Gas-chromatographic study of the solution thermodynamics of

J. Phys. Chem. 1982, 86, 4605-4618

under contract No. F33615-78-C-2075,and by the Division of Chemical Sciences, Office of Basic Energy Sciences,U.S. Department of Energy, under contract W-7405-eng-26 with the Union Carbide Corp. M.S. is grateful for financial

4605

assistance from Norges Teknisk-Naturvitenskapelige Forskningsrld. We note with thanks the technical assistance of J. Cobb and D. Goff, and helpful advice from J. Brynestad and C. A. Angell.

Gas-Chromatographic Study of the Solution Thermodynamics of Hydroxylic Derivatives and Related Compounds Stanley H. Langer;

Richard J. Sheehan,t and Jan-Chan Huangt

Department of Chemical Engineering, Universlty of Wisconsin, Medison, Wisconsin 53706 (Recelved: January 26, 7982; I n Final Form: June 28, 1982)

Applications of gas chromatography have been enhanced through conversion of many chemical compounds with suitable reagents to volatile derivatives. This study was conducted to resolve vapor pressure and solution effect contributions to the volatility factor (hence, separation) for a number of model hydroxylic derivatives with low molecular weight stationary phases. The latter include qualane, a phthalate ester, a tetrachlorophthalate ester, a phosphate ester, a polyphenyl ether (PPE) and a tetracyanoethyl ether. The derivatives chosen were the trimethylsilyl ethers (TMSE's), trifluoroacetates (TFA's) and pentafluoropropionates of butyl alcohol (aliphatic),cyclohexanol (cyclic),and m-and p-methylphenols (aromatics);n-butyl tert-butyl ether was included for comparison with the trimethylsilyl ether of butyl alcohol. Activity coefficients as well as excess partial molar functions were measured for the solutes in the stationary phases at infinite dilution by using gas-chromatographic techniques at ca. 100 O C . Many of the solution interactions were found to involve "dual-character" molecules (e.g., comprising two parts with dissimilar properties) which have been neglected to date. The dual character of many derivatives results in vapor pressure and solution interaction effects which can assist isomer separation. Study of excess entropy and enthalpy solution effects was facilitated by taking into account combinatorial (size) contributions using Flory-Huggins (FH) type calculations. Many of the thermodynamic results could then be interpreted in terms of specific solute-solvent interactions. The results of this study support an approach to selecting derivatives for separations with particular stationary phases. Both the vapor pressures and the solvent interactions of derivatives are shown to play a significant role in separation. Entropic factors also can be important.

Introduction The popularity of gas-liquid chromatography for separation and identification stems from the possibility of utilizing both vapor pressure and solute3olvent (stationary phase) interaction effects with efficient, simple apparatus.'+ Where vapor pressure data are available, gas chromatography is readily adapted to the study of solute-solvent interactions through the measurement of solute activity coefficients a t infinite dilution as well as related excess partial molar functions fo the solution process.613 However, resolution of the vapor pressure and solute-solvent interaction effects has been uncommon outside of studies of hydrocarbon solutions1"6 and specific complexation interaction^."-'^ Applications of gas chromatography have been further expanded by the possibility of converting or "derivatizing" many chemical compounds with suitable reagents to give volatile products.2*22 Derivative formation may impart increased stability. It also can be used to facilitate difficult separations of closely related isomers, to aid in identification or detection,21to minimize adsorption on liquidchromatographic supports,23and to alter the "volatility" of the parent compounds.24 The volatility factor is ambiguous in that it includes both vapor pressure and solution interaction e f f e ~ t s . ~ ~Surprisingly, J~J~ the consequence Present address: Amoco Research Laboratories, Naperville, IL 60540. *Department of Physics, Kent State University, Kent, OH.

of derivative formation has received little attention with regard to examining these effects separately despite their (1) James, A. T.;Martin, A. J. P. J. Appl. Chem. 1956, 6 , 105-15. (2) Porter, P. E.; Deal, C. H.; Stross, F. J. Am. Chem. SOC.1956, 78, 2999-3006. (3) Langer, S.H.Anal. Chem. 1967, 39,524-5. (4) Laneer. S.H.:Sheehan. R. J. Adu. Anal. Chem. Znstrum. 1968.6. , . 289-323. (5) Laub, R. J.; Purnell, J. H. J. Chromatogr. 1975, 112, 71-9. (6)Everett, D.H.; Stoddard, C. T. H. Trans. Faraday SOC.1961,57, 746-54. (7) Lanner. S. H.:Purnell. J. H. J . Phvs. Chem. 1963. 67. 263-70. (8) CruGkshank, A.J. B.; Windsor, M. Young, C. L. h o c . R . SOC. London, Ser. A 1966,295, 259-70. (9) Conder, J. R.; Purnell, J. H. Trans. Faraday SOC.1968,64,1505-12; 1969,65,839-48. (10) Martire, D. E.; Pecsok, R. L.; Purnell, J. H. Trans. Faraday SOC. 1965,61, 2496-508. (11) Locke, D. C. Adu. Chromatogr. 1976,14, 87-198. (12) Laub, R. J.; Pecsok, R. L. "Physiochemical Applications of Gas Chromatogrphy";Wiley: New York, 1978. (13) Conder, J. R.; Young, C. L. "Physiochemical Methods by Gas Chromatography"; Wiley: New York, 1979. (14) Young, C. L. Chromatogr. Reu. 1968, 10, 129-58. (15) Ashworth, A. J.; Everett, D. H. Trans. Faraday SOC.1960, 56, 1-tim-1 - - - -R-. (16) Parcher, J. F.;Weiner, P. H.; Hussey, C. L.; Westlake, T.N.J . Chem. Eng. Data 1975,20, 145-51. (17) Langer, S.H.; Johnson, B. M.; Conder, J. R. J. Phys. Chem. 1968, 72,4020-30 (18) Martire, D.E.; Riedl, P. J. Phys. Chem. 1968, 72, 3478-88. (19) Purnell, J. H.;de Andrade, J. M. V. J . Am. Chem. SOC.1975,97, 3585-90. (20) Burchfield, H. P.; Storrs, E. E. "BiochemicalApplications of Gas Chromatography";Academic Press: New York, 1962.

c.;

0 1982 American Chemical Society

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The Journal of Physical Chemistry, Vol. 86, No. 23, 1982

importance in the design and selection of gas-chromatographic liquid p h a s e ~ . ~ pMany ~ * ~ ~of the solution interactions involve "dual-character" molecules (e.g., compqising two parts with dissimilar properties such as aliphatic,esters of fluorinated materials) which have been neglected to date. Such dual-character molecules might be expected to be oriented in some liquid phases to affect excess thermodynamic properties. Studies of the solution thermodynamics of derivatives have broad implications since both solutes and solvents (liquid phases) can be varied systematically to provide opportunities for recognizing important solution effects. A long-term interest in solution interactions and the design of gas-chromatographic liquid phases (solvents), as well as the unusual character of many derivatives, led to the present study of the thermodynamics of solutions of representative derivatives of hydroxylic compounds with a number of stationary phases. For comparison, several hydrocarbons and an ether were included. The stationary phases were selected to include a variety of functional groups and potential interactions but were restricted to lower molecular weight compounds. In addition to resolving vapor pressure and solution interaction effects, the results provide opportunities for refining current solution theories. The derivatives selected as representative were the trimethylsilyl ethers, trifluoroacetates, and pentafluoropropionates of the following solutes: butyl alcohol (aliphatic), cyclohexanol (cyclic),and m- and p-methylphenols (aromatics); n-butyl tert-butyl ether was included for comparison with the trimethylsilyl ether of butyl alcohol. The low molecular weight stationary phases were squalane, a phthalate ester, a tetrachlorophthalate ester, a phosphate ester, a polyphenyl ether, and a tetracyanoethyl ether.

Theory

Langer et al.

