseous and condensed states for TFC12OH. Furthermore, information on the solute-solvent interaction in the adsorbed film as well as in the bulk solution and on that the condensed state of the adsorbed film resembles the solid state was derived from the volume change of adsorption. The latter has been already confirmed by the electron density and film thicknessvaluesobtainedbytheX-rayreflectivitymeasurement.14–16 Another example of usefulness of pressure effect was recently demonstrated as follows: the partial molar volumes of 1H,1Hperfluorononanol (FDFC9OH) and its ω-hydrogenated analogue, 1H,1H,9H-perfluorononanol (HDFC9OH), in the adsorbed films were evaluated and suggested that HDFC9OH molecules tend to tilt by around 15° from interface normal for ω-dipoles to interact effectively with water molecules in the interfacial region and to reduce the repulsive interaction between neighbors arranging parallel in the adsorbed film.17,18 Bolaform surfactants with two head groups at both ends of the hydrophobic chain shows a characteristic behavior at soft interfaces.19–23 Chattoraj et al. studied the adsorptions of hydrocarbon (HC) dibasic acids and their salts at oil/water interfaces by means of interfacial tensiometry and concluded that bolaform surfactants show “wicket-like” conformation in

10.1021/jp9056434 CCC: $40.75  2009 American Chemical Society Published on Web 10/09/2009

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which the hydrophobic chain forms a loop and two head groups which are anchored at the interface because of the flexible nature of the HC chain.22,23 In the previous study on the adsorption of 1H,1H,10H,10H-perfluorodecane-1,10-diol (FC10diol) at the hexane/water interface, we have investigated the effect of the rigidity of the hydrophobic chain and two terminal hydroxyl groups on the adsorption behavior of the FC compound from the viewpoint of entropy and energy of adsorption.24 One of the important findings was that the FC10diol molecules form a condensed monolayer with parallel molecular orientation, which is striking contrast to the “wicket-like” conformation of bolaform surfactant with HC chain. Another noticeable point is that the molecules pile spontaneously and successively form a multilayer at high concentrations and low temperatures. The evaluated entropy and energy changes of adsorption suggested that the FC10diol molecules are not so densely packed in the upper layer of the multilayer compared with the first condensed monolayer, and therefore the multilayer is not a simple pile of condensed monolayer. In the present study, we aim at examining more closely the adsorption behavior, especially phase transition and multilayer formation, of FC10diol in terms of the volume change of adsorption. The interfacial tension of the hexane solution of FC10diol against water was measured as a function of pressure and molality at 298.15 K. The interfacial density and partial molar volume change of adsorption were evaluated and compared with those of TFC10OH. Furthermore, in the course of the interfacial tension measurement, a solid deposit of FC10diol was observed in the bulk hexane solution, and thus the adsorption behavior of FC10diol from the solid state was also discussed from the viewpoint of volume. Experimental Section 1. Materials. 1H,1H,10H,10H-Perfluorodecane-1,10-diol (FC10diol) purchased from Azmax Co., Ltd. was purified by recrystallization once from chloroform solution. Its purity was checked by observing no time dependence of interfacial tension between the hexane solution of FC10diol and water, and by liquid-gas chromatography. Hexane (Aldrich Chemical Co. Inc.) was distilled once and water three times; the second and third stages were done from dilute alkaline permanganate solution. 2. Interfacial Tension Measurement. The equilibrium interfacial tension γ of the hexane solution of FC10diol against water was measured as a function of pressure p and molality m1 at 298.15 K by the shape analysis of pendant drops described elsewhere.25 The pressure range was from atmospheric pressure (0.1 MPa) to about 150 MPa. In Figure 1 is shown the schematic diagram of the apparatus designed originally in our laboratory.26,27 The pressure vessel is a cylinder of chrome-molybdenum steel in which two sapphire windows are equipped for capturing the image of pendant drop profiles through them by the CCD camera. The measurement cell is made of quartz and consists of plunger, syringe, drop forming tip, and cylinder. The syringe and cylinder are filled with water and hexane solution, respectively. Temperature was kept constant by circulating thermostatted water in the jacket around the pressure vessel. Pressure is generated by use of a hand-screw pump and measured with a Heise Bourdon gauge. As pressure is raised, the plunger is moved down by the decrease in volumes of water and hexane solution phases, and a pendant drop is automatically formed at the tip of capillary. The error in γ value was estimated within (0.05 mN m-1. The densities of pure hexane and water at respective

