Usual and Unusual Surface Tensions of Perfluorocarbon-Containing Binary Liquid Mixtures near a Critical Endpoint

Usual and Unusual Surface Tensions of Perfluorocarbon-Containing Binary Liquid Mixtures near a Critical Endpoint

JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO. 203, 31–40 (1998) CS985497 Usual and Unusual Surface Tensions of Perfluorocarbon-Containing Bi...

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JOURNAL OF COLLOID AND INTERFACE SCIENCE ARTICLE NO.

203, 31–40 (1998)

CS985497

Usual and Unusual Surface Tensions of Perfluorocarbon-Containing Binary Liquid Mixtures near a Critical Endpoint Ian A. McLure, 1 Richard Whitfield, 2 and James Bowers 3 Department of Chemistry, The University, Sheffield S3 7HF, United Kingdom Received October 8, 1996; accepted February 26, 1998

on established simple molecular models, e.g. the quasicrystalline model (1), with well-understood pathways for accounting for deviations from ideality. These deviations can often, although always with care, be interpreted in terms primarily of the relative strength of the interaction between the unlike molecules in the mixture and, when that primitive line of reasoning fails, of secondary molecular factors such as size, chain length, flexibility, shape, or local correlation of molecular orientation. However, although there is no similarly rigorous route to surface tension ideality, the nearlinearity in mole fraction x of the surface tension s of argon / krypton (2), the archetypal real but effectively ideal liquid mixture, reminds us that a linear s(x) dependence relationship offers an equally useful operational benchmark for surface ideality—and a simpler one than those previously suggested (3) —from which deviations can be as readily understood in terms of intermolecular forces as those from Raoult’s law. The use of alternative definitions of surface ideality, such as that suggested by Rusanov (4) in which the surface tension is necessarily concave, would little alter our conclusions here since nearly all of our mixtures display markedly negative deviations, no matter the definition of ideality adopted. Essentially as much as this was pointed out, although cast then in terms of the composition dependence of the boiling temperature Tb of mixtures, by Hildebrand and Scott in 1948 (5). Then and now it was clear that as much can be learned about intermolecular forces in mixtures from surface tensions as from vapor pressures. Our purpose here is to explore some of the limits to this assertion with specific examples that both confirm and contradict it. The paper opens then with a short background summary of the qualitative features of the behavior of the surface tension of binary liquid mixtures, chiefly but not restricted to the dependence on concentration, using the related behavior of vapor pressures as a guide to interpretation and in seeking new phenomena. The experimental procedure for measuring the surface tensions of four mixtures containing a perfluoroalkane which illustrate the complexity of behavior exhibited by mixtures of even relatively simple substances is outlined, and the results for each mixture studied and

The surface tension of binary mixtures near critical endpoints is discussed with detailed focus on the composition dependence. The similarity with the corresponding composition dependence of the vapor pressure is explored. The differences between mixtures in which the more volatile component is of lower surface tension, i.e. is less tense—known as usual mixtures—and those in which the more volatile component is more tense—known as unusual mixtures—are analyzed. As a basis of discussion, a limited review of the related literature is presented along with some fresh results for two usual mixtures (octamethylcyclotetrasiloxane / perfluoropentane and heptane / perfluorohexane) and two unusual mixtures (pentane / perfluoroheptane and 2-methylpentane / perfluorotributylamine). These mixtures display a variety of horizontal inflections characteristic of the behavior of the noncritical interface near a critical endpoint. The form of the horizontal inflection is uniformly related to the sign of the difference between the surface tensions of the pure components, i.e. with the overall negative slope towards the less tense component. A number of the mixtures also exhibit aneotropy or surface azeotropy. All these results are shown to be well described by the Surface Regular Solution theory. q 1998 Academic Press Key Words: Surface tension; perfluorocarbon; critical endpoint.

1. INTRODUCTION

Although equally common, the variety of maxima, minima, and points of inflection exhibited by the vapor/liquid surface tension isotherms of binary liquid mixtures of nonelectrolytes enjoys much less recognition and understanding than the corresponding features of the more familiar vapor pressure isotherms. This arises partly perhaps because, unlike surface tensions, the theory for vapor pressure ideality, i.e. the linear dependence on mole fraction x known as Raoult’s law, rests 1

To whom correspondence should be addressed. Current address: Birchall Centre for Inorganic Chemistry and Materials Science, Chemistry Department, Keele University, Staffordshire ST5 5BG, United Kingdom. 3 Current address: Department of Chemistry, The University, Durham DH1 3LE, United Kingdom. 2

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0021-9797/98 $25.00 Copyright q 1998 by Academic Press All rights of reproduction in any form reserved.

