6548
J. Phys. Chem. B 2002, 106, 6548-6553
Calorimetric Studies of Aggregate Formation of Oleyl Alcohol in Oil Solutions Ryo Murakami,*,† Youichi Takata,† Akio Ohta,‡ Masao Suzuki,§ Takanori Takiue,† and Makoto Aratono† Department of Chemistry and Physics of Condensed Matter, Graduate School of Sciences, Kyushu UniVersity, Fukuoka 812-8581, Japan, Department of Chemistry and Chemical Engineering, Faculty of Engineering, Kanazawa UniVersity, Ishikawa 920-8667, Japan, and AdVanced Science and Technology Center for CooperatiVe Research, Kyushu UniVersity, Kasuga-shi, Fukuoka 816-8580, Japan ReceiVed: April 18, 2001; In Final Form: March 20, 2002
The enthalpies of mixing of oleyl alcohol and oils (cyclohexane, benzene) were measured as a function of the concentration at fixed temperatures by the use of a high-accuracy isothermal calorimeter. By applying the thermodynamic equations to the enthalpy of mixing, the differential enthalpies of solution of oleyl alcohol in the oil solution were evaluated. The enthalpies are positive and decrease with increasing concentration in both oils, indicating that the aggregate formation is exothermic. However, the enthalpy of aggregate formation in the cyclohexane solution is much larger than that in the benzene solution and has a magnitude corresponding to the hydrogen bond formation, which was supported by the infrared spectra. Furthermore, the infrared spectra of the benzene solution showed that the hydroxyl group of alcohol attractively interacts with benzene molecule. These experimental results suggested that oleyl alcohol molecules associate themselves through the hydrogen bond formation between the hydroxyl groups in the cyclohexane solution, whereas with keeping interaction between hydroxyl group and benzene molecule in the benzene solution.
Introduction In the recent studies on the adsorption of oleyl alcohol (9cis-octadecene-1-ol) at the oil/water interfaces, we presented that alcohol molecules form aggregates in the oil solutions and the aggregation behavior is strongly affected by the chemical structure of the oil molecules. For example, the average aggregation numbers were estimated to be 10∼20 for the benzene system, whereas 2∼4 for the cyclohexane system.1 Because the tension was measured at the water-saturated oil/ oil-saturated water interfaces, a larger amount of water in the benzene solution than in the cyclohexane solution may cause this remarkable difference. To draw the conclusion, we need information on the structure of the aggregates and the molecular interaction that drives the aggregate formation, and so on. It is well-known that calorimetry is one of the most powerful methods to obtain information on the molecular interaction rather directly.2-6 Also, we have estimated and reported the differential enthalpy of solution of nonionic surfactant and the enthalpy of micelle formation by the use of the high precision isothermal titration microcalorimeter.2-4 In this study, we applied these technique and methodology to the oleyl alcoholoil systems. Because the aggregate formation in the oil solutions does not occur critically, which is different from the ordinary micelle formation, the thermodynamic equations in our previous * To whom correspondence should be addressed. Mailing address: Ryo Murakami, Department of Chemistry and Physics of Condensed Matter, Graduate School of Sciences, Kyushu University, Hakozaki 6-10-1, Higashiku, Fukuoka 812-8581, Japan. E-mail: ryo1scc@ mbox.nc.kyushu-u.ac.jp. † Department of Chemistry and Physics of Condensed Matter, Graduate School of Sciences, Kyushu University. ‡ Department of Chemistry and Chemical Engineering, Faculty of Engineering, Kanazawa University. § Advanced Science and Technology Center for Cooperative Research, Kyushu University.
