Langmuir 2005, 21, 5085-5093
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Alkane/Alcohol Mixed Monolayers at the Solid/Liquid Interface Loic Messe, Ana Perdigon, and Stuart M. Clarke* BP Institute and Department of Chemistry, University of Cambridge, Madingley Rise, Madingley Road, Cambridge CB3 0HE, U.K.
Akira Inaba Department of Chemistry, Graduate School of Science, Osaka University, Toyonaka, Osaka 560, Japan
Tom Arnold Chemical Sciences Division, Oak Ridge National Laboratory, Tennessee Received January 17, 2005. In Final Form: March 11, 2005 In this work, we present the behavior of solid monolayers of binary mixtures of alkanes and alcohols adsorbed on the surface of graphite from their liquid mixtures. We demonstrate that solid monolayers form for all the combinations investigated here. Differential scanning calorimetry (DSC) is used to identify the surface phase behavior of these mixtures, and elastic neutron incoherent scattering has been used to determine the composition of the mixed monolayers inferred by the calorimetry. The mixing behavior of the alcohol/alkane monolayer mixtures is compared quantitatively with alkane/alkane and alcohol/alcohol mixtures using a regular solution approach to model the incomplete mixing in the solid monolayer with preferential adsorption determining the surface composition. This analysis indicates the preferential adsorption of alcohols over alkanes of comparable alkyl chain length and even preferential adsorption of shorter alcohols over longer alkanes, which contrasts strongly with mixtures of alkane/alkane and alcohol/ alcohol of different alkyl chain lengths where the longer homologue is always found to preferentially adsorb over the shorter. The alcohol/alkane mixtures are all found to phase separate to a significant extent in the adsorbed layer mixtures even when molecules are of a similar size. Again, this contrasts strongly with alkane/alkane and alcohol/alcohol mixtures where, although phase separation is found for molecules of significantly different size, good mixing is found for similar size species.
Introduction The mixing of molecules adsorbed from solution to different interfaces is central to many phenomena of both industrial and academic relevance. It is often found, for example, that the surface tension of a mixture of two surfactants is lower than either of the two pure materials. Clearly, the mixing behavior at the interface is key to understanding this and many other effects. Recently, we and others have presented data on the behavior of solid monolayers adsorbed from solutions of binary mixtures of linear alcohols and binary mixtures of linear alkanes (for example, refs 1-4). In this paper, we report a study of the behavior of solid monolayers of mixtures of linear alkanes and alcohols adsorbed from their solutions to graphite. We address several key issues including the extent of preferential adsorption in these systems and an interpretation of the monolayer mixing behavior. In this work, we present a combination of calorimetry and incoherent elastic neutron scattering (IQENS) data on the phase behavior of solid monolayers of binary mixtures of linear alcohols and alkanes adsorbed on
graphite. Phase diagrams of mixed adsorbed layers are obtained by calorimetry by investigation of the composition variation of the monolayer melting point. Incoherent neutron scattering is used to determine the composition of the mixed monolayers that is generally different from the bulk solution due to preferential adsorption of one or other component and compared with the composition deduced by calorimetry. Experimental Section Calorimetry. The application of differential scanning calorimetry (DSC) for the study of phase behavior in adsorbed layers has been given elsewhere.5 In outline, the composition dependence of the monolayer melting point is used as an indicator of the adsorbed layer mixing behavior. The DSC measurements were performed on a Pyris 1 Power compensation system at the BP Institute, University of Cambridge, as discussed previously. The heating rate used was 10 °C/min.6 Incoherent Neutron Scattering. The high resolution backscattering spectrometer, IN107 at the ILL, Grenoble, France, was used for these experiments as described elsewhere.8 In outline, neutrons can exchange energy with nuclei in a sample. If the nuclei are moving, for example, in a liquid, then the neutrons will be sped up or slowed. If the nuclei are essentially immobile,
* To whom correspondence should be addressed. (1) Gilbert, E. P.; Reynolds, P. A.; Thiyagarajan, P.; Wozniak, D. G.; White, J. W. Phys. Chem. Chem. Phys. 1999, 1, 2715-2724. (2) Messe, L.; Clarke, S. M.; Inaba, A.; Dong, C. C.; Thomas, R. K.; Castro, M. A.; Alba, M. Langmuir 2002, 18, 9429-9433. (3) Findenegg, G. H.; Koch, C.; Liphard, M. Adsorption from Solution, Conference in Honour of D. H. Everett, Bristol, Sept 8-10, 1982. (4) Clarke, S. M.; Messe, L.; Adams, J.; Inaba, A.; Arnold, T.; Thomas, R. K. Chem. Phys. Lett. 2003, 373, 480-485.