Here

Pi and Poare column inlet and outlet pressures, B22and B23 are the second virial coefficient of the solute and the crossed virial coefficient between the solute and the carrier gas, respectively, and u i and 13; are the molar volume and the partial molar volume of the solute, respectively. Usually, I3; does not differ from u; by more than 5%; therefore, it may be replaced in the correction term of eq 3 by ui. The last term of eq 3 tends to be insignificant at low column pressure, especially with helium carrier gas. BZ3for hydrocarbon-helium mixtures usually lies between +30-60 cm3/mol, tending to cancel the 0; term.27x2s,33 However, with nitrogen carrier gas, hydrocarbon retention ~~ volumes may be lowered by as much as 1 - 1 . 5 7 ~ . To obtain the most precise calculation, we used here the last term in eq 3. Excess partial molar functions for a solute at infinite dilution in the stationary phase are then given by3J-14J7 AG: = RT In yf"

(4)

(51

AG; =

fl: - TAS;

(6)

where AGJ is the partial molar excess free energy of mixing, AH: is the partial molar excess enthalpy of mixing, and AS: is the partial molar excess entropy of mixing. Second virial coefficients were computed with the equation of McGlashan and ~ o - w o r k e r s ~ ~ ~ ~ ~

B22/Vc = 0.43 - O.866TL1 - O.694Tc2 The mole fraction based activity coefficient for a solute - 0.0375(n - l)T;4.5 (7) at infinite dilution in a stationary phase, y;, can be related to the corrected retention volume per gram of liquid phase where T, is the reduced temperature, V, is the critical at column temperature, by the e q ~ a t i o n ~ ~ ~ ~ ~ J ' volume, and n is the number of carbon atoms. Pure hydrocarbons appear to be "normal" and obey this equation. For use with other solutes, a "pseudo" carbon number obtained from vapor pressure data and correlations discussed by Guggenheim and Wormald must be employed.31 where M, is the molecular weight of the stationary phase For the crossed second virial coefficients the following (solvent) and po is the vapor pressure of the pure solute. The relative retention of two solutes, L Y ~ ,is~ ,then2-4i7p25 combining rules were used for the critical temperatures and volumes: 32

c,

For a more rigorous thermodynamic treatment, the fugacity-based activity coefficient at infinite dilution, r:, corrected for gas-phase imperfection to zero pressure is obtained from the

These equations were employed earlier to predict differences between retention volumes of hydrocarbons in nitrogen and helium to within a few tenths of a percent.2' (26) Cruickshank,A. J. B.;Gainey, B. W.; Young, C. L. Trans. Faraday SOC. 1968, 64, 337-48.

(21) Ahuja, S. J. Chromatogr. Sci. 1979, 17, 168-72. (22) Knapp, D. R. 'Handbook of Analytical DerivatizationReactions"; Wiley: New York, 1979. (23) Langer, S. H.; Hein, D. T.; Bolme, M. W. Anal. Chem. 1978,50, 1578-9. (24) Sheehan, R. J.; Langer, S. H. J. Chem. Eng. Data 1969, 14, 248-50. (25) Baiulescu, G. E.; Ilie, V. A. "Stationary Phases in Gas Chromatography";Pergamon Press: New York, 1975.

(27) Conder, J. R.; Langer, S. H. Anal. Chem. 1967, 39, 1461-4. (28) Laub, R. J.; Pecsok, R. L. J. Chromatogr. 1974, 98, 511-26, (29) McGlashan, M. L.; Potter, D. J. B. Proc. R. SOC.London, Ser. it. 1962,267, 478-500. (30) McGlashan, M. L.; Wormald, C. J. Tram. Faraday SOC.1964,60, 646-52. (31) Guggenheim, E. A.; Wormald, C . J. J . Chem. Phys. 1965, 42, 3775-80. (32) Hudson, G. M.; McConbrey, J. C . Trans. Faraday Soc. 1960,56, 761-6. (33) Langer, S. H.; Patton, J. E. J. Phys. Chem. 1972, 76, 2159-69.

The Journal of Physical Chemistry, Vol. 86, No. 23, 1982 4607

Solution Thermodynamics of Hydroxylic Derivatives

Experimental Section Apparatus. The gas chromatograph was fabricated to ensure constant, uniform temperature for the whole column. It is similar to the one described earlier.33 A wellinsulated case enclosed a 21.6-cm diameter by 91.5-cm cylindrical chamber containing a supported, centered, 16.5-cm diameter by 83.3-cm copper cylinder. The Ushaped columns were located inside the latter. Nichrome heating elements were supported in the annular space on the cylinder exterior. A high-speed fan pulled air down the cylinder and pushed it up the annular section. A nickel resistance thermometer was used to sense temperature for the controller circuit. Measurements in the area around the column revealed no short-term temperature variations as detected by a potentiometer sensitive to 0.01 OC. Temperature gradients throughout were less than f0.04

"C. A National Bureau of Standards calibrated thermometer with 0.1 OC graduations was read to 0.01 "C with a magnifier to measure temperature. Helium carrier gas flow was regulated by a needle valve-diaphragm combination and measured by a soap bubble meter. Column pressure drop and atmospheric pressure were determined with a mercury manometer and barometer. All columns were fabricated from 5-mm i.d. type 304 stainless-steel tubing. The thermal conductivity cell and power supply were from Gow-Mac Instrument Co. The injection system was a heated aluminum block with direct carrier gas flow into the column. Procedures. Chromatographic data were measured by using careful procedures described earlier.' All measurements were made after a 3-h or longer equilibration period. Before each run,the carrier gas flow rate was checked twice and room temperature was measured. In general, mixtures of four solutes which were particular derivatives of four parent compounds were injected with a toluene standard. Total samples ranged from 0.03 pL for rapidly eluting compounds to 0.1 pL for slower ones. Timing started at the maximum of the air peak, with each solute peak timed at several points on the leading and trailing edges. Column pressure drops on the order of 0.4-1 atm and temperature were monitored during the run, and the gas flow rate was measured twice afterward. Barometric pressure was measured several times during the day. Reported data were replicated and checked to within 0.1 mL or 0.1 s whichever was greater. Where appropriate, the toluene standard allowed corrections for slight liquid-phase evaporation. Materials. Squalane, tetracyanoethylated pentaerythritol (TCNP), polyphenyl (five ring) ether (Anspec), dionyl (3,3,5-trimethylhexyl)phthalate(May and Baker), and tris(2,4-dimethylphenyl)phosphate (TXP) were obtained from standard suppliers. Pure di-n-butyl tetrachlorophthalate (DBTCP) was prepared in our laboratories. n-Butyl pentafluoropropionate (Peninsular ChemResearch) was a commercial product. Reagent such as hexamethyldisilazane,trifluoroacetic anhydride (Aldrich), and pentafluoropropionic anhydride (Pierce) were commercial products. Silanized firebrick and Celite (Anspec) nonadsorbing solid supports of mesh 100/120 or 60/80 were used. Trimethylsilyl ethers of hydroxylic compounds were prepared by refluxing with hexamethyldisilazane with a little sand.34 Fluoroesters were prepared by reacting fluorinated anhydrides with alcohols and phenols.35 (34)Freedman, R. W.; Croitoru, P. P. Anal. Chem. 1964,36,1389-90. (35)Shulgin, A. T. Anal. Chem. 1964,36,920-1.

