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Correlation between surface and bulk structures of alcohol–water mixtures
Journal of Colloid and Interface Science 284 (2005) 255–259 www.elsevier.com/locate/jcis
Correlation between surface and bulk structures of alcohol–water mixtures Yohko F. Yano ∗ Department of Chemistry, Gakushuin University, 1-5-1, Toshima-ku, Tokyo 1718588, Japan Received 4 June 2004; accepted 21 September 2004 Available online 13 December 2004
Abstract Adsorption isotherms of binary aqueous solutions of methanol, ethanol, 1-propanol, 2-propanol, tert-butanol, and 1-butanol are demonstrated, being calculated by using the Gibbs adsorption equation with experimental data of surface tension and vapor pressure found in the literature. For all of the alcohol–water mixtures, the maximum value in the adsorption isotherm, namely, the maximum surface excess is about that expected for the formation of a monolayer. Furthermore, the composition of the mixture for the maximum surface excess coincides with that corresponding to the minimum in the excess partial molar volume of the solutes. These results indicate that the hydrophobic hydration in bulk induces the surface excess of the alcohols and after a monolayer is formed, the hydrophobic hydration itself is no longer retained. 2004 Elsevier Inc. All rights reserved. Keywords: Surface structure; Alcohol–water mixtures; Adsorption isotherm; Hydrophobic hydration; Surface tension; Activity; Monolayer; Surface excess; Partial molar volume; Gibbs adsorption equation
1. Introduction Is there any structural correlation between the surface and bulk of aqueous solutions? Although various studies of aqueous solutions have been performed, it seems that no one has given any answers to this question. In the previous study on aqueous solutions of 2-butoxyethanol (hereafter BE) demonstrated by X-ray reflectivity and surface tension measurements, we found that the surface excess of BE only exists when the hydrophobic hydration (i.e., the presence of hydrophobic solute caused an increase in the order of the water surrounding the solute) occurs in the bulk [1]. This phenomenon seems quite natural because the “surface excess of solute” is essentially caused by the strong hydrogen bond network in the solvent water. Covering the water surface with the solutes having weaker molecular interactions reduces surface energy observed as surface tension [2]. Generally, the hydrophobic hydration [3] and the surface excess * Fax: +81-3-5992-1029.
E-mail address: [email protected]. 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.09.059
are known to occur in most of the alcohol–water mixtures. However, both of them have been studied independently and not related to each other. Our purpose in the present paper, therefore, is to figure out correlation between surface and bulk structures that exists generally in the alcohol–water mixtures by demonstration of the adsorption isotherms, that is, the solute mole fraction dependence of the surface excess. The surface excess of alcohol in alcohol–water mixtures is given by the Gibbs adsorption equation [2]: ∂γ 1 wa . Γal = − (1) RT ∂ ln aal T To evaluate it quantitatively, a reliable data set of two parameters, the surface tension γ and the activity of alcohol aal , is necessary for calculation. In most previous works, Γalwa were calculated with using molar concentrations instead of the activities. Lavi et al. calculated adsorption isotherms for several alcohol–water mixtures by using activity coefficients and observed the nonideality in high concentrations [4]. However, they used theoretical fits of the experimental data and, therefore, doubtful maxima or singularities were produced. Thus, in this paper, numerical calculations are carried
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out by using more accurate experimental data. Comparing the results with the partial molar volume of the solutes, we are going to discuss correlation between the surface and bulk structures.
2. Determination of the surface excess The surface tension data of several alcohol–water mixtures at 25 ◦ C were collected from Refs. [5–11]. These are shown as the closed symbols in Figs. 1b–6b. The fitting values in the Connors equation [12] that Lavi et al. used are slightly off from the experimental data and these differences make the position of maxima away from their original one in the derivatives of γ . We decided, therefore, to take a numerical method by using the original experimental data. On the other hand, the activity data at 25 ◦ C shown as the open circles were calculated from the partial vapor pressure ∗ , where p is the partial vapor pres[13,14] as aal = pal /pal al ∗ is the vapor pressure sure of alcohol in the solution and pal of pure alcohol. The crosses are data from DECHEMA [15] that Lavi et al. used. The data taken from Refs. [13,14] have much more data points that will give the adsorption isotherm with higher accuracy. The solid curves are the best fit of them
with the van Laar equation [16], 2 Axal aal = xal exp A 1+ , B(1 − xal )
(2)
where xal is the mole fraction of alcohol and A and B are empirical constants as fitting parameters. They fit very well to the data for methanol, ethanol, and 2-propanol as shown in Figs. 1b, 2b, and 3b, while not so well around the inflection points for 1-propanol and tert-butanol in Figs. 3b and 5b. We calculated Γalwa , shown as the closed circles in
Fig. 2. (a) Adsorption isotherm of ethanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for ethanol–water mixtures at 25 ◦ C: (") Ref. [7], (Q) Ref. [5], (a) Ref. [6], (!) Ref. [13], (×) Ref. [15].