(5) Clarke, S. M.; Inaba, A.; Arnold, T.; Thomas, R. K. J. Therm. Anal. Calorim. 1999, 57, 641-651. (6) Castro, M. A.; Clarke, S. M.; Inaba, A.; Arnold, T.; Thomas, R. K. J. Phys. Chem. 1998, B102, 10528-10534. (7) ILL “Neutron Research Facilities at the ILL High Flux Reactor”, Institut Laue-Langevin, 1996. (8) Castro, M. A.; Clarke, S. M.; Inaba, A.; Thomas, R. K. Physica B 1998, 241-243, 1086-1088.
10.1021/la0501280 CCC: $30.25 © 2005 American Chemical Society Published on Web 04/22/2005
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for example, in a solid phase, then the neutrons are scattered without energy changesso-called “elastic” scattering. Scattering from a protonated adsorbate is much greater than that from the graphite substrate, optimizing the sensitivity to the adsorbed layers. Hence, the temperature variation of the elastic incoherent scattering intensity reveals the quantity of solid adsorbate in the sample. In addition, scattering is also dominated by a protonated component in a mixture, if the other is deuterated, allowing us to probe each component of these binary mixtures. To optimize the sensitivity to the scattering from the adsorbed monolayers, the amount of bulk fluid was kept to a minimium. The adsorbent used was recompressed exfoliated graphite Papyex (Le Carbone Lorraine). Our particular sample was characterized by the adsorption of nitrogen and found to have a specific surface area of 31.6 m2 g-1. Protonated alkanes and alcohols were obtained from Aldrich and used without further purification. The deuterated alcohols and alkanes were prepared using isotope exchange of the corresponding carboxylic acid and reduction to the alcohol and alkane. The deuteration levels are approximately >98%. The graphite substrates were outgassed under vacuum in an oven at 350 °C before known quantities of alcohol/alkane mixtures were added as liquid by microsyringe and annealed onto the surface at a temperature of approximately 40 °C below the bulk boiling point. We express the amount of each alcohol adsorbed in terms of the number of equivalent monolayers adsorbed. This is estimated from the areas per molecule, taken from the work of Groszek9 and Morishige,10 and the specific surface area of the graphite. For the calorimetry measurements presented here, the total coverage was approximately 40 monolayers and the error in the estimate of the amount in an equivalent monolayer is small.
Results Calorimetry. Differential scanning calorimetry thermograms from monolayers adsorbed from liquids and liquid mixtures have been reported elsewhere.11 Generally, the large endothermic melting transitions from the bulk adsorbates are readily distinguished from the high temperature melting points of the solid adsorbed monolayers. Figure 1a presents representative examples of the DSC thermograms of mixtures of heptanol and nonane (C7OH/ C9H). This figure highlights the temperature region of the monolayer melting point and shows clear depression of freezing point and even a weak eutectic invariant near the minimum. The bulk melting transitions are at lower temperatures, the tails of which can just be seen at the low temperature side of some traces. Figure 1b-f presents the composition dependence of the monolayer melting peaks identified in these DSC thermograms of binary mixtures of alcohols and alkanes. In each part, we present data for several alcohols mixing with a common alkane. In outline, the mixing behavior of the components in the solid monolayer is reflected in the composition dependence of the monolayer melting point. Combinations which mix well in the liquid but phase separate in the solid are identified by a pronounced minimium (eutectic) in the phase diagram (e.g., Figure 1b for the C5OH/C8H mixture). However, good mixing in both solid and liquid phases is usually indicated by a smooth variation in monolayer melting point that almost follows a straight line joining the melting points of the pure monolayers. We can use elementary models of phase separation (fully miscible in the liquid state but complete phase separation in the solid) to predict the monolayer phase behavior.12 This approach requires an estimate of the monolayer melting enthalpies which we determine from the inte(9) Groszek, A. J. Proc. R. Soc. London 1970, A314, 473. (10) Morishige, K.; Kato, T. J. Chem. Phys. 1999, 111, 7095-7102. (11) Castro, M.; Clarke, S. M.; Inaba, A.; Arnold, T.; Thomas, R. K. Phys. Chem. Chem. Phys. 1999, 1, 5017-5023. (12) Kondepudi, D.; Prigogine, I. Modern Thermodynamics; Wiley: Chichester, U.K., 1998.