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Figure 1. Schematic diagram of the apparatus of interfacial tension measurement under high pressure: (1) pressure pump, (2) valve, (3) Heise Bourdon gauge, (4) pressure vessel, (5) sapphire glass window, (6) quartz cell, (7) thermostatted water, (8) light source, (9) CCD camera, (10) PC, (11) plunger, (12) drop forming tip, (13) cylinder, (14) water, and (15) hexane solution.

pressures were used for the calculation of interfacial tension instead of those of hexane and aqueous solutions,28,29 because the solution was very dilute and their mutual solubility was negligibly small. 3. Density Measurement. The densities F of the hexane solutions of FC10diol and TFC10OH were measured as a function of m1 at 298.15 K by using a digital density meter, Anton Paar DMA 60/602, to evaluate the partial molar volume V1O of the solutes in the hexane solutions. The V1O value was calculated by using the equation

VO1 ) φV + m1

( ) ( ) ∂φV ∂m1

)

T,p

∂m1φV ∂m1

(1) T,p

and

φV )

1000(F - F0) F + 0 M m1FF 1

(2)

where φV is the apparent molar volume, F0 is the density of pure hexane, and M1 is the molar mass of the solute. The error in V1O value was estimated to be (20 cm3 mol-1 for FC10diol and (5 cm3 mol-1 for TFC10OH. Results and Discussion Figure 2a shows the time, t, dependence of interfacial tension γ measured at m1 ) 0.030 mmol kg-1 and 99.4 MPa. The γ value decreases with time, and a plateau region appears on the γ versus t plot at around 40.8 mN m-1. As has already been discussed in our previous paper,24 the plateau is caused by the coexistence of two phases during the phase transition in the adsorbed film. Similar plots were obtained at several pressures. The γ versus t plots measured at m1 ) 0.1675 mmol kg-1 and 11.0 MPa (Figure 2b) shows an oscillation region at around 33.8 mN m-1, which is also due to a phase transition but probably due to a different kind of one from that observed in Figure 2a. The equilibrium interfacial tension γ is drawn as a function of pressure p at given molalities m1 and 298.15 K in Figure 3.

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Figure 4. Interfacial tension vs molality curves at constant pressure: p ) (1) 0.1, (2) 10, (3) 20, (4) 40, (5) 60, (6) 80, (7) 100, and (8) 120 MPa.

Figure 2. Interfacial tension vs time plots at given concentration and pressure: (a) m1 ) 0.030 mmol kg-1 and p ) 99.4 MPa, (b) m1 ) 0.1675 mmol kg-1 and p ) 11.0 MPa.

Figure 5. (a) Equilibrium interfacial tension vs pressure curves: (1) expanded-parallel condensed transition; (2) parallel condensed-multilayer transition. (b) Equilibrium molality vs pressure curves: (1) expanded-parallel condensed transition; (2) parallel condensed-multilayer transition, and (3) solubility mS1 of FC10diol in hexane. Figure 3. Interfacial tension vs pressure curves at constant molality: m1 ) (1) 0, (2) 0.00125, (3) 0.0025, (4) 0.005, (5) 0.0075, (6) 0.010, (7) 0.015, (8) 0.020, (9) 0.025, (10) 0.030, (11) 0.035, (12) 0.040, (13) 0.0447, (14) 0.050, (15) 0.0599, (16) 0.067, (17) 0.0749, (18) 0.085, (19) 0.0875, (20) 0.095, (21) 0.105, (22) 0.110, (23) 0.115, (24) 0.1175, (25) 0.120, (26) 0.130, (27) 0.140, (28) 0.1445, (29) 0.1525, (30) 0.155, (31) 0.1675, (32) 0.170, (33) 0.180, (34) 0.190, (35) 0.1999, and (36) 0.205 mmol kg-1.