For n-butyl tert-butyl ether, NaH and tert-butyl alcohol were reacted for 72 h after which n-butyl bromide was added and refluxed for 40 h to complete the Williamson synthesis. Sodium tert-butoxide has a low reactivity. All synthesized compounds were distilled at least twice. Chromatographic analyses showed 99% minimum purity except for the tert-butyl ether (4% impurity). Densities of the viscous stationary phases were determined by using a pycnometer calibrated with mercury at temperatures of interest. A large-bore needle was used to inject these liquids into the pycnometer bulb. The method of Lipkin et al.36was used to determine solute densities. Results Values of for the n-alkanes, aromatics, and four types of derivatives are listed in Tables I and I1 for the six stationary phases studied (see paragraph at end of text regarding supplementary material). Since the vapor pressures of some cresol derivatives are quite low, their retention volumes were not measured for some strongly interacting solvents. Densities and thermal expansion coefficients of solutes are listed in Table I11 (supplementary material). The vapor pressures of the derivatives calculated from a previous reportz4and those of n-alkanes and aromatics calculated from the standard reference37are shown in Table I11 for 80 "C and Table VI1 for 100 "C. Second virial Coefficients for solutes and cross second virial coefficients for solutes and the carrier gas were calculated with eq 7. For those compounds for which critical properties were not available in the literature, a group method% was used for estimation. Values of yf" calculated with eq 3 are listed in Table IV. With eq 4-6, excess partial molar quantities were calculated and listed in Table V. Errors of the orde? of 0.2% in y; result in f2 cal/mol error in calculated AG; values. However, the same error in yf" will cause about 60 cal/mol error for Al?; and TAS; at the temperatures of this s t ~ d y . ~ While ? ' ~ retention volumes can generally be reproduced to better than 0.2%, some caution is appropriate with the vapor pressure data and the vapor-phase imperfection correction in order to obtain the best values for the excess thermodynamic functions. The importance of the vapor-phase imperfection correction can be illustrated with the squalane data. A rf"/r," ratio of 1.036 for n-heptane calculated at 80 "C can be compared with that of 1.056 at 100 "C. Without the imperfection correction, the calculated excess enthalpy of mixing for n-heptane will be positive. It has been observed that the partial molar excess enthalpy of mixing of nhexane in n-hexadecane is positive at low temperature, becoming negative around 60 0C.39 Similar temperature dependence has been observed in other alkane and the negative values of excess enthalpy for n-alkanes in squalane here are consistent with those results. The vapor-phaseimperfection correction, which depends mainly on the product of the vapor pressure and the second virial coefficient of the solutes, increases with increasing temperature. Therefore, the excess enthalpy calculated without this correction tends to be high; the excess entropy is subject to a related systematic error. However, such errors have only minor influence in com-

vhf

~~

(36)Lipkin, M. R.; Davison, J. A.; Harvey, W. T.; Kurtz, S. S. Ind. Eng. Chem., Anal. Ed. 1944,16,55-8. (37)Rossini, F. P.; Mair, B. J.; Streiff, A. J. "Hydrocarbons from Petroleum"; Reinhold: New York, 1953. (38)Reid, R. C.; Prausnitz, J. M.; Sherwood, T. K. 'The Properties of Gases and Liquids", 3rd ed.; McGraw-Hill: New York, 1977. (39)McGlashan, M. L.;Morcom, K. W. Trans. Faraday SOC. 1961,57, 581-7. (40)Hijmans, J.; Holleman, T. Adu. Chem. Phys. 1969,16, 223-81.

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The Journal of Physical Chemistty, Vol. 86, No. 23, 1982

Langer et al.

TABLE IV: Corrected Activity Coefficients at Infinite Dilution, 7 ; squalane

DBTCP

DNP

TXP

TCNP

80 "C 100 "C 80 "C 1 0 0 "C 80 "C 100 "C 80 "C 100 "C 80 "C

1. n-heptane 2. n-octane 3. n.nonane 4. benzene 5. toluene 6. o-xylene 7. 1-methyl-3-ethylbenzene 8. n-butyl acetate 9. cyclohexyl acetate 10. m-tolyl acetate 11.p-tolyl acetate 12. n-butyl trimethylsilyl ether 13. cyclohexyl trimethylsilyl ether 14. m-tolyl trimethylsilyl ether 15. p-tolyl trimethylsilyl ether 16. n-butyl trifluoroacetate 17. cyclohexyl trifluoroacetate 18. m-tolyl trifluoroacetate 19. p-tolyl trifluoroacetate 20. n-butyl pentafluoropropionate 21. cyclohexyl pentafluoropropionate 22. m-tolyl pentafluoropropionate 23. p-tolyl pentafluoropropionate 24. n-butyl tert-butyl ether

0.658 0.684 0.707 0.600 0.621 0.660 0.698 1.015 0.977 2.287 2.244 0.915 0.819 0.957 0.900 1.953 1.372 1.823 1.862 2.507 1.847

0.661 0.688 0.711 0.581 0.607 0.647 0.687

1.614 1.706 1.794 0.475 0.492 0.475 0.666 0.898 0.951 0.858 1.984 1.968 0.903 1.789 0.812 1.606 0.958 0.908 1.755 1.773 1.287 1.323 1.652 1.699 2.269 2.549 1.664 1.956

1.554 1.640 1.716 0.496 0.522 0.514 0.696 0.914 0.859

1.172 1.257 1.342 0.535 0.577 0.609 0.688 0.737 0.743

1.148 1.221 1.297 0.536 0.581 0.613 0.693 0.741 0.741

2.408 2.669 2.951 0.666 0.745 0.802 0.975 1.032 0.968

1.753 1.552 0.978 0.936 1.723 1.276 0.982 0.944 2.465 1.833

1.282 1.269 1.143 1.267 30.28 1.228 1.197 0.973 1.035 35.63 0.483 11.49 0.481 11.19 1.117 1.103 1.987 1.912 11.95 0.879 0.880 1.451 1.410 12.00 0.855 0.857 1.313 1.303 6.350 0.863 0.866 1.282 1.263 6.282 1.524 1.512 3.097 2.956 23.66 1.245 1.198 2.379 2.200 25.82

PPE

100 "C 80 "C 100 "C

2.254 38.13 32.54 2.473 52.66 44.03 2.714 72.28 59.38 0.661 2.176 2.176 0.741 3.126 3.103 0.796 3.995 3.917 0.961 6.430 6.184 1.037 3.784 3.790 0.963 4.622 4.502

2.135 1.934 1.333 1.080 1.085 2.020 1.959 13.88 2.093 1.895 1.220 1.032 1.037 1.821 1.761 13.23 0.831 0.820 1.479 1.469 1.118 1.103 2.063 1.972 20.77

2.719 3.039 3.382 6.644 0.743 0.809 0.959 0.865 0.763

2.528 2.804 3.081 0.649 0.743 0.804 0.950 0.898 0.789 0.901 0.906 2.721 2.272 1.504 1.410 3.071 2.064 2.054 2.158 5.190 3.620

28.03 32.22 11.28 11.08 11.16 11.13 6.368 6.272 22.09 22.81

2.767 2.330 1.469 1.370 3.231 2.136 2.130 2.282 5.509 3.924

13.42 12.77 19.22

3.661 3.432 3.624 3.402 2.033 1.987

10,000 c c m

I

IOoo[ 100,

t

I

i

I

I

10

100

I

1000

10,000

I

20

C 'O0

Figure 1. log-log plot of Vioofor solutes of this study (see Table I V for number assignments) eluted from squalane and dibutyl tetrachlorophthalate: (-) alkanes, (- - -) aromatics.

parisons of solutes of similar structure because any relative differences are less affected by these c o r r e ~ t i o n s . ~ J ~

Discussion Correlation of The logarithms of Vi" for solutes in three solvent pairs are plotted and compared in Figures 1-3. Since the ratio of values of any solute in two solvents reflects the inverse ratio of activity coefficients (eq 2), log-log plots of are related to plots of excess free energies of mixing for solutes in two different solvents. While the molecular weights of solvents, as well as resolved contributions from excess enthalpy or excess entropy values of solutes are not considered, this approach provides a simple means by which to compare interactions in two solvents. Log-log plots of values for aromatic solutes generally produce straight lines for solvent pairs of similar properties, such as 7,8-benzoquinoline vs. ~ h e n a n t h r e n e .Such ~ linearity is a result of a compensation relation between

q.

q

q

q

1 -11_.1

100

L

I:_

1000

(cm3/gi f o r DBTCF

Figure 2. log-log plot of Vioo for solutes of Table I V eluted from dinonyl phthalate and dibutyl tetrachlorophthalate: (-) alkanes, (- - -) aromatics.