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grated areas under the monolayer melting peaks.13 However, largely due to uncertainties of background measurements, estimates of the specific surface areas of the graphite, and the molecular area, there is considerable uncertainity in these values. Alcohol/Alcohol Mixtures. Figure 2a and b presents the variation in monolayer melting point as a function of bulk mixture composition for alcohols C6OH/C9OH and C6OH/ C8OH on graphite (data taken from ref 14). The measured enthalpy of monolayer melting is found to be approximately 1.1 J/g of graphite or 16 kJ mol-1. The lines on the plot illustrate the predicted depression of freezing point15 for a model with complete phase separation in the solid monolayer. For these mixtures, although the composition of the minimium is displaced, the magnitude of the predicted depression of freezing point is in reasonable agreement with experiment. Other binary combinations of alcohols show much better mixing and hence far lower depressions of freezing point.4 Indeed, in some cases, a molecular compound is formed.2,14,16 At this stage, we conclude that approximately 16 kJ mol-1 is a reasonable estimate of the monolayer melting enthalpy for alcohol/ alcohol combinations. Alkane/Alkane Mixtures. Figure 2c presents the variation in monolayer melting point as a function of bulk mixture composition for the alkane/alkane mixture C8H/ C9H on graphite. As observed, we see a pronounced minimum in this phase diagram, clearly suggesting a significant extent of phase separation or at least a significant extent of nonideal mixing. This is supported by neutron diffraction data.11 The enthalpy of monolayer melting for alkanes obtained from DSC measurements is found to depend on the particular alkane in question. The lines in Figure 2c illustrate the predicted depression of freezing point for an enthalpy of melting of 7 kJ mol-1. It is evident that the model overpredicts the extent of the depression of freezing point. Even with significantly larger values of the monolayer melting enthalpy, well above the experimental error (e.g., 10 kJ mol-1), we observe a magnitude of the freezing depression which is still significantly smaller than that predicted by these simple models. This overprediction of the depression of freezing point suggests either that our estimates of monolayer enthalpies are grossly in error for the alkanes or that there is significant mixing in the monolayers not captured by the simple models we have used. In particular, there may be some mixing, probably at the extremes of composition (i.e., some octane dissolving in the essentially pure nonane). To model the observed depression of freezing point for alkane mixtures, we have considered regular solution models where we include an additional excess enthalpy of mixing term to restrict mixing in the solid monolayers relative to the ideal mixing case. In this simplest model, we assume there is ideal mixing in the adsorbed liquid. The chemical potential of species A must be the same in both solid and liquid adsorbed states:
gA(S) + RT ln xA(S) ) gA(L) + RT ln xA(L) where gA(L or S) is the standard chemical potential of species A in state L or S (liquid or solid) and xA(L) is the (13) Clarke, S. M.; Arnold, T. Appl. Phys. A 2002, 74, s1371-s1372. (14) Messe, L.; Clarke, S. M.; Inaba, A.; Arnold, T.; Dong, C. C.; Thomas, R. K. Langmuir 2002, 18, 4010-4013. (15) Atkins, P. W. Physical Chemistry, 5th ed. (International Student Edition); Oxford University Press: Oxford, U.K., 1994. (16) Messe, L.; Perdigon, A.; Clarke, S. M.; Inaba, A.; Castro, M. A. J. Colloid Interface Sci. 2002, 266, 19-27.
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Figure 1. (a) Representative DSC thermograms from mixtures of C7OH and C9H adsorbed on graphite in the region of the monolayer melting showing the depression or freezing point and the weak eutectic invarient. Monolayer melting temperature as a function of bulk solution composition for binary mixtures of alcohols and alkanes adsorbed on graphite. Mixtures of alcohols with (b) octane, (c) nonane, (d) decane, (e) undecane, and (f) dodecane.
mole fraction of species A in state L. Here, we assume that the two species mix ideally in the liquid (activity coefficient of unity) but have activity coefficient γA,S in the solid phase
gA(S) + RT ln(γA,SxA(S)) ) gA(L) + RT ln xA(L) with a similar expression for the other component B.