studies were modified so as to be applicable to the present systems. The infrared spectroscopy was also employed to obtain information on the hydrogen bond formation of alkanol molecules in oil solutions.6-10 To elucidate the influence of water molecules to the aggregation behavior, furthermore, the water content in the oil solution was determined by the Karl Fischer method.11 Experimental Section Materials. Oleyl alcohol (9-cis-octadecene-1-ol) of very high purity (>99.5% by a gas-liquid chromatography) was supplied by Nippon Oil and Fats Co. Ltd. (Amagasaki, Japan) and used without further purification. Benzene (Wako Pure Chemical Industries Ltd., Super Special Grade) was refluxed with metallic sodium for 12 h and then distilled. Cyclohexane (Kanto Chemical Co. Inc., JIS Special Grade Reagent) was used after a simple distillation. Water was distilled three times, the second and third steps being done from alkaline permanganate solution. Infrared Spectroscopy. The fundamental OH-stretching vibration region was measured at room temperature with PerkinElmer Spectrum BX FT-IR System with a transmission cell with CaF2 windows and a 0.1 mm spacer. Sixteen scans were accumulated at a resolution of 2 cm-1. Calorimetry. The enthalpy of mixing of oil saturated with water and oleyl alcohol was measured by the isothermal titration microcalorimeter (TAM2277; Thermometric AB, Sweden) controlled by Digitam 3.0 software. A 2.5 µL portion of liquid oleyl alcohol was injected into a 4 mL stainless steel ampule filled with ∼3 mL of oil by using a computer controlled syringe pump (612 Lund Pump 2) from a gastight syringe (Hamilton 1725LT) through a stainless steel cannula. The weight of liquid injected was accurately calculated from the density value of the liquid. The solution in the ampule was stirred by the turbine
10.1021/jp011466m CCC: $22.00 © 2002 American Chemical Society Published on Web 06/04/2002
Aggregate Formation of Oleyl Alcohol
J. Phys. Chem. B, Vol. 106, No. 25, 2002 6549
HM ) [noho + n1sh1s + naha + nwhw] - [(noh/o + n/wh/w) +
SCHEME 1: Mixing process of oil and alcohol
nsh0s + n0wh0w] (4) Here, n1s is the numbers of moles of monomer, na is that of aggregate having an average aggregation number Na, and h1s and ha are the corresponding partial molar enthalpies, respectively. By substituting the mass balance equation
ms ) m1s + Nama at the constant speed of 120 rpm. The heat flow was detected to 0.15 µW by high-sensitive thermopiles surrounded by a heat sink stabilized at the desired temperature (2 × 10-4 K within an experimental error of 0.5 µW. The electrical calibration performance made the results quantitative. The titration measurements were performed at least two runs at a given temperature. Water Content Measurement. The water contents of dry benzene, the water-saturated benzene, benzene solutions of oleyl alcohol, and cyclohexane were measured by the MKS-1s Karl Fischer Moisture Meter (Kyoto Electronics Manufacturing Co. Ltd.) at 298.15 K under atmospheric pressure. Theoretical Let us consider the mixing process of ns moles of liquid oleyl alcohol and the oil phase which contains no moles of oil and is saturated with n/w moles of water under the presence of an excess water phase. The process is shown in Scheme 1. A certain amount of water n0w is expected to be transferred from the excess water phase to the oil solution during this mixing process and hence, the oil solution contains n/w + n0w(t nw) moles of water at the given ns. The enthalpy of mixing HM at a given temperature T and pressure p is given by
into eq 4, where m1s and ma are respectively the molalities of monomer and aggregate, hM is given by
(
)
ho - h/o ha HM ) + m1s(h1s - h0s ) + Nama - h0s + noMo Mo Na
hM )
m/w(hw - h/w) + m0w(hw - h0w) (6) Differentiating hM with respect to ms, we have
( ) ∂hM ∂ms
) ∆A0 hs - (∆A0 hs - ∆10hs)
T, p
( ) ( ) ∂m1s ∂ms
+
T, p ∂m0w
∂ms
( )
hama ∂Na Na ∂ms
-
T, p
(hw - h0w) (7)
T, p
where we introduced the partial molar enthalpy change accompanied by the dissolution of pure liquid alcohol into the oil phase as monomers, ∆10hs, defined by
∆10hs ) h1s - h0s
(8)
and that as aggregates, ∆A0 hs, defined by
∆A0 hs ) ha/Na - h0s
H ) [noho + nshs + nwhw] M
[(noh/o + n/wh/w) + nsh0s + nwh0w], (1) where hi is the partial molar enthalpy of component i in the oil solutions after the mixing, h0i the molar enthalpy of pure liquid i, and h/o and h/w are the partial molar enthalpy of oil and that of water in the oil phase before the mixing, respectively. Then the enthalpy of mixing per unit mass of oil hM is given by
