J. Phys. Chem. 1992, 96,2407-2409
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p ,T,x Surface of Liquid-Liquid Immiscibility in Aqueous Solutions of Tetraalkylammonium Salts Hermann Weingartner* and E k e Steinle Institut fur Physikalische Chemie und Elektrochemie der Universitat Karlsruhe, Kaiserstrasse 12, 0-7500Karlsruhe, Germany (Received: November 25, 1991; In Final Form: January 24, 1992)
Aqueous solutions of higher homologues of tetraalkylammonium salts exhibit liquid-liquid phase separation. A model study of the pressure-temperatureomposition (p,T,x) surface of immiscibility of tetraisopentylammonium bromide + H20up to 370 K and 200 MPa yielded a closed miscibility gap at atmospheric pressure with its lower part suppressed by crystallization, and a very unusual hyperbolic shape of the p,T,x surface. The results reflect a very peculiar behavior of the thermodynamic excess functions of aqueous solutions of hydrophobic ions which is discussed in relation to known regularities in the thermodynamic properties of the lower homologues which are completely miscible with water.
Introduction Symmetrical quarternary ammonium salts (R4N+X-, where R stands for alkyl chains) form an interesting class of 1:1 electrolytes which are capable of subtle and nearly continuous structure variations. Thermodynamic aspects of their hydration and mutual interaction in water are of broad interest, as these salts may serve as model compounds for hydrophobic electrolytes with solution properties lying somewhere between those of simple alkali metal salts and those of surface-active ammonium salts with long alkyl chains. Vast research effort in the past four decades has resulted in a comprehensive characterization of the thermodynamic properties of the lower homologues with alkyl chains R ranging from methyl to n-butyl (or in a few cases to n-pentyl) under ambient condition^.^-^ From these investigations an extensive data base is now available for the principal thermodynamic functions of these systems and for their major derivatives. There remains, however, much to be explored at high temperatures and high pressures, where changes in the structural features of liquid water may lead to new phenomena. Recently detected liquid-liquid immiscibilities in aqueous solutions of these salts a t elevated temperatures4-* represent such an interesting phenomenon. In general, liquid-liquid unmixing in electrolyte solutions is very unusual, but we have recently demonstrated6s7that it is a common feature of aqueous solutions of higher tetraalkylammonium salts a t elevated temperatures. At room temperature most of these gaps are suppressed by crystallization. A thermodynamic analysis6v7as well as model calc u l a t i o n ~of~ these phase equilibria suggest that specific forces owing to hydrophobic effects are the driving force for phase separation. This distinguishes this type of unmixing sharply from the phase separations known to be present for electrolytes dissolved in solvents of low dielectric constant,7J0 which appear to be driven by the long-range Coulombic interactions. In this paper we report on a pilot study of the pressure-temperature-composition (p,T,x) surface of the liquid-liquid immiscibility of R4NX + H20systems, using tetraisopentylammonium bromide, i-Pe4NBr, as a model compound. This system is particular suited, as its upper critical solution temperature of 369 K at 0.1 MPa is the lowest found so far in R4NX H20 system^,^ and the salt is sufficiently stable at this temperature. It will turn out that the p,T,x surface shows rather extravagant features, resulting from the distinct behavior of the thermodynamic functions of hydrophobic electrolytes. We have also performed some additional experiments with tetra-n-butylammonium bromide (Bu,NBr) and other lower homologues which at atmospheric pressure are completely miscible with water above the crystallization curve.
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Experimental Section Details on sample preparations and on measurements at atmospheric pressure are given elsewhere.' Phase separation at high
pressures was studied with a simple high-pressure optical cell with sapphire windows" which enabled measurements up to 480 K and 250 MPa. The p,T,x surface was measured by a point-by-point visual determination of the pressure and temperature of transition from the homogeneous to the heterogeneous phase for samples of known composition.