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others from the literature are discussed in detail. The discussion of the results and the literature survey will focus on the behavior of the inflection near the critical molefraction xc and on the incidence of surface azeotropy or aneotropy. Although our chief purpose was not to describe results of our surface tension measurements in quantitative terms using a molecular theory, we have further tested the solubility version of the Surface Regular Solution theory which we have recently shown to predict with some success the surface tension behavior of other alkane or dimethylsiloxane / perfluorocarbon mixtures. 2. BACKGROUND

Two simple qualitative observations form the basis for a vapor pressure-linked discussion of the surface tension of mixtures. The first reflects the intermolecular forces in pure liquids and states that in general the less strongly cohesively bound of the components of a binary mixture is both the more volatile and the less tense, i.e. has the higher vapor pressure and the lower surface tension, respectively. If the comparison is made at the same actual temperature this assertion is not invariably reliable, notably for the alkanes and perfluoroalkanes to be discussed below, but it is essentially valid when the comparison is made at the same corresponding temperature, no matter how defined. The second observation reflects the intermolecular forces in mixed liquids and so is necessarily more complex and rather less reliable. Usefully cast in terms of the deviation factor j in the Berthelot or geometric-mean rule for the characteristic energies, eij , between a pair of molecules i and j, i.e. eij Å j( eiiej j ) 1 / 2 , the general observations are that mixtures in which j exceeds unity, i.e. mixtures in which complexing or a specific attractive interaction exists between the unlike molecules, exhibit negative deviations from Raoult’s law and positive deviations from surface tension ideality and that the more common mixtures for which j is less than unity display positive deviations from Raoult’s law and negative deviations from surface tension ideality. 2.1. Extrema Two further general observations can be made, both depending on the magnitude of j. The first is that the more j departs from unity, the greater are the deviations from Raoult’s law and provided that the vapor pressures of the pure components pi* (where the subscript i denotes component i) are not too dissimilar, the mixture vapor pressure isotherms develop extrema which may be either negative or positive depending on whether j exceeds or is less than unity, respectively. This is known as azeotropy. The effect on the surface tensions is similar but of opposite sign. Values of j markedly different from unity can also cause extrema in surface tension, provided again that the surface tensions

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of the pure components s i* are not too dissimilar, although in this case the extrema are positive or negative depending on whether j is less than or exceeds unity, respectively. This has been termed surface azeotropy or aneotropy (6) and occurs quite widely. Negative aneotropy is much more common than positive aneotropy, reflecting the greater prevalence of positive deviations from Raoult’s law (7). As indicated above, the surface tensions and vapor pressures of the pure liquids are somewhat coupled, but they do not necessarily vary with temperature in the same way, nor do the vapor pressures and surface tensions of mixtures depend on composition in the same way. Thus although tempting, it is mistaken, as Prigogine and Defay have pointed out (8), to infer from the observation in the last paragraph that azeotropy and aneotropy must occur simultaneously—i.e. at the same temperature in a given mixture—and even if they do, and this is not uncommon, to further assume that they occur in a mixture of the same composition. 2.2 Inflections The second generalization concerns mixtures in which j takes low values compared to unity, say around 0.9. Limited miscibility then usually occurs with a limit of complete miscibility in the presence of the coexisting vapor at a critical endpoint (CEP). Most CEPs are upper critical endpoints (UCEP), below which the mixture separates into two liquid phases, rather than lower critical endpoints (LCEP), above which the mixture phase-separates. These occur at upper or lower critical solution temperatures, TUCS or TLCS , respectively. For present purposes there is little need to distinguish UCEPs and LCEPs since, although our present discussion entails only the former it, applies equally well for the most part to both. At such endpoints, provided that the pi* of the pure components i are not too similar, there is a discernible point of horizontal inflection in the vapor pressure isotherm at the composition, xc , of the critical mixture, and provided that the si* are, again, not too similar there is a discernible point of horizontal inflection in the surface tension isotherm at xc . The vapor pressure isotherm is a thermodynamic requirement at a CEP, although in the presence of azeotropy it can be hard to discern (9). 2.3. Modern Treatments The origin of the foregoing extrema and inflections in vapor pressure isotherms have been given quantitative expression in terms of the strictly regular solution theory of mixtures by Prigogine and Defay (10) and of the extrema in surface tension isotherms by Prigogine, Defay, and Bellemans using the same theory (11). However, for a theoretical discussion of the inflections in surface tensions near a CEP we must turn to more recent work. In 1977 Widom investigated the behavior of the surface tension and density profile of a noncritical interface near a

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critical endpoint using a mean-field theory (12). The theory was general, but in the context of this article, the critical endpoint that we focus on is that which occurs in a binary liquid mixture coexisting with its vapor. Widom predicted inter alia that the mixture surface tension s at the critical solution temperature TCS should exhibit a horizontal inflection at xc , i.e., it should behave like a typical critical vapor pressure isotherm. Furthermore, this version of the theory predicted that at the critical point the surface tension should always increase in the direction of increasing concentration of the less volatile component. Since, as indicated above, there is a general but no direct connection between volatility and surface tension, this latter prediction was deemed unsatisfactory, which led to Ramos-Go´mez and Widom (13) modifying the theory using a less restrictive model for the free energy functional. With this modified theory they found that ( Ìs / Ìx *2 )T õ 0 where s1* ú s2* (with si* the surface tension of component i) regardless of the volatility ratio of the components. The surface tension behavior predicted by Widom has also been predicted by Telo da Gama and Evans (14) using a microscopic theory, by Rusanov on different grounds (4), and by Bowers and McLure (15) using a phenomenological Surface Regular Solution theory. All of these approaches allow the calculation of a surface tension isotherm across the entire composition range, whereas Widom’s treatment was restricted to the near-critical region. 2.4. Immediate Purposes In this paper our chief concern is to explore the generality of these observations, especially those concerning the behavior of surface tensions at critical endpoints. We also seek to detail and account for some exceptions to them. In particular, we are concerned with deviations from the common case, which Widom has termed usual mixtures, i.e. those identified in the Introduction in which the more volatile component of a mixture is also the less tense, and, in mixtures of nonelectrolytes, the less common case, termed unusual by Widom in which the more volatile component is the more tense. Although this second class of mixtures is relatively uncommon in nonelectrolyte mixtures, it is almost the rule in surfactant solutions in which the less tense surfactant is also usually by far the less volatile. In nonelectrolyte mixtures, almost the only classes of mixtures which readily offer unusual behavior are mixtures of an alkane or a dimethylsiloxane with a perfluoroalkane, and both of our unusual mixtures are drawn from these groups. There are few examples of surface tension determination for unusual mixtures available in the literature, so we endeavored to measure the surface tension isotherms of two unusual mixtures near a CEP. To complement these measurements we also present some surface tension isotherms for two usual mixtures.