Fig. 1. (a) Adsorption isotherms of methanol–water mixtures at 25 ◦ C. The closed circles were calculated using the data in (b) and the continuous dashed curve is a guide for the eyes. The scale on the right-hand side is the corresponding molecular area of the surface excess solute. The horizontal dash-dotted line corresponds to Γalwa of a monolayer. The vertical dash-dotted arrow is the mole fraction of the minimum in the excess partial molar volume of the solute and it coincides with that corresponding to the maximum of the adsorption isotherm. The shaded area is the range of transition where the hydrophobic hydration is lost (see text). (b) Mole fraction xal dependence of surface tension γ and activity aal for methanol–water mixtures at 25 ◦ C: (") Ref. [5], (!) Ref. [13], (×) Ref. [15]. The solid curve is the van Laar fit of aal , whereas the dashed line corresponds to the ideal aal . The dotted line is drawn using Eq. (3).
Fig. 3. (a) Adsorption isotherm of 1-propanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for 1-propanol–water mixtures at 25 ◦ C: (") Ref. [7], (a) Ref. [8], (!) Ref. [13], (×) Ref. [15].
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Fig. 4. (a) Adsorption isotherm of 2-propanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for 2-propanol–water mixtures at 25 ◦ C: (") Ref. [5], (a) Ref. [9], (!) Ref. [13], (×) Ref. [15].
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Fig. 6. (a) Adsorption isotherm of 1-butanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. The vertical dash-dotted arrow shows not only the mole fraction of the minimum in the excess partial molar volume of 1-butanol, but also the solubility limit. (b) Mole fraction xal dependence of surface tension γ and activity aal for 1-butanol–water mixtures at 25 ◦ C: (") Ref. [10], (—) Ref. [17].
dash-dotted lines) indicates that the excess alcohols form a monolayer because it approximately corresponds to the area per CH2 chain in close-packed configuration.
3. Results 3.1. Methanol and ethanol
Fig. 5. (a) Adsorption isotherm of tert-butanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for tert-butanol–water mixtures at 25 ◦ C: (") Ref. [11], (!) Ref. [14], (×) Ref. [15].
Figs. 1a–6a, numerically by using the raw data points of γ and the corresponding values of aal obtained by the leastsquares fit of Eq. (2). In the case of 1-propanol, 2-propanol, and tert-butanol, we also calculated by using a polynomial fit of aal near the inflection points to avoid artificial errors and drew them as the dashed curves. For 1-butanol, we used the NRTL equation (shown as the solid curve) with parameters at 25 ◦ C taken from Ref. [17] that Lavi et al. used. The scales on the right-hand side of Figs. 1a–6a are the molecular area of alcohol calculated from the inverse of Γalwa . The molecular area of 20 Å2 (shown as the horizontal
Figs. 1 and 2 show the activity, aal , surface tension, γ , and calculated surface excess, Γalwa , at 25 ◦ C for methanol and ethanol aqueous solutions, respectively. The dashed straight lines are aal for the ideal solutions that obey Henry’s law. For methanol, aal is almost ideal over the entire concentration. On the other hand, the deviations from ideality are quite substantial for ethanol. For these two alcohols, the van Laar equation describes the experimental data very well. The Γalwa for ethanol calculated using a van Laar fit reproduced the previous works [6,18,19] very well. The surface tension decreases with the mole fraction of alcohol. This rapid decrease is typical for the aqueous system with surface-active solutes and this character increases with the length of the hydrocarbon chain. Therefore, the surface excess of alcohol Γalwa for ethanol increases more rapidly than that for methanol as shown in Figs. 1a and 2a. For both of them, the maximum values are around 0.8 × 10−5 mol/m2 (denoted by the horizontal dash-dotted lines) corresponding to a monolayer. For ethanol, this result is supported by the neutron reflection study, which directly observed a surface monolayer completed near xal = 0.1 [18]. We recognize that the mole fraction of the maximum Γalwa exactly coincides with that corresponding to the minimum
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in the excess partial molar volumes of alcohols reported in Refs. [3,20], as shown by the vertical arrows in these figures. This is very striking because both the Γalwa and aal curves are smooth at these mole fractions. 3.2. 1-Propanol, 2-propanol, and tert-butanol Clear inflection points in the aal curves of these three mixtures appear in Figs. 3b–5b. The derivatives of aal become very small at xal ≈ 0.2 and they are much smaller for 1-propanol and tert-butanol than for 2-propanol. This behavior is very similar to that predicted for a typical surfactant under micelle formation [21]. Actually, Debye’s correlation lengths (i.e., radii of the space distribution of the fluctuation of electron density) obtained by small-angle X-ray scattering measurements show maxima around this concentration due to the formation of micelle-like aggregates for 1-propanol and clathrate–hydrate-like aggregates for tertbutanol and 2-propanol [22]. Except for 2-propanol, the van Laar equation does not describe the experimental data very well around xal ≈ 0.2. The NRTL equation, which has more advantage in consideration with the interaction between two components gave almost the same curves. The deviations from the experimental data caused by a van Laar fit make the values of Γalwa around xal ≈ 0.2 scatter. We also tried a polynomial fit near the inflection points and confirmed that neither the maximum for 2-propanol nor singularities for 1-propanol and tert-butanol around xal ≈ 0.2 reported by Lavi et al. existed. They were probably caused by underestimation of ∂aal /∂xal . We drew the dashed curves as guides for eyes that were also considered with the polynomial fits. All of the adsorption isotherms rapidly increase and show a maximum at xal = 0.07 for 2-propanol and at xal = 0.04 for others. The maxima also coincide with the minima in the excess partial molar volumes of alcohols [23,24] denoted by the arrows as described above. 