Results and Discussion Figure 1 shows the p , T j surface of liquid-liquid immiscibility of i-Pe4NBr + H20.For convenient representation we use in this figure the weight fraction, w,, of the salt rather than the mole fraction, x l , as a composition variable, as this enables a quite symmetric representation of the temperature-composition projection. If plotted in terms of xI,the gaps are highly unsymmetrical and confined to the water-rich regime? The p , T j surface in Figure 1 is constructed from about 120 experimental data points. From our previous results' on the phase behavior of RINX systems at atmospheric pressure it has become evident that the higher homologues form closed liquid-liquid immiscibility gaps with their lower parts suppressed by crystallization. In the system considered here, the upper critical solution temperature (UCST) is at 369.2 K and a mole fraction x , = 0.035. Below about 320 K, the gap narrows again, thus indicating a closed miscibility loop. Crystallization interferes a t 303 K. If plotted in weight fraction units, the lower part of the gap and the lower critical solution temperature (LCST) can be reasonably estimated by symmetrical extrapolation of the visible part, as has been confirmed for similar system^^^^ where larger parts of the loop can be monitored. The LCST is found by this extrapolation to lie at about 273 K. The dashed line in Figure 1 shows the extrapolated part of the coexistence curve at 0.1 MPa. The complete p,T,x surface in Figure 1 shows that with rising pressure the zone of immiscibility first exhibits a slight decrease, followed by an increase above 60 MPa, thus resulting in a wcalled (1) Huot, J.-Y.; Jolicocur, C. In The Chemical Physics of Solvation; Dogonadze, R., Kalman, E., Kornyshev, A. A., Ulstrup, J., E&.; Elsevier: Amsterdam, 1985; Part A, Chapter 11, and references cited therein. (2) Franks, F.; Reid, D. S. In Water. A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, Chapter 5. (3) Wen, W.-Y. In Water and Aqueous Solutions; Horne, R. A., Ed.; Wiley: New York, 1972. (4) Mugnier de Tobriand, A.; Lucas, M. J . Inorg. Nucl. Chem. 1979,41, 1214.
( 5 ) Glasbrenner, H.; Weingirtner. H.J . Phys. Chem. 1989, 93, 3378. (6) Weingirtner, H. Eer. Eunsenges. Phys. Chem. 1989, 93, 1058. (7) Weingkrtner, H.; Merkel, T.; Maurer, U.; Conzen, J.-P.; Glasbrenner, H.; Kashammer, S. Eer. Eunsenges. Phys. Chem. 1991, 95, 1579. (8) Japas, M. L.; Levelt-Scngers,J. M. H. J. Phys. Chem. 1990,945361. Friedman, H. L. J. Solurion Chem. 1991, 20, (9) Xu,H.; Raineri, F. 0.; 739. (10) Friedman, H. L.; Larsen, B. J . Chem. Phys. 1979, 70, 92. (1 1) (a) Schneider, G. M. Eer. Eumenges. Phys. Chem. 1966,70,497. (b)
Schneider, G. M. In Chemical Thermodynamics, A Specialist Periodical Report; McGlashan, M. L., Ed.; The Chemical Society: London, 1978.
Author for correspondence.
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Letters
2408 The Journal of Physical Chemistry, Vol. 96, No. 6, 1992
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Figure 2. Pressure dependence of the upper (0)and extrapolated lower (---) critical solution temperatures in the system i-Pe,NBr + H,O. For
details see text.
hyperbolic tube of immiscibility in the p,T,x space."-'3 This becomes also evident from Figure 2, which displays a minimum in the pressure dependence of the UCST at about 60 MPa. Based on the rough extrapolation, the corresponding maximum of the LCST appears to occur at a slightly higher pressure. The zone of immiscibility is well removed from the liquid-gas critical line. In the generally accepted nomenclature this corresponds to type VI behavior.13 From nonelectrolyte thermodynamics we know that type VI mixtures are invariably composed of complex molecules exhibiting strong intermolecular forces or hydrogen bonding, and in most cases water is one of the component^.^^^,^^ Four possible types of phase diagrams are known within the class of type VI mixtures, from which the hyperbolic tube observed here appears to be the most rare one, so far only observed for solutions of certain methyl-substituted pyridines and piperidines in H20 and D2O.I1J3In general, the observation of a hyperbolic type of (12) The particular shape of the tube in the p,T,x space shown in Figure 1 was first observed in an aqueous nonelectrolyte mixture" and for vividness it has been denoted as 'hyperbolic tube"."," This does imply that any of the projections corresponds to a hyperbola in the mathematical sense. (1 3) See e.g.: Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures; Butterworths: London, 1982.