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2.5. Choice of Mixture Our goal was to determine the surface tensions of some binary mixtures which would illustrate the variety of composition dependences instanced above, in particular near-critical behavior, usual and unusual behavior, and aneotropy but only if of insufficiently marked character to mask the effect of near-criticality. For the sake of useful comparison and eventual consistent description in terms of the same molecular theory, the mixtures ideally would be drawn from the same molecular class. Alkane / perfluoroalkane mixtures meet all these criteria. For example, all known mixtures of this class of mixture, except ethane / perfluoroethane whose unusually high melting point completely masks the region of limited miscibility (9), exhibit an upper critical endpoint. This wide variety of behavior, even within the framework of the relatively limited availability of perfluoroalkanes of reasonable purity, made the choice of mixtures for our purposes reasonably straightforward. We chose two mixtures that are usual in the sense defined above and two that are unusual. Alkane / perfluoroalkane mixtures containing components of equal chain length n have been termed symmetrical. In all such mixtures with n ú 3, the perfluoroalkane is the more volatile and the less tense; these mixtures are thus usual. Oddly enough, mixtures with n õ 3 are also usual, for example, methane / perfluoromethane (16, 17), but in this case the perfluoroalkane and the alkane exchange roles, i.e. the perfluoroalkane rather than the alkane is much less volatile and more tense. Hydrocarbon / perfluorocarbon mixtures involving globular rather than open chain molecules, e.g. methylcyclohexane / tetradecafluoromethylcyclohexane (18), are also usual in the same fashion as larger symmetrical alkane / perfluoroalkane mixtures. Taking any convenient symmetrical mixture drawn from this class as a basis, the effects of lengthening the alkane chain are to diminish the volatility and raise the tenseness of the alkane, i.e. to make the mixture more usual in the sense of this paper and, for corresponding reasons, shortening the alkane chain tends to make the mixture less usual. The effect of lengthening the perfluoroalkane chain length mixture is to diminish the volatility and raise the tenseness, but less markedly so than for alkanes, i.e. to make the mixture less usual in character, and vice versa for shortening the perfluoroalkane chain. The consequence of lengthening either of the component chains is to increase the upper critical solution temperatures TUCS with TUCS more sensitive to changes in alkane chain length than to those in perfluoroalkane chain length. Thus if we designate hexane / perfluorohexane, in many respects the archetypal alkane / perfluoroalkane mixture at ambient temperatures—or at least the most intensely studied, largely because of its convenient TUCS Å 237C—as a convenient benchmark of usual behavior, we can develop a

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rationale for the choice of more or less usual or even unusual mixtures. For example, the modest composite change of replacing hexane by the much less volatile octamethylcyclotetrasiloxane—not an alkane but in many respects thermodynamically similar in mixtures to a large globular hydrocarbon—and replacing perfluorohexane by the shorter and more volatile perfluoropentane produces a mixture whose usual character is reinforced over that of the benchmark mixture. Similarly, the modest increase in the alkane chain length to yield heptane / perfluorohexane results in a somewhat more usual mixture than hexane / perfluorohexane. Thus we adopted octamethylcyclotetrasiloxane / perfluoropentane and heptane / perfluorohexane as our usual mixtures. The same reasoning suggests that unusual mixtures can be generated from the benchmark mixture by decreasing the chain length of the alkane or, equivalently, increasing the chain length of the perfluoroalkane, or both. Thus we adopted for our unusual mixtures one with a smaller alkane / a larger perfluoroalkane than the benchmark, and one with a substantially larger perfluoroalkane and an alkane of unchanged chain length. The first of these mixtures—pentane / perfluoroheptane—is effectively the counterpart of our first usual mixture—heptane / perfluorohexane. The second mixture—2-methylpentane / perfluorotributylamine—takes advantage of the essentially nonbasic character of the perfluorochemical which thus can be taken as a large perfluoroalkane. This is advantageous because perfluoroalkanes of chain length greater than eight are scarce. The rise in TUCS occasioned by the use of perfluorotributylamine is partly compensated by the use of a branched alkane which lowers the TUCS compared to that of the analogous mixture containing an unbranched alkane of equal total number of carbon atoms. Thus we adopted pentane / perfluoroheptane and 2-methylpentane / perfluorotributylamine as our unusual mixtures. These choices are supported by the relatively accessible upper critical solution temperatures (19–21). The choice was further supported by the outcome of our previous calculations of surface tensions by the Surface Regular Solution theory (15). We made no effort to seek aneotropy, accepting as a gift the aneotropy which accompanied our choices of mixtures made on other grounds. 3. EXPERIMENTAL

3.1. Differential Capillary Rise, Cell, and Cleaning Procedure The orthobaric capillary constants a 2 Å 2s / rg, where r is the density of the liquid phase, strictly speaking the difference in densities of the coexisting liquid and vapor phases but well enough approximated here the density of the liquid alone, and g is the acceleration of free fall in our laboratory,

