J . Chem. SOC., Faraday Trans. I , 1982, 78, 2251-2257 Surface Tension of Per fluor opropane, Perfluoro-n-but ane, Perfluoro-n-hexane, Perfluoro-oc tane, Perfluorotributylamine and n-Pentane Application of the Principle of Corresponding States to the Surface Tension of Perfluoroalkanes BY I A N A. MCLURE,* V I R G ~ L I O A. M. SOAREST AND BERYL E D M O N D S ~ Department of Chemistry, The University, Sheffield S3 7HF Received 14th October, 198 1 The orthobaric surface tensions of C,F,, n-C,F,,, n-C,F,,, C8FIB, (C,F,),N and n-C,H,, have been measured by the differential capillary-rise technique over various ranges of temperatures. The results for the perfluoroalkanes have been analysed in terms of the van der Waals equation, the Brock and Bird equation incorporating Pitzer’s acentric factor and the phenomenological corresponding-states treatment of Patterson and Rastogi; the data are fitted with varying degrees of success. The phenomenological principle of corresponding states to which the surface tensions for the perfluoroalkanes conform is not identical to that for the n-alkanes and some other homologous series, but it is similar to it, in particular in the need for at least three reduction parameters.The most successful approaches to the interpretation of both the surface thermo- dynamics and the bulk thermodynamics of chain-molecule liquid mixtures rest on the assumption of the conformity of appropriate properties of both the pure components and the mixture to the principle of corresponding states.l12 For mixtures the demonstration of conformity is not straightforward since the assumption of conformity is usually intractably involved with the particular form of mixture theory necessarily introduced at this stage of the analysis.By contrast, the demonstration of the conformity of the pure substances is reasonably simple, requiring essentially a knowledge of suitable physical properties of the pure substances over wide ranges of temperature; for a very demanding test, density data over very wide ranges of temperatures are required. To assist in the analysis of the results of our measurements of the surface tension of some alkane + perfluoroalkane liquid mixtures3$ * we have measured the orthobaric surface tension of perfluoropropane, perfluoro-n-butane, perfluoro-n-hexane, per- fluoro-octane, perfluorotributylamine and n-pentane.We have analysed the results with varying degrees of sophistication in terms of the principle of corresponding states. We have compared the outcome of this analysis with that performed for the n-alkanes and other substances by Patterson and Rastogi.5 t Present address: Instituto Superior Tecnico, Centro de Quimica Estrutural, Complexo I, Av. Rovisco 9 Present address: The Institution of Chemical Engineers, 165-171 Railway Terrace, Rugby CV 21 3HQ. Pais, 1096 Lisbon Codex, Portugal. 13-2 225 12252 SURFACE TENSION OF PERFLUOROALKANES EXPERIMENTAL APPARATUS A N D PROCEDURE The measurements of surface tension were carried out in a closed Pyrex glass cell using the differential capillary-rise technique. The technique was chosen for two reasons.The first is that it yields accurate surface tensions for liquids that wet, as do all those studied in this programme, the walls of the capillaries. The second is that it readily lends itself to closed-cell operation, thus preventing the loss of the materials under study and the ingress of unwanted substances, notably air and (as here for sub-ambient temperature work), water. Avoiding losses is important if, again as here, the materials are volatile, hard-to-obtain in acceptable purity and expensive; furthermore, for mixtures of liquids of differing volatility, for which the same apparatus has been used, losses can lead to undetected changes in composition. If unwanted substances are excluded from the cell the interpretation of the orthobaric data so produced is uncoloured by doubts arising from their presence at the gas-liquid interface. Details of the apparatus and the procedure used are available elsewhere.6, During each measurement the temperature was held constant to within & 0.1 K for temperature below 273 K and f 0.02 K at higher temperatures.MATERIALS Perfluoropropane was supplied by Air Products Ltd with a claimed purity > 95 mol %. Perfluoro-n-butane was supplied by Fluorochem Ltd with a claimed purity > 97.8 rnol %. Perfluoro-n-hexane was supplied by the Imperial Smelting Co with an isomeric impurity level revealed by gas-liquid chromatography to be < 1 mol %. The perfluoro-octane was obtained from a variety of sources: K and K Laboratories, Peninsular Chemicals and Pfalz and Bauer.No sample was of high purity; gas-liquid chromatography suggested an isomeric impurity content of up to 10 rnol %. In view of dismal past experience of separating isomeric perfluoroalkanes no attempt at purification was made and it was hoped that little adverse effect on the measurements would result. The perfluorotributylamine was obtained from Koch-Light Laboratories Ltd with a purity claimed to exceed 99 mol % in terms of perfluorinated (C,F,),N. Proton n.m.r. measurements revealed the absence of partially fluorinated substances. All materials were degassed vigorously in view of the high solubility of air in perfluorochemicals. For measurements below 303 K, Fisons Ltd n-pentane of purity 99.4 rnol % was used after distillation; for measurements above 303 K, Phillips research grade (lot no.1789) of purity > 99.9 mol % was used; both samples were dried with sodium and degassed before measurement. RESULTS The surface tension o was calculated from the equation 0 = ri rj dg[3Ahij + (ri - r j ) ] / 6 (ri - r j ) where Ahij is the difference in the height of the menisci in the capillaries of radius ri and rj, d is the density of the liquid phase and g is the acceleration of free fall in our laboratory (9.813 42 m s - ~ ) , for which an estimate was supplied by the Geological Survey in London. We believe that the error in our results is of the order k0.05 mN m-l for surface tensions reported to within kO.01 mN m-l and of the order f 0.1 mN m-l otherwise. The results obtained at different temperatures for each substance were fitted by a least-squares procedure to two types of equation, namely o = a-bT (2) and ( 3 ) where a, b, oo and p are empirical parameters and T, is the gas-liquid critical temperature of the substance taken from the compilation of Ambrose and Townsend.8I. A.MCLURE, V. A. M. SOARES A N D B. E D M O N D S 2253 TABLE 1 .-ORTHOBARIC SURFACE TENSIONS T/K a/mN m-l a[eqn (2)]/mN m-l o [eqn (3)]/mN m-l a(lit)/mN m-l 233.9 240.9 246.9 253.1 260.1 268.9 233.5 237.7 243.4 247.1 25 1.4 258.9 261.9 265.4 298.0 303.0 3 13.0 3 18.0 323 328 338 303 306 313 318 328 333 337 303 313 318 323 237.9 241.5 249.4 256.7 261.5 266.9 303.0 3 13.0 10.97 9.99 9.33 8.5 1 7.77 6.92 14.00 13.62 12.88 12.41 11.96 11.17 10.94 10.60 11.34 11.0 10.0 9.55 9.1 8.6 7.4 perfluoropropane [density from ref.(9)] 10.89 10.89 10.03 10.01 9.33 9.3 1 8.62 8.60 7.80 7.80 6.80 6.84 13.97 14.00 13.52 13.54 12.40 12.91 12.50 12.52 12.04 12.05 11.23 11.25 10.90 10.92 10.52 10.55 11.46 1 1.46 10.97 10.94 9.99 9.92 9.50 9.42 9.01 8.92 8.52 8.44 7.59 7.49 perfluoro-n-butane [density from ref. (1 O)] perfluoro-n-hexane [density from ref. (1 l)] perfluoro-octane [density from ref. (9)] 13.4 13.41 13.37 13.2 13.18 13.13 12.6 12.64 12.59 12.3 12.26 12.21 11.5 11.49 11.44 11.1 11.11 11.06 10.8 10.80 10.76 16.3 16.30 15.4 15.40 14.95 14.95 14.5 14.5 22.23 22.23 22.22 perfluorotributylamine [density from ref. (1 3)] n-pentane [density from ref. (1 5)] 21.89 21.81 20.81 20.9 1 20.11 20.07 19.56 19.52 18.85 18.89 1 5.0a 14.75 13.9a 13.68 21.80 20.88 20.05 19.50 18.88 14.88 13.80 10.9811 10.0511 9.1 1" 1 3.912 12.712 11.312 16.114 22.1 316 21 .7416 20.8216 20.0616 19.5316 1 8.9416 14.9416 13.8416 a These points were not included in the fitting procedure for eqn (2) or (3).2254 SURFACE TENSION OF PERFLUOROALKANES TABLE 2.-vALUES OF CONSTANTS OF EQN (2) AND (3) a b OSD 6 0 IU OSD substances ~~ C3F8 37.88 0.1156 0.10 43.07 1.22 0.09 n-C,F,o 39.23 0.1084 0.08 42.97 1.21 0.08 51.4 1.37 0.15 n-C,F,, 36.65 0.07668 39.1 1.16 0.1 n-C,H,, 49.56 0.1149 0.06 52.34 1.21 0.06 nGF1, 40.62 0.09786 - (C,F,)3N 43.57 0.0900 - - - - - In table 1 we show the measured values of the surface tensions together with the values calculated from (2) and (3).In table 2 we present the values of a, b, a. and ,u obtained for each compound and the respective standard deviations asu for the calculated surface tensions.No surface tensions have been reported previously for C3F, or n-C,F,,. Skripov and Firsov17 present surface tensions for n-C,F,,, n-C,F,,, n-C,F,,, n-C,F,,, n-C,F,, and n-C10F2,. Their surface tensions are low for n-C,F,, and n-C,F,, and show a temperature dependence different from those of other authors. Since they assumed the constancy of the parachor with temperature it seemed to us that if the densities they used were corrected better agreement might be found. We tried to