Including the activity coefficient for the solid phase to include the nonideality gives
gB(S) + RT ln(γB,SxB(S)) ) gB(L) + RT ln xB(L) or
{gA(L) - gA(S)}/RT ) R ) ln(γA,SxA(S)) - ln xA(L)
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Figure 2. Experimental monolayer phase diagrams for alcohol/alcohol mixtures of (a) hexanol and nonanol (C6OH/C9OH) and (b) hexanol and octanol (C6OH/C8OH). The diamonds are the experimental points. The solid lines represent calculations for completely phase separated monolayers without preferential adsorption. The solid lines with small circles represent calculations for completely phase separated monolayers with preferential adsorption of the longer alcohol. Comparison of experimental monolayer phase diagram for an alkane/alkane mixture of octane and nonane (c) with a completely phase separated monolayer model without preferential adsorption. (d) Comparison of the experimental data with the regular solution model with preferential adsorption.
giving eR ) γA,SxA(S)/xA(L) and similarly, for B, eβ ) γB,SxB(S)/xB(L). Re-expressing xA(S) ) 1 - xB(S) and xA(L) ) 1 - xB(L) gives
eR ) γA,S(1 - xB(S))/(1 - xB(L)) and xB(L) ) γB,SxB(S)/eβ (1) In the regular solution model, the activity coefficient is given by RT ln γA,S ) ΩxB,S2 (and similarly for B),17 where Ω is an interaction parameter related to the difference in energy between A-B pairs and the mean of A-A and B-B pairs and is related to the excess enthalpy of mixing: Hex ) ΩxAxB. A value of Ω of zero would recover the ideal mixing case, and increasing values of Ω indicate increasingly poor mixing in the solid monolayers. The temperature dependence of the free energy difference {gA(L) - gA(S)} can be given by ∆Hf,A{1 - T/Tm,A}, where ∆Hf,A is the enthalpy of fusion of the pure material A. (17) Everett, D. H. An Introduction to the Study of Chemical Thermodynamics; Longmans, Green and Co Ltd: London, 1959.
Given a value for Ω (J mol-1), the enthalpies of fusion, and the melting points of the pure monolayers, determined by DSC measurements, eq 1 can be solved to find xB,S at each temperature and hence a phase diagram can be plotted. In addition, we have also included a correction for preferential adsorption. This is based on the equilibrium outlined by Everett.
long(bulk) + short(ads) T long(ads) + short(bulk) where long and short refer to long and short alkanes and “(bulk)” and “(ads)” refer to molecules in the bulk mixture or adsorbed on the surface. Hence, this equilibrium represents the exchange of an adsorbed short molecule by a longer molecule. The equilibrium coefficient is given by
K ) xlong(ads)xshort(bulk)/xlong(bulk)xshort(ads) Here, we have ignored any difference in the sizes of the adsorbed molecules.18 When both species are equally (18) Everett, D. H. In Adsorption from Solution; Ottewill, R. H., Rochester, C. H., Smith, A. L., Eds.; Academic Press: London, 1982.
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Figure 3. Experimentally determined variation of (a) Ω and (b) ln K with relative size ratio for alkane/alkane monolayer mixtures. (c) Experimentally determined variation of Ω with relative size ratio for alcohol/alcohol monolayer mixtures. (d) Variation of Ω against RT ln K. See text for discussion.
adsorbed, K will be unity. Preferential adsorption of the longer component will be reflected by a K value greater than unity. Everett18 has shown that RT ln(K) is related to (σB* - σA*)a, where (σB* - σA*) is the difference in free energies, and hence interfacial tensions of the pure monolayers, and a is the area per molecule. Figure 2d presents the experimental and calculated variation in monolayer melting point as a function of bulk mixture composition for the alkane/alkane mixture C8H/ C9H on graphite with the regular solution model and preferential adsorption. Figure 3a and b presents the values of Ω and the ln K against the relative size ratio of the components obtained by fitting the DSC data from this and several other alkane/alkane mixtures (data taken from ref 19). The “relative size ratio” is a measure of mismatch in molecule size compared to the overall sizes of the molecules calculated as the difference in alkyl chain lengths of the two components divided by the average chain length. The low values of Ω and the positive gradient of the data in Figure 3a indicates that for a small mismatch in size there is good mixing in the solid alkane/alkane monolayers. With increasing mismatch in alkane size, there is a larger excess enthalpy and hence poorer mixing in the monolayer. This supports the conclusion that only more similar molecules are able to mix effectively. The additional point of (0,0) should also be added to this graph to account for the ideal mixing of alkanes with themselves. Such a point does indeed follow the general trend of the other data of Figure 3a. There is rather a lot of scatter in the data, and we cannot conclude with any confidence if there is a linear or other mathematical form to this data set. However, we would expect Ω to increase with increasing mismatch, as observed, but then to saturate (19) Arnold, T. Ph.D. Thesis, Oxford, 2001.