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were measured using a four-capillary device which has been described elsewhere, as have the cell cleaning and filling methods and the general technique (22). 3.2. Materials All the perfluorocarbons were obtained from Fluorochem and used without further purification. The stated purities of the linear perfluoroalkanes were ú99% of which a minimum of 85% was the n-isomer. The heptane and pentane were from Fisons and Aldrich, respectively, with stated purity ˚ molecular sieves. The 2-methylú99%, and dried using 4 A pentane was obtained from Aldrich with purity ú99.9% and was used after drying with sodium. The octamethylcyclotetrasiloxane was a gift from Dow Corning Ltd with stated purity ú95%. 3.3. Densities The densities were calculated using the pure component densities and an orthobaric excess volume correction when available. The densities used for heptane were from Christopher et al. (23), for pentane from Curtice et al. (24), for 2-methylpentane from Francis (25), and for octamethyltetracyclosiloxane from Hurd (26) and McLure and BarbarinCastillo (27). The fluorocarbon densities used for perfluorotributylamine were from Edmonds and McLure (28), for perfluoropentane from Simons and Dunlap (29), for perfluorohexane from Dunlap et al. (30), and for perfluoroheptane from Oliver et al. (31). The only excess volume data available were from Edmonds for heptane / perfluorohexane ( 32 ) . The neglect of the excess volume correction does not alter the qualitative isotherm shape, so we did not undergo the time-consuming task of measuring the excess volumes for the other mixtures. 4. RESULTS AND DISCUSSION

4.1. Surface Tension of Pure Components The pure component surface tensions were measured and compared with the literature values in Jasper’s compilation (33) or with those of other workers within this research group (Neville (34) and Edmonds (32)). No great discord was found between the values, and any small differences could be attributed to variations in sample purity. The surface tensions as a function of temperature were fitted to the van der Waals form, s Å s0 (1 0 T/Tc ) m ,

[1]

where s0 is a critical amplitude and the critical exponent m takes the value Å 1.26 now widely accepted (35), and Tc is the gas/liquid critical temperature taken from Ambrose’s

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TABLE 1 Orthobaric Capillary Constants a2 for (1 0 xF) (Octamethylcyclotetrasiloxane) / xF (Perfluoropentane) at 50.0, 55.4, and 59.87Ca a2/mm2 xF

50.07C

55.47C

59.87C

0 0.190 0.416 0.540 0.622 0.690 0.780 0.905 1

3.573 2.890 2.039 1.617 1.454 1.375 1.286 1.156 0.979

3.500 2.867 2.050 1.628 1.456 1.356 1.244 1.102 0.938

3.433 2.831 2.064 1.640 1.449 1.336 1.201 1.088 0.891

a xF is the perfluoropentane mole fraction. The critical solution temperature, TUCS, is 49.97C at a critical mole fraction xF,c Å 0.84.

compilation of critical properties (36). These expressions for the temperature dependence of s were used in our Surface Regular Solution theory calculations. 4.2. Surface Tension of Mixtures The results for the individual mixtures studied here are reported below under separate subheadings of usual and unusual mixtures. The incidence of the critical inflection and aneotropy is discussed when applicable. The TUCS of each mixture was determined and used as input information in the Surface Regular Solution theory calculations.

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est to TUCS , and the result is displayed on the figure as a dashed line. As can be seen, the qualitative features of the isotherm are predicted well except in mixtures dilute in perfluoroalkane where the theory overestimates the surface tension of the mixture. This poor degree of fit was also found for the predicted surface tensions in the series linear dimethylsiloxane / perfluorohexane for the dimer, trimer, and tetramer (22). The generation of a maximum in the surface tension has been discussed and observed elsewhere (3). Heptane / perfluorohexane, TUCS Å 42.97C. This mixture comprises two chain – molecular substances of all-butequal chain lengths. The capillary constants measured at 45.0, 50.0, and 55.07C are given in Table 2 with respect to perfluorohexane mole fraction. The surface tension isotherms are sketched in Fig. 2. A similar treatment to that discussed above reveals an inflection in the 45.07C isotherm in the region near xF Å 0.45, compared with the coexistence curve critical composition value of xF,c Å 0.36 ( 38 ) . The Surface Regular Solution theory-calculated isotherm nearest TUCS , previously reported ( 15 ), is shown in the figure, showing pleasing agreement between the theory and experiment. The disagreement between theory and experiment noted above persists, but here the theory predicts a surface tension in mixtures dilute in perfluoroalkane lower than is observed.

4.2.1. Usual Mixtures In the usual mixtures studied here the perfluoroalkane is the less tense and the more volatile component. Octamethylcyclotetrasiloxane / perfluoropentane, TUCS Å 59.87C. This mixture comprises a large globular cyclic dimethylsiloxane and a relatively short linear perfluoroalkane; the surface tension of the dimethylsiloxane is relatively large and that of the perfluoroalkane particularly small. Table 1 shows the measured capillary constants at 50.0, 55.4, and 59.87C. Surface tension isotherms based upon a zero excess volume are plotted in Fig. 1. The isotherm nearest TUCS is (TUCS / 7C / 0.1), and it exhibits a horizontal inflection. From fitting the data with a polynomial expression, the value of xF at which ( Ìs / Ì x2 )T is closest to zero is determined to be xF Å 0.75, which compares with the crude coexistence curve critical composition of xF,c Å 0.84 (37); this apparent inconsistency is not particularly serious since a much greater number of data points would be required to more precisely determine xc from surface tension isotherms, and that was not one of our main goals. The Surface Regular Solution theory has been used to calculate the surface tension isotherm clos-

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FIG. 1. Surface tension isotherms of (1 0 xF ) (octamethylcyclotetrasiloxane) / xF (perfluoropentane) at 50.0 ( L ), 55.0 ( s ), and 60.07C ( h ), near the upper critical solution temperature TUCS Å 49.87C. The isotherms at 50.0 and 55.07C have been displaced upward by 5 and 2.5 mN m01 , respectively. The solid lines are polynomial fits to the data, intended solely to guide the reader’s eye. The dashed line is the surface tension isotherm at 50.07C calculated using the Surface Regular Solution theory.

