Proc. Natl. Acad. Sci. USA Vol. 76, No. 12, pp. 6040-6041, December 1979 Chemistry

An improvement in the theory of regular solutions (solubility parameters/methyl groups/iodine solubility/London forces) J. H. HILDEBRAND Department of Chemistry, University of California, Berkeley, California 94720 Contributed by Joel H. Hildebrand, September 5, 1979

ABSTRACT In constructing the theory of regular, nonpolar, binary solutions, the partial molal energy of mixing has been expressed by the square of difference between "solubility pa- rameters," usually evaluated by the molal energy of vaporization per cubic centimeter, (AEV/ V)1/2 = 6, at approximately 250C. We have found, however, that liquids whose molecules contain methyl groups do not conform to these parameters; to account for their solvent power for iodine requires parameters increased in proportion to the number of methyl groups per molecule. The anomaly may be attributed to the absence of outer nonbonded electrons able to exert London attractive force between neigh- boring molecules. Parameters derived from solubility for iodine -h in both methyl-containing liquids and fluorochemicals greatly improve the predictive power of the theory of regular solu- .A, tions. C1 k The theory of solubility of nonelectrolytes set forth in the book Regular and Related Solutions, by Hildebrand, Prausnitz, and Scott (1), is based upon two concepts: (i) that the components are randomly mixed by thermal agitation, to give the entropy of solution, and (ii) that the energy of mixing can be calculated by solubility parameters, 6, that are square root of the energy of vaporization per cubic centimeter of the liquid, (Ev/V)1/2 = 3. The basic equation is, for component 2, RT in a2/x2 = V2k (2 - I1] in which a is activity referred to the pure liquid, x2 is mole V2 p(2-61)2, kcal fraction, V2 is molal liquid volume, is the molal volume FIG. 1. Solubility of iodine in different groups of solvents, de- 0l scribed in the text. Coordinates are the members ofEq. 1. (One kilo- fraction of the other component. Fig. 1 (from page 148 of ref. = in ref. 5). 1) is a plot of the solubility of iodine in different groups of sol- calorie 4.184 kilojoules.) (Originally printed vents at 250C. The activity of solid iodine at this temperature for all but the two paraffins, n-C7H16 and 2,2,4-tri- is 0.258, its under-cooled liquid volume is 59 cm3, and 62 = 14.1. theory Reverse subscripts for component 1. methylpentane." The points on line A are for the solubility of iodine at 250C Scott (4) in 1958 published "The anomalous behavior of in CS2, CHC13, TiCl4, cis-decalin, trans-decalin, CC14, cyclo- fluorocarbon solutions." C6H12, cyclO-C5Hlo, SiCl4, and CCl3CF3. The three points off In ref. 1, p. 98 and following, we wrote, "Regular solution the line at the top are for solutions in (C4F9)3N, C7F16, and theory is useful for semiquantitative work; for quantitative cyclO-C6F11CF3. The three points G are for polar liquids, those "results it is necessary to make empirical modifications. While on line F are for aromatics that form brown complexes with such modifications can be made in several ways, the most direct iodine; neither of these groups obeys Eq. 1, nor should they. way is to introduce corrections to the geometric mean." This They are treated as deviants from line A. But the points BCDE, is involved in (31 - 62)2 = 62 + 23132 + 62. We discussed this at all alkanes, and the lone point to the right, for octamethylcy- some length. This hypothesis was unsatisfactory because it was clotetrasiloxane, cyclo-(SiO)4(CH3)8, all form violet solutions. not predictive; it had no theoretical basis. Dymond and I (5) in This requires explanation. 1965 published "Effect of methyl groups upon solvent power In 1950 I published a paper (2) on "An irregularity in the of aliphatic liquids." For this there is a theoretical explanation, solvent powers of paraffins." In the same year, Fisher, Benesi, which I pointed out in 1978 (6) under the title "Absence of outer and I (3) published five liquid-liquid solubility curves with nonbonding electrons in methyl groups affects solubility pa- perfluoroheptane and stated in a summary that, "Solubility rameters." London (7), in 1930, explained the van der Waals results attraction between nonpolar molecules as a quantum theory parameter differences calculated from the experimental perturbation between electrons in outer orbitals of neighboring were in close agreement with values predicted by solubility molecules. The electrons in methane and methyl groups are all in tight bonds; the ionization potention of methane, 13.0 eV, The publication costs of this article were defrayed in part by page are charge payment. This article must therefore be hereby marked "ad- is extraordinarily large, and the intermolecular attractions vertisement" in accordance with 18 U. S. C. §1734 solely to indicate so small that AEv/V is too small to measure their attraction with this fact. molecules like those of iodine. 6040 Downloaded by guest on September 26, 2021 Chemistry: Hildebrand Proc. Natl. Acad. Sci. USA 76 (1979) 6041

