Langmuir 1997, 13, 2167-2170
2167
Notes Surface Composition Studies on (n-Hexane + Perfluoro-n-hexane) by Specular Neutron Reflection James Bowers, Ian A. McLure,* and Richard Whitfield Department of Chemistry, The University, Sheffield S3 7HF, U.K. Andrew N. Burgess and Archibald Eaglesham ICI Chemicals and Polymers, The Heath, Runcorn, Cheshire WA7 4QD, U.K. Received July 24, 1995. In Final Form: August 2, 1996
Introduction According to the Gibbs adsorption isotherm, GAI, at constant temperature T the relative adsorption Γ2,1 in a binary liquid mixture of components 1 and 2swith 2 the less tense or lower surface tension componentsis given by
Γ2,1 ) -x2(∂σ/∂x2)T/[RT(1 + x2(∂ ln γ2/∂x2)T)]
(1)
where σ is the surface tension, γ2 is the bulk activity coefficient, usually calculated from vapor pressure data, and x2 is the mole fraction of component 2. The symmetrical quantity Γ2,1/x2 has been termed the total surface segregation, TSS.1 At the critical end point, CEP, of a binary liquid mixture two coexisting liquid phases β and γ, say, merge identity to become a single liquid phase βγ in the presence of a coexisting vapor. At the CEP both the numerator and denominator of eq 1 vanish. It is a necessary condition for phase separation that the denominator vanishes, and the identification that ∂σ/∂x2 ) 0 at the CEP was first made by Widom2 and has subsequently been substantiated by experiment and other theories.3 The quantity Γ2,1 behaves along the critical isotherm according to
Γ2,1 ∼ |x2 - x2,c|-0.934
(2)
such that the limiting value is infinity at the CEP; the theoretical treatment of this has been given elsewhere.1,4 Since TSS ) Γ2,1/x2 ) (Γ2/x2) - (Γ1/x1) and all the other quantities are positive and both x1 and x2 are nonzero, the simplest interpretation of the divergence Γ2,1 is therefore that Γ2 itself diverges and so, in effect, a layer of “infinite” thickness is formed at the critical composition x2,c. This phenomenon is known as critical adsorption and was originally predicted by Fisher and de Gennes.5 (Alkane + perfluoroalkane) mixtures are almost unique among nonpolar mixtures in exhibiting large positive deviations from ideality usually attributed to uniquely * To whom correspondence should be addressed. (1) McLure, I. A.; Soares, V. A. M.; Williamson, A.-M. Langmuir 1993, 9, 2190. (2) Widom, B. J. Chem. Phys. 1977, 67, 872. (3) For example see: Bowers, J.; McLure, I. A. Langmuir 1996, 12, 3326 and references therein. (4) Rowlinson, J. S.; Widom, B. Molecular Theory of Capillarity; Clarendon Press: Oxford, 1982. (5) Fisher, M. E.; de Gennes, P. G. C R. Acad. Sci. (Paris), Ser. B 1978, 287, 207.
S0743-7463(95)00611-1 CCC: $14.00
weak unlike molecular forces; the nonideality is most manifest in the partial miscibility common up to temperatures near the normal boiling point. This research note presents the results of a pilot study of neutron reflectivity measurements on the surface of the (n-hexane + perfluoro-n-hexane) mixture across the composition range close to its upper critical end point temperature, TUCS ) 22.86 °C.6 The coexistence curve for this mixture shown in Figure 1, identifying the CEP, and the experimental path chosen in this study is based on the measurements of Bedford and Dunlap,7 who measured the critical temperature as 22.65 °C. The small discrepancy between the two values of TUCS is not uncommon in accounts of alkane + perfluoroalkane mixtures; although irrelevant to our present purposes, it will be addressed at a later date. The wetting characteristics of (alkane + perfluoroalkane) mixtures are not yet wholly characterized experimentally. Of the most likely reporter techniques, ellipsometry and neutron reflectivity, the former lacks the simple relationship between refractive index and structure profiles which the latter enjoys. Specifically, the neutron reflectivity experiment yields results from which the composition profile normal to the interface can be modeled to within a single-angstrom resolution. The chief aim of this study was to use specular neutron reflectivity profiles to trace the onset of the critical adsorption at the liquid-vapor interface and to identify the nature of the adsorbed species. Materials and Methods The experiment was conducted on the neutron reflectometer CRISP at the ISIS spallation source at the Rutherford-Appleton Laboratory (Oxfordshire). The details of neutron reflectivity experiments are given elsewhere.8 We have eschewed for now the opportunity to employ deuterium substitution in the hexane to highlight structural details, since we have discovered a marked isotope effect on TUCS which introduces unwelcome complications into the experiment. Particularly, the opportunity is lost to reduce the reflectivities from the isotopically substituted mixtures to a common model basis. Materials. The n-hexane was obtained from Aldrich Chemical Co. (+99%), and the perfluoro-n-hexane, 99% (85% n-isomer), from Fluorochem Ltd. Both were used without further purification. Mixtures. The mixtures were prepared by mass to a prescribed perfluoro-n-hexane mole fraction x2. Before transferring the mixture, it was warmed gently until it formed a single liquid phase. Sample Environment. The mixtures were contained within open Teflon troughs, mounted within stainless-steel blocks. The troughs were located inside a common aluminum housing assembly and maneuvred across the path of the incident neutron beam using remote-control servo motors. Although the trough holders could be partially-sealed using Viton O-rings, some evaporation of the relatively volatile components proved to be a problem during the course of these measurements. Close temperature management was also of some concern due to the demanding requirements of the near-critical system. The temperature of the experiment was thus set at 24.5 °C, sufficiently distant from the TUCS to avoid accidental phase separation. The trough used carried no provision for sample stirring when the cell was closed; mixing was therefore limited to manual stirring (6) Block, T. E.; Judd, N. F.; McLure, I. A.; Knobler, C. M.; Scott, R. L. J. Phys. Chem. 1981, 85, 3282. (7) Bedford, R. D.; Dunlap, R. G. J. Am. Chem. Soc. 1958, 80, 282. (8) Penfold, J.; Thomas, R. K. J. Phys. Condens. Matter 1990, 2, 6024.