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TABLE 2 Orthobaric Capillary Constants a2 for (1 0 xF) (Heptane) / xF (Perfluorohexane) at 45.0, 50.0, and 55.07Ca

TABLE 3 Orthobaric Capillary Constants a2 for (1 0 xF)(Pentane) / xF (Perfluoroheptane) at 10.0, 15.0, 20.0, 25.0, and 40.07Ca

a2/mm2

a2/mm2

xF

45.07C

50.07C

55.07C

xF

10.07C

15.07C

20.07C

25.07C

40.07C

0 0.112 0.209 0.309 0.403 0.493 0.596 0.751 0.877 0.904 1

5.449 3.258 2.444 2.097 1.883 1.770 1.623 1.428 1.338 – 1.610

5.324 3.225 2.434 2.079 1.825 1.713 1.580 1.396 1.271 1.234 1.155

5.238 3.231 2.431 2.022 1.802 1.668 1.543 1.336 1.201 1.194 1.129

0 0.104 0.188 0.298 0.394 0.535 0.609 0.706 0.825 0.909 1

5.521 3.467 2.824 2.458 2.199 1.985 1.845 1.791 1.672 1.659 1.630

5.391 3.410 2.787 2.396 2.144 1.923 1.771 1.747 1.640 1.606 1.566

5.255 3.324 2.734 2.328 2.081 1.857 1.679 1.684 1.584 1.588 1.534

5.129 3.252 2.682 2.275 2.009 1.785 1.669 1.616 1.534 1.527 1.496

4.703 2.997 2.423 2.020 1.812 1.616 1.492 1.448 1.400 1.397 1.376

a xF is the perfluorohexane mole fraction. The critical solution temperature, TUCS, is 42.97C at at a critical mole fraction xF,c Å 0.36.

4.2.2. Unusual Mixtures In the unusual mixtures discussed here the perfluorocarbon is both the less tense and the less volatile component, i.e. rather than the less common case for an unusual mixture

FIG. 2. Surface tension isotherms of (1 0 xF ) (heptane) / xF (perfluorohexane) at 45.0 ( h ), 50.0 ( L ), and 55.07C ( s ), near the upper critical solution temperature TUCS Å 42.97C. The isotherms at 45.0 and 50.07C have been displaced upward by 5 and 2.5 mN m01 , respectively. The solid lines are polynomial fits to the data, intended solely to guide the reader’s eye. The dashed line is the surface tension isotherm at 45.07C calculated using the Surface Regular Solution theory.

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a xF is the perfluoroheptane mole fraction. The critical solution temperature, TUCS, is 6.57C at a critical mole fraction xF,c Å 0.31.

of this class with the perfluorocarbon both the more tense and the more volatile. Pentane / perfluoroheptane, TUCS Å 6.57C. The mixture is composed of two linear substances of different chain lengths but with the perfluoroalkane the longer unlike the earlier mixture of this kind. The capillary constants are tabulated in Table 3 for temperatures of 10.0, 15.0, 20.0, 25.0, and 40.07C, well above the TUCS at 6.57C. The surface tensions of the components are very similar, thus making aneotropy almost inevitable, and the surface tension isotherms displayed in Fig. 3 confirm that this mixture does indeed exhibit aneotropy but of a very small magnitude. The aneotrope almost masks the critical inflection, thereby making the location of the critical composition uncertain in this manner. The isotherms at higher temperature show clearly how the critical contribution drops out, leaving isotherms showing clear aneotropy. Again a Surface Regular Solution theory calculation has been made showing outstanding agreement with experiment. 2-Methylpentane / perfluorotributylamine, TUCS Å 46.17C. This mixture comprises a near-linear hydrocarbon and a large globular perfluorocarbon. This particular mixture was chosen because (a) the perfluorotributylamine has a particularly low vapor pressure at the temperatures of our experiments for a perfluorochemical, here effectively a perfluoroalkane since the nitrogen in such ternary perfluoroamines confers no significant basic character, and (b) the 2-methylpentane lowers the mixture TUCS into a favorable experimental range. The capillary constants are given in Table 4. The surface tensions have been calculated assuming excess volume of mixing is zero and are shown in Fig. 4 for isotherms at 46.2, 50.0, 55.0, and 60.07C. The shape of the observed isotherms

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cule with a globular molecule with the globular molecule indifferently the more or less tense. This implies that the chain-molecule properties are adequately incorporated into the thermodynamic properties of the pure components and of the mixture of critical composition at the critical temperature. General Comments