The γ value increases slightly at low concentrations, decreases slowly at intermediate ones, and decreases steeply at high concentrations with increasing pressure, respectively. It is noted that the γ versus p curves have one or two break points where the slope changes faintly at the first while abruptly at the second break point. In Figure 4 are shown the γ versus m1 curves at given pressures. The γ value decreases gradually with increasing m1, and the curves have one or two break points depending on pressure. The interfacial tension at the break points coincide with the values at the plateaus and oscillation on the γ versus t plots, and thus these breaks are due to phase transitions in the adsorbed FC10diol film. The interfacial tension γeq and the corresponding m1eq at the break points are plotted against pressure in Figure 5a,b, respectively. The γeq value increases

and the m1eq decreases with increasing pressure. Furthermore, it should be noted that other break points were observed on the γ versus m1 curves at high concentrations m1S, above which the γ value is independent of m1 as shown by dotted lines in Figure 4. We will look closely at this finding in the latter part of this paper. Now let us analyze the results mentioned above by using thermodynamic equations briefly described in the following. The fundamental equation describing the interfacial tension γ is given by

dγ ) -sHdT + VHdp - ΓH1 dµ1

(3)

where sH, VH, and Γ1H are respectively the interfacial excess entropy, volume, and the number of moles of solute per unit area defined with reference to the two dividing planes making the excess numbers of moles of water and hexane zero simultaneously.30 Assuming the hexane solution to be ideally dilute, the total differential of γ is expressed as

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dγ ) -∆sdT + ∆Vdp - ΓH1 (RT/m1)dm1

Takiue et al.

(4)

Here, ∆s and ∆V are the entropy and volume changes associated with the adsorption of FC10diol from the hexane solution defined by

∆y ) yH - ΓH1 yO1 y ) s, V

(5)

where yH and y1O are the interfacial excess thermodynamic quantity and the partial molar quantity of FC10diol in the hexane solution, respectively. To characterize the state of the adsorbed film, we first evaluate the interfacial density Γ1H of FC10diol by applying the equation

ΓH1 ) -(m1 /RT)(∂γ/∂m1)T,p

(6)

to the γ versus m1 curves in Figure 4. The results are shown as Γ1H versus m1 curves at constant pressures in Figure 6. The Γ1H value increases with increasing m1 and changes discontinuously to around 2 µmol m-2 just above the first phase transition, and then to 6-11 µmol m-2 at the second transition. It should be noted that the Γ1H value further increases steeply by a small concentration change above the second transition while it is almost constant in a wide concentration range below the transition. This manifests that the film states are totally different from each other at concentrations below and above the second transition. The interfacial pressure π versus the mean area per adsorbed molecule A curve provides us information on the states of adsorbed film. Here, the π and A values are calculated, respectively, by

π ) γ0 - γ

Figure 7. Interfacial pressure vs mean area per adsorbed molecule curves at constant pressure: p ) (1) 0.1, (2) 10, (3) 20, (4) 40, (5) 80, (6) 100 MPa; (7) TFC10OH at 0.1 MPa, and (8) TFC10OH at 80 MPa.

(7)

and

A ) 1/NAΓH1

Figure 6. Interfacial density vs molality curves at constant pressure: p ) (1) 0.1, (2) 10, (3) 20, (4) 40, (5) 60, (6) 80, (7) 100, and (8) 120 MPa; (•) ΓH1 at mS1 .