excess entropy and excess enthalpy in solution processes. Usually, families of solutes differ in their enthalpy-entropy relations, so that distinct family curves are observed.li Therefore, the linear logarithmic plot is a criterion for homogeneity and regularity of family interactions. Retention data for two standard gas-chromatographic liquid phases, squalane and di-n-butyl tetrachlorophthalate (DBTCP), are shown in Figure 1. Squalane, consisting of saturated hydrocarbon units, retains n-alkanes; DBTCP, a well-known charge-transfer ~ o l v e n t ,retains ~ ~ J ~aromatic ~~~ hydrocarbons and other compounds with aromatic rings. Regular patterns are found for n-alkanes and aromatics; n-heptane, n-octane, and n-nonane fall on a straight line with constant intervals, indicating that methylene group additions to n-alkanes contribute in a regular fashion to log with each solvent. This applies for almost all solvents, being the basis for the reference Kovats index for non-alkane The aromatics exhibit

q



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4609

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Figure 3. log-log plot of Vioofor solutes of Table I V eluted from tris(2,4-dimethylphenyl) phosphate and tetracyanoethylated pentaerythritol: (-) alkanes, (- - -) aromatics.

irregular methylene intervals although the family curve parallels that for the n-alkanes. o-Xylene is retained as can be seen by the extent of its separation from toluene in Figure 1. This can be explained by the dipole moments of ortho aromatic derivatives, which can result in attractive interactions with s ~ l v e n t s . ~n-Alkanes J~ and aromatic hydrocarbon plots shown as solid and dashed lines in Figure 1bound the solutes here except for small deviations by fluoroester derivatives of two methylphenols. The molecular weight of m-tolyl pentafluoropropionate is 2.26 times that of l-methyl-3-ethylbenzene, but it has a retention volume comparable to that of the latter because fluoro derivatives exhibit relatively high vapor pressures. With the squalane column, m-tolyl trifluoroacetate and m-tolyl pentafluoropropionate actually are eluted earlier than 1-methyl-3-ethylbenzene. A comparison with acetates and trimethylsilyl ethers further shows that TFA and PFP groups form advantageous hydrocarbon hydroxylic derivatives which tend not to be retained by a number of solvents despite their molecular weight. In Figure 2, trifluoroacetate and pentafluoropropionate derivatives of n-butyl alcohol and cyclohexanol are found to be eluted outside the n-alkane and aromatic limits in the plot for two aromatic stationary phases, dinonyl phthalate (DNP) and DBTCP. This reflects some "squeezing" from solution. Comparison of Figures 1and 2 shows that the butyl fluoroesters move across two limits: in Figure 1 the representative points are close to the aromatic line, while in Figure 2 they fall outside the n-alkane line. Fluoroester derivatives thus have higher solubilities in DNP than in DBTCP, possibly reflecting expected strong dipole-dipole interaction^.'^ This effect is prominent with butyl derivatives which are shifted significantly. Both n-alkane and aromatic lines in Figures 1and 2 are parallel with slopes close to unity. The constancy of slopes indicates that a linear excess free energy relation for the solution process exists for n-alkanes and aromatics with both solvents. Since these figures include a common solvent, DBTCP, the solvent similarity involves all three solvents: squalane, DNP, and DBTCP. The difference between them manifested by the area between the two parallel lines stems from the interactions of the aromatic (41)Kovats, E. Helu. Chim. Acta. 1958, 41, 1915-32.

Langer et ai.

rings of solutes with solvents. The proximity of n-alkane and aromatic lines in Figure 2 relative to Figure 1 reflects the similarity of DNP and DBTCP as well as the nonselective nature of the former. DNP retains fluoroesters and TMSE (trimethylsilyl ether) derivatives, as can be seen in Figure 2 , where almost all data points, other than aromatics, fall on a single straight line. Thus, DNP is a nonselective solvent with high compatibility with a variety of solutes, a consequence of its molecular composition of multiple, varied, closely interspersed groups (as discussed below). Plots in Figure 3 for tris(2,4-dimethylphenyl) phosphate (TXP) and tetracyanoethylated pentaerythritol (TCNP) reflect a range and variety of specific interactions for these extremely polar solvents. Using bounding n-alkanes and aromatic lines, data points in Figure 3 can be divided into three classes. The central zone contains three pairs: tolyl TMSE deri~atives,'~J~ butyl fluoroesters,'6,20and cyclohexyl f l u o r ~ e s t e r s . 'These ~ ~ ~ ~molecules have the common feature of comprising two significant parts with different properties; one is polar or polarizable and another is less so. The retention behavior of these compounds lies between those that consist of polarizable groups and those with nonpolar or less polarizable groups. Above the central clusters, there are 10 points close to the aromatic line, all containing an aromatic ring. In contrast, compounds essentially expelled by TCNP fall on the alkane line and contain no aromatic ring. The molecules in the central zone are molecules of dual character with moderate solubilities in both solvents. Dual-character effects are also a feature of Figures 1 and 2 but they are less distinctive than in Figure 3. Almost all derivatives of this study can exhibit a dual character with appropriate solvents. Dual character, where identifiable, is helpful for separating mixtures of derivatives, such as TFA and TMSE of methylphenols from hydrocarbons, because derivatization can impart properties which differ from the basic character of parent compounds. The dual characteristics can speed the elution rate but still allow moderate retention so that gas-chromatographic separations based on interactions are possible to achieve. The slopes of n-alkane and aromatic lines differ from unity in Figure 3, being slightly lower for alkanes and slightly higher for aromatics, reflecting specific interaction of the latter with the TCNP liquid phase. Since the characteristic vapor pressure of each solute is constant in any solvent, the trend of the retention behavior reveals a large change of activity coefficients as well as of excess free energies in the two solvents (eq 4). With these highly nonideal solutions, the excess of enthalpy of mixing, which may be as large as 1 kcal/mol, cannot be correlated simply with the excess entropy of solution. Excess Free Energy and Its Components. Most gaschromatographic thermodynamic studies involve small solute molecules dissolved in solutions of larger solvent molecules. For interpretation, Flory-Huggins-type treatments for mixtures of different molecular size are often employed following that of Ashworth and Everett; 2,7~15 the infinite-dilution activity coefficient, y:, is expressed as the product of the thermal activity coefficient (7;) and athermal activity coefficient (7:) terms. The thermal term is associated with the excess enthalpy of solution while the athermal term is related to an excess entropy of solution, i.e.

rf" = r,"rt"

(11)

In y ," = - A S ; / R

(12,

In y; = m ; / R T

(13)



The athermal contribution to the activity coefficient has been assigned by frequently using the Flory-Huggins expression for the combinatorial entropy 7,"= ( l / m ) exp(1- l / m ) (14) where m is the size ratio of the solution molecules, approximated as the volume ratio of solvent to solute. Such treatment may be valid on occasion but it ignores other contributions to the excess entropy and is open to question. I t has not been adequate for explaining solution behavior.7-9J4 An alternate attractive approach can come from Guggenheim and Flory's t r e a t m e n t ~ ~ by~considering v~ the residual activity coefficient remaining after factoring out the size correction now, 7iH. Then, x, the free energy of interaction, involves contributions x = XH -k XI-S (15) where xH = -T(dx/dT) = Al?;/RT (16) = d(Tx)/dT = -ASE/R

(17) Then, AS; is a residual entropy of solution associated with all entropy effects other than size correction. According to F l ~ r yXH , ~and ~ x1-S are correlated with each other. A negative XH is compensated by a positive x1-s which frequently causes x to fall in a narrow range (e.g., 0.3-0.55) for most miscible polymer-solvent mixtures.42b Here, then, the activity coefficient is expressed as rf"= 6 H 7 % f S (18) where T F ~ H = r,"(eq 14) (19) x1.S

7F = exP(XH)

(20)

