Langmuir 2008, 24, 4833-4844
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Mixing in Adsorbed Monolayers: Perfluorinated Alkanes J. E. Parker and S. M. Clarke* BP Institute and Department of Chemistry, UniVersity of Cambridge, Cambridge, United Kingdom ReceiVed September 3, 2007. In Final Form: February 13, 2008 The mixing behavior of binary combinations of perfluoroalkanes in the bulk and in solid monolayers adsorbed at the graphite/liquid interface, determined by calorimetry and powder diffraction, is reported. The perfluoroalkanes are found to generally have a smaller excess enthalpy of mixing on the surface than in the bulk, and their relative size ratio is a good parameter to predict the mixing behavior. The excess enthalpy of mixing for perfluoroalkanes is found to be significantly smaller than that of the closely related hydrocarbons. The preferential adsorption of longer homologues over shorter ones is observed. Interestingly, the extent of preferential adsorption with relative size ratio is very similar to that of the hydrocarbons. These results can be understood in terms of the increased compressibility and lower polarizability of the perfluoroalkanes compared to hydrocarbons.
Introduction Adsorption of molecules at the solid/liquid interface can occur with the formation of a solid monolayer, even though the bulk phase is liquid. These monolayers are of considerable interest due to their role in interfacial phenomena such as lubrication, adhesion, and detergency. In this work, the absorption of perfluoroalkanes from their pure liquids and from binary mixtures onto the surface of graphite will be investigated using a combination of techniques. Perfluoroalkanes are interesting candidates for study due to the differences in their molecular structure and properties compared to the normal alkanes that are expected to have a significant effect on their adsorption and mixing behavior. In particular,1 they have weak intermolecular forces, low surface tensions (the lowest of all organic liquids), and high compressibility, and they exhibit near ideal behavior (as defined below) in their liquid mixtures.2 The adsorption of long chain alkanes, alcohols, carboxylic acids, and other species has been studied using a variety of approaches including calorimetry, adsorption isotherms, scanning tunneling microscopy (STM), X-ray and neutron diffraction, and incoherent neutron scattering.3-13 For example, the structures of the crystalline monolayers of adsorbed alkanes have been determined using neutron and X-ray diffraction studies and STM.6,10,11,14-18 Adsorbed layers formed by short ( 0.10 and in the monolayer for ∆n/n > 0.25. Figure 8b also indicates that alkane mixtures with ∆n/n less than approximately 0.07 essentially mix ideally. Figure 9 compares the reduced interaction parameters in the (a) monolayers and (b) bulk perfluoroalkane/perfluoroalkane and alkane/alkane combinations. As discussed above, in all cases, the extent of nonideal behavior increases with the relative size (40) Arnold, T. The adsorption of alkanes from their liquids and binary mixtures. Ph.D., University of Oxford, 2001.
Mixing BehaVior of Perfluorinated Alkanes
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im ) 1 - ∆m/Γm
ratio. Significantly, the values of Ω/2RT for the F/F mixtures are lower than those of the corresponding H/H mixtures, indicating more ideal behavior in the F/F monolayers. Perfluoroalkanes are highly compressible, due to the weak cohesive forces, which gives rise to a relatively large free volume.41 Such large free volumes may also be expected to impact the mixing behavior of the materials where the space available to an impurity molecule in the lattice is a key factor. This may explain why the perfluoroalkanes should have a lower reduced interaction parameter than the relative hydrocarbon mixtures. In understanding the behavior and developing rules to predict mixing or phase separation in the solid monolayers, a number of approaches from the bulk have been adapted. Essentially all of these approaches for mixing in the solid state are based on the crystal structures and symmetries of the pure materials39 and the conceptual idea that one molecule needs to be of a similar size and shape to fit in the lattice of another and form an ideal22,42 mixture or a continuous series of solid solutions. Kitaigorodskii39 has outlined rules for mixing in 3D alkane crystals which are reviewed by Dorset.27 There are a number of criteria that must be met for the solid state to show ideal mixing or a continuous series of solid solutions. These include the criteria that the pure materials must have similar crystal symmetry and be sufficiently similar in size, as represented by an isomorphism coefficient. For bulk mixtures, this is defined as
