ARTICLE pubs.acs.org/JPCC
Concentration-Induced Wetting Transition in WaterTetrahydrofuranIsobutane Systems Lars Boewer, Michael Paulus, Felix Lehmk€uhler,*,† and Metin Tolan Fakult€at Physik/DELTA, Technische Universit€at Dortmund, Maria-Goeppert-Mayer-Str. 2, D-44227 Dortmund, Germany ABSTRACT: The pressure-dependent wetting of isobutane at the aqueous tetrahydrofuran (THF) solutionisobutane interface was studied by means of X-ray reflectivity measurements. Using pure water and mixtures at low THF concentrations, a completely wetting isobutane layer is adsorbed onto the substrate. The pressuredependent layer thickness can be described by a simple adsorption isotherm. In contrast, the formation of thick layers with low electron density is observed at high THF concentrations. The film growth shows an unpredictable behavior. This finding can be explained by the formation of partially wetting isobutane droplets on the water/THF substrate caused by a decrease of the liquid’s surface tension with increasing THF concentration.
’ INTRODUCTION The knowledge of the structure of gasliquid interfaces is relevant for both technology and fundamental research. Especially, the formation of thin liquid films and their wetting behavior has been under examination in the past years.15 In particular, wetting and wetting transitions of alkanes on water systems are the subject of various experimental610 and theoretical11,12 studies. Wetting transitions from partial to complete wetting and vice versa typically have a first-order character, including, for example, hysteresis effects, but deviations were reported resulting in more complicated wetting transitions and phases.13,14 In the case of a bare interface between a liquid substrate and a gaseous phase, gas molecules are adsorbed onto the substrate’s surface, forming a thin complete wetting layer.3 Assuming van der Waals interactions between the substrate and the gas phase, the interface is mathematically described by the interfacial free energy per unit area ! Aeff p0 þ dΔFkB T ln ð1Þ F ¼ γ1 þ γ2 12πd2 p where γ1 and γ2 are the surface tensions of the substrate and the adsorbed layer, respectively; Aeff the effective Hamaker constant, which is a measure of the interaction between the substrate and the gas;15 d the thickness of the layer; ΔF the density difference between adsorbed and the gas phase; p the gas pressure; and p0 the condensation pressure of the gas at temperature T. In Figure 1, the free energy is shown as a function of layer thickness d. The different curves correspond to different gas pressures p. The adsorption of stable layers requires minima of F. This results in an adsorption isotherm, a so-called a FrenkelHalseyHill (FHH) isotherm1618 !1=3 Aeff dðpÞ ¼ ð2Þ 6πΔFkB T logðp=p0 Þ An increase of the absolute value of the Hamaker constant leads to an increase of F at fixed d and vice versa. Changes of the surface tensions r 2011 American Chemical Society
lead to a shift of F only; the layer thickness at a given pressure is not affected. In this scenario, a complete wetting is possible for negative Hamaker constants only while the surface and interfacial tensions are not considered. In contrast, following Young’s equation,13 only interfacial and surface tensions of the attending phases determine the wetting state; the Hamaker constant is not taken into account. In both models, wetting transitions can be described by either a change of the sign of Aeff or a change of the interfacial or surface tensions. In this paper, we study the wetting transition at the water/THF isobutane interface in order to test both wetting models. For a detailed investigation of such interfaces, experimental techniques providing high resolution are necessary. X-ray reflectivity or ellipsometry can provide adequate data and are thus frequently used. The advantage of X-ray reflectvity is the possibility to study interfacial density profiles normal to the surface,19 in particular, surface and interface roughness of liquids with sub-angstrom resolution. Furthermore, X-ray reflectivity allows extreme sample conditions and environments, such as high-pressure sample cells to study pressuredependent gas adsorption.4 The Hamaker constant of a given sample system can be calculated based on Lifshitz theory to15 εsub εlay 3 Aeff th ≈ kB T 4 εsub þ εlay
!