FIG. 3. Surface tension isotherms of (1 0 xF ) (pentane) / xF (perfluoroheptane) at 10.0 ( h ), 15.0 ( L ), 20.0 ( s ), 25.0 ( n ), and 407C ( , ), near the upper critical solution temperature TUCS Å 6.57C. The isotherms at 10.0, 15.0, 20.0, and 25.07C have been displaced upward by 10.0, 7.5, 5, and 2.5 mN m01 , respectively. The solid lines are polynomial fits to the data, intended solely to guide the reader’s eye. The dashed line is the surface tension isotherm at 50.07C calculated using the Surface Regular Solution theory.

is striking, displaying both a horizontal inflection and a modest negative aneotrope. The isotherm nearest TUCS is at (TUCS / 7C / 0.1), and the inflection occurs near xF Å 0.21, which agrees well with the critical composition xF,c Å 0.24 crudely extracted from the limited coexistence curve data (21). Aneotropy occurs at xF É 0.58. Usually in mixtures in which the pure component surface tensions are very similar, aneotropy is present, and in most cases it obscures the horizontal inflection in the critical isotherm. As seen in Fig. 4, the critical inflection for this mixture is not masked by the presence of the aneotrope. The Surface Regular Solution theory isotherm is shown. The agreement at first glance does not seem outstanding, but closer examination of the scale shows that the theory predicts the qualitative behavior of the surface tension in the critical region reasonably well but fails to distinguish the aneotrope from the critical point. To summarize all these results, the resulting critical compositions and aneotropic compositions are given in Table 5 for the four mixtures studied. The success of the Surface Regular Solution theory applied to the mixtures, two of which were examined in the original paper (15), is worthy of a further comment. The theory seems to work well for mixtures of chain molecules with equal chain lengths or with either the alkane or the perfluoroalkane the longer, and for mixtures of a linear mole-

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A variety of surface tension isotherm shapes near a CEP is found in nature. The surface tension measurements shown above demonstrate the diversity of isotherm shapes which can occur. The four mixtures display four different basis shapes. In an attempt to classify the types of mixture that exhibit certain isotherm shapes, the list in Table 6 has been formulated from a review of the literature and work carried out in this group. The four types of isotherm have been further subdivided to account for usual and unusual behavior. Figure 5 shows the commonly found isotherm shapes for both usual and unusual mixtures. From top to bottom, the isotherms shown represent an operational ideality (faute de mieux linearity with mole fraction) and have been classified as Types 1–4. Returning to the mixtures studied here, the surface tensions of all four mixtures studied exhibit a clearly discernible horizontal inflection with a near-vanishing ( Ìs / Ì x2 )T at or close to xc as predicted by Ramos-Go´mez and Widom. The inflection progressively ‘‘washes out’’ as the temperature rises above TUCS , most notably this is shown for pentane / perfluoroheptane. Two of the mixtures exhibit aneotropy to a greater or lesser extent and shed light on the interplay between the inflection and the aneotrope, particularly when the aneotrope is broad or the aneotropic composition is similar TABLE 4 Orthobaric Capillary Constants a2 for (1 0 xF) (2-Methylpentane) / xF (Perfluorotributylamine) at 46.2, 50.4, 55.0, and 60.07Ca a2/mm2 xF

46.27C

50.47C

55.07C

60.07C

0 0.095 0.153 0.203 0.303 0.403 0.496 0.599 0.701 0.931 1

4.813 3.017 2.633 2.407 2.093 1.900 1.764 1.645 1.604 1.598 1.605

4.719 2.957 2.581 2.359 2.059 1.855 1.725 1.608 1.565 1.565 1.579

4.601 2.883 2.529 2.293 1.998 1.799 1.678 1.566 1.537 1.532 1.553

4.466 2.806 2.461 2.224 1.943 1.749 1.628 1.528 1.493 1.498 1.515

a xF is the perfluorotributylamine mole fraction. The critical solution temperature, TUCS, is 46.17C at a critical mole fraction xF,c Å 0.24.

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TABLE 5 Summary of Critical Parameters and Surface Tension Featuresa Mixture

xC

xC(s 0 x)

xan(s 0 x)

TUCS/7C

Octamethyltetracyclosiloxane / perfluoropentane Heptane / perfluorohexane Pentane / perfluoroheptane 2-Methylpentane / perfluorotributylamine

0.84 0.36 0.31 0.24

0.75 0.40 0.20 0.21

– – 0.55 0.58

59.8 42.9 6.5 46.1

a xC is the critical composition and is the perfluorocarbon mole fraction xF; xC(s 0 x) is the value determined from the slope of the surface tension isotherm; xan(s 0 x) is the aneotropic composition when relevant determined from the slope of the surface tension isotherm; and TUCS is the upper critical solution temperature.

to the critical composition. From these results and the results of the literature review, we are able to ascertain some conditions for the observation of the horizontal inflection. If the mixture exhibits aneotropy, i.e. when s1* É s2*, the inflection is not necessarily apparent if the aneotropic and critical compositions are similar. There is a simple analogy here with the behavior of the vapor pressure of a liquid mixture near a critical point, which was mentioned in the Introduction, in which an azeotrope can all but conceal the thermodynamically necessary horizontal inflection in the vapor pressure isotherm at the critical temperature. Generally, however, if the critical surface tension lies between the surface tensions of the two pure components the inflection is observable.