(8)

where γ0 is the interfacial tension at the pure hexane/water interface and NA is Avogadro’s number. The π versus A curves are shown at constant pressures in Figure 7. The curves (except at 100 MPa) consist of three parts connected by two discontinuous changes. It is noted that the π versus A curves in the middle state are almost vertical, and the A values converge into around 0.82 nm2. This value is very close to the cross sectional area of FC10diol along its major axis and thus indicates that the FC10diol molecules are densely packed and form a condensed film with molecular orientation parallel to the interfacial plane. Furthermore, the A value just above the second phase transition is smaller than the cross sectional area of FC chain (A ≈ 0.28 nm2) and decreases further to 0.16 nm2 with increasing π, suggesting that the FC10diol molecules pile spontaneously and form a multilayer. Therefore, the three states are assigned as expanded, parallel condensed, and multilayer states in the order of decreasing A value. The π versus A curves at 0.1 and 80 MPa of the adsorbed TFC10OH film are also drawn in Figure 7.12 The difference of A values in the condensed state, A ≈ 0.3 nm2 for TFC10OH and A ≈ 0.8 nm2 for FC10diol, clearly proves the different molecular orientation at the interface from each other. Furthermore, the higher transition pressure πeq between

the expanded and the condensed states for FC10diol than for TFC10OH also manifests the different molecular orientation that in the parallel orientation of FC10diol, the hydrophobic chain contacts with water and hexane molecules and thus the dispersion interaction between hydrophobic chains of FC10diol molecules is weaker than that of TFC10OH molecules where they are surrounded by other six molecules in the perpendicular condensed film. Now let us examine the adsorption of FC10diol from the viewpoint of the volume. The variable ∆V defined by eq 5 is evaluated by applying

∆V ) (∂γ/∂p)T,m1

(9)

to the γ versus p curves shown in Figure 3, and plotted against m1 at various pressures in Figure 8. The ∆V value in the expanded state decreases from positive to negative with increasing molality and thus increasing Γ1H, and then changes discontinuously but slightly to the one in the condensed state at the first phase transition point. ∆V in the condensed state is almost independent of pressure and molality, which corresponds to the almost constant values of Γ1H there, and then discontinuously goes down to largely negative values of the multilayer states having large Γ1H values. Judging from these correspondence between ∆V and ΓH1 , it is obvious that the adsorption of FC10diol lowers ∆V. The chain-dotted line represents the volume change

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Figure 8. Volume change associated with adsorption vs molality curves at constant pressure: p ) (1) 0.1, (2) 10, (3) 20, (4) 40, (5) 60, (6) 80, (7) 100, and (8) 120 MPa; (solid line) ∆V vs p, (dashed dotted line) ∆V(S) vs p, ([) ∆Vcal.

Figure 9. Partial molar volume change of adsorption vs interfacial density curves at constant pressure: (1) FC10diol at 0.1 MPa, (2) FC10diol at 80 MPa, (3) TFC10OH at 0.1 MPa, and (4) TFC10OH at 80 MPa.

TABLE 1: Partial Molar Volume at the Expanded-Condensed Transition at 0.1 MPa

associated with adsorption from the solid state and thus is different in nature as will be examined in the latter part. The relation between adsorption Γ1H and ∆V value is clarified by evaluating the partial molar volume change of adsorption Vj1H - V1O. According to our thermodynamics of interfaces,30 ∆V consists of three terms originating from oil, water, and alcohol components as

∆V ) ΓIo(VjIo - VOo ) + ΓwI(VjwI - VwW) + ΓH1 (VjH1 - VO1 ) (10) where ΓIi (i ) o, w) is the number of moles of oil and water inherent in the interface, VjIi (i ) o, w) and Vj1H are, respectively, the mean partial molar volume of solvents and that of solute in the interface, and VRj (R ) O, W; j ) o, w, 1) is the partial molar volume of component j in the bulk phase R. Thus, according to further thermodynamic formulation, VjH1 - VO1 value is estimated by12,30

VjH1 - VO1 ) [∆V - (1 - ΓH1 a1)(∂γ/∂p)T,ΓH1 ]/ΓH1

(11)