εgas εlay εgas þ εlay
!
ðn2sub n2lay Þ 3 þ hνe pffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiqffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3 8 2 n2 þ n2 n2 þ n2 sub
lay
gas
lay
ðn2gas n2lay Þ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð n2sub þ n2lay þ n2gas þ n2lay Þ
ð3Þ
Received: May 19, 2011 Revised: June 30, 2011 Published: August 11, 2011 18235
dx.doi.org/10.1021/jp204663w | J. Phys. Chem. C 2011, 115, 18235–18238
The Journal of Physical Chemistry C
ARTICLE
Figure 1. Free energy as a function of layer thickness for different pressures (blue, high pressure; red, low pressure). The minima are shown as black circles.
Figure 2. Calculated effective Hamaker constant of the water/ THFisobutane system as a function of THF concentration. Aeff becomes negative above 5.5 mol % THF.
Here, nsub, nlay, and ngas are the indexes of refraction of the substrate, layer, and gas, respectively, at a wavelength of 589 nm; εsub, εlay, and εgas are the accompanying static dielectric constants; and νe ≈ 3 1015 Hz.15 To determine the wetting state of the water/THFisobutane system, we used literature values,20 yielding a positive effective Hamaker constant of Aeff = 1.1 1021 J, suggesting only partial wetting of isobutane on pure water. For THFwater mixtures, the corresponding values were interpolated from literature values.20,21 With increasing THF fraction, the Hamaker constant decreases and changes sign at a concentration of cTHF ≈ 5.5 mol %, indicating a transition from partial to complete wetting. The calculated Hamaker constant is shown in Figure 2. In contrast, the thermodynamic interpretation via the interfacial tensions of the involved phases suggests a complete wetting at low THF concentration considering an interfacial tension between water and liquid isobutane of γw/i = 50.0 mN/m at T = 290 K from interpolation of interfacial tensions of alkanes.22,23 Because the surface tension of water/THF mixtures drops rapidly with increasing THF fraction,24 following Young’s equation, the wetting state is expected to change from complete to partial wetting by increasing the THF fraction in the mixture. Unfortunately, data on interfacial tension of water/THF mixtures and alkanes are missing so that the fraction of THF that results in a concentration-induced wetting transition cannot be estimated beforehand. We used X-ray reflectivity to study the adsorption of isobutane onto the surface of water and water/THF mixtures as a function of gas pressure. For water and low concentrations of THF (cTHF ≈ 1 mol %), we found the formation of complete wetting films that can be modeled by an adsorption isotherm. In contrast, at THF concentrations around 5 mol %, thick adsorbed layers with a significantly lower electron density compared with liquid isobutane are formed at pressures well below the condensation pressure of isobutane. These layers are in fact isobutane islands caused by the partial wetting state.