© 1997 American Chemical Society
2168 Langmuir, Vol. 13, No. 7, 1997
a
Notes beforehand. Bearing such inadequacies in mind, we can realistically attribute an accuracy of ca. (0.05 to the volume fractions of the prepared mixtures, since for this particular mixture the two components have very similar vapor pressures and the mixture itself exhibits a pronounced very broad azeotrope in the vapor pressure isotherm.9
Results and Discussion The reflectivity profiles were measured at T ) 24.5 °C, just above the two-liquid-phase region. Figure 2 shows some reflectivity spectra for mixtures (a) rich in n-hexane (x2 ) 0.115), (b) at the critical composition (x2 ) 0.36), and (c) rich in perfluoro-n-hexane (x2 ) 0.812). Since these reflectivity spectra are relatively featureless, it is critical that the model used in the fitting procedure be thermodynamically valid. Although the outcomes presented here are unlikely to be unique, we have found that essentially one model only could be found which was consistent both with the observed reflectivity and with the expected thermodynamics of the mixture. The results tabulated in Table 1 were inverted from the reflectivities using the optical matrix method. The neutron-scattering length densities for n-hexane and perfluoro-n-hexane were calculated to be Nbh ) -0.05 × 10-5 Å-2 and Nbf ) 0.354 × 10-5 Å-2, respectively, using the densities of 0.65 g‚cm-3 for n-hexane and 1.67 g‚cm-3 for perfluoro-n-hexane. The volume fraction, φ2, of perfluoro-n-hexane derived from the reflectivity data was calculated using eq 3.
φ2(Nbf) + (1 - φ2)(Nbh) ) (Nbm)
b
Figure 1. (T-x2) (a) and (T-φ2) (b) coexistence curves for (n-hexane + perfluoro-n-hexane) near the upper critical end point, UCEP. The CEP is marked b together with the thermodynamic conditions which specify it, i.e. the critical temperature TUCS and the critical composition x2,c. The figure also identifies the one-(1L) and two-liquid-phase regions (2L) and the experimental path (- - -) chosen for this study.
(3)
Nbm is the measured neutron-scattering length density obtained from the best fit for the data. This treatment neglects the positive excess volume of mixing (about 3% of the ideal mixture volume for the equimolar mixture) which is characteristic of alkane + perfluoroalkane mixtures. Analysis of the reflectivity data suggested that the adsorption was relatively small for mixtures at compositions far from x2,c ) 0.36 of the phase diagram,6 i.e. x2 ∼ 0.2 and 0.8. For mixtures in the middle of the composition range, near x2,c, it was possible to model the observed data by assuming the presence of a monolayer at the liquidvapor interface. The optimum fits were established when the layer was 9-11 Å thick with a scattering length density of 0.34 × 10-5 Å-2. These parameters are consistent with a monolayer composed of essentially pure perfluoro-nhexane. For higher x2 the reflectivity was best modeled using a bare subphase with no capping perfluoro-n-hexane monolayer. We recognize that it is difficult to assert unambiguously that this is a real feature of the surface and not simply a consequence of the diminished sensitivity of the fitting procedure as the mixture becomes more perfluoro-n-hexane rich. However, given that this feature was not anticipated in advance, we prefer to offer it here as a working hypothesis of reasonably high probability that remains to be confirmed absolutely in the near future by more detailed reflectivity measurements. Figure 3 depicts the variation in neutron-scattering length density (and hence composition) for an x2 ) 0.36 mixture on passing from the vapor to the bulk phase via the surface region. The higher scattering length densities just above the liquid-vapor interface (defined at z ) 0) can be attributed to the presence of a perfluoro-n-hexanerich layer. The surface tensions of Rodriguez-Nun˜ez et al.10 in Figure 4 clearly show the horizontal inflection in the near(9) Dunlap, R. D.; Bedford, R. G.; Woodbrey, J. C.; Furrow, S. D. J. Am. Chem. Soc. 1959, 81, 2927. (10) Rodriguez-Nun˜ez, E.; McLure, I. A. Unpublished results.