hM )
(5)
m/w(hw
-
h/w)
+
m0w(hw
Because the change of the water concentration in the oil phase accompanied by the mixing process, (∂m0w/∂ms)T, p is negligibly small (see Figure 6), eqs 3 and 7 are reduced respectively to
( ) ∂hM ∂ms
∂hM ∂ms
-
h0w)
) hs - h0s
(10)
T, p
and
( )
HM 1 ) (h - h/o) + ms(hs - h0s ) + noMo Mo o
(9)
T, p
) ∆A0 hs - (∆A0 hs - ∆10hs)
( ) ∂m1s ∂ms
T, p
-
( )
hama ∂Na Na ∂ms
T, p
(2)
(11)
where Mo is the molar mass of oil, ms is the molality of oleyl alcohol, and m/w and m0w are the molalities of water corresponding to n/w and n0w, respectively. Then the variation of hM with respect to ms is given by
Equation 10 shows that (∂hM/∂ms) is the differential enthalpy of solution of oleyl alcohol in the oil solution. Furthermore, eq 11 explains explicitly the differential enthalpy by using the terms related to the aggregate formation. Hereafter, (∂hM/∂ms) at a given ms is written by ∆hs(ms). At a low concentration where aggregates are absent, we have
( ) ∂hM ∂ms
T, p
) hs - h0s +
( ) ∂m0w ∂ms
(hw - h0w)
(3)
T, p
where we used the Gibbs-Duhem equations of the oil phases. Although eq 3 is a general one for the present sytem, it is more appropriate to express separately the contribution of monomer and aggregate of oleyl alcohol in HM as
∆hs(ms f 0) ) ∆10hs
(12)
from eq 11. Then the enthalpy of aggregate formation at a given molality ms defined by
∆A1 hs(ms) ) ha/Na - h1s
(13)
6550 J. Phys. Chem. B, Vol. 106, No. 25, 2002
Figure 1. FT-IR Spectra of oleyl alcohol. (a) cyclohexane solution: (1) ms ) 14.93, (2) 29.54, (3) 39.88, (4) 50.11, (5) 59.14, and (6) 68.97 mmol kg-1; (b) benzene solution: (1) ms ) 19.92, (2) 58.38, and (3) 119.3 mmol kg-1.
Murakami et al.
Figure 2. Enthalpy of mixing vs molality curves of oleyl alcohol (a) cyclohexane system: (1) T ) 288.15, (2) 293.15, (3) 298.15 K, (b) sat. benzene system: (1) T ) 288.15, (2) 293.15, (3) 298.15 K.
is estimated by
[
( )] [ ( )]
∆A1 hs(ms) ) ∆hs(ms) - ∆hs(ms f 0) +
hama ∂Na / Na ∂ms T, p ∂m1s 1(14) ∂ms T, p
where ∆10hs was assumed to be independent of ms. Results and Discussions Infrared Spectroscopy. The infrared spectra of the fundamental OH-stretching absorption band of oleyl alcohol are shown at various concentrations in Figure 1, respectively. In the cyclohexane solution (Figure 1a), a sharp absorption band was observed and centered at about 3644 cm-1 over the whole concentrations. This is assigned to the free OH-stretching vibration.9,10 Furthermore, two notable absorption bands were observed at lower wavelengthes at higher concentrations: the bands centered at about 3535 and 3340 cm-1 are assigned to the OH-stretching in open-chain aggregates and that in cyclic aggregates, respectively.9,10 Therefore, the hydrogen bond are formed through the hydroxyl groups of oleyl alcohol molecules at higher concentrations in the cyclohexane solution. In the benzene solution (Figure 1b), however, the band of free OH-stretching at 3644 cm-1 was obviously shifted to a lower wavelength, suggesting that almost all hydroxyl groups attractively interact with benzene molecules.12 In addition, the band of cyclic aggregates is hardly observed and that of openchain aggregates is only weakly observed even at a very high
Figure 3. Comparison between values of δhM / δms and ∂hM/∂ms at 298.15 K: (1) cyclohexane system, (2) water-saturated benzene system: (O) δhM / δms, (b) ∂hM / ∂ms.
concentration (about 120 mmol kg-1). Therefore, the aggregation behavior of oleyl alcohol molecules in the benzene solution is expected to be much different from that in the cyclohexane solution. The titration calorimetry and the measurement of water content of the oil solutions give further information on the origin of the difference. Enthalpy of Mixing. The enthalpy of mixing HM was measured as a function of ns at fixed temperatures from 288.15 to 298.15 K under atmospheric pressure. The heat per one injection is calculated from the corresponding peak area of the thermal power vs time curve by the program of Digitam 3.0 software. Then the HM value at a given ns is estimated by summing up the area from the first peak to the one at which
Aggregate Formation of Oleyl Alcohol
J. Phys. Chem. B, Vol. 106, No. 25, 2002 6551
Figure 6. Nw vs Ns curve in water-saturated benzene solution of oleyl alcohol; Ns ) 8 corresponds to ms ) 102.4 mmol kg-1.