profile of surfaces and interfaces. In an X-ray reflectivity experiment, the intensity of a reflected X-ray beam is measured as a function of the wave vector transfer qz = (4π)/(λ) sin(αi) normal to the sample surface. Here, λ denotes the wavelength and αi the incident angle. In the first Born approximation, the reflectivity R of a surface is given by
’ EXPERIMENT X-ray reflectivity is an interface-sensitive scattering technique that provides information on the laterally averaged electron density
Z 2 1 dFðzÞ Rðqz Þ ¼ RF ðqz Þ expðiqz 3 zÞdz Fs dz
ð4Þ
with the electron density profile F(z), the electron density of the substrate Fs, and the Fresnel reflectivity RF.19 Thus, the density profile of the sample surface is accessible with subnanometer resolution. The measurements were carried out at the beamline BW1 at DORIS III (DESY) using an X-ray scattering setup for liquid surfaces.25 The wavelength of the X-rays was λ = 1.304 Å. Furthermore, additional X-ray reflectivities were recorded using a Bruker AXS Advance diffractometer at a wavelength of 1.54 Å. For pressure-dependent measurements, a stainless steel sample cell was used, which allows gas pressures up to 6 bar (for details, see ref 3). The water (ultrapure, resistivity = 18.2 MΩ 3 cm) and water/THF mixtures were placed on a stainless steel plate with a diameter of 12 cm. This allows the formation of flat liquid surfaces, not disturbed by a meniscus. The water depth was about 1 mm. Water/THF mixtures were prepared with 1, 4.5, and 5.9 mol % THF (purity > 99.9%, Sigma Aldrich) fractions. After closing the cell, it was flushed by gaseous nitrogen in order to remove the air. Subsequently, a reflectivity of the waternitrogen interface was recorded to measure the roughness of the water surface without an adsorbed layer. Afterward, the cell was flushed with isobutane (purity > 99.95%, Messer) and reflectivities at different gas pressures between 1 bar and the respective condensation pressure of isobutane were recorded. The temperature was set to 290.15 K and was stabilized by a Lakeshore temperature controller with an accuracy of ΔT = ( 0.02 K. This temperature leads to a condensation pressure of p0 = 2.75 bar. To obtain the truely reflected signal, the diffusely scattered radiation— predominantly originating from the dense gas atmosphere—was 18236
dx.doi.org/10.1021/jp204663w |J. Phys. Chem. C 2011, 115, 18235–18238
The Journal of Physical Chemistry C
Figure 3. Pressure-dependent X-ray reflectivities of the water/THF isobutane system at cTHF = 5.9%. Solid lines represent fits. The pressures vary from 1 (red) to 2.6 bar (blue). The black circles represent the measurement at 2.7 bar, where a macroscopic thick layer was found.
measured by a detector offset of 0.1° with respect to the specular condition. The pressure stability during one reflectivity scan, including the measurement of the diffusely scattered signal, was Δp = 0.02 bar. Because of the small expected layer thicknesses, an effective density model in combination with the well-known Parratt algorithm was applied to model the electron density profiles.19,26
’ RESULTS AND DISCUSSION Similar to previous experiments on watergas interfaces,4,8 the waterisobutane interface exhibits the adsorption of isobutane on the water surface. The thickness of the adsorbed layer increases with rising pressure. A fit of the adsorption isotherm following eq 2 yields an effective Hamaker constant of Aeff,0 = (8.0 ( 0.5) 1021 J. Here, the small increase of layer thickness due to capillary wave motion of the interface was also taken into account.3 Analogous results were found for the measurements at 1 mol % THF concentration. Again, isobutane adsorbes onto the surface, yielding a complete wetting layer. The effective Hamaker constant for this system can be refined to Aeff,1 = (1.2 ( 0.1) 1020 J. However, contrary to the prediction of eq 3, the constant is negative in both cases, and complete wetting was observed. This is supported by the measured electron density of the layer that equals the density of liquid isobutane. Nevertheless, it is in line with Young’s equation by comparing interfacial and surface tensions of the accompanying substances. This situation changes at high THF concentrations. Corresponding reflectivity data are shown in Figure 3. The data are normalized by the Fresnel reflectivity RF. With increasing pressure, first, the reflectivity drops rapidly. Oscillations are visible, becoming more pronounced at high pressures. Such oscillations indicate a growing layer at the liquid gas interface. The electron density profiles for the whole series are shown in Figure 4. The profiles are normalized to the water density. In contrast to water and low THF concentrations, the electron densities of the layers are well below the density of liquid isobutane, which is expected in the case of complete wetting due to adsorption.3 X-ray reflectivity experiments probe the laterally averaged density profile so that such low electron densities can only be originated
ARTICLE
Figure 4. Electron density profiles of the water/THFisobutane system at high THF concentrations of one experimental run at cTHF = 5.9%. The colored curves show the density profiles between 1 and 2.55 bar of isobutane (red to blue), indicating a growing film with increasing pressure up to d = 59 Å. The dashed black line shows the density profile for 2.6 bar of isobutane, the dashed-dotted black line the density profile after raising the pressure above 2.6 bar. The solid black line represents the reference density profile with 1 bar of nitrogen as the gas phase. The horizontal thin black dashed line marks the electron density of liquid isobutane.