7% = exp(x1-s) (21) Equation 18 is essentially an untested expression for 7;; yiH is the Flory-Huggins size effect correction; and 7; is essentially the 7;of eq 13. However, to avoid confusion with the symbols used earlier which are based on eq 11, the subscript T is used to indicate that 73 is based on the assumptions of eq 18. includes all entropy effects (other than size effects) which arise from the interaction between solutes and solvents. I t involves at least two important contributions: an orientation entropy due to specific interactions7J2J3or different molecular shapes,44 and an equation of state e n t r ~ p y . ~ ~ ? ~ ~ The activity coefficients in Table IV, then, have been utilized with eq 5 , 14, 16, and 17 to calculate the three contributions to the infinite-dilution activity coefficients. These are shown for the solutes used here at 90 OC in Table VI. Vapor Pressure of Derivatives. The net interaction between the enthalpy and entropy factors in both the pure liquid state and the solution state is a major consideration in isomer s e p a r a t i ~ n . ~ * ~Liquid-state J ~ J ~ p ~ ~ interaction for pure solutes may be reflected in the vapor pressure data. It should be remembered that excess thermodynamic solution properties are referred to that pure state. When one examines the derivative concept for gas chromatography, two consequences of derivatization are of special note. One is that derivatization substantially changes the vapor (42) (a) Guggenheim, E.A. Trans. Faraday SOC.1948,44,1007-12. (b) Miller, M. "The Structure of Polymers";Reinhold: New York, 1966; pp 150-1. (43) Flory, P.J. Discuss. Faraday SOC.1970,49, 7-29. (44) de st. Romain, P.; Van, H. T.; Patterson, D. J . Chem. SOC.,Faraday Trans. 1 1979, 75,1700-7. (45) Flory, P. J.; Orwoll, R. A.; Vrij, A. J. J . Am. Chem. SOC.1964,86, 3515-20.

pressure of the parent compounds, especially phenols.24 Another is that derivatization can facilitate isomer separation, a major concern of gas chromatography. The advantage of the increase of solute vapor pressures can be understood with eq 1, which indicates that elution speed is approximately inversely proportional to the vapor pressure of the solute. The vapor pressure behavior of some homologous series relevant to gas chromatography was studied early by Pierotti et al.46 They showed that plots of the logarithm of vapor pressure vs. carbon number were linear for homologous series, providing a basis for formulating group behavior approaches. The vapor pressure plots for most monosubstituted organic compounds are parallel, which indicates that each methylene group decreases the vapor pressure by a constant ratio. The zero carbon number intercept of each homologous series line is a characteristic property of the functional group. The vapor pressures of fluoroesters are considerably higher than corresponding aliphatic analogues, e.g., tolyl trifluoroacetates vs. tolyl acetates. The vapor pressures of the tolyl acetates are lower than that of toluene by a factor equivalent to about five methylene units. The vapor pressure of toluene is decreased by the equivalent of four methylene groups on substitution of a TMSE group despite an increase in molecular weight of ca. 103. Vapor pressures of derivatives can be rationalized from their molecular structures. Both acetate and fluoroacetate derivatives contain two groups of differing nature. In tolyl acetates, the polar ester group interacts with the polarizable tolyl group to give liquids of relatively low vapor pressure. In corresponding fluoroesters, the aromatic core and the derivatizing group have low interaction energy leading to high vapor pressure. Alternatively, tolyl fluoroesters can be considered as a composite of three parts rather than two: an aromatic ring, the ester, and the fluorocarbon. The ester group and the aromatic core have high affinity as reflected by the low acetate vapor pressures. But the fluorocarbon esters, or fluorocarbon derivatives, are so dissimilar that the ester-aromatic ring interaction is o f f ~ e t . Molecules ~ ~ ~ ~ ~with three or more differing groups, (e.g., a multicharacter molecule) will possess properties resulting from group arrangement within the molecular structure and the net balance of intermolecular interactions. A simple additive rule for molecular properties often fails for the lower molecular weight members of homologous This is because the functional group can have a dominant effect on overall properties when the molecule is small. The molecules considered here consist of hydrocarbon and derivative parts which are both of comparable size. The simple summation ru1e38,46,48 is not expected to hold for these molecules and the effect of derivatization on vapor pressure may not be the same for each parent compound. However, the vapor pressures of the derivatives can be estimated by considering the derivatizing group as a single, simple unit. The estimated vapor pressure can serve as a guide for a derivative choice; solution properties are more difficult to predict. Dual character can also be observed from comparison of the entropy of vaporization and the solubility parameter of pure liquids. In a dual-character liquid molecule, portions of the molecule may tend to repel each other so (46) Pierotti, G. J.;Deal, C. H.; Derr, E. L.; Porter, P. E. J . Am. Chem. SOC.1956, 78,2989-98.

(47) Simons, J . H.; Mausteller, J. W. J . Chem. Phys. 1952,20,1516-9. (48) Purnell, J. H."Gas Chromatography"; Wiley: New York, 1962; p 43.

4612


Langer et al.

ri00oooooFi

m w c909

I:

-m ??

mw

a-

0 0

0 0

w

w

z

Solution Thermodynamics of

Hydroxylic Derivatives


TABLE VII: Calculated Entropies of Vaporization at Normal Boiling Points (AS:) with Solubility Parameters (6 , m o ~ and ) Vapor Pressures a t 100 "C for Solutes Used Here

1. n-heptane 2. n-octane 3. n-nonane 4. benzene 5. toluene 6. o-xylene 7. l-methyl-3-ethylbenzene 8. n-butyl acetate 9. cyclohexyl acetate 10. m-tolyl acetate 11.p-tolyl acetate 12. n-butyl trimethylsilyl ether 13. cyclohexyl trimethylsilyl ether 14. m-tolyl trimethylsilyl ether 15. p-tolyl trimethylsilyl ether 16. n-butyl trifluoroacetate 17. cyclohexyl trifluoroacetate 18. m-tolyl trifluoroacetate 19. p-tolyl trifluoroacetate 20. n-butyl pentafluoropropionate 21. cyclohexyl pentafluoropropionate 22. m-tolyl pentafluoroproprionate 23. p-tolyl pentafluoropropionate 24. n-butyl tert-butyl ether

21.7 22.0 22.3 21.6 21.7 22.0 22.3 23.0 24.2 27.9 28.0 23.1 23.8

6.7 6.8 6.9 8.3 8.1 8.1 8.0 7.7 8.1 9.0 9.0 6.4 6.8

795.8 351.1 158.2 1. 3 5 1 556.6 198.6 114.5 342.5 66.27 14.63 14.30 351.9 80.06

25.2 25.0 23.7 23.8 25.0 24.7 23.4

7.2 7.2 6.9 7.1 7.7 7.7 6.4

27.96 26.70 661.7 161.2 76.64 70.87 448.5

25.4

6.9

111.3

25.3

7.0

59.14

24.6

7.1

57.48

22.6

6.7

356.7

that local centers of similar groups will form. The liquid structure of some dual-character molecules, therefore, can resemble a solution of surfactants with micellar structure. The entropy of such an organized liquid will be lower than that of a random liquid structure. In Table VI1 the entropies of vaporization at the normal boiling point (A%) and the solubility parameter of 100 O C (61,ec) for the solutes studied here are calculated with the vapor pressure equations previously m e n t i ~ n e d . ~It~ appears ~~' that the entropies of vaporization of dual-character derivatives re usually higher than those of simple liquids (i.e., 21-22 eu). This is true for four derivatizing groups. However, entropies of vaporization alone do not distinguish between two types of dual character because both attractive and repulsive interactions between molecules enhance liquid structure o r g a n i ~ a t i o n . ~The ~ solubility parameter (the square root of the cohesive energy density) can serve as an additional criterion for characterizing the molecular interaction. Molecules with strong attractive interactions in the pure liquid state will tend toward high solubility parameters with low vapor pressures. Dual-character molecule desirable for gas-chromatographic applications should have high vapor pressures with low solubility parameters, a consequence of low cohesive energy density. Examination of both entropies of vaporization and solubility parameters shows that acetates interact attractively in the pure liquid state, the high values of AsV, resulting from organization associated with the interaction between molecules. The TMSE, TFA, and PFP derivatives do not have high solubility parameters. The high AS; values can stem from a change of significant orientation or organization in the pure liquid to the more random vapor state. (49)Pople, J. A. Discuss. Faraday SOC.1953, 15, 35-43.