Some of the measurements referenced in Table 6 were made long before the theory of Widom, for example those of Rusanov et al. in 1969 (39), Morgan and Egloff in 1916 (40), and Campbell and Annand in 1972 (41). However, as might have been expected, Widom’s theory did encourage fresh experimental measurements, such as those of Khosla and Widom (42) and McLure and co-workers (16, 18, 22, 38). Returning briefly to the incidence of the horizontal inflection, now that we have established when it may be observ-

TABLE 6 Summary of Surface Tension Behavior near a Critical Endpoint Based on the Isotherm Shapes Given in Fig. 5, Subdividing Types 1–4 into Usual and Unusual Mixtures Type

Ref.

Usual Mixtures 1. 2,6-Lutidine / water Hexadecane / acetone Hexane / nitrobenzene Octane / perfluorohexane Octamethyltetracyclosiloxane / perfluoropentane Decamethyltetrasiloxane / perfluorohexane Propanenitrile / (pentane, hexane, or heptane)

43 44 39 32 This work 22 46

2. Triethylamine / water Nitroethane / 3-methylpentane Heptane / perfluorohexane Octamethyltrisiloxane / perfluorohexane

40 42 This work 15

3. Hexane / perfluorohexane Hexamethyldisiloxane / perfluorohexane Methylcyclohexane / perfluoromethylcyclohexane 4. Methanol / cyclohexane Methane / perfluoromethane Pentane / perfluorotributylamine

38 22 18 41 16, 17 32

Unusual Mixtures FIG. 4. Surface tension isotherms of (1 0 xF ) (2-methylpentane) / xF (perfluorotributylamine) at 46.3 ( h ), 50.0 ( L ), 55.0 ( s ), and 60.07C ( n ), near the upper critical solution temperature TUCS Å 46.27C. The isotherms have not been displaced. The solid lines are polynomial fits to the data, intended solely to guide the reader’s eye. The dashed line is the surface tension isotherm at 46.37C calculated using the Surface Regular Solution theory.

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1. 2-Butoxyethanol / water 2. Isobutyric acid / water

44, 45 42

3. 2-Methylpentane / perfluorotributylamine

This work

4. Pentane / perfluoroheptane

This work

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endpoint is not dependent on the relative volatilities of the two components. An interesting situation is the crossover between usual and unusual mixtures. This occurs, for example, when the vapour pressures of the two components are identical. Such mixtures are known as Bancroft mixtures and azeotropy is inevitable no matter how small the deviations from bulk ideality. McLure and Ferna´ndez (47) have measured the surface tension of tetrachloromethane / perfluoromethylcyclohexane near the UCEP. Despite the coincidental uniqueness of the vapour pressures, the outward appearance of the isotherms is no different from those of otherwise comparable usual or unusual mixtures. 5. CONCLUSIONS

The main points of this study and review are listed below:

FIG. 5. The four main types of surface tension isotherm which occur near a critical endpoint. The dashed straight line is the operational ideality, i.e., linearity with mole fraction x2 . From top to bottom at x2 Å 0.5, the isotherms are for types 1, 2, 3, and 4. Examples of mixtures of each type of isotherm are given in Table 6.

able we can discuss the range of temperatures over which it is observable from the references cited in Table 6. Privat et al. (43) stated that they observed the inflection 14 K below TLCS of (2,6-lutidine / water). Pegg (44) observed the inflection 9 K below TLCS of 2-butoxyethanol / water and 7 K above TUCS of hexadecane / acetone. However, he did not look any further away. Knecht and Woermann (45) also examined 2-butoxyethanol / water near the lower critical endpoint. For propanenitrile / heptane, Arriaga-Colina (46) found the inflection was still apparent 10 K above its TUCS . Bowers and McLure have shown that the signature of the inflection remains in the surface tension isotherms for hexamethyldisiloxane / perfluorohexane nearly 20 K above TUCS (22). From the literature and the presented work, it appears that the sign of ( Ìs / Ì x2 )T near xc with respect to ( s 1* 0 s2*),where s1* ú s2*, is always negative, in agreement with the Ramos–Go´mez and Widom theory, where the subscripts 1 and 2 refer to the components of the mixture, i.e. s should always increase near xc with the increasing composition of the component of higher surface tension. This observation still possibly requires further qualification by experiment for both usual and unusual mixtures, but the results of this survey and the current experiments indicate that the prediction is correct, i.e., the surface tension near the critical

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(i) We have reviewed and classified the composition dependence of the surface tension of binary liquid mixtures near a critical endpoint and briefly compared the outcome with the behavior of the vapor pressure in the same region. (ii) The horizontal inflection in the near-critical surface tension isotherm s has been observed in the cases of study and the sign of ( Ìs / Ì x2 )T with respect to x2 , where component 2 is the less tense, is found to be in agreement with the theory that it is negative. (iii) We have further tested the solubility parameter version of the Surface Regular Solution theory and have found that it is able to generate the four types of behavior often observed in near-critical mixtures, and that it works equally well for usual and unusual mixtures. The theory ably reproduces the experimental surface tensions in relation to two crucial factors: the difference in the surface tensions of the pure component and the measure of the weakness of the unlike intermolecular interaction represented in the calculation by the observed critical solution temperature. ACKNOWLEDGMENTS The authors are grateful for the award of United Kingdom Engineering and Physical Sciences Research Council postgraduate studentships to R.W. and J.B. and of a European Union International Scientific Cooperation postdoctoral award to J.B.