3.3. 1-Butanol In a series of n-alcohols in increasing order of the number of carbon atoms, 1-butanol is the first that exhibits a limited solubility in water. Phase separation occurs at xal = 0.018 and 25 ◦ C. The partial molar volume of 1-butanol decreases with its mole fraction and shows the minimum at the phase boundary [25]. The activity data shown as the solid line in Fig. 6b is the NRTL equation with the parameters at 25 ◦ C taken from DECHEMA [17]. It slightly deviates from a straight line near the phase boundary. The absorption isotherm shows a saturation state expected from the monolayer type of Langmuir adsorption isotherm observed typically in aqueous solutions of a surfactant. Li et al. reproduced the adsorption isotherm well by the neutron reflection measurements, and furthermore, they speculated that the structure of the monolayer was rough, since the observed thickness was larger than the molecular length [26].
4. Discussion All of the adsorption isotherms in Figs. 1a–6a show similar behavior. First, Γalwa increases with the alcohol mole fraction and then decreases (except for 1-butanol). This is very reasonable because the surface excess of solute decreases with xal beyond the maximum and should be zero for the pure solute. Actually, none of them reaches zero due to continuous decrease observed in γ . Second, the maximum values of Γalwa for all mixtures are around 0.8 × 10−5 mol/m2 corresponding to a monolayer. It had been already known in the early 20th century that the most of the surface excess n-alcohols form monolayers at some concentration [27]. Third, the mole fraction of the maximum Γalwa exactly coincides with that corresponding to the minimum in the excess partial molar volumes of alcohols (we hereafter call the mole fraction xal∗ ). This is very interesting discovery because the molecular space of alcohols both in the bulk and the surface show minima simultaneously! This implies that there exists some correlation between the surface and bulk structures. In the case of BE not shown here, the mole fraction of the minimum in the excess partial molar volumes of BE [28] also is located near that corresponding to the Γalwa of a monolayer that is about half of its maximum value. To explain about the third behavior, we are going to discuss what the maximum Γalwa is caused by. Addison mentioned that below the γ of 55 mN/m, the γ is a linear function of the logarithm of concentration for each n-alcohol, and this part of the curve is represented by the relation γ = α − β log xal ,
(3)
where α and β are constants [27]. The β value is constant irrespective of chain length and has the value β = γw B, with B = 0.407 and the surface tension of pure water γw . This is why all of the alcohols show the same maximum value of Γalwa . In fact, |dγ /d log xal | for all of the solutions, as shown in Figs. 1b–6b, increases with the alcohol concentration and is equal to β (the dotted lines) at the maximum, and then abruptly becomes small. It is very important to notice that dγ /d log xal = −β at xal∗ . Additionally, aal starts to turn below the straight dashed line at xal∗ for all of the alcohols. The maximum Γalwa is, therefore, found to be caused by these two factors: the largest dγ /d log xal and d log aal < d log xal . In other words, xal∗ is the mole fraction at which the solutions starts to deviate from ideal. In the case of tert-butanol, Omelyan reported that the concentration xal∗ ≈ 0.03 corresponds to that the solute alcohols filling up the cavity in the solvent water start to aggregate [29]. In the present study, we find that the surface monolayer completes at xal∗ . Recently, Koga et al. proposed that hydrophobic hydration (they used the word “iceberg formation”) locally enhances the hydrogen bond network but associates with the reduction of the hydrogen bond probability of bulk H2 O that are relatively far away from solutes [23,30]. And they
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clarified the ranges of transition where the percolation of hydrogen bond network (i.e., the continuous hydrogen-bonded network formed by water molecules) is lost. They are shown as shaded areas in Figs. 1–5. The width of these ranges gives the strength of the effect of alcohol on water—the narrower is the stronger. The order of relative hydrophobic nature of alcohols established by Koga et al. as methanol < ethanol < 2-propanol < 1-propanol < tert-butanol < BE is also observed in the order of xal∗ . It is interesting to notice that all of the curves of surface tension break like the critical micelle concentration for surfactants at the end point of these ranges as shown in Figs. 1b–5b. We consider that the aggregations of the solute alcohols formed at xal∗ grow and finally destroy the percolation of hydrogen bond network (hereafter HBN) at this concentration. As a result, the surface excess of the solute alcohols decreases, because it is no longer necessary for covering the surface with the solutes when the molecular interactions in the bulk weaken. In the case of the interfaces of mutually saturated aqueous 1-butanol solutions studied by Monte Carlo simulations, a dense 1-butanol monolayer remained at the surface of the water-rich phase, in contrast with no enrichment of water at the surface of the 1-butanolrich phase [31]. This result also supports the idea that the surface monolayer forms only when the percolation of HBN in water is retained.