where ∆m is the volume due to the nonoverlapping parts (when the two unit cells are positioned so as to achieve maximum overlap) and Γm is the volume due to the overlapping parts.43 When the value of im for a pair of alkanes is approximately 0.8 or above,27 the two alkanes are found to be completely miscible in the solid phase. For monolayers, an equivalent 2D isomorphism coefficient can be defined in terms of unit cell areas rather than volumes, and it has been used to assess the mixing behavior in alkane monolayers.22,25 The 2D crystal structure of the solid monolayer of perfluorododecane has already been determined36 from the neutron diffraction patterns. We have obtained diffraction patterns from a number of other perfluoroalkane monolayers that have also been solved.38 For the perfluoroalkane mixtures studied here, the symmetry of all of the longer perfluoroalkanes is the same: a centered unit cell, with the molecular backbones parallel to each other and to the unit cell long axis (“a” direction). The “b” distance of the unit cell remains approximately the same for all chain lengths, as it corresponds to the lateral separation of the molecules. Hence, the unit cell area will be linearly proportional to the length of the molecule, and there is effectively no difference in using the isomorphism coefficient to the relative size ratio as a measure of similarity for these mixtures. The bulk phase diagrams and X-ray diffraction data presented above can be compared to those previously reported in the literature by Dorset27 and Visjager et al.44 The forms of the phase diagrams for FC12/FC14 and FC14/FC16 resemble those already reported for these systems. No phase diagram for FC10/FC12 could be found; however, the form of the phase diagram presented here is very similar to that of FC12/FC14, and it seems reasonable that the mixing behavior in the bulk will be closely related. It is noted for theses systems27 that the continuity of melting point lines and lamellar spacing over the concentration series indicate the formation of solid solutions. The melting point lines diverge from those predicted for an ideal mixture, suggesting that the solid solutions are nonideal. For larger chain length differences, eutectic behavior has been reported in bulk perfluoroalkane mixtures. For example, FC12/FC16 and FC14/FC20 exhibit the depression of freezing point of an ideal phase separated system,27 as do our results presented above. Significantly, some perfluoroalkane mixtures exhibit more complex behavior than that observed here. For example, X-ray diffraction data for the FC12/FC16 system44 shows three constant lamellar spacings in the concentration range XFC16 ) 0.3-0.5. The intermediate lamellar spacing in the eutectic solid, in between those of the two pure components, was interpreted to be a secondary crystallization of an incommensurate solid of randomly alternating lamellae of separated pure components. This was then consistent with the solidus line in the phase diagram not extending all the way to the pure FC16 at X ) 1; a metastable solid solution is formed at high FC16 concentrations, which later fractionates. For other systems, Visjager et al.44 have also reported complicated phase behavior, with several peaks in the DSC thermograms, many of which were found to depend on the cooling rate of the samples and the conclusion that DSC thermograms did not necessarily reflect equilibrium behavior. None of the samples prepared in this present work showed any of these additional transitions. This may be attributed to the sample
(41) Lemal, D. M. J. Org. Chem. 2004, 69, 1-11. (42) Sloutskin, E.; Bain, C. D.; Ocko, B. M.; Deutsch, M. Faraday Discuss. 2005, 129, paper 24.
(43) Rajabalee, F.; Espeau, P.; Haget, Y. Mol. Cryst. Liq. Cryst. Sci. Technol., Sect. A 1995, 269, 165-173. (44) Visjager, J.; Tervoot, T. A.; Smith, P. Polymer 1999, 40, 4533-4542.
Figure 9. Reduced interaction parameter, Ω/2RT, as a function of relative size ratio for (a) alkane/alkane (open circles) and perfluoroalkane/perfluoroalkane (filled triangles) mixtures in the monolayer and (b) alkane/alkane (filled circles) and perfluoroalkane/perfluoroalkane (open triangles) mixtures in the bulk.
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Figure 10. Thermal expansion of the 2D monolayers of an alkane (open circles) and a perfluoroalkane (filled triangles) determined by neutron diffraction.
preparation method: annealing the samples at high temperature and allowing them to cool very slowly to form the monolayer, during which time the bulk phase may be better equilibrated. The nonideal behavior suggested for these mixtures is supported by the calculated values of Ω/2RT.