for species that completely phase separate. This could explain the additional point at a relative size ratio of 0.4, suggesting that completely phase separated alkanes have a Ω value of approximately 3000 J mol-1. Figure 3c gives similar data for alcohol/alcohol monolayer mixtures adsorbed on graphite. These data illustrate the same general trends as Figure 3a for alkane/alkane mixtures and more clearly illustrates the approximately constant value of Ω for the strongest phase separated mixtures. When the interaction parameter is bigger than 2RT or 5000-6000 J mol-1 (depending upon the temperature),20 there should be complete phase separation and no further depression of freezing point, as observed. Figure 3b indicates that K for all the alkane/alkane mixtures investigated is larger than unity, and hence, we conclude that the longer homologue is preferentially adsorbed. The extent of preferential adsorption is observed to generally increase with larger relative differences in alkyl chain length, although there is significant scatter in these data. Such behavior may be expected on an entropy basis, as we can replace many smaller molecules on the surface with fewer larger molecules, although there has been some discussion of the relative energetics of adsorbed methyl and methylene groups in this context.9 Using our measured values of the equilibrium constant, K, we calculate the free energy, ∆G, of the surface exchange process using -RT ln K. Figure 3d illustrates a comparison of these calculated free energies with the values of Ω we obtained independently from the fitting procedure. Interestingly, other than one point, these data lie approximately on a straight line of gradient unity, which passes through the origin. This could be an entirely coincidental agreement between two essentially different energies (the free energy of exchanging short molecules (20) Everett, D. H. J. Chem. Soc., Faraday Trans. 1965, 61, 2478.
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for long ones on the surface and the excess enthalpy of mixing parameter, Ω). However, in some respects, mixing and partitioning are both relatively size dependent. Everett has formulated the chemical potentials of the adsorbed phases to include a contribution from the interfacial tensions18
gA(S) + RT ln(γA,SxA(S)) - (σ - σA*(S))aA(S) ) gA(L) + RT ln xA(L) - (σ - σA*(S))aA(L) where aA(S) is the area per mole of species A in the solid monolayer. Proceeding as before,
{gA(L) - gA(S)} ) RT ln(γA,SxA(S)/xA(L)) (σ - σA*(S))aA(S) + (σ - σA*(S))aA(L) If we assume that the areas per molecule in the liquid and solid monolayer are the same, then aA(L) ) aA(S) ) a, giving
{gA(L) - gA(S)} ) RT ln(γA,SxA(S)/xA(L)) + {σA*(S) σA*(S)}a Re-expressing the activity coefficient RT ln γA,S ) ΩxB,S2 gives
{gA(L) - gA(S)} ) RT ln(xA(S)/xA(L)) + (ΩxB,S2) + {σA*(S) - σA*(S)}a In comparison to the earlier model, we have replaced the regular solution interaction term ΩxB,S2 with two terms, ΩxB,S2 + {σA*(S) - σA*(S)}a. We have seen that {σA*(S) σA*(S)}a equals RT ln K. If Ω is small, then the experimentally determined parameter will be dominated by the differences in interfacial free energy arising from RT ln K. This could give rise to the equivalence between the measured Ω and RT ln K we observed. Alkane/Alcohol Mixtures. Using the experimentally determined phase diagrams and quantitative estimates of the monolayer melting enthalpies, we now consider the mixing behavior of the alkane/alcohol combinations given in Figure 1. Considering first C5OH/C8H in Figure 1a, we see a pronounced minimum suggesting predominantly phase separation, which might be expected for such dissimilar molecules. However, calculations using models, assuming complete phase separation, again indicate that the experimentally measured depression of monolayer freezing point is significantly less than that predicted from the enthalpies of melting of the pure monolayers of the alcohol and alkane. This suggests that either the measured enthalpies are considerably in error (by more than a factor of 2) or there is significant mixing in the solid monolayer. Again, we have used the regular solution model with preferential adsorption to fit these DSC surface phase diagrams. Figure 4a shows the variation of ln K with relative size ratio for all the alkane and alcohol combinations. It is clear from this figure that alcohols are preferentially adsorbed over alkanes. For example, an alcohol of chain length n can adsorb equally as strong as an alkane two methylene groups longer. The equivalence point, K ) 1, when both species are equally adsorbed corresponds to a relative size ratio of 0.2. Figure 4b reexpresses the data of Figure 4a as the free energy of the exchange equilibrium against relative size parameter. This graph also indicates that a relative size ratio of 0.2 will give approximately equal preferential adsorption between an alcohol and an alkane. The gradient of the best fit
Figure 4. Experimentally determined variation of (a) ln K, (b) ∆G, and (c) Ω with relative size ratio for alcohol/alkane monolayer mixtures. The lines are guides to the eye only.