5. Summary and conclusions We performed a demonstration of the adsorption isotherms of several alcohol–water mixtures (methanol, ethanol, 1-propanol, 2-propanol, tert-butanol, 1-butanol) calculated using surface tension and vapor pressure data taken from the literature. For all of the alcohols, the value of the maximum in the adsorption isotherm indicates the formation of a monolayer and this concentration coincides with that corresponding to the minimum in the excess partial molar volume of the alcohol. This also coincides with the bulk solution losing ideality. Furthermore, the critical micelle concentrationlike breaks are also observed in the surface tension at which the hydrogen bond percolation is lost. From these observations, we conclude that a correlation really exists between the surface and bulk structures of alcohol–water mixtures as summarized below. In dilute alcohol aqueous solutions, hydrophobic hydration induces a surface excess of the alcohol. When a monolayer is completely formed, the solute molecules, either on the surface or in the bulk, feel tightest and the bulk solution starts to lose ideality; that is, the solute molecules starts to aggregate. Gradually, the hydrogen bond network in water is destroyed by the growing aggregations. Consequently, the surface excess decreases as the molecular interactions in bulk weaken.
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Acknowledgments The author is grateful for helpful discussions with Professor Takao Iijima of Gakushuin University and Professor Yoshikata Koga of the University of British Columbia.
References [1] Y.F. Yano, J. Chem. Phys. 116 (2002) 8093. [2] A.W. Adamson, A.P. Gast, Physical Chemistry of Surfaces, sixth ed., Wiley–Interscience, New York, 1997, p. 48. [3] F. Franks (Ed.), Water: A Comprehensive Treatise, vol. 2, Plenum, New York, 1973. [4] P. Lavi, A. Marmur, J. Colloid Interface Sci. 230 (2000) 107. [5] G. Vazquez, E. Alvarez, J.M. Navaza, J. Chem. Eng. Data 40 (1995) 611. [6] E.A. Guggenheim, N.K. Adam, Proc. R Soc. London Ser. A 139 (1933) 218. [7] R. Strey, Y. Viisanen, M. Aratono, J.P. Kratohvil, Q. Yin, S.E. Friberg, J. Phys. Chem. B 103 (1999) 9112. [8] J. Glinski, G. Chavepeyer, J.K. Platten, J. Chem. Phys. 104 (1996) 8816. [9] B.C. Hoke, J.C. Chen, J. Chem. Eng. Data 36 (1991) 322. [10] W.D. Harkins, R.W. Wampler, J. Am. Chem. Soc. 53 (1931) 850. [11] J. Glinski, G. Chavepeyer, J.K. Platten, J. Chem. Phys. 102 (1995) 2113. [12] K.A. Connors, J.W. Wright, Anal. Chem. 61 (1989) 194. [13] J. Hu, C.A. Haynes, A.H.Y. Wu, C.M.W. Cheung, M.M. Chen, E.G.M. Yee, T. Ichioka, K. Nishikawa, P. Westh, Y. Koga, Can. J. Chem. 81 (2003) 141. [14] Y. Koga, W.W.Y. Siu, T.Y.H. Wong, J. Phys. Chem. 94 (1990) 7700. [15] J. Gimehling, U. Onken, Vapor–Liquid Equilibrium Data Collection Aqueous Organic System, in: Chemistry Data Series, vol. 1, Dechema, Frankfurt/Main, 1977, part 1. [16] J.M. Prausnitz, R.N. Lichtenthaler, E. Gomes de Azevedo, Molecular Thermodynamics of Fluid-Phase Equilibria, Prentice–Hall, Englewood Cliffs, NJ, 1986. [17] J.M. Sorensen, W. Arlt, Liquid–Liquid Equilibrium Data Collection Binary System, in: Chemistry Data Series, vol. 5, Dechema, Frankfurt/ Main, 1979, part 1, p. 236. [18] Z.X. Li, J.R. Lu, D.A. Styrkas, R.K. Thomas, A.R. Rennie, J. Penfold, Mol. Phys. 