Figure 4. Partial molar enthalpy change of oleyl alcohol vs molality curves. (a) cyclohexane system: (1) T ) 288.15, (2) 293.15, and (3) 298.15 K, (b) benzene system: (O) water-saturated benzene, (b) dry benzene: (1) T ) 288.15, (2) 293.15, and (3) 298.15 K.
Figure 5. Enthalpy of mixing vs molality curves of oleyl alcohol dry benzene system: (1) T ) 288.15, (2) 293.15, and (3) 298.15 K.
the total amount of oleyl alcohol reaches ns. Figure 2 shows the enthalpy of mixing per kilogram of oil hM vs molality ms curves at each temperature. It is seen that the mixing process is endothermic and the hM value increases with increasing concentration. Furthermore, we note that the hM value of the benzene system decreases, while that of the cyclohexane increases, with increasing temperature. The differential enthalpy of solution ∆hs(ms) at a given ms was evaluated by two methods at 298.15 K. First, according to its thermodynamic definition given by eq 10, the derivative (∂hM/ ∂ms) was estimated from the hM vs ms curves in Figure 2 and plotted against ms in Figure 3 (full circles). Second, taking into account that the titration was performed at a very small
concentration increment δms, δhM / δms may be approximately equal to the derivative (∂hM/∂ms) in its value; δhM / δms values are plotted by the open circles in Figure 3. It is said that the values from two methods are coincide with each other within the reproducibility of (0.25 kJ mol-1. However, as we have verified in our previous paper,4 the δhM / δms value even at very small δms is not equal to the (∂hM/∂ms) value unless the titrant is pure material. Therefore the coincidence observed in Figure 3 is not general but special for the present case where the titrant is pure liquid alcohol. To keep the generality of the calculation in our papers on the titration calorimetry, we evaluated the differential enthalpy of solution by the first method, (∂hM/∂ms). The ∆hs(ms) values are plotted against ms in Figure 4. The positive values of ∆hs(ms) suggest the weaker intermolecular interaction between oleyl alcohol molecules and oil molecules compared to that between the same species. It was found that the values of ∆hs(ms) are almost constant at low concentrations, and therefore, the oil solutions of oleyl alcohol are reasonably assumed to be ideally dilute and all alcohol molecules are dispersed as monomers. Furthermore, the less positive values of ∆hs(msf0) in the benzene solution substantiates the more attractive solute-solvent interaction, which is suggested from the IR spectra, compared to that in the cyclohexane solution. Now, let us estimate the enthalpy of aggregate formation ∆A1 hs(ms ) 100) by using eq 14. For doing this, we have to evaluate the dependence of average aggregation number on the total concentration (∂Na/∂ms)T, p and the dependence of monomer concentration on the total concentration (∂m1s/∂ms)T, p. Taking account of small aggregation number, (∂Na/∂ms)T, p was assumed to be negligibly small. The (∂m1s/∂ms)T,p value for the cyclohexane solution was estimated roughly to be about 0.22∼0.26 at 100 mmol kg-1 from the dependence of the maximum of the absorbance intensity at 3644 cm-1 A3644 on the concentration given in Figure 1a as follows: A3644 increases linearly with increasing the total concentration at low concentrations, A3644 ) Rms. However, at high concentrations, A3644 was by shifted ∆A3644 to a lower intensity from the straight line A3644 ) Rms. By assuming that this shift is proportional to the concentration of alcohol in aggregates, the monomer concentration m1s is estimated by using the relation ∆A3644/Rms ) (ms - m1s)/ms and then the derivative (∂m1s/∂ms)T, p is also estimated by the relation (∂m1s/∂ms)T, p ) 1 - (1/R)(∂∆A3644/ms). For the benzene solution, (∂m1s/∂ms)T, p could not be evaluated by using the same way because the adsorption band around 3644 cm-1 involve the contribution not only from monomers but also
6552 J. Phys. Chem. B, Vol. 106, No. 25, 2002
Murakami et al.