straight line through these data gives a 19.3 kJ mol-1 free energy increment for a unit change in the relative size parameter. Again, using the relation between RT ln K and the differences in interfacial tensions of the pure monolayers, (σA* - σB*)a, we can compare the results from different combinations of adsorbed species. This approach has been proposed by Everett.21 For example, the difference between RT ln K for C8OH/C8H (4537 J mol-1) and C8OH/C9H (2462 J mol-1) should be equal to
(σC8OH* - σC8H*)a - (σC8OH* - σC9H*)a ) (σC8H* - σC9H*)a where (σC8H* - σC9H*)a ) RT ln K for C8H/C9H (2051 J mol-1) if we assume the areas per molecule, a, are approximately equal. The RT ln K calculated from the difference is 2075 J mol-1, in very good agreement with (21) Brown, C. E.; Everett, D. H.; Morgan, C. J. J. Chem. Soc., Faraday Trans 1975, I 71, 883.
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Figure 5. Surface composition as a function of solution composition for binary mixtures of C8OH/C10H (alcohol/ alkane). The solid circles are the experimental points. The diamonds are the calculations with preferential adsorption. The diagonal line represents the case where surface and bulk compositions are the same.
the observed value 2051 J mol-1. This is the only combination of species where we can make this comparison without making corrections for differences in molecular size. Everett et al. report that, at 298 K, (σC2OH* - σC7H*)a/RT (for ethanol/heptane) is 2.43, corresponding to 6020 J mol-1, in reasonable agreement with that found here for alcohol/alkane mixtures with a similar relative size ratio (0.57) of 6200 J mol-1. Figure 4c gives the variation of the regular solution excess enthalpy parameter with the difference in alkyl chain length. Significantly, this figure indicates that this Ω parameter is large and approximately constant with relative size ratio, although there is significant scatter in the data. This is in marked contrast to the alkane/alkane mixtures and the alcohol/alcohol mixtures where Ω is found to increase with mismatch for similar sized molecules. Hence, this figure indicates that there is a dominant unfavorable interaction simply arising from mixing an alcohol and an alkane in the solid monolayer independent of the differences in chain lengths of the two species. There is a similar, approximately constant, behavior when the data is plotted against relative size ratio. Alkane/alkane and alcohol/alcohol combinations can mix effectively in the monolayer when they are sufficiently similar in size. This is reflected here by the small excess parameter, Ω, we observe for combinations with small relative size ratios. The combinations with larger relative size ratios predominantly phase separate and have a much larger excess parameter, Ω. The large Ω seen for all alkane/ alcohol combinations suggests that essentially all these combinations phase separate to a significant extent. Incoherent Neutron Scattering. In Figure 5, we present the variation in the surface composition as a function of bulk solution composition for a binary mixture of an alcohol and an alkane, C8OH/C10D, adsorbed on graphite obtained from incoherent elastic neutron scattering. The data in Figure 5 illustrate that to obtain a surface composition with equal amounts of both components the bulk mixture must be significantly in excess in the alkane. This is the case even though the alkane has a longer alkyl chain than the alcohol and is in excellent agreement with the DSC analysis above. The behavior of alkane/alcohol mixtures is clearly more subtle than the alkane/alkane or alcohol/alcohol mixture with the shorter
Figure 6. Variation of ln K with relative size ratio for monolayer mixtures of (a) alcohol/alkane, (b) alkane/alkane, and (c) alcohol/alcohol mixtures adsorbed on graphite. These data combine analysis of both DSC and INS data.