Here, a1 is the partial molar area of the solute molecule and assumed to be the mean area in the condensed monolayer with the most closed molecular packing, a1) 0.82 nm2, because the contribution of solvents to ∆V is negligibly small there and thus we have

VjH1 - VO1 ≈

∆V ΓH1

(12)

The results at 0.1 and 80 MPa are shown as Vj1H - V1O versus curves together with the corresponding ones of TFC10OH in Figure 9. The Vj1H - V1O value of FC10diol is negative, and therefore the FC10diol molecule has smaller volume at the interface than in the bulk solution because of the restricted molecular orientation, partial loss of hydrocarbon-fluorocarbon contact, and so on. The prominent feature is that the Vj1H - V1O value of the condensed state is much smaller, and thus the discontinuous change in Vj1H - V1O at the expanded-condensed phase transition point is quite larger for TFC10OH than for FC10diol. This is clearly due to the difference in molecular orientation in the condensed films of TFC10OH and FC10diol Γ1H

from each other as already explained by comparing their π versus A curves. Here, let us provide information on molecular orientation in the adsorbed film on the basis of the partial molar volume at the interface VjH1 evaluated by subtracting VO1 from VjH1 - VO1 . Here, V1O was calculated from the densities of solution through eqs 1 and 2 at 0.1 MPa, and almost constant V1O ) 261 cm3 mol-1 for FC10diol and V1O ) 286 cm3 mol-1 for TFC10OH within the experimental concentration ranges. First, with respect to the condensed monolayer, the VjH1 values at the expanded-condensed phase transition point are summarized in Table 1. The most remarkable finding is that, although the V1O value of FC10diol is much smaller than that of TFC10OH, the Vj1H value of FC10diol is close to and even slightly larger than that of TFC10OH in the condensed state even if the error in Vj1H is taken into account. This finding supports the view that, although FC chains of TFC10OH are surrounded by FC chains of TFC10OH molecules and almost escaped from the contacts with hexane in the condensed films, those of FC10diol remain their contact with hexane even in the condensed film due to their parallel orientation to the interface. With respect to the multilayer, prior to the evaluation of the partial molar volume in the multilayer Vj1H.M, the ∆V value at 0.1 MPa is compared in Figure 8 to ∆Vcal calculated by

∆Vcal ) ΓH1 (VjH1 - VO1 )first

(13)

under the assumption that the multilayer is formed just by piling condensed monolayers, where (Vj1H - V1O)first ≈ -7.3 cm3 mol-1 for the condensed monolayer was employed. It is evident that the ∆V value is much smaller than ∆Vcal, which indicates the

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TABLE 2: Partial Molar Volume of FC10diol at 0.1 MPaa

∆y(S) ) yH1 - ΓH1 yS1 y ) s, V

(16)

where y1S is the molar thermodynamic quantity of solid FC10diol. The ∆V(S) evaluated from the γS versus p curve is shown by the chain-dotted line in Figure 8. The ∆V(S) value passes through a minimum for the multilayer above, while almost constant for the condensed monolayer below m1 ) 0.04 mmol kg-1. By using eqs 5 and 16, we have

VO1 - VS1 ) [∆V(S) - ∆V(O)]/ΓH,S 1

a

c S VO1 ≈ 261 cm3 mol-1 at all concentrations. b νjH,C 1 . ν1 .