REFERENCES 1. Guggenheim, E. A., ‘‘Mixtures.’’ Clarendon Press, Oxford, 1952. 2. Nadler, K., Zollweg, J., Streett, W. B., and McLure, I. A., J. Colloid Interface Sci., 122, 530 (1988). 3. Edmonds, B., and McLure, I. A., J. Chem. Soc., Faraday Trans. 1 78, 3319 (1982). 4. Rusanov, A. I., ‘‘Phasengleichgewichte und Grenzfla¨schenerscheinungen.’’ Akademie-Verlag, Berlin, 1978. 5. Hildebrand, J. H., and Scott, R. L., ‘‘The Solubility of Nonelectrolytes,’’ p. 411. Reinhold, New York, 1950.

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6. McLure, I. A., Edmonds, B., and Lal, M., Nature (London) 212, 283 (1966). 7. McLure, I. A., Pegg, I. L., and Soares, V. A. M., in ‘‘Colloid Science’’ (D. H. Everett, Ed.), Royal Society of Chemistry Specialist Periodical Report 4, Chap. 6. Royal Society of Chemistry, Cambridge, 1983. 8. Defay, R., Prigogine, I., and Bellemans, A., ‘‘Surface Tension and Adsorption,’’ p. 179. Longmans, London, 1966. 9. Gilmour, J. B., Zwicker, J. O., Katz, J., and Scott, R. L., J. Phys. Chem. 71, 3259 (1967). 10. Defay, R., and Prigogine, I., ‘‘Chemical Thermodynamics’’, Chap. 25. Longmans, London, 1954. 11. Ref. 7, p. 179. 12. Widom, B., J. Chem. Phys. 67, 872 (1977). 13. Ramos Go´mez, F. F., and Widom, B., Physica 104A, 595 (1980). 14. Telo da Gama, M. M., and Evans, R., Mol. Phys. 48, 229 (1983). 15. Bowers, J., and McLure, I. A., Langmuir 12, 3326 (1996). 16. Higgins, R. A., M.Sc. Thesis, University of Sheffield, 1985. 17. McLure, I. A., Soares, V. A. M., Almeida, B. de J. V. S., and Higgins, R. A., Fluid Phase Equilibria 32, 9 (1986). 18. Ferna´ndez, J., McLure, I. A., and Williamson, A. M., J. Chem. Thermodyn. 26, 897 (1994). 19. Hicks, C. P., Hurle, R. L., Toczylkin, L. S., and Young, C. L., Aust. J. Chem. 31, 19 (1978). 20. McLure, I. A., Mohktari, A., and Bowers, J., J. Chem. Soc. Faraday Trans. 93, 249 (1997). 21. Munson, M. S. B., J. Phys. Chem. 68, 796 (1964). 22. Bowers, J., and McLure, I. A., J. Chem. Soc. Faraday Trans. [In press] 23. Christopher, P. M., Laukhuf, W. L. S., and Planck, C. A., J. Chem. Eng. Data 21, 443 (1976). 24. Curtice, S., Felton, E. G., and Prengle, H. W., J. Chem. Eng. Data 17, 192 (1972).

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25. Francis, A. W., Chem. Eng. Sci. 10, 37 (1959). 26. Hurd, C. B., J. Am. Chem. Soc. 68, 364 (1946). 27. McLure, I. A., and Barbarin-Castillo, J.-M. J. Chem. Eng. Data 39, 12 (1994). 28. Edmonds, B., and McLure, I. A., J. Chem. Eng. Data 22, 127 (1977). 29. Simons, J. H., and Dunlap, R. D., J. Chem. Phys. 18, 335 (1950). 30. Dunlap, R. D., Murphy, C. J. Jr., and Bedford, R. G., J. Am. Chem. Soc. 80, 83 (1958). 31. Oliver, G. D., Blumkin, S., and Cunningham, C. W., J. Chem. Eng. Data 73, 5722 (1951). 32. Edmonds, B. E., Ph.D. Thesis, University of Sheffield, 1972. 33. Jasper, J. J., J. Phys. Chem. Ref. Data 1, 841 (1972). 34. Neville, J. F., Ph.D. Thesis, University of Sheffield, 1979. 35. Moldover, M. R., Phys. Rev. 31, 1022 (1985). 36. (a) Ambrose, D., ‘‘Vapour–Liquid Critical Properties,’’ Report Chem 107. National Physical Laboratory, 1980. (b) See also supplement of same name by same author (1983). 37. Bowers, J., Ph.D. Thesis, University of Sheffield, 1995. 38. Whitfield, R., Ph.D. Thesis, University of Sheffield, 1996. 39. Rusanov, A. I., Levichev, S. A., and Mikhalenko, O. N., Russ. J. Phys. Chem. 43, 1461 (1969). 40. Morgan, J. L. R., and Egloff, G., J. Am. Chem. Soc. 38, 844 (1916). 41. Cambell, A. N., and Annand, S. C., Can. J. Chem. 50, 1109 (1972). 42. Khosla, M. P., and Widom, B., J. Colloid Interface Sci. 76, 375 (1980). 43. Privat, M., Tene`bre, L., Bennes, R., Tronel-Peyroz, E., Douillard, J. M., and Ghaicha, L., Langmuir 4, 1151 (1988). 44. Pegg, I. L., Ph.D. Thesis, University of Sheffield, 1982. 45. Knecht, B., and Woermann, D., Ber. Bunsenges. Phys. Chem. 99, 1067 (1995). 46. Arriaga-Colina, J. L., Ph.D. Thesis, University of Sheffield, 1985. 47. McLure, I. A., and Ferna´ndez, J., J. Chem. Thermodyn. 28, 767 (1996).

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