alcohol sometimes competing effectively with a longer alkane. The data in Figure 5 can also be used to estimate the exchange equilibrium constant, K, of the species for the surface. In Figure 5, the experimental data (b) is compared with such an analysis ([) with K ) 0.1 for this alcohol/alkane mixture. This value of K is in reasonable agreement with that determined by DSC (K ) 0.24). We have also used IQNS to investigate the mixture C7OH/ C10D and find a value of K ) 3.44 determined by IN10, again in reasonable agreement with that determined by DSC (7.5). In Figure 6, we present a combination of DSC and IQNS data showing the ln K values as a function of relative size ratio for (a) alcohol/alkane, (b) alkane/alkane, and (c) alcohol/alcohol mixtures. In preparing this figure, we have taken IQNS data from alkane/alkane mixtures adsorbed on graphite determined by incoherent elastic neutron scattering which have been presented elsewhere19 and IQNS data from adsorbed alcohol/alcohol mixtures. For
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all these combinations, we see there is reasonable agreement between the extent of preferential adsorption between the DSC and IQNS measurements. Clearly, we also expect that molecules can compete with themselves equally for the surface and hence the data must also pass through the point (0,1.0) on the log graph, as indeed we observe for alkane/alkane and alcohol/alcohol mixtures. The trend in these data is clear with longer molecules being preferentially adsorbed. Interestingly, this is different from recent MD computer simulation of binary alkane mixtures on graphite where the shorter analogue was preferentially adsorbed.22 However, there may be an issue of kinetic versus thermodynamic preferences in the relatively short times scales of the MD simulation. For the alkane/alcohol mixtures, Figure 6a, it is evident that the curve does not pass through the origin but well to the right of that point, clearly indicating that the alcohols are preferentially adsorbed over alkanes of a similar chain length. However, it is clear that, by changing conditions, such as increasing the bulk solution composition or increasing the length of the alkane molecules, the alkane can be made to be present as the major component on the surface, even if the other is still preferentially adsorbed. In understanding the difference in behavior of homoand heteromixtures, one principle factor is the nature of the OH group of the alcohol which can form strong hydrogen bonds. One approach can be to consider that such intermolecular association can be considered to effectively increase the length of the alcohol molecules by dimerization making the alcohols appear “longer”, leading to a stronger adsorption. However, the data presented above seem to indicate that the equivalence in adsorption is not between an alcohol of length n and the alkane with a length of 2n but only with an alkane 10-15% longer. This clearly suggests more subtle effects are important. Discussion and Conclusions This work has clearly indicated that binary mixtures of simple linear alcohols and alkanes form solid adsorbed monolayers above the melting point of the bulk mixtures. In addition, we have characterized the extent of preferential adsorption in alkane/alkane, alcohol/alcohol, and alkane/alcohol binary mixtures. Generally, we identify that, for homomixtures, the longer homologue is preferentially adsorbed. However, in the heteromixtures, a shorter alcohol can compete effectively with a longer alkane for the graphite surface. The mixing behavior for these mixtures has been presented in terms of a regular solution model. For homomixtures (alkane/alkane and alcohol/alcohol mixtures), we find a significant extent of mixing depending upon the relative sizes of the species. This is in contrast with the alkane/alcohol mixtures where extensive phase separation seems to be the norm. The adsorption of alcohol molecules from dilute binary mixtures of alcohols in alkanes and has been reported previously3 where the formation of a close packed layer of alcohol (decanol) is identified on adsorption from heptane which melts some 40-50 K above the bulk melting point, in good agreement with the results presented here. The enthalpies of displacement were determined to be approximately 5 kJ mol-1 for mole fractions over 10 × 10-3 but depend on composition and temperature. It was deduced that the adsorption of individual alcohol molecules from heptane was not particularly favorable. Only ad(22) Smith, P.; Lynden-Bell, R. M.; Smith, W. Mol. Phys. 2000, 98, 255-260.