80 (1993) 925. [19] M. Aratono, T. Toyomasu, M. Villeneuve, Y. Uchizono, T. Takiue, K. Motomura, N. Ikebe, J. Colloid Interface Sci. 191 (1997) 146. [20] F. Franks, D.J.G. Ives, Quart. Rev. (1966) 1. [21] K. Shinoda, E. Hutchinson, J. Phys. Chem. 66 (1962) 577. [22] H. Hayashi, K. Nishikawa, T. Iijima, J. Phys. Chem. 94 (1990) 8334. [23] Y. Koga, P. Westh, K. Nishikawa, Can. J. Chem. 81 (2003) 150. [24] M. Sakurai, Bull. Chem. Soc. Jpn. 60 (1987) 1. [25] K. Tamura, J. Hu, C. Trandum, P. Westh, C.A. Haynes, Y. Koga, Phys. Chem. Chem. Phys. 2 (2000) 355. [26] Z.X. Li, J.R. Lu, R.K. Thomas, A.R. Rennie, J. Penfold, J. Chem. Soc. Faraday Trans. 92 (1996) 565. [27] C.C. Addison, J. Chem. Soc. (1945) 98. [28] Y. Koga, J. Phys. Chem. 96 (1992) 10,466. [29] I. Omelyan, A. Kovalenko, F. Hirata, J. Theor. Comput. Chem. 2 (2003) 193. [30] Y. Koga, K. Nishikawa, P. Westh, J. Phys. Chem. A 108 (2004) 3873. [31] B. Chen, J.I. Siepmann, M.L. Klein, J. Am. Chem. Soc. 125 (2003) 3113.
Correlation between surface and bulk structures of alcohol–water mixtures Yohko F. Yano ∗ Department of Chemistry, Gakushuin University, 1-5-1, Toshima-ku, Tokyo 1718588, Japan Received 4 June 2004; accepted 21 September 2004 Available online 13 December 2004
Abstract Adsorption isotherms of binary aqueous solutions of methanol, ethanol, 1-propanol, 2-propanol, tert-butanol, and 1-butanol are demonstrated, being calculated by using the Gibbs adsorption equation with experimental data of surface tension and vapor pressure found in the literature. For all of the alcohol–water mixtures, the maximum value in the adsorption isotherm, namely, the maximum surface excess is about that expected for the formation of a monolayer. Furthermore, the composition of the mixture for the maximum surface excess coincides with that corresponding to the minimum in the excess partial molar volume of the solutes. These results indicate that the hydrophobic hydration in bulk induces the surface excess of the alcohols and after a monolayer is formed, the hydrophobic hydration itself is no longer retained. 2004 Elsevier Inc. All rights reserved. Keywords: Surface structure; Alcohol–water mixtures; Adsorption isotherm; Hydrophobic hydration; Surface tension; Activity; Monolayer; Surface excess; Partial molar volume; Gibbs adsorption equation
1. Introduction Is there any structural correlation between the surface and bulk of aqueous solutions? Although various studies of aqueous solutions have been performed, it seems that no one has given any answers to this question. In the previous study on aqueous solutions of 2-butoxyethanol (hereafter BE) demonstrated by X-ray reflectivity and surface tension measurements, we found that the surface excess of BE only exists when the hydrophobic hydration (i.e., the presence of hydrophobic solute caused an increase in the order of the water surrounding the solute) occurs in the bulk [1]. This phenomenon seems quite natural because the “surface excess of solute” is essentially caused by the strong hydrogen bond network in the solvent water. Covering the water surface with the solutes having weaker molecular interactions reduces surface energy observed as surface tension [2]. Generally, the hydrophobic hydration [3] and the surface excess * Fax: +81-3-5992-1029.