Table 1. Solubility of iodine and derived parameters Table 2. Parameters of isooctane/(C4F9)3N mixture Line Phase XA XB 'OA 'kB (Fig. 1) Solvent 100X2 61 (AE1v/V1)1/2 Isooctane 0.277 0.9663 0.1038 0.8771 B Cyclohexane 0.918 8.2 8.2 (C4F9)3N 0.723 0.0335 0.8962 0.1029 B Methylcyclohexane 0.920 8.3 8.1 B Ethylcyclohexane 1.036 8.4 8.0 0.16, V1 = 196, V2 - 312, from which we obtain 62- 61 = 2.36. B Dimethylcyclohexane 0.937 8.3 7.8 The old values are 6b = 6.4 and 62 = 6.1, which are quite in- C n-Heptane 0.679 7.9 7.4 consistent with the C n-Pentane 0.595 7.7 7.1 limited solubility, but the iodine-based pa- D 2,3-Dimethylbutane 0.567 7.9 7.0 rameters give 8.2 - 5.6 = 2.6, in reasonable agreement with D 2,2-Dimethylbutane 0.469 7.7 6.7 2.36. E 2,2,3-Trimethylbutane The curve for C7F16 and isooctane obtained by Fisher and (triptane) 0.621 8.0 7.0 Benesi (3), critical temperature = 23.70C, permits calculating E 2,2,4-Trimethylpentane at 20°C to give 62 - 61 = 2.52; the revised parameters give 7.9 (isooctane) 0.592 7.9 6.8 - 5.6 = 2.3. * Octamethylcyclotetrasiloxane 0.813 8.2 6.4 An accurate test of parameters is to be had in the composition n-C7F16 0.01834 5.6 6.0 of the two phases at 25°C of the mixture of isooctane and (C4F7)3N 0.0232 5.6 5.9 (C4F9)3N directly determined from their different densities by Cyclo-C7FjjCF3 0.0201 5.7 6.1 Fujishiro and Hildebrand (11). See Table 2. I calculated values The column 10Ox2 is the solubility of iodine in mol % at 250C. Two of 4 using V1 = 108.5 and V2 = 359. These values substituted values for the solubility parameters for liquids whose molecules in the equation for two liquid phases in equilibrium give 61- contain methyl groups are (i) Sl calculated from solvent power for 62 = 2.4. The 6 values in Table 1 are 7.9 - 5.6 = 2.3. iodine and (ii) calculated from cohesion, as measured by (AE1V/VI)1/2. Another test of a parameter based upon solvent power for iodine is the formula for the partial molal volume of a solute I show in Table 1 the values of the parameters that these liquid at high dilution. On p. 186 of ref. 1 there are 19 liquid methyl compounds must have in order to account for their pairs in which the excess of the partial molal volume of the di- solvent power for iodine. The increase is proportional to the lute solute over its pure molal volume V° agrees with the re- number of methyl groups in molecules of the solvent as shown lationship: in Fig. 2. Shinoda and I (8) calculated, similarly, the solubility V2- V2 (62 -b)2 parameters of the fluorochemicals that place on the line the [2] three points near the top of line A in Fig. 1 and are included in vo (ElayV)7' Table 1. in which T indicates Kelvin temperature. The measured ex- The question next arises, will these new parameters serve to pansions of isooctane in CS2 and in CCI4, 0.037 and 0.009, re- predict solubility relationships of these liquids with other sub- spectvely, are not calculated correctly by using the value stances? The first test is the solubility of SnI4 in isooctane (AEV/V)l/2 = 6.8, but by using its iodine-based parameter 7.9 measured in 1937 by Negishi (9), who obtained X2 = 0.0032. gives 0.049 with CS2 and 0.006 with CC14. [The value of (dE1 With the old parameter for isooctane the calculated value of dy), is 89.0 for CS2 and 81.0 for CC14.] X2 = 0.000215; the new parameter yields 0.0028. The evidence seems to show that the solubility parameters Next, I use liquid-liquid solubilities for C6F1jCF3 with cy- derived from solvent power for iodine can predict with rea- clo(SiO)4(CH3)8 with its eight methyl groups, determined by sonable accuracy the solubility relationships of the solvents with Jolly and Hildebrand (10) in 1957. Its critical mixing temper- each other. ature is 440C and there are enough solubility points on the A Although the London concept of the mechanism of the at- and B branches to yield A and B values of x for each component tractive forces between nonpolar molecules is not yet quanti- at 40°C. This makes it possible to calculate a value of (62 - 61)2 tative, the solubility parameters of regular solution theory ad- more reliable than a value calculated from the critical tem- justed to solvent power for iodine yield predictions that are good perature, as has been the custom. We use formula 10.3 from approximations. 174 of ref. 1. = = = = page XIA 0.84, XIB 0.39, X2B 0.61, x2A 1. Hildebrand, J. H., Prausnitz, J. M. & Scott, R. L. (1970) Regular and Related Solutions (Van Nostrand-Reinhold, New York). 2. Hildebrand, J. H. (1950) J. Chem. Phys. 18, 1337-1339. ic0 - T 3. Hildebrand, J. H., Fisher, H. & Benesi, H. A. (1950) J. Am. Chem. Soc. 72, 4348-4351. 8- 4. R. L. 75a) Scott, (1958) J. Phys. Chem. 62, 136-145. 5. Dymond, J. & Hildebrand, J. H. (1965) Proc. Nati. Acad. Sci. USA E 6- 54,1001-1003. a' 6. Hildebrand, J. H. (1978) IEC Fundam. 17,365-366. V1 4O 7. London, F. (1930) Z. Physik. Chem. BRl, 222. 8. Shinoda, K. & Hildebrand, J. H. (1958) J. Phys. Chem. 62, 292-294. 9. Hildebrand, J. H. & Negishi, G. R. (1937) J. Am. Chem. Soc. 59, 339-341. 0 0.4 0.8 1.2 1.6 2.0 Y. 10. Jolly, J. E. & Hildebrand, J. H. (1957) J. Phys. Chem. 54, 1 - (EvV,) 1001-1003. FIG. 2. Increases in solubility parameters of solvents for iodine 11. Fujishiro, R. & Hildebrand, J. H. (1962) J. Phys. Chem. 66, in relation to the number of methyl groups in a molecule. 573. Downloaded by guest on September 26, 2021