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A thermodynamic model for bulk alkane/alkane mixing was developed by Matheson and Smith.45 In this model, the free volume of a molecule in its own pure crystal lattice is greater than the van der Waals size of the actual molecule. The total volume it has available is deduced from the molar volume in the liquid and the volume change on freezing. This approach has been adopted to include all the contributions to space available to a molecule in a lattice, including defects and grain boundaries. Impurity molecules can be accommodated into this volume without energy penalty if they are small enough. This would correspond to ideal mixing. However, if the impurity molecule is too big, then some elastic distortion of the host lattice is required with an energy penalty. In this way, nonideal mixing can be included in the model. The model has been used to compute mixing in both bulk alkane and perfluoroalkane mixtures.44,45 To make a similar comparison for the 2D layers of interest here, some estimate of the elastic energy cost of distorting the 2D crystal lattice is required. This has been estimated from the thermal expansion45 of the 2D crystals obtained from neutron diffraction data of the alkanes and perfluoroalkanes presented in Figure 10. The figure indicates that the thermal expansion of the perfluoroalkane monolayer is much greater than that of the alkane monolayer. This echos the higher bulk compressibility of perfluoroalkanes over alkanes.
Figure 11. Loci to the solutions of eq 5 from ref 46 with f ) 0, ideal mixing (filled symbols) and f ) 0.4, phase separation (open symbols) for (a) bulk perfluoroalkane mixtures, (b) monolayer perfluoroalkane mixtures, and (c) a comparison of the predicted mixing behavior of perfluoroalkane mixtures (triangles) and alkane mixtures (circles) in the monolayer phase. The behaviors of combinations indicated by crosses are discussed in the text.
Mixing BehaVior of Perfluorinated Alkanes
A convenient method of displaying the solubility of a longer homologue in the solid phase of a shorter one is to plot this on a graph. This graph has two lines representing (a) the maximum length of the longer impurity that can mix ideally in the lattice of the shorter and (b) the maximum chain length of the longer impurity before phase separation occurs in the mixture. An illustration for both the bulk and monolayer calculations is given in Figure 11a and b, respectively. In Figure 11a, the thermal expansion coefficients for the bulk perfluoroalkanes, (dV/dT)TdTm, have been taken to be in the range 0.5-1.3 cm3/K and present these boundary lines for f ) 0 and 0.4, where f is a scaling factor for the extent of compressibility in the free energy of mixing. This is essentially a recalculation of Figure 2 from Visjager et al.,44 except that slightly different f values have been used. In Figure 11, Cs and Ct are the number of carbons in the shorter and longer (“taller”) mixture components, respectively. The predicted phase behavior from this model agrees with the experimentally determined phase behavior for perfluoroalkane bulk binary mixtures as described previously.44 For example, the positions of the crosses in Figure 11a predict that FC15/FC16 will form an ideal mixture, FC12/FC15 is nonideally mixed, and FC14/FC20 is phase separated, in excellent agreement with the Ω/2RT values extracted from the phase diagrams using the regular solution model. The thermal expansion coefficient calculated for the perfluoroalkane monolayer was used to construct a similar phase map for the perfluoroalkane monolayer mixtures. It is clear that, for a given short molecule, a much longer molecule is required for phase separation to occur than for the bulk phase. Nonideal mixing behavior is also predicted for a wider range of chain length differences than the bulk. Figure 11b predicts that a mixture of FC12/FC21 will be phase separated in the solid monolayer; this is in excellent agreement with the results from the regular solution model, which predicted that this combination would have an Ω/2RT value of 1. The data of Matheson and Smith45 for the thermal expansion of bulk alkanes and the thermal expansion coefficient calculated for alkane monolayers obtained here have also been used to calculate the phase map of the bulk and monolayer alkane/alkane mixtures. This comparison is given in Figure 11c and indicates that the model predicts that perfluoroalkanes mix better than the corresponding alkanes, in excellent agreement with the experimental results presented here. The preferential adsorption coefficient, K, has been obtained from the thermodynamic data above and is given in Figure 12a as -RT ln K plotted against the relative size ratio for F/F monolayer mixtures. Figure 12a presents -RT ln K, which is equal to the Gibbs energy of long molecules replacing short molecules on the surface, and thus, a negative value indicates that the longer mixture component is preferentially adsorbed. The value of -RT ln K is negative for all mixtures, suggesting that a longer perfluoroalkane is preferentially adsorbed over a shorter one. The increasingly negative value of -RT ln K with increasing size ratio illustrates that the amount of preferential absorption increases with the increasing relative size ratio of the components. The uncertainty in the determination of K for different systems is reflected by the error bars. Preferential absorption of the longer component is also reported for alkane/alkane mixtures20,40,21 and is presented with the perfluoroalkane data in Figure 12b. Interestingly, the data for these two systems essentially follow the same trend with mixtures with the same relative size ratio having the same preferential absorption behavior. This behavior indicates that, as the chain (45) Matheson, R. R.; Smith, P. Polymer 1985, 26, 288-292.