Notes
Langmuir, Vol. 13, No. 7, 1997 2169 Table 1. Neutron Reflectivity Results Taken at 24.5 °C, Just above the Critical End Point at 22.65 °C, from across the Composition Range in the Mixture n-Hexane + Perfluoro-n-hexanea x2
φ2
φ2(subphase) ex reflectivity
C6F14 capping layer
0.12 0.20 0.36 0.50 0.81 0.87 1.0
0.17 0.28 0.47 0.61 0.87 0.91 1.0
0.17 0.21 0.57 0.60b 0.85 0.81 1.00
no no yes yes no no no
a x is the mole fraction and φ the volume fraction of perfluoro2 2 n-hexane. The two right-hand columns originate from modeling the data as described in the text; φ2(subphase) is the subphase composition resulting from the data-fitting procedure, and the final column indicates the presence of a capping layer of C6F14 required by the fit. b Recently measured on the reflectometer SURF at the ISIS Facility, RAL by J. Bowers, A. N. Burgess, P. J. Clements, and Ian A. McLure.
Figure 2. Reflectivity spectra for the mixture (1 - x2)n-hexane + x2perfluoro-n-hexane at 24.5 °C above TUCS ) 22.86 °C: (a) n-hexane-rich mixture with x2 ) 0.115; (b) mixture of critical composition x2,c ) 0.36; (c) perfluoro-n-hexane-rich mixture with x2 ) 0.812.
critical isotherm predicted by Widom.2 From these results and the vapor pressures of Dunlap et al.9 the calculated TSS at 25 °C displays perfluoro-n-hexane enrichment at the liquid-vapor interface, in confirmation of the results of the neutron reflectivity experiment. But the outstanding question is whether this monolayer is due to critical adsorption or to primitive surfactancy. In Figure 5 the perfluoro-n-hexane volume fraction of the subphase calculated from the reflectivity measure-
Figure 3. Neutron-scattering length density profile through the liquid-vapor interface of the mixture x2,c ) 0.36 for (1 - x2)hexane + x2perfluoro-n-hexane at T ) 24.5 °C, close to the critical end point at TUCS ) 22.65 °C; z is the coordinate normal to the interface with z < 0 for the bulk liquid and the interface at z ) 0.
ments is plotted versus the perfluoro-n-hexane volume fraction of the bulk mixture. The line drawn on the figure is freely fitted by least-squares to the data points: it is satisfying that the line almost passes through the points (0,0) and (1,1), as it should. There are two points which fail to fall close to this line once the errors are taken into consideration. The first is the point corresponding to x2 ) x2,c which lies above the fitted line. It is clear that the subphase is here enriched with perfluoro-n-hexane with respect to the bulk mixture, and this we are inclined to identify as critical adsorption. The other off-line point corresponding to x2 ) 0.87 suggests
2170 Langmuir, Vol. 13, No. 7, 1997
Notes
Figure 5. Volume fractions φ2R for (1 - φ2)hexane + φ2perfluoro-n-hexane derived from the fitting of the measured reflectivities as a function of the bulk mixture volume fractions φ2.
Summary
Figure 4. Orthobaric surface tension σ of (1 - x2)n-hexane + x2perfluoro-n-hexane at 25 °C close to the critical end point TUCS ) 22.65 °C.
that the subphase is enriched with n-hexane with respect to the bulk mixture. This observation is not inconsistent with the experimental surface tensions in this region shown in Figure 4, where according to the fitting polynomial dσ/dx2 is just positive. The surface tension isotherm in Figure 4 possibly exhibits an aneotrope, or surface azeotrope, at x2 ) 0.8: or at least a region of composition for which dσ/dx2 ) 0. At an aneotrope, TSS vanishes, indicating that the surface composition and the bulk composition are identical. Unsurprising perhaps, but gratifying certainly, the results of the neutron reflectivity measurements at x2 ) 0.81 are in agreement with this observation.
In the noncritical regions, around x2 ∼ 0.2 and 0.8, the surface composition appears similar to that of the bulk. However, in the intermediate composition range, from modeling the reflectivity data, the surface is apparently composed of a perfluoro-n-hexane monolayer with a thickness of about 10 Å. Near the critical composition itself the subphase is enriched with perfluoro-n-hexane. An aneotropic region has also plausibly been identified. These results are consistent with the calculated total surface segregation. Further work is in progress which will hopefully resolve the practical prblems of the thermostating and the sample environment and strengthen the observations, especially the speculation surrounding the aneotropic region. Acknowledgment. The authors thank the EPSRC for the award of beam time on the CRISP reflectometer at the Rutherford Appleton Laboratory and of postgraduate studentships to J.B. and R.W. They also wish to record their appreciation of the assistance of the staff at CRISP. LA950611I