One important consequence of derivatization is that suitable groups can be used with geometric isomers to alter their vapor pressure ratios. Thus, in Table VI1 the trifluoroacetates of methylphenols are found to have a high vapor pressure ratio (P,/P; = 1.093 at 100 "C). Meta isomers usually have higher vapor pressure than para isomers, explained by the more organized structure of the latter. However, this structure effect can be small and offset the dipole moment as in chlor~toluene.~ Understanding and identifying factors which determine the vapor pressure ratios of isomers facilitate derivative selection. The isomeric aromatic vapor pressure ratio for acetates is lower than that for TMSE's, a result of the nonspecific interaction between the aromatic core and the acetate group. Thus, the low vapor pressures of these derivatives would make the acetates a questionable choice. One would prefer an extreme dual-character molecule which contains two parts with different properties to minimize nonspecific interaction^.^ Fluoroesters fit this category. Both trifluoroacetate (TFA) and pentafluoropropionate (PFP)derivatives give higher vapor pessure ratios than acetate and TMSE derivatives. TFA gives higher isomeric vapor pressure ratios than PFP. Tolyl PFP's have a derivatizing portion comparable to the aromatic core, so that they are packed in a less dense structure than the TFA derivatives, reflected in the thermal expansion coefficients, a,of the solutes which are listed in Table 111. According to the theories of F l o e and Simha,5l an expanded liquid has a higher expansion capacity than a condensed liquid. They treated the liquid expansion as a reduced volume, the ratio of molar volume to core volume (usually greater than unity). The core volume, similar to the van der Waals volume, represents the exclusion volume of the molecule and can be calculated from density data of liq~ids.4~ As temperature increases, the reduced volume increases. Flory and Simha also presented formulas for thermal expansion coefficients which imply that higher thermal expansion coefficients are associated with higher reduced volumes as is the case with tolyl pentafluoropropionates relative to trifluoroacetateq. The low vapor pressure ratio of tolyl pentafluoropropionate isomers can be interpreted as a consequence of an expanded liquid structure which diminishes the contact between the aromatic core and the derivatizing group, thus reducing specific interaction influences which cause their vapor pressures to differ. This is further supported by the data of Table VII, where lower solubility parameters are found for the aromatic pentafluoropropionate derivatives than for corresponding trifluoroacetates. Solute-Solvent Interaction. Many of the activity coefficients of Tables IV and VI follow the "like-dissolves-like" maxim. This is most evident in Table VI, where alkane solutes give thermal activity coefficients, y;, and interaction activity coefficients, yEs, close to unity in squalane, while simple aromatics behave similarly in DNP and TXP. Comparison of DBTCP and DNP data of Table V shows the negative excess enthalpy of aromatics in DBTCP relative to DNP. DBTCP apparently favors certain structures and related interactions. This is especially true for aromatics where strong interactions are accompanied by preferred configuration^.'^ In fact, DBTCP gives the lowest excess enthalpies for aromatics, presumably a result of charge-transfer i n t e r a ~ t i o n . ' ~ J ~ J ' ~ ~ ~ In contrast, TCNP solutions generally exhibit the lowest excess entropies for aromatics. Negative excess entropies (50) Flory, P. J.; Orwoll, R.A.; Vrij, A. J. A m . Chem. SOC.1964, 86, 3507-14. (51)Simha, R.;Havlik, A. J. J. A m . Chem. SOC. 1964, 86,197-204.

4614


might be anticipated from interference with the polar structure of TCNP. Such a nonselective interaction is usually not favorable for subtle separations. Aromatics generally give moderately negative excess free energies with polyphenyl ether since the latter consists of ether-connected aromatic rings. However, n-alkanes show higher positive excess enthalpies with polyphenyl ether than aromatics in squalane. This reflects some alkane substitution on aromatics other than benzene. The TMSE derivatives which present many methyl groups for interactions generally exhibit relatively high rf" values in aromatics and polar phases. The comparison of the butyl ether derivatives in DBTCP is most revealing in that the trimethylsilyl oxygen is less likely to participate in "charge-transfer" interaction. The low rf"values of the TMSE's in squalane reflect low solution enthalpies from the methyl-alkane interactions. Comparing TMSE derivatives with the tert-butyl ether shows that the carbon ether generally gives a lower activity coefficient than the silyl group except with the organic phosphate. Some difference results from size effects, with the carbon ether being smaller. In TXP, unusual behavior is observed since TMSE derivatives evidently interact strongly with solute orientation. The slightly larger n-butyl TMSE has a shape similar to the tert-butyl ether, but solution excess enthalpy is 1.94 kcal/mol lower and excess entropy 4.3 eu lower. The specific interaction of solutes with T X P is also manifested in isomer separations discussed later. The acetates show a mixed behavior, the tolyl acetates giving large activity coefficients in the alkane stationary phase. These derivatives usually show the smallest rf" values among esters of saturated parent compounds. The acetates can participate in strong interactions because of the unhindered concentration of available electrons in the ester group. It can interact with polar or aromatic stationary phases with low excess enthalpies even with nonpolar butyl and cyclohexyl groups attached. Such dualcharacter molecules give low excess free energies in DBTCP, TCNP, and TXP. The TFA and PFP derivatives exhibit more extreme dual properties with higher activity coefficients, being less readily accommodated in these solvents. Most important, the pentafluoropropionate (PFP) derivatives and trimethylsilyl ethers (TMSE's) generally give highest rf"values in the solvents studied here (Table IV); therefore, they are attractive derivatives in that they give low retention volumes and rapid separations. The high rf"values for the fluoroesters result from repulsive interactions involving fluorine as reflected by the high excess enthalpies in many solvents, especially squalane. PFP derivatives, with more fluorine, always have higher values than the trifluoroacetates (TFA's). The contributions of a fluorocarbon unit, CF2,to the excess properties can be gauged by comparing the difference between the properties of PFP and TFA derivatives of the same compound. This approach gives a different CF2contribution for each parent compound; the fluorocarbon unit always gives the highest excess free energy contribution in TCNP. Excess free energies of solution are often amenable to group method treatments. Pierotti et al.46classified interactions between two monofunctional molecules into six types. Infinite-dilution activity coefficients measured by gas chromatography were used to determine coefficients characteristic of each functional group. The underlying concept was that each functional group contributed to the excess free energy of solution either in a constant manner or through o simple term. While the original group method

Langer et al.