the p,T,x surface suggests the existence of two overlapping immiscibility regions, namely a low-pressure immiscibility which disappears with rising pressure, and a high-pressure immiscibility which increases with rising pressure.I13l3 It is of large interest to examine how this phase behavior is related to the properties of the lower homologues like Bu4NBr which under ambient conditions are completely miscible with water. We have therefore searched for unmixing at higher pressures and temperatures in solutions of the lower homologues, but we could not detect any immiscibility region in the case of Bu4NBr and the corresponding tetraethyl and tetrapropyl salts up to 250 MPa. On the other hand, it is well-known that the thermodynamic properties of the lower members in the homologous R4NX series show certain reg~larities,'-~ and search for interrelations between these regularities and the observed phase behavior of the higher homologues is expected to give important new insight into electrolyte thermodynamics of hydrophobic ions. First, we note that by combining the thermodynamic stability criteria with semiempirical approaches for the osmotic or activity coefficient, one may deduce conditions for unmixinga6 For example, Pitzer's equations often used in electrolyte thermodynamics incorporates a modified Debye-Hiickel law plus a virial coefficient series truncated after the second or third virial coefficient term.14 With these equations one finds that largely negative second osmotic virial coefficients are required to obtain unmixing.6 This is just what is reflected by the known14Pitzer parameters of the lower R4NX homologues, where with increasing chain lengths the contribution due to the second virial term becomes increasingly n e g a t i ~ e . ~Such J ~ negative virial coefficients are usually interpreted in terms of attractive specific interactions, and more specifically, they are considered to be manifestations of the hydrophobic On a more quantitative basis this has recently been confirmed by statistical-mechanical calculations under the hypernetted chain (HNC) approximation of the phase behavior of hydrophobic model electrolytes characterized by ion-ion pair potentials of the Friedman-Gurney type? The observation of a closed immiscibility loop and its peculiar pressure-dependence draws attention now to some new, hitherto largely unknown aspects of the solution thermodynamics of hydrophobic electrolytes. Let us first examine consequences of the existence of a closed loop in the T,x plane for the behavior of the thermodynamic excess functions. As is ~ell-known,'~ the simultaneous existence of a LCST and UCST requires the second derivative of the molar excess enthalpy with respect to composition, ( C ~ ~ H E , / Cto~ change X ~ ~ ) sign from plus to minus with rising temperature at constant pressure. With the usual assumption concerning the absence of inflection points in the excess functioncomposition relationships,11+13 the sign of the second derivative determines that of H", itself; Le., H ", must change sign from negative to positive with rising temperature. While there is no information on these quantities for the system considered here, and for other homologous systems with liquid-liquid phase separation, this general behavior can be inferred from the enthalpies of the completely miscible lower homologues like Bu4NBr + H 2 0 near room temperature in conjunction with the unusually large and positive heat capa~ities.~-~ More directly, it follows from vapor pressure data for Bu4NBr H 2 0 at elevated temperatures," which indicate a change in sign of H", a t about 373 K. We note that in particular the large heat capacities are a specific feature of aqueous solutions of hydrophobic Hence, in this respect the existence of a closed loop appears to reflect the thermodynamic pecularities of the lower homologues. In this context it is also interesting that detailed considerations of the thermodynamics of hydrophobic nonelectrolytes in aqueous solutions2 have indicated that in certain cases conditions are right for the Occurrence of an LCST. From thermodynamic arguments this implies 71ASEl > I Pl, where ASE is the excess entropy. Changes in the phase behavior of homologous solutes with chain length then arise from lASEl increasing faster than l e i , due
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(14) Pitzer, K . S.; Mayorga, G. J . Phys. Chem. 1973, 77, 2300. (15) Mayrath, J . E.; Wood,R. H.J . Chem. Thermodyn. 1983, 15, 625.