E-mail address: [email protected]. 0021-9797/$ – see front matter 2004 Elsevier Inc. All rights reserved. doi:10.1016/j.jcis.2004.09.059
are known to occur in most of the alcohol–water mixtures. However, both of them have been studied independently and not related to each other. Our purpose in the present paper, therefore, is to figure out correlation between surface and bulk structures that exists generally in the alcohol–water mixtures by demonstration of the adsorption isotherms, that is, the solute mole fraction dependence of the surface excess. The surface excess of alcohol in alcohol–water mixtures is given by the Gibbs adsorption equation [2]: ∂γ 1 wa . Γal = − (1) RT ∂ ln aal T To evaluate it quantitatively, a reliable data set of two parameters, the surface tension γ and the activity of alcohol aal , is necessary for calculation. In most previous works, Γalwa were calculated with using molar concentrations instead of the activities. Lavi et al. calculated adsorption isotherms for several alcohol–water mixtures by using activity coefficients and observed the nonideality in high concentrations [4]. However, they used theoretical fits of the experimental data and, therefore, doubtful maxima or singularities were produced. Thus, in this paper, numerical calculations are carried
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out by using more accurate experimental data. Comparing the results with the partial molar volume of the solutes, we are going to discuss correlation between the surface and bulk structures.
2. Determination of the surface excess The surface tension data of several alcohol–water mixtures at 25 ◦ C were collected from Refs. [5–11]. These are shown as the closed symbols in Figs. 1b–6b. The fitting values in the Connors equation [12] that Lavi et al. used are slightly off from the experimental data and these differences make the position of maxima away from their original one in the derivatives of γ . We decided, therefore, to take a numerical method by using the original experimental data. On the other hand, the activity data at 25 ◦ C shown as the open circles were calculated from the partial vapor pressure ∗ , where p is the partial vapor pres[13,14] as aal = pal /pal al ∗ is the vapor pressure sure of alcohol in the solution and pal of pure alcohol. The crosses are data from DECHEMA [15] that Lavi et al. used. The data taken from Refs. [13,14] have much more data points that will give the adsorption isotherm with higher accuracy. The solid curves are the best fit of them
with the van Laar equation [16], 2 Axal aal = xal exp A 1+ , B(1 − xal )
(2)
where xal is the mole fraction of alcohol and A and B are empirical constants as fitting parameters. They fit very well to the data for methanol, ethanol, and 2-propanol as shown in Figs. 1b, 2b, and 3b, while not so well around the inflection points for 1-propanol and tert-butanol in Figs. 3b and 5b. We calculated Γalwa , shown as the closed circles in
Fig. 2. (a) Adsorption isotherm of ethanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for ethanol–water mixtures at 25 ◦ C: (") Ref. [7], (Q) Ref. [5], (a) Ref. [6], (!) Ref. [13], (×) Ref. [15].
Fig. 1. (a) Adsorption isotherms of methanol–water mixtures at 25 ◦ C. The closed circles were calculated using the data in (b) and the continuous dashed curve is a guide for the eyes. The scale on the right-hand side is the corresponding molecular area of the surface excess solute. The horizontal dash-dotted line corresponds to Γalwa of a monolayer. The vertical dash-dotted arrow is the mole fraction of the minimum in the excess partial molar volume of the solute and it coincides with that corresponding to the maximum of the adsorption isotherm. The shaded area is the range of transition where the hydrophobic hydration is lost (see text). (b) Mole fraction xal dependence of surface tension γ and activity aal for methanol–water mixtures at 25 ◦ C: (") Ref. [5], (!) Ref. [13], (×) Ref. [15]. The solid curve is the van Laar fit of aal , whereas the dashed line corresponds to the ideal aal . The dotted line is drawn using Eq. (3).
Fig. 3. (a) Adsorption isotherm of 1-propanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for 1-propanol–water mixtures at 25 ◦ C: (") Ref. [7], (a) Ref. [8], (!) Ref. [13], (×) Ref. [15].
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Fig. 4. (a) Adsorption isotherm of 2-propanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for 2-propanol–water mixtures at 25 ◦ C: (") Ref. [5], (a) Ref. [9], (!) Ref. [13], (×) Ref. [15].
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Fig. 6. (a) Adsorption isotherm of 1-butanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. The vertical dash-dotted arrow shows not only the mole fraction of the minimum in the excess partial molar volume of 1-butanol, but also the solubility limit. (b) Mole fraction xal dependence of surface tension γ and activity aal for 1-butanol–water mixtures at 25 ◦ C: (") Ref. [10], (—) Ref. [17].
dash-dotted lines) indicates that the excess alcohols form a monolayer because it approximately corresponds to the area per CH2 chain in close-packed configuration.
3. Results 3.1. Methanol and ethanol
Fig. 5. (a) Adsorption isotherm of tert-butanol–water mixtures at 25 ◦ C. See the caption of Fig. 1 for details. (b) Mole fraction xal dependence of surface tension γ and activity aal for tert-butanol–water mixtures at 25 ◦ C: (") Ref. [11], (!) Ref. [14], (×) Ref. [15].