TABLE 1: Enthalpy of Aggregate Formation ∆A1 hs(ms
) 100) / kJ mol
-1
T/K
cyclohexane
sat. benzene
dry benzene
288.5 293.15 298.15
-20.66 ( 0.51 -18.95 ( 0.50 -16.34 ( 0.53
-2.39 ( 0.40 -2.27 ( 0.48 -1.95 ( 0.36
-1.95 ( 0.34 -1.80 ( 0.36 -1.53 ( 0.38
TABLE 2: Water Content in Pure Oils water content / ppm oil
cyclohexane
sat. benzene
dry benzene
80
705
110
from aggregates. However, taking into account that ∆hs(ms) ∆hs(ms f 0) is much smaller in the benzene solution than that in the cyclohexane solution, the influence of the factor 1 (∂m1s/∂ms)T, p on the value of ∆A1 hs(ms) was assumed to be very small in the benzene system. The values of ∆A1 hs(ms ) 100) are presented in Table 1 as a function of temperature. It is realized that the aggregate formation in the oil phase is attended by a decrease of enthalpy and its magnitude in the cyclohexane solution is about 16∼21 kJ mol-1, being much larger than that in the benzene solution. Because the hydrogen bond formation usually accompanies -10∼-40 kJ mol-1,13 it is suggested that the hydrogen bond acts effectively through hydroxyl groups of oleyl alcohol molecules in the cyclohexane solution at high concentrations. In the benzene solution, on the other hand, such a strong interaction is not predicted even at 100 mmol kg-1 judging from the small decrease of enthalpy (about 2 kJ mol-1). Therefore, it is probable that hydrogen bond formation is not responsible for the aggregate formation in the benzene solution. These findings are totally consistent with those in the FT-IR study given in Figure 1. To clarify the aggregation in the benzene solution, the influence of water molecules dissolved in it was examined. We measured the enthalpy of mixing of oleyl alcohol and almost dry benzene containing water molecules of only 110 ppm, which is much smaller than that in the water-saturated benzene but similar to that in the water-saturated cyclohexane as shown in Table 2. Figures 5 and 4b show the hM and ∆hs(ms) vs molality curves, respectively. Also the values of ∆A1 hs(ms ) 100) are given in Table 1. It is important to note that the ∆hs(ms) value vs molality curves are similar to those in sat. benzene and the difference in ∆A1 hs(ms ) 100) is not so significant. Therefore, it is said that water molecules hardly affect the aggregation behavior of oleyl alcohol although the aggregates formed in the water-saturated benzene are slightly stabler than that in dry benzene. This finding denies the formation of a reversed micelle of oleyl alcohol molecules in the benzene solution even in the presence of water molecules under the saturation condition. Water Content Measurement. There exists a large quantity of water molecules in the benzene solution compared to the cyclohexane solution; Table 2 shows that the water content in the water-saturated benzene solution is about seven times of that in the dry benzene even in the absence of oleyl alcohol molecules. In Figure 6, the number of water molecules Nw per one thousand solvent molecules is plotted against that of alcohol molecules Ns. Here Ns ) 8 corresponds to the molality of 102.4 mmol kg-1. It is important to note that Nw proportionally increases with Ns even at concentrations where the aggregate formation takes place (Ns > 4.7).14 Furthermore, the ratio Nw / Ns is about 0.076 and expected to be too small for reversed micelle formation to take place in the benzene solution.