applied only to infinitely dilute solutions, recent modifications have been refined to incorporate analytical expressions which predict excess free energies over all concentration ranges.% At present, group methods are limited in three respects: (a) They provide parameters for only common organic groups such as methyl, methylene, hydroxyl, ketone, and amino, etc. The properties of silicon- and fluorine-containing groups, contained in the derivative compounds of this study, are not well characterized and may not conform to simple solution theories. (b) Most do not treat isomer effects.52 Usually, the retention volumes of alkyl isomers can be predicted approximately by an addition or subtraction operation on the retention volume of parent a l k a n e ~ . ~This ~ J method ~ ~ ~ ~ is less applicable to systems where specific interactions occur. Here, for example, even in the inert squalane solvent, differences between the excess free energies of para and meta isomeric compounds vary among derivative types, depending on the nature of substituents. (c) Group methods usually consider the number of groups involved in terms of molar interaction but not group concentration. Most solution models consider the mole fraction of molecules or groups, but not their densities. It is pertinent to note that the density of n-hexane decreases by 18% from the melting point to the normal boiling point, affecting the solubility parameter and other mixture properties. Since the liquid density is a function of temperature, simple parameters obtained at one temperature (corresponding to one density) may not be applicable at other temperatures. In gas-chromatographic systems, consideration of molar volume is important because the mixed solute-solvent systems involve volatile solutes and highly condensed liquid phases. In the solution process, the volatile solute expands the solvent structure; the influence of the solute molar volume change on solution excess properties has been discussed by Hildebrand et al.53and Flory et a1.43,45 In addition to expanding the solvent, the solute, especially one of dual character, may orient in an organized form in the solvent. The orientation effect for alkanealkane mixtures has been demonstrated by using solutes with different shapes in a solvent with a linear structure.44 With the added possibility of stronger specific interactions, orie,itation effects encountered in this study can be significantly higher than those of alkane-alkane systems. The overall excess entropy for the solution process includes at least three contributions: destruction of solute structures, expansion of the solvent, and orientation of solute within solvent structure. Excess enthalpy also is associated with these processes, but the enthalpy involvement for each process may vary. For instance, in a polymer solution, the combinatorial entropy may not involve associated enthalpy. In the orientation and interaction processes discussed here, enthalpy and entropy may both be important. Therefore, it might be expected that simple group methods would have limited applicability to the dual-character molecules of this study. Examination of the differences between derivatives and related isomers through solution excess thermodynamic properties can provide further insights on molecular interactions. Excess Enthalpies and Entropies. Correlation between measured enthalpies and excess entropies has been suggested as a criterion for examining specific solute-solvent interaction^.^ In an athermal liquid mixture with no (52) Hiranuma, H. Ind.Eng. Chem., Process Des. Deu. 1977, 16, 427. (53) Hildebrand, J. H.; Prausnitz, J. M.; Scott, R. L. 'Regular and Related Solutions"; Van Nostrand-Reinhold: New York, 1970.



IO

i

t

I

lox\

li

x

\

4

\\

0

I

0.I

10

1

1

YT

I

1

I

I + 15 I .o

Flgure 4. Plot of thermal contribution to activity coefficient (7;)vs. the athermal contribution (7:) in squalane, uncorrected for size. Calculated from eq 11 and 13.

contact energy difference, there is still a combinatorial entropy of mixing which does not correlate with any enthalpy quantity. Since it can be calculated from the molar volume ratio of the solute and the solvent (eq 14), when interacting solutesolvent systems are examined over wide size ranges, it seems reasonable to remove this combinatorial entropy from treatment of the enthalpy-entropy relations though this is seldom done. The remaining excess entropy term, or the “residual entropy” here,43would be more closely associated with solute-solvent interactions. With the large molecular weight solvents or polymeric liquid phases used in gas-chromatographic studies, differences between the overall excess entropy and residual entropy should be considered. Such differences can be examined with the moderate molecular weight solvent, squalane, of this study. In the nonpolar and only slightly polarizable squalane solvent, specific interactions with solutes (which might mask other effects) are minimal. The two types of enthalpy-entropy compensation relations for squalane are illustrated in Figures 4 and 5. In Figure 4, log-log plots of overall excess enthalpy vs. overall excess entropy are represented. Rather than using enthalpy and entropy as coordinates, dimensionless 7; and 7,”are plotted. The experimental value of 7; is obtained through eq 5 and 1 3 , ~ ;being obtained from eq 11. The logarithmic scale reflects the enthalpy-entropy relation. The abscissa of Figure 5 is yrs (obtained from eq 18) which corresponds to the interaction and orientation entropy alone. The plot of Figure 4 is more scattered. The data for benzene, the smallest molecule of this study, demonstrate the size correction effect. There is a low excess entropy in Figure 4; but, with the size effect correction, it falls on a linear plot. In Figure 5, in fact, almost all data fall on a straight line, which is more striking bcause they encompass two classes of hydrocarbons and four types of derivatives, each with considerably different properties. The steep negative slope of the plot in Figure 5 is indicative of the enthalpy changing more rapidly than the residual entropy. Since there is little specific interaction between solute and solvent for an infinitely dilute solution of squalane, the excess thermodynamic properties relate

’i-5 Figure 5. Plot of thermal contribution to activity ccefficient (7;) vs. slze-conected contribution (7;) in squalane (see Table I V for number assignments). Calculated with eq 18, 14, and 20.

to the altered interactions of solute molecules from the pure solute state. Applying such reasoning to Figure 5 , the tolyl acetates would have the highest excess solution enthalpy because of the largest “altered-state”interaction for these solutes. Strong interactions are also manifested by the low vapor pressures for pure solutes. Cyclohexyl acetate is a related analogue to tolyl acetates. The separation between tolyl acetates and cyclohexyl acetate in Figure 5 is an indication of the influence of the interaction between the acetate and aromatic groups. Similarly, the difference between tolyl trifluoroacetate and tolyl acetate in Figure 5 reflects the influence of fluorine substitution. Fluoresters interact to a smaller degree than do the acetates, with the differences between tolyl and cyclohexyl derivatives diminished. This is a result of the balance between the three types of interactions due to the aromatic ring, the ester, and the fluorocarbon portion of the molecules. The two structurally similar ether compounds, n-butyl trimethylsilyl ether and n-butyl tert-butyl ether almost coincide in Figure 5 (compare Figure 7). These two compounds participate in similar interactions in the pure and solution states; the proximity of the calculated results gives an indication of the precision of the measurements. Results may also be compared in Figure 4. The data for these and other compounds thus support the procedure of separating the combinatorial entropy correction from the entropy associated with interaction, expressed here in terms of ris. The enthalpy-entropy relation for dinonyl phthalate has been plotted in Figure 6 for solute residual properties. The solution excess thermodynamic properties are so small that net residual activity coefficients (product of 7; and 7;s) fall between 1 and 2, and indication of the high compatibility of DNP with many solute types which effectively minimize solute dual-character effects. DNP and similar multicharacter solvents have been employed as gas-chro-

4616


Langer et al.

L a 7re

= 2.0 \ \

\

2 .o

\

YT

1.0

0.5

1.0

2.0

YI-5

0.

j I

‘12

I IO 0

I O YI-8

Figure 6. Plot of thermal contribution to activity coefficient (7;) vs. size-corrected contribution (yT4) from dinonyl phthalate. Calculated with eq 18, 14, and 20. 7; = yzsyy. Compare with Figure 7 for meaning of symbols.

Flgure 7. Plot of thermal contribution to activity coefficient (7;) vs. size-corrected athermal contribution (yTs)for tris(2,4dimethylphenyl) phosphate. Calculated with eq 18, 14, and 20.

matographic stationary phases when specific interactions were not to be invoked. Solutes, exhibiting a narrow range of activity coefficients, are eluted then in order of decreasing vapor pressures in a “distillation-type” separation. The fact that activity coefficients are close to unity for the solutes studied here with DNP is a result of the multicharacter nature of this solvent, composed of two branched aliphatic side chains, ester groups, and an aromatic core. Upon solute solution in DNP, both solute and solvent are oriented to facilitate suitable contacts with little energy expenditure. The solution process is neither “demanding” nor highly exothermic. For example, the acetate portion of cyclohexyl acetate can contact the aromatic core or ester portion of DNP, while the cyclohexyl group can contact the branched nonyl groups of DNP. Such local contact only slightly nonideal tends to be “regular”;therefore, it is not surprising that the solution process involves small positive residual excess free energies which illustrates further the advantage of considering the combinatorial entropy in calculations. Without a size correction, some net negative excess free energies would be difficult to interpret in a regular solution theory framework. Even with the understanding accorded above, regular solution theory is of limited applicability to DNP solutions since the activity coefficient range is more narrow than predicted from solute solubility parameters. As recognized early, the simple regular solution treatment of Hildebrand and Scatchardmdoes not adequately take into account the volume effects on mixing and accommodate the entropy of The volume effect has been treated extensively in the l i t e r a t ~ r e , ~while ~ f ’ ~the other discussion of excess entropy components has been limited. The solution data for squalane and DNP suggest that residual entropies are a result of at least two effects, orientation and interaction. The enthalpy-entropy relation for squalane stationary phase reflects the fact that pure liquids do indeed exist in an interacting, organized form to a variety of degrees. When functional molecules are vaporized and condensed in an infinitely dilute form in squalane, a positive excess enthalpy and a positive excess