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sorption to form favorable alcohol-alcohol interactions leads to preferential adsorption. The relative size ratio for decanol and heptane is approximately 0.36. Using Figure 6a, we would expect a K value of approximately 10.0 for this system, at the eutectic minimium. Estimating the relevant temperature to be 20 °C, this corresponds to a free energy of exchange of 5.6 kJ mol-1. In our calculations for K, we consider the eutectic composition where the solid and liquid monolayers are in equilibrium. This differs from the work of Findenegg et al. where the adsorption of the alcohol over the alkane also corresponds to a phase change to a solid monolayer, so direct comparison with the early work is not straighforward. The formation of solid monolayers of alcohols has also been reported by workers using diffraction.10,23,24 The molecular structures are found to involve a “zigzag” herringbone arrangement of molecules in the solid monolayers. Given that most of the monolayer structures of alkanes25-27 contain molecules that are essentially parallel to each other and are not arranged in a zigzag, it is perhaps not unexpected that the alkanes and alcohols do not mix. The shorter alkanes with an even number of carbons (4, 6, 8, and 10) do have a zigzag arrangement of molecules and might be more likely to mix. However, the data presented here would indicate that even in these most favorable circumstances the adsorbed alcohols and alkanes separate on the surface. In the mixing model used here, we have assumed that the adsorbed liquid solutions are ideal. While this may be a reasonable approximation for homomixtures, like alkane/alkane mixtures, it is known that mixtures of alkanes and alcohols are not ideal in the bulk and are unlikely to be ideal on the surface. The excess functions for some bulk alcohol/alkane mixtures28,29 have been reported. In the context of the regular solution model used here, nonideal behavior in the adsorbed liquid mixture will reduce the value of Ω experimentally determined. This indicates that the Ω values we obtain are lower estimates of the true values in the mixed monolayers. Typical values of the maximum excess enthalpy observed experimentally in the bulk are in the range 400-700 J mol-1 which would correspond to Ω values of 1600-2800 J mol-1 if translated directly into the monolayers. In addition, there can also be excess entropy contributions but these are generally much smaller than the excess enthalpy terms. However, we consider it unlikely that the extent of nonideality will be the same in the surface and the bulk and that these bulk estimates represent an upper estimate of the extent of the issue. Our approach is very similar to that of Sloutskin et al.30 except they study the air/liquid and liquid/liquid interfaces rather than the solid/liquid interface studied here. They report essentially the same behavior, with a related regular solution type approach, with the mixing behavior depending upon the relative mismatch in molecule size. They find a linear dependence of the interaction parameter (23) Morishige, K.; Takami, Y.; Yokota, Y. Phys. Rev. 1993, B48, 8277-8281. (24) Morishige, K.; Sakamoto, Y. J. Chem. Phys. 1995, 103, 2354. (25) Herwig, K. W.; Newton, J. C.; Taub, H. Phys. Rev. B 1994, 50, 15287-15297. (26) Arnold, T.; Thomas, R. K.; Castro, M. A.; Clarke, S. M.; Messe, L.; Inaba, A. Phys. Chem. Chem. Phys. 2002, 4, 345-351. (27) Arnold, T.; Dong, C. C.; Thomas, R. K.; Castro, M. A.; Perdigon, A.; Clarke, S. M.; Inaba, A. Phys. Chem. Chem. Phys. 2002, 4, 34303435. (28) Wieczorek, S. A. J. Chem. Thermodyn. 1978, 10, 187-199. (29) Wieczorek, S. A. J. Chem. Thermodyn. 1979, 11, 239-245. (30) Sloutskin, E.; Bain, C. D.; Ocko, B. M.; Deutsch, M. Faraday Discuss. 2005, 129, paper 24.
Alkane/Alcohol Mixed Monolayers
with (∆n/n)2. This dependence is interpreted in terms of free volume for kink and gauche formation in molecules of different lengths. These authors do not include the free energy differences of the pure monolayers in the calculation of chemical potential. There appears to be reasonable agreement between our results and theirs; for example, they find that for the alkane/alkane mixture C26:C36 with a relative size parameter of 0.31 (their parameter δ ) 0.096) they find an interaction parameter of approximately 1.2 KBT, from their Figure 4. From Figure 3a in this work, we find that Ω is 3500 J mol-1 or Ω/RT ) 1.4 (where T is approximately 300 K). It is interesting that the interaction parameters in solid monolayers adsorbed at the air/liquid and liquid/liquid interfaces are clearly similar to those at the solid/liquid interface. Interestingly, these authors report that the shorter homologue in the homomixtures is preferentially adsorbed unlike in our case where it is the longer molecule. Molecules are reported
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to adsorbed in an upright orientation at the air/liquid interface. Hence, the area per molecule is essentially the same for long or short alkanes. Hence, there is no entropy gain upon adsorbing a longer molecule, over a shorter one, at the air/liquid interface which is found at the solid/ liquid interface where the molecules have their carbon backbone parallel to the surface. Acknowledgment. The authors thank The Leverhulme Trust (S.M.C.) and JSPS (Grant No. A-16205001) (A.I.) for financial support and the staff and scientists at ILL for beam time and technical assistance. Division of Materials Sciences, Office of Basic Energy Sciences, U.S. Department of Energy, under Contract No. DE-AC0500OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC. LA0501280