by the presence of an additional component with a lower density than liquid isobutane. Because the densities of THF and water are larger than that of liquid isobutane, we conclude that, instead of a closed adsorbed layer, partially wetting islands are formed. After increasing the pressure to 2.6 bar, which is still well below the condensation pressure of isobutane, a thick layer of approximately 97 Å in thickness is formed. It is remarkable that also its density increases (see Figure 4) but does not exceed the density of liquid isobutane. As such thicknesses at the applied pressure cannot be understood in the framework of pure gas adsorption, we conclude that the formed partially wetting islands are growing rapidly at this pressure. A further increase of pressure leads to smooth reflectivity curves (black circles in Figure 3) without any oscillations. Thus, only one single interface was resolved by the reflectivity experiment. In addition, the electron density of this surface is decreased compared to water, but still higher than that in liquid isobutane. Therefore, we interpret this finding as a very thick layer that wets the substrate completely. Regarding the resolution of our setup, the layer thickness is in the region above 3000 Å. However, due to the fact that the density is higher than the density of pure liquid isobutane, we assume that it consists of a mixture of THF and isobutane. The experiment was repeated several times for the two high concentrations, leading to large thicknesses in each run. In Figure 5, the measured layer thicknesses, which are obtained by the fits of the reflectivity curves, are shown as a function of gas pressure. As mentioned above, for water and low THF concentrations (1 mol % in this case), an adsorption isotherm could be fitted to the data (black circles and green diamonds). The data for the high THF concentrations demonstrate that the pressure at which the thickness increases drastically is found to vary for each run, although the sample preperation and experiment conditions were all the same. It is important to note that the divergency of 18237
dx.doi.org/10.1021/jp204663w |J. Phys. Chem. C 2011, 115, 18235–18238
The Journal of Physical Chemistry C
ARTICLE
’ REFERENCES
Figure 5. Layer thickness as a function of pressure for water, 1 mol % THF, and high THF concentrations. Each run is represented by the same symbol (triangles, circles, diamonds). The black and blue solid lines are fits of eq 2, while the red solid lines are guides to the eyes.
layer thickness was observed in every experimental run if high THF concentrations were used, but the pressure where this divergency sets in seems to be stochastic. Furthermore, a complete wetting following eq 2 fails to describe the data because the constant p0, which actually represents the condensation pressure, varies for each measurement.
’ CONCLUSION We studied the wetting behavior of isobutane at water/ THFisobutane interfaces by means of X-ray reflectivity. Pure water and water/THF mixtures at low THF concentrations as substrates result in adsorption of completely wetting isobutane layers. At THF concentrations between 4.5 and 6 mol %, we found the formation of partially wetting islands. At a certain pressure threshold, which is quite below the condensation pressure of isobutane, the island thicknesses show a rapid gowth and an accumulation of THF. Thus, a transition from complete to partial wetting by increasing the THF concentration and pressure was detected. Our finding is a contradiction to the theoretical model for the effective Hamaker constant,15 but it can be understood by taking into account the change of interfacial tensions. The increase of THF in the substrate lowers the surface tension so that complete wetting becomes impossible. Afterward, the adsorbed islands grow until they merge to a macroscopic thick closed layer.