recalculate their surface tensions for n-C,F,, using correct density values but the improvement was negligible. A close inspection of the boiling points of their material shows them to be lower than those reported by Ambrose and Townsend by as much as 2-12 K, suggesting that the material was highly impure.Therefore we do not include the data of Skripov and Firsov in our discussion. For n-C,F,, the agreement between our results and those of Stiles and Cadyll is very good. The comparison of our results for n-C,F,, with those of Haseldine and Smith12 shows also fairly good agreement, giving some support to our hope that the effect of the presence of the known impurity in our material is small. DISCUSSION The simplest form of expression for the principle of corresponding states for the surface tension of simple fluids is where the function 6(0 of reduced temperature Fis universal for the reduced surface tension 6. The first explicit expression was that of van der WaalP 6 = 6(F) 6 = a/a* = [l -(T/?3]P where o* and p are constants.This equation is a statement of a two-parameter principle of corresponding states. Using combinations of gas-liquid critical constants for a*, simple dimensional analysis yields three choices of o* proportional to V;2/3, P, V:I3 or Tk/3pEi3. Guggenheim found that using the first choice the critical index p for the rare gases is close to 1 1/9.19 For substances similar to the rare gases, for which the critical compressibility 2, is a constant, the choice of form of a* in terms of critical constants is a matter of indifference. For more complex substances 2, is not a constant, and different choices of the form of o* give rise to different functional dependences of a* on F.I. A. M C L U R E , V. A. M. S O A R E S AND B.E D M O N D S 2255 For the perfluoroalkanes we find that the dependence of o on T is equally well described by eqn (2) or (3). This is, however, scarcely an exacting test since at T/T, far from unity the expansion of eqn (3) in powers of T / q produces an expression essentially linear in T. However, within the limits of the test p is not excessively far from the currently accepted best value of 1.26 for T/ q close to unity. More seriously from the point of view of the principle of corresponding states, no combination of critical constants of the kind given above for o* produces a universal function of T/ T, for the perfluoroalkanes studied here. Clearly, therefore, recourse to a more complicated form of corresponding-states principle must be taken.We now turn to a consideration of the most simple of these forms of corresponding- states principle, which involves three parameters characteristic of the substances. Three parameters have been found necessary to bring the bulk properties of n-alkanes, linear dimethylsiloxanes and linear perfluorocarbons in to conformity with the principle of corresponding states. A convenient empirical t hree-parameter form of corresponding-states principle for the surface tension of complex substances has been described by Brock and Bird20 6’ = (a/mN m-1)(pc/atm)-2/3( T,/K)-l13 = (0.491 5 + 0.6529co)( 1 - T)l1/’ where o is Pitzer’s acentric factor defined as CL) = log [p,/lO p(T = 0.7 731. Fig. 1 shows 6’ as a function of co at = T/T, = 0.65 for perfluoropropane to perfluorononane.For comparison, the line of Brock and Bird is also shown. Lack of low-temperature data makes impossible a comparison with the test of Stie121 at = 0.6. For the sake of completeness, we include in fig. 1 even these data which do not enjoy our full confidence. The sources of data not reported in this paper for perfluoropentane are in ref. (22) and for perfluoroheptane and perfluorononane in ref. (12). The points for perfluoropropane fall close to the line of Brock and Bird, but those for perfluoro-octane and perfluorononane fall below the line by 8 and 12%, respect- ively: well above the Stiel criterion of 5% from ‘normal’ liquids. It is unlikely, although not impossible, that these deviations are due to errors in the measurements of o or in the densities needed to obtain o from the observed capillary heights.The question of impurity is relatively simple to settle, since for perfluoropentane and perfluorohexanell at least, branching causes o to increase rather than, as here, to decrease. Although the data for perfluoroalkanes are few we believe that the deviation reveals the onset of the failure of the correlation of Brock and Bird to describe the surface tensions of this homologous series. By contrast