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J . Phys. Chem. 1992, 96, 2409-2410 to a different sensitivity of both quantities to hydrophobic and hydrophilic contributions.2 At least part of these more phenomenological arguments also apply to the systems considered here. It is more difficult to relate the unusual pressure dependence of the miscibility gap to available thermodynamic data for the lower homologues. The pressuredependence of the critical solution temperatures (LCST’s and UCST’s) is given by1I9l3
where V, is the molar volume, t“, the molar excess volume, and subscript c means at the critical solution point. To a first approximation this implies a change of sign of v“, from minus to plus with rising pressure along the critical loci. If the usual regularities in the homologous series hold also for v“,,our results imply that either such a change in sign is also present for the lower homologues, or that there is at least a tendency toward such a change within the homologous series. Unfortunately, the available molar volume and compressibility datal” are too limited to test this prediction. Finally, we note that some results of detailed studies of various types of phase behavior of nonelectrolyte mixtures” are of direct relevance for the present work. Generalizing this results to electrolyte systems, and assuming regularities in the thermodynamic properties of the homologues series, the following general conclusions on the phase behavior of R4NX-water systems can be drawn. There are two regions of immiscibility at high and low pressure, respectively. For the higher homologues, as represented by iPe4NBr, both regions overlap, leading to the recently observed immiscibilities at atmospheric pressure7 and, at least for i-Pe4NBr, to the hyperbolic shape of the p,T,x surface reported here. Increase of the length of the alkyl chains leads to a broadening of both immiscibility zones,resulting in the increase of the gaps a t atmospheric pressure reported r e ~ e n t l y .Decrease ~ of the chain length results in complete miscibility of the lower homologues in the entire (p,T,x) range accessible by our experiments (480 K, 250 MPa). This may be interpreted as a separation of both immiscibility zones. The low-pressure immiscibility shifts to lower pressures and eventually is displaced completely to the region of negative pressures, while the high-pressure immiscibility shifts toward higher pressures, thus resulting in complete miscibility in an intermediate regime including atmospheric pressure. Due to the lack of a sufficient data base, it is difficult to give more definite predictions. The hypothetical immiscibility regions at negative pressure, predicted for the lower homologues, are well-known from none-
lectrolyte thermodynamics.11J3 In the case of Bu4NBr, some support for this interpretation comes from the observation16that under ambient conditions the addition of small amounts of typical “salting-out” salts like Na2S04or KCl to aqueous Bu4NBr results in liquid-liquid phase separation. In analogy to similar observations on salting-out out of hydrophobic nonelectrolytes in aqueous solutions (e.g., in the system 3-methylpyridine + H20 salt”) this may be interpreted as a displacement of the hypothetical immiscibility region from negative toward positive pressures upon addition of salting-out electrolytes. In conclusion, we can state that the observed phase behavior appears to be closely related to the known thermodynamic pecularities of the completely miscible lower homologues which are usually attributed to the presence of hydrophobic effects, thus suggesting that phase separation is mainly driven by hydrophobic forces. This reconfirms our earlier a n a l y ~ i sand ~ , ~the results of the calculations of Friedman and co-workers? in which unmixing has been attributed to the presence of cation-cation and cationanion pairs as manifestations of the hydrophobic effect in such systems. We may therefore speak of hydrophobic (or solvophobic) phase separation,'^^ in contrast to the Coulombic phase separation due to long-range Coulombic forces observed in certain electrolyte solutions in solvents of low dielectric c ~ n s t a n t . ~ ~ ~ ~ ~ ’ ~ The nature of the driving force for unmixing is of special interest for interpreting the unusual critical behavior of some ionic fluids. Recent experiments by Singh and PitzerIs and ourselves19 in electrolyte solutions exhibiting Coulombic unmixing have given evidence that the near-critical behavior of some ionic fluids is quite different from that of nonelectrolyte systems in that apparently classical critical behavior is observed rather than the king behavior found at liquid-gas and liquid-liquid critical points of nonelectrolytes. This contrasts, however, sharply with an Ising-like behavior observed by Japas and Levelt-Sengers* for the system tetra-n-pentylammonium bromide + water. A possible rationale is that the different driving forces lead to this discrepant behavior. In contrast to the nonaqueous electrolyte systems, hydrophobic forces appear to dominate the critical behavior in R4NX H 2 0 systems, Coulombic forces playing a minor role.
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Acknowledgment. Financial support by the Deutsche Forschungsgemeinschaft is gratefully acknowledged. (16) Weingartner, H. Unpublished results. (17) For a more detailed discussion of the differences of the molecular structures leading to Coulombic and hydrophobic unmixing see for example refs 7 and 9. (18) Singh, R. R.; Pitzer, K. S.J . Chem. Phys. 1990, 92, 6775. (19) Weingartner, H.; Wiegand, S.; Schrkr, W. J. Chem. Phys. 1992,96, 848.
“Hardness Profile” of a Reaction Path Dipankar Datta Department of Inorganic Chemistry, Indian Association for the Cultivation of Science, Calcutta 700 032, India (Received: November 22, 1991; In Final Form: January 21, 1992)
The variation of the hardness of a chemical species along a reaction path, which we call the “hardness profile”, is shown to go through a minima at the transition state. The hardness values are calculated by the MNDO method.
(1) Parr, R. G.; Pearson, R. G . J . Am. Chem. SOC.1983, 105, 7512.
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(2) Pearson, R. G. Proc. Narl. Acad. Sci. U.S.A. 1986, 89, 1827.
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