(1) Bonn, D.; Kellay, H.; Wegdam, G. H. Phys. Rev. Lett. 1992, 69, 1975–1978. (2) Ragil, K.; Meunier, J.; Broseta, D.; Indekeu, J. O.; Bonn, D. Phys. Rev. Lett. 1996, 77, 1532–1535. (3) Paulus, M.; Gutt, C.; Tolan, M. Phys. Rev. E 2005, 72, 061601. (4) Lehmk€uhler, F.; Paulus, M.; Sternemann, C.; Lietz, D.; Venturini, F.; Gutt, C.; Tolan, M. J. Am. Chem. Soc. 2009, 131, 585–589. (5) Bonn, D.; Eggers, J.; Indekeu, J.; Meunier, J.; Rolley, E. Rev. Mod. Phys. 2009, 81, 739–805. (6) Rafai, S.; Bonn, D.; Bertrand, E.; Meunier, J.; Weiss, V. C.; Indekeu, J. O. Phys. Rev. Lett. 2004, 92, 245701. (7) Kwon, O.-S.; Jing, H.; Shin, K.; Wang, X.; Satija, S. K. Langmuir 2007, 23, 12249–12253. (8) Paulus, M.; Gutt, C.; Tolan, M. Surf. Interface Anal. 2008, 40, 1226–1230. (9) Bertrand, E.; Dobbs, H.; Broseta, D.; Indekeu, J. O.; Bonn, D.; Meunier, J. Phys. Rev. Lett. 2000, 85, 1282–1285. (10) Pfohl, T.; Riegler, H. Phys. Rev. Lett. 1999, 82, 783–786. (11) Weiss, V. C. J. Chem. Phys. 2006, 125, 084718. (12) Boinovich, L. B.; Emelyanenko, A. M. Russ. Chem. Bull., Int. Ed. 2008, 57, 263–273. (13) Bonn, D.; Ross, D. Rep. Prog. Phys. 2001, 64, 1085–1163. (14) Bonn, D.; Bertrand, E.; Shahidzadeh, N.; Ragil, K.; Dobbs, H. T.; Posazhennikova, A. I.; Broseta, D.; Meunier, J.; Indekeu, J. O. J. Phys.: Condens. Matter 2001, 13, 4903–4914. (15) Israelachvili, J. Intermolecular & Surface Forces; Academic Press: San Diego, CA, 2000. (16) Frenkel, J. Kinetic Theory of Liquids; Oxford University Press: New York, 1946. (17) Halsey, G. D. J. Chem. Phys. 1948, 16, 931–937. (18) Hill, T. L. J. Chem. Phys. 1949, 17, 590. (19) Tolan, M. X-ray Scattering from Soft-Matter Thin Films; Springer: Berlin, 1999. (20) Lide, D. R., Ed. CRC Handbook of Chemistry and Physics, 84th ed.; CRC Press: Boca Raton, FL, 20032004. (21) Nayak, J. N.; Aralaguppi, M. I.; Kumar Naidu, B. V.; Aminabhavi, T. M. J. Chem. Eng. Data 2004, 49, 468–471. (22) Mitrinovic, D. M.; Tikhonov, A. M.; Li, M.; Huang, Z.; Schlossman, M. L. Phys. Rev. Lett. 2000, 85, 582–585. (23) Zeppieri, S.; Rodríguez, J.; Lopez de Ramos, A. L. J. Chem. Eng. Data 2001, 46, 1086–1088. (24) Cheong, W. J.; Carr, P. W. J. Liq. Chromatogr. Relat. Technol. 1987, 10, 561–581. (25) Frahm, R.; Weigelt, J.; Meyer, G.; Materlik, G. Rev. Sci. Instrum. 1995, 66, 1677–1680. (26) Parratt, L. G. Phys. Rev. 1954, 95, 359–369.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected]. Present Addresses †
Deutsches Elektronen Synchrotron (DESY), Notkestr. 85, 22607 Hamburg, Germany.
’ ACKNOWLEDGMENT The authors thank Bernd Struth for technical support and HASYLAB (DESY Hamburg) for providing synchrotron radiation. 18238
dx.doi.org/10.1021/jp204663w |J. Phys. Chem. C 2011, 115, 18235–18238