Therefore, it is suggested that the situation of one oleyl alcohol molecule in aggregate is similar to that in the monomeric state from the viewpoint of hydration. Conclusions 1. In the cyclohexane solution, the aggregation of oleyl alcohol takes place through the hydrogen bond formation between the hydroxyl groups. At a high concentration, cyclic aggregates are predominant over open chain aggregates. 2. In the benzene solution, the hydrogen bond formation between alcohol molecules is not so important but oleyl alcohol molecules are expected to associate themselves with keeping interaction between hydroxyl groups and benzene molecules even in the presence of water molecules under the saturation condition. Therefore, the aggregate formation similar to reversed micelle formation is denied. Nomenclature 1. Concentrations no ) Total number of moles of oil ns ) Total number of moles of oleyl alcohol n/w ) Number of moles of water in a pure oil phase before the mixing. n0w ) Number of moles of water transferred from an excess water phase to an oil solution during the mixing process. nw ) n/w + n0w ) Total number of moles of water in an oil solution after the mixing. n1s ) Number of moles of monomer in an oil solution. na ) Number of moles of aggregate in an oil solution. m/w ) Molality of water corresponding to n/w. m0w ) Molality of water corresponding to n0w. ms ) Molality of oleyl alcohol. m1s ) Molality of monomer in an oil solution. ma ) Molality of aggregate in an oil solution. Na ) Average aggregation number. Mo ) Molar mass of oil. (∂Na/∂ms)T, p ) Dependence of average aggregation number on total concentration. (∂m1s/∂ms)T, p ) Dependence of monomer concentration on total concentration. 2. Thermodynamic Quantities hM ) HM/noMo ) Enthalpy of mixing. hi ) Enthalpy of mixing per unit mass of oil. h/o ) Partial molar enthalpy of component i in an oil solution after the mixing. h0i ) Molar enthalpy of pure liquid i. h/i ) Partial molar enthalpy of oil in an oil phase before mixing. h/w ) Partial molar enthalpy of water in an oil phase before mixing. h1s ) Partial molar enthalpy of monomer. ha ) Partial molar enthalpy of aggregate. ∆hs(ms) ) (∂hM/∂ms)T,p ) hs - h0s ) Differential enthalpy of solution of oleyl alcohol in an oil solution at a given ms. ∆10hs ) h1s - h0s ) Partial molar enthalpy change accompanied by the dissolution of pure liquid alcohol into the oil phase as monomers. ∆A0 hs ) ha/Na - h0s ) Partial molar enthalpy change accompanied by the dissolution of pure liquid alcohol into the oil phase as aggregates. ∆A1 hs(ms) ) ha/Na - h1s ) Enthalpy of aggregate formation at a given molality ms.
Aggregate Formation of Oleyl Alcohol ∆A1 hs(ms ) 100) ) Enthalpy of aggregate formation at ms ) 100 mmol kg-1. References and Notes (1) Aratono, M.; Murakami, R.; Ohta, A.; Ikeda, N.; Takiue, T. J. Colloid. Interface Sci., submitted for publication. (2) Aratono, M.; Ohta, A.; Ikeda, N.; Matubara, A.; Motomura, K.; Takiue, T. J. Phys. Chem. B. 1997, 101, 3535. (3) Ohta, A.; Takiue, T.; Ikeda, N.; Aratono, M. J. Phys. Chem. B. 1998, 102, 4809. (4) Ohta, A.; Murakami R.; Takiue, T.; Ikeda, N.; Aratono, M. J. Phys. Chem. B. 2000, 104, 8592. (5) Kimura, T.; Ozaki, T.; Nakai, Y.; Takeda, K. Takagi, S. Thermochimica Acta. 1998, 54, 285. (6) Costas, M.; Patterson, D. J. Chem. Soc., Faraday Trans. 1985, 81, 635.
J. Phys. Chem. B, Vol. 106, No. 25, 2002 6553 (7) Aveyard, R.; Briscoe, B. J.; Chapman, J. J. Chem. Soc. Fraday Trans. I 1973, 69, 1772. (8) Iwahashi, M.; Hachiya, N.; Ozaki, Y.; Mtuzawa, H.; Liu, Y.; Czarnecki, M. A.; Ozaki, Y.; Horiuchi, T.; Suzuki, M. J. Phys. Chem. 1995, 99, 4155. (9) Førland, G. M.; Libnau, F. O.; Kvalheim, O. M.; Høiland, H. Applied Spectroscopy 1996, 50, 1264. (10) Førland, G. M., Liang, Y., Kvalheim, O. M., Høiland, H., Chazy, A., J. Phys. Chem. B 1997, 101, 6960. (11) Kitahara, A., AdV. Colloid Interface Sci. 1980, 12, 109. (12) Van Ness, H. C.; Van Winkle, J.; Richol, H. H.; Hollinger, H. B. J. Phys. Chem. 1967, 71, 1483. (13) Israelachvili, J. N., Intermolecular and Surface Forces; Academic Press: London, 1985; Chapter 8. (14) Aratono, M.; Mitsutake K.; Murakami R.; Takiue, T. 10th International Conference On Colloid and Interface Science, 23-28 July 2000 in Bristol, p. 84.