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Figure 12. Gibbs free energy (-RT ln K) of replacing a shorter molecule with a longer one on the surface of graphite for (a) perfluoroalkane/perfluoroalkane mixtures and (b) a comparison of perfluoroalkane (filled triangles) and hydrocarbon (open circles) mixtures.
length of the molecule increases, a -CF2- group has the same relative effect on the preferential absorption of the longer perfluoroalkane that a -CH2- group has for an alkane. Given the very different interactions of the perfluoroalkanes and hydrocarbons with the surface and the differences in surface mixing behavior, it is very interesting that the relative adsorption behavior is essentially identical. The preferential adsorption of longer homologues is also found for homomixtures of other species such as alcohols and carboxylic acids.23,24 Interestingly, heteromixtures25 may not follow this simple rule: a shorter alcohol can adsorb in preference to a longer alkane due to the association of the alcohol molecules by hydrogen bonding. The preferential adsorption behavior has a number of potential origins. It could be entropic; adsorbing fewer longer molecules onto the surface releases more shorter molecules into the bulk, each of which will have a favorable translational entropy contribution. By releasing more molecules, the total entropy will be increased. On this basis, it is expected that the alkanes and perfluoroalkanes will exhibit similar behavior. However, alkanes are much more conformationally flexible than the perfluoroalkanes, a factor this simple model ignores. The preferential adsorption coefficient, K, defined above also includes a contribution from the differences in interfacial tension on adsorbing the longer or shorter species. Here, it is assumed that there are minimal changes in the interfacial tension on replacing a perfluoroalkane with another perfluoroalkane.
Conclusions Thermodynamic and scattering data on the mixing behavior of perfluorinated alkanes in the bulk and at the solid/liquid
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interface are presented. It is found that the perfluoroalkanes generally mix more ideally on the surface than in the bulk and that the relative size ratio is a good parameter to predict the behavior. The reduced interaction parameters in Table 1, Ω/2RT, can be related to the coordination number of the crystal lattice, as described in the Theoretical Models section. The most simple approach is to assume that the energies of interaction (2EAB EAA - EBB) and T are the same for the surface and the bulk. Typical coordination numbers in the solid bulk and monolayer can be taken as 12 and 6, respectively, if the objects are spheres or approximately 6 and 2, respectively, if the molecules are considered as long linear species. It is therefore expected that the ratio of the reduced interaction parameter in the bulk and the monolayer should be in the range of approximately 2-3. This is reasonably shown by the majority of experimental samples (Table 1) that give an interaction parameter ratio of approximately 1.4-3.0, except where one of the experimentally determined interaction parameters (monolayer) is rather small and there is a large error in the ratio. The average reduced interaction parameter ratio, excluding those with a large error, is approximately 2.2, in good agreement with this simple model. Hence, this analysis gives comfort that the experimentally determined reduced
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interaction parameters of the bulk and monolayer bear a reasonable relationship to one another. The mixing in perfluoroalkanes, both in the bulk and adsorbed layer, is also found to be significantly more ideal than that of the closely related hydrocarbons. The enhanced mixing of the perfluoroalkanes is attributed partly to their enhanced compressibility and hence ease of accommodating molecules of a different size into their crystal lattice. The preferential adsorption of longer homologues over shorter ones is also observed; however, interestingly, the extent of preferential adsorption is very similar to that of the hydrocarbons. This latter behavior is qualitatively consistent with a simple entropic model of preferential adsorption. Acknowledgment. We thank the instrument scientists and staff at ILL for the allocations of beam time and assistance with the neutron experiments. We thank EPSRC and the Department of Chemistry, Cambridge University, for a DTA Studentship for J.E.P. Supporting Information Available: Additional thermodynamic data. This material is available free of charge via the Internet at http://pubs.acs.org. LA703995U