Figs. 1a–6a, numerically by using the raw data points of γ and the corresponding values of aal obtained by the leastsquares fit of Eq. (2). In the case of 1-propanol, 2-propanol, and tert-butanol, we also calculated by using a polynomial fit of aal near the inflection points to avoid artificial errors and drew them as the dashed curves. For 1-butanol, we used the NRTL equation (shown as the solid curve) with parameters at 25 ◦ C taken from Ref. [17] that Lavi et al. used. The scales on the right-hand side of Figs. 1a–6a are the molecular area of alcohol calculated from the inverse of Γalwa . The molecular area of 20 Å2 (shown as the horizontal
Figs. 1 and 2 show the activity, aal , surface tension, γ , and calculated surface excess, Γalwa , at 25 ◦ C for methanol and ethanol aqueous solutions, respectively. The dashed straight lines are aal for the ideal solutions that obey Henry’s law. For methanol, aal is almost ideal over the entire concentration. On the other hand, the deviations from ideality are quite substantial for ethanol. For these two alcohols, the van Laar equation describes the experimental data very well. The Γalwa for ethanol calculated using a van Laar fit reproduced the previous works [6,18,19] very well. The surface tension decreases with the mole fraction of alcohol. This rapid decrease is typical for the aqueous system with surface-active solutes and this character increases with the length of the hydrocarbon chain. Therefore, the surface excess of alcohol Γalwa for ethanol increases more rapidly than that for methanol as shown in Figs. 1a and 2a. For both of them, the maximum values are around 0.8 × 10−5 mol/m2 (denoted by the horizontal dash-dotted lines) corresponding to a monolayer. For ethanol, this result is supported by the neutron reflection study, which directly observed a surface monolayer completed near xal = 0.1 [18]. We recognize that the mole fraction of the maximum Γalwa exactly coincides with that corresponding to the minimum
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in the excess partial molar volumes of alcohols reported in Refs. [3,20], as shown by the vertical arrows in these figures. This is very striking because both the Γalwa and aal curves are smooth at these mole fractions. 3.2. 1-Propanol, 2-propanol, and tert-butanol Clear inflection points in the aal curves of these three mixtures appear in Figs. 3b–5b. The derivatives of aal become very small at xal ≈ 0.2 and they are much smaller for 1-propanol and tert-butanol than for 2-propanol. This behavior is very similar to that predicted for a typical surfactant under micelle formation [21]. Actually, Debye’s correlation lengths (i.e., radii of the space distribution of the fluctuation of electron density) obtained by small-angle X-ray scattering measurements show maxima around this concentration due to the formation of micelle-like aggregates for 1-propanol and clathrate–hydrate-like aggregates for tertbutanol and 2-propanol [22]. Except for 2-propanol, the van Laar equation does not describe the experimental data very well around xal ≈ 0.2. The NRTL equation, which has more advantage in consideration with the interaction between two components gave almost the same curves. The deviations from the experimental data caused by a van Laar fit make the values of Γalwa around xal ≈ 0.2 scatter. We also tried a polynomial fit near the inflection points and confirmed that neither the maximum for 2-propanol nor singularities for 1-propanol and tert-butanol around xal ≈ 0.2 reported by Lavi et al. existed. They were probably caused by underestimation of ∂aal /∂xal . We drew the dashed curves as guides for eyes that were also considered with the polynomial fits. All of the adsorption isotherms rapidly increase and show a maximum at xal = 0.07 for 2-propanol and at xal = 0.04 for others. The maxima also coincide with the minima in the excess partial molar volumes of alcohols [23,24] denoted by the arrows as described above. 3.3. 1-Butanol In a series of n-alcohols in increasing order of the number of carbon atoms, 1-butanol is the first that exhibits a limited solubility in water. Phase separation occurs at xal = 0.018 and 25 ◦ C. The partial molar volume of 1-butanol decreases with its mole fraction and shows the minimum at the phase boundary [25]. The activity data shown as the solid line in Fig. 6b is the NRTL equation with the parameters at 25 ◦ C taken from DECHEMA [17]. It slightly deviates from a straight line near the phase boundary. The absorption isotherm shows a saturation state expected from the monolayer type of Langmuir adsorption isotherm observed typically in aqueous solutions of a surfactant. Li et al. reproduced the adsorption isotherm well by the neutron reflection measurements, and furthermore, they speculated that the structure of the monolayer was rough, since the observed thickness was larger than the molecular length [26].