partial molar volume in the multilayer Vj1H.M is smaller than that in the condensed monolayer. Although the physical meaning of a partial molar area a1 is rather ambiguous for the multilayer, let us assume a1 ) 1/Γ1H in eq 11 for this moment, which will be verified later by examining the volume change associated with multilayer adsorption from solid state, and evaluate Vj1H.M by using ΓH1 and VO1 . Table 2 shows VjH.M together with the partial 1 molar volume in the condensed monolayer VjH.C 1 and that of solid V1S evaluated later from eq 17. It is essential that the Vj1H.M value just above the phase transition point, where Γ1H is 6.19 µmol m-2 and almost three times of Γ1H in the condensed monolayer, is more than 10% smaller than Vj1H.C but almost equal to V1S, and that further increase in ΓH1 due to molecular piling accompanies the increase in Vj1H.M. These observations produce a scenario of layering that FC10diol molecules are closely packed in a first few layers just above the phase transition and gradually a little loosely packed in upper layers of the multilayer. Therefore, it is concluded that the upper part of multilayer is not grown up simply by the piling of condensed monolayers but by leaving contact of FC chains with hexane molecules, which is good correspondence to the conclusion from the entropy change of adsorption estimated in our previous paper.24 Now, let us examine the adsorption above m1S. Since a tiny deposit was found in the hexane solution above m1S, therefore, m1S is referred to the solubility of FC10diol at a given pressure. The filled circles in Figure 3 are the interfacial tensions γS measured under the existence of the deposit. The γS value increases with pressure, and the γS versus p curve has a break point at around 87 MPa where the γeq versus p curve of the condensed monolayer-multilayer transition disappears; the deposit is in equilibrium with multilayer below and with condensed monolayer above this pressure. By assuming the deposit to be a crystal of FC10diol alone and substituting its chemical potential

dµ1 ) -sS1 dT + VS1 dp

(14)

into eq 3, the total differential of γS is expressed as

dγS ) -∆s(S)dT + ∆V(S)dp

(17)

where ∆V(O) and Γ1H,S are respectively the volume change associated with adsorption from the hexane solution and the interfacial density at mS1. Then, the molar volume of solid FC10diol V1S was calculated to be 224 cm3 mol-1 by substituting V1O()261 -2 cm3 mol-1) and ΓH,S 1 ()11.2 µmol m ) under atmospheric pressure as given in Table 2. The magnitude is in the order of Vj1H.C > Vj1H,M g V1S, and V1S is very close to Vj1H,M at m1 ) 0.185 mmol kg-1 as already discussed above. Finally, let us show that the minimum of ∆V(S) for the multilayer is understood using the V1S value estimated above. Since an isothermal compressibility of solid phase is usually very small (≈1.0 × 10-5 MPa-1), it is reasonably assumed that V1S is 224 cm3 mol-1 and Vj1H,M is determined solely by Γ1H as demonstrated in Table 2 irrespective of pressure. Thus, ∆V(S) can be calculated by using

∆V(S)cal ) ΓH,S jH,M - VS1 ) 1 (V 1

(18)

H where ΓH,S 1 is a value of Γ1 when the multilayer is in equilibrium with the deposit as given by solid circles in Figure 6, and Vj1H,M is read from the relation between Vj1H,M and Γ1H in Table 2. The ∆V(S)cal values are plotted by solid circles in Figure 8. It should be noted that ∆V(S)cal almost perfectly traces the ∆V(S) estimated experimentally. This finding substantiates that Vj1H,M was estimated appropriately by eq 12 with the assumption of a1 ) 1/ Γ1H even in the multilayer and therefore that, the larger Γ1H is, the larger value Vj1H,M has. Furthermore, it is concluded that the minimum in ∆V(S) against m1S is primarily due to the minimum in Γ1H,S as shown in Figure 6 and thus due to that in Vj1H,M. Therefore, a question why ∆V(S) has a minimum continues with the other question why Γ1H,S has a minimum. The answer is as follows. The Γ1H value just above the phase transition point increases with raising pressure as seen in Figure 6. However, since the increment in bulk concentration from m1eq to m1S is gradually diminished with raising pressure as shown in Figure 5b, a further increment in Γ1H to Γ1H,S is also diminished. Therefore, it is likely that the minimum in Γ1H,S comes from the competition between these two opposite trends.

Acknowledgment. This work was supported in part by the Grant-in Aid for Scientific Research (C) (No. 19550021) and Japan-U.S. Cooperative Science Program of JSPS, and The Asahi Glass Foundation. References and Notes

(15)

Here, we introduced the thermodynamic quantity change associated with the adsorption from the solid state ∆y(S) defined by

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