the correlation works well for n-alkanes up to n-dodecane. A fuller test of the Brock and Bird expression at more than one temperature is afforded from the plot of the quantity o/pE13 Tk/3 (0.491 5+0.6539 co) against T/Tc. Not surprisingly, a universal curve is found for perfluoropropane to perfluoroheptane, but again the data for perfluoro-octane and perfluorononane fall below the line and increasingly so as T/T, increases.Our (admittedly limited) analysis of the surface tensions of the perfluoro-n-alkanes suggests that at least three reduction parameters are needed for a successful principle of corresponding states. Although the Brock and Bird equation formally meets this criterion it fails to give good predictions for the surface tensions of substances of high chain length or at reduced temperatures. A further objection, although one of principle only, is that co lacks a clear molecular significance similar to that enjoyed by pressure, volume and temperature reduction factors and their combinations.2256 SURFACE TENSION OF PERFLUOROALKANES T 0.23 -2 b. 0.2 1 0.20 I 1 I 1 0.3 0.4 0.5 0.6 w FIG.1.-Reduced surface tension cp;2/3 C1l3 plotted against the Pitzer acentric factor o at (T/T,) = 0.65 following the treatment of Brock and Bird. The points in increasing order of co are C,F, to n-C,F,,. A more searching phenomenological test, in which the reduction parameters do have some physical significance, is that described by Patterson and R a ~ t o g i . ~ In their analysis the reduced surface tension 6” = aPg3 ag3 is a universal function of the measure of reduced temperature apT, where a p is the isobaric thermal expansion coefficient and is the isothermal compressibility. Owing to lack of pVT data for the other perfluorocarbons our analysis using the method of Patterson and Rastogi has been restricted to perfluoro-n-hexane.In the absence of a good reason for discarding either of the discordant pVT data of Stiles and Cady and Dunlap and coworker^^^^^^ 6’’ was calculated using both sets and the results are shown in fig. 2. Clearly, although the results fall close to the curve of Patterson and Rastogi they do not fall on it within the scatter of the points for the substances considered by these authors. They also fall below the theoretical lines obtained by Patterson and Rastogi for various models of the liquid state. On the basis of this test, it looks as if perfluoro-n-hexane surface tensions do not obey exactly the same phenomenological principle of corresponding states as do those of the n-alkanes, linear dimethyl- siloxanes and other homologous series. Without more extensive p VT data little more on this matter can be added.The foregoing analysis suggests that the perfluoroalkanes do require a three- parameter corresponding-states treatment and that it is similar but not identical to that which applies to the n-alkanes and other chain molecule series. Further measurements of surface tension and p VT quantities on material of dependable purity and over wider ranges of temperature and density would be welcome to permit a test of acceptable stringency.I. A. MCLURE, V. A . M. SOARES A N D B. EDMONDS 2257 FIG. 2.-Reduced surface tension aapy;2/3 k-ll3 plotted against a T following the treatment of Patterson and Rastogi for perfluoro-n-hexane; (0) denotes points calculated using the density data of Rohrback and Cady and (0) denotes points calculated using the density data of Dunlap and Scott.The curves (a), (6) and (c) refer to the different models used by Patterson and Rastogi using the following ( m , n) choices for the intermolecular potential function: (a) (6, 12), (b) (3, co) or Flory model, (c) (6, a). 1 2 3 4 5 fi 0 9 10 11 1 2 13 I4 15 16 17 1.3 19 20 21 22 23 1 4 I. Prigogine, The Molecular Theory of Solution (North-Holland, Amsterdam, 1957), chap. 8. R. Defay, I. Prigogine, A. Bellemans and D. H. Everett, Surface Tension and Adsorption (Longmans, London, 1966), chap XII. I. A. McLure and B. Edmonds, J . Chem. Soc., Faraday Trans. I , to be submitted. V. A. M. Soares and I. A. McLure, J . Chem. Soc., Faraday Trans. 1, 1982, 78, in press. D. Patterson and R. A. 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Bird, AIChE J., 1955, 1, 174. L. I . Stiel, Ind. Eng. Chem., (London), 1968, 60, 50. G. H. Rohrback and G. H. Cady, J . Phys. Chem., 1979, 71, 1938. R. D. Dunlap, R. G. Bedford, J. C. Woodbary and S . D. Furrow, J . Am. Chem. SOC., 1959,81,2927. R. D. Dunlap and R. L. Scott, J. Phys. Chem., 1962,66, 631. (PAPER 1 / 1603)