4. Discussion All of the adsorption isotherms in Figs. 1a–6a show similar behavior. First, Γalwa increases with the alcohol mole fraction and then decreases (except for 1-butanol). This is very reasonable because the surface excess of solute decreases with xal beyond the maximum and should be zero for the pure solute. Actually, none of them reaches zero due to continuous decrease observed in γ . Second, the maximum values of Γalwa for all mixtures are around 0.8 × 10−5 mol/m2 corresponding to a monolayer. It had been already known in the early 20th century that the most of the surface excess n-alcohols form monolayers at some concentration [27]. Third, the mole fraction of the maximum Γalwa exactly coincides with that corresponding to the minimum in the excess partial molar volumes of alcohols (we hereafter call the mole fraction xal∗ ). This is very interesting discovery because the molecular space of alcohols both in the bulk and the surface show minima simultaneously! This implies that there exists some correlation between the surface and bulk structures. In the case of BE not shown here, the mole fraction of the minimum in the excess partial molar volumes of BE [28] also is located near that corresponding to the Γalwa of a monolayer that is about half of its maximum value. To explain about the third behavior, we are going to discuss what the maximum Γalwa is caused by. Addison mentioned that below the γ of 55 mN/m, the γ is a linear function of the logarithm of concentration for each n-alcohol, and this part of the curve is represented by the relation γ = α − β log xal ,
(3)
where α and β are constants [27]. The β value is constant irrespective of chain length and has the value β = γw B, with B = 0.407 and the surface tension of pure water γw . This is why all of the alcohols show the same maximum value of Γalwa . In fact, |dγ /d log xal | for all of the solutions, as shown in Figs. 1b–6b, increases with the alcohol concentration and is equal to β (the dotted lines) at the maximum, and then abruptly becomes small. It is very important to notice that dγ /d log xal = −β at xal∗ . Additionally, aal starts to turn below the straight dashed line at xal∗ for all of the alcohols. The maximum Γalwa is, therefore, found to be caused by these two factors: the largest dγ /d log xal and d log aal < d log xal . In other words, xal∗ is the mole fraction at which the solutions starts to deviate from ideal. In the case of tert-butanol, Omelyan reported that the concentration xal∗ ≈ 0.03 corresponds to that the solute alcohols filling up the cavity in the solvent water start to aggregate [29]. In the present study, we find that the surface monolayer completes at xal∗ . Recently, Koga et al. proposed that hydrophobic hydration (they used the word “iceberg formation”) locally enhances the hydrogen bond network but associates with the reduction of the hydrogen bond probability of bulk H2 O that are relatively far away from solutes [23,30]. And they
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clarified the ranges of transition where the percolation of hydrogen bond network (i.e., the continuous hydrogen-bonded network formed by water molecules) is lost. They are shown as shaded areas in Figs. 1–5. The width of these ranges gives the strength of the effect of alcohol on water—the narrower is the stronger. The order of relative hydrophobic nature of alcohols established by Koga et al. as methanol < ethanol < 2-propanol < 1-propanol < tert-butanol < BE is also observed in the order of xal∗ . It is interesting to notice that all of the curves of surface tension break like the critical micelle concentration for surfactants at the end point of these ranges as shown in Figs. 1b–5b. We consider that the aggregations of the solute alcohols formed at xal∗ grow and finally destroy the percolation of hydrogen bond network (hereafter HBN) at this concentration. As a result, the surface excess of the solute alcohols decreases, because it is no longer necessary for covering the surface with the solutes when the molecular interactions in the bulk weaken. In the case of the interfaces of mutually saturated aqueous 1-butanol solutions studied by Monte Carlo simulations, a dense 1-butanol monolayer remained at the surface of the water-rich phase, in contrast with no enrichment of water at the surface of the 1-butanolrich phase [31]. This result also supports the idea that the surface monolayer forms only when the percolation of HBN in water is retained.
5. Summary and conclusions We performed a demonstration of the adsorption isotherms of several alcohol–water mixtures (methanol, ethanol, 1-propanol, 2-propanol, tert-butanol, 1-butanol) calculated using surface tension and vapor pressure data taken from the literature. For all of the alcohols, the value of the maximum in the adsorption isotherm indicates the formation of a monolayer and this concentration coincides with that corresponding to the minimum in the excess partial molar volume of the alcohol. This also coincides with the bulk solution losing ideality. Furthermore, the critical micelle concentrationlike breaks are also observed in the surface tension at which the hydrogen bond percolation is lost. From these observations, we conclude that a correlation really exists between the surface and bulk structures of alcohol–water mixtures as summarized below. In dilute alcohol aqueous solutions, hydrophobic hydration induces a surface excess of the alcohol. When a monolayer is completely formed, the solute molecules, either on the surface or in the bulk, feel tightest and the bulk solution starts to lose ideality; that is, the solute molecules starts to aggregate. Gradually, the hydrogen bond network in water is destroyed by the growing aggregations. Consequently, the surface excess decreases as the molecular interactions in bulk weaken.
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Acknowledgments The author is grateful for helpful discussions with Professor Takao Iijima of Gakushuin University and Professor Yoshikata Koga of the University of British Columbia.
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