entropy are generally observed. The overall process is unfavorable in many instances here because the enthalpy effect is greater than the entropy effect. In DNP solution, the (unfavorable) disrupting process for the pure liquid structure is compensated by the orderly solution interaction process. DNP molecules with interspersed varied groups orient and contact solute molecules almost in a like-dissolves-likemanner with the result that the mixture behavior is not far from ideal. log-log plots of 7;vs. 7s; for solutes in TXP are shown in Figure 7. Most data fall on a straight line with a slope slightly lower than -1. Thus, for equivalent excess enthalpy there is a larger change of entropy in TXP (which is of a more diverse character) than in squalane. In multicharacter DNP, the entropy effect is essentially proportional to that for the enthalpy. Squalane, a single-character solvent, gives a slope lower than -2, while a good multicharacter solvent has a slope equal to ca. -1 (reflecting a net residual activity coefficient close to unity), as required by net properties similar to those of ideal solutions. Therefore, the slope of the enthalpy-entropy line for dual-character solutes appears to be a useful criterion for solvent dualism. If the slope of the excess solution enthalpy-entropy plot approaches -1 for dualcharacter solutes, the solvent may be of dual character or multicharacter, and vice versa. TXP, with some dual character as well as polarity, is not strongly selective for particular derivative types and consequently most data points are grouped together. Exceptions are the large negative 7;values for trimethylsilyl ethers of n-butyl and cyclohexyl groups. The size of these deviations for two compounds which both contain the TMSE group removes the possibility of experimental error (ArF/rF I hO.1). The deviation must be associated with the derivative group. The Si-0 bond contains some *-bond properties due to the d-orbital electrons of the silicon atom. Silicones are known to participate to some extent in hydrogen bonding and have affinity for ketone groups.* The abnormal low excess entropies for trimethylsilyl ethers possibly originate from an unusual interaction between the Si-0 bond and

Solution Thermodynamics of Hydroxylic Derivatives -A

1.10

0 I .05

X

0

9

y&A I .oo

A

+ 0 X

0

0.95

z

v,

I

I-

I. P

m-

/P

p-

Figure 8. Plot of activity coefficient ratios at 100 OC for meta and para derivatives of methylphenol vs. vapor pressure ratios of these derivatives to demonstrate the effect of liquid phases on the activity coefficient ratio (contribution to separation factor): (+) TXP, (A)TCNP, (X) squalane, (0) DBTCP, (0)PPE, (0)DNP. Separation factor a2,, is the product of the activity coefficient ratio and vapor pressure ratio.

the polar phosphate ester. With solute molecules oriented within the T X P structure, a large negative excess entropy could result. The negative excess enthalpy accompanying the solution process leads to a small net excess solution free energy. Separation of Isomers. Specific interactions can be examined further through the separation factor for derivatives of meta and para isomers. The separation factor of eq 2 depends both on the characteristic vapor pressures of solutes and on their activity coefficients in solution. A comparison plot of the meta/para vapor pressure ratios of isomer derivatives and corresponding activity coefficient ratios in solution at 100 "C is shown in Figure 8, for the systems studied here. The vapor pressure ratios reflect solute-solute interactions while the activity coefficients reflect solute-solvent interactions. Both tetrachlorophthalate and phosphate show a less selective net attraction for the meta fluoroesters. There is, however, a marked preference for the para isomers reflected by the positive excess entropies associated with orientation. This is evidence that the strong interaction between T X P and solutes involves special steric requirements. The acetate isomers here are of limited value for affecting separation, probably because the rather strong solute-solute and solute-solvent interactions are nonspecific. The low vapor pressures of the parent acetates and low m-/p-tolyl separation factors mitigate against their use as derivatives with the solvents used here. Acetate data were not obtained in some solvents because of long retention times. The TMSE derivatives give advantageous vapor pressure ratios for some separations. Unfortunately, the more favorable vapor pressure ratio of the TMSE isomer de-


rivatives can be countered by a less favorable activity coefficient ratio. These derivatives show relatively low activity coefficienh in the solvents of this study, with vapor pressures often one-half of those of the fluoroesters (including n-butyl, cyclohexyl, and tolyl derivatives). However, the net favorable meta/para separtion factors with squalane, DBTCP, and PPE phases make them useful for separation at higher gas flow rates. Polyphenyl ether and squalane yield high activity coefficient ratios for TMSE derivatives. These two solvents with homogeneous structural units may have little interaction with solutes. Net differences in the isomer activity coefficients must originate from an altered pure solute interaction. Indeed, in these phases, TMSE derivatives may exhibit dual character. Thus, dual-character derivatives can facilitate separations with structurally simple liquid phases because solute-solute interactions of the pure liquids are altered. The best derivative group for separation of those examined here is the pentafluoropropionate. Advantageous activity coefficient ratios are observed, although the pure solute vapor pressure ratios are not the most favorable. There is a marked difference between the TFA and PFP vapor pressure ratios; however, the activity coefficient ratios for TFA derivatives generally are less favorable (being less than or close to unity) in contrast to those for PFP derivatives. Thus, there can be trade-off between favorable vapor pressures and the activity coefficient ratios where the stationary phase essentially moderates solutesolute interactions favorable to separation. The TFA and PFP derivatives usually are eluted in close proximity. The additional fluorine atoms on the PFP derivatives result in higher activity coefficients, offsetting reduced vapor pressures from increased molecular weight. The PFP derivatives show low retention volumes in the two phthalates, TXP, TCNP, and PPE. Constancy of the fluoroester retention volumes results from a balance between vapor pressure decrease and increased activity coefficient. Where the activity coefficient ratios are higher than unity there is a desirable reinforcement to the vapor pressure ratios with activity coefficient ratios. This reinforcement is evident with the phosphate phase, where the favorable steric atmosphere for para isomers together with the vapor pressure ratios gives a para/meta retention ratio of 1.14 for PFP derivatives at 100 "C. This is impressive in view of the isomer similarity. The TFA derivatives with phosphate also show a good separation ratio, but retention volumes are larger than for PFP derivatives. The latter show favorable ratios along with low retention volumes with TCNP. Para/meta retention ratios of 1.125 for these derivatives and 1.124 for the PFP derivatives a t 100 OC with DBTCP are also high, but the retention volumes considerably exceed those of the phosphate phase.

Conclusions In the gas-chromatographic study of the thermodynamics of solutions of derivatives, molecules of dual character are encountered. To some extent, the dual-character classification is dependent upon the liquid phases. The thermodynamic properties of these solutions are less readily described by simple solution theories which have been used for molecules of globular or homogeneous structures. Gas chromatography is an attractive method for obtaining accurate data for complex molecules of mixed character when appropriate vapor pressure data are available. Examination of vapor pressure and activity coefficient data for derivatives revealed that separation of isomeric derivatives is generally a consequence of both effects. The study of the thermodynamics of derivative solutions not

4818

J. Phys. Chem. 1982, 86, 4618-4622

only aids the selection of stationary phases for gas chromatography but also appears to suggest a category of mixtures wherein entropy from orientation is of comparable importance to associated excess enthalpy. Further research in this direction should reveal new areas of experimental thermodynamics which can stimulate the development and refinement of appropriate solution theories. It has been suggested that strong selective interactions or solvent solubility parameters differing from those of solutes are desirable liquid-phase features for resolving similar isomer^.^,^ DBTCP is an example of a selective phase which gives a favorable activity coefficient ratio for cresol derivatives, while TCNP with a high cohesive energy density (solubility parameter) exemplifies a potential liquid-phase choice from solubility parameter considerations. Cohesive energy density differences alone, however, do not account for the activity coefficient ratios of TMSE derivatives in squalane and P P E (see Figure 8). Favorable activity coefficient ratios of the dual-character tolyl fluoroesters with T X P are due to entropic factors which can be as important as the energy factor (see Table V). The values of excess entropies of mixing are less favorable for the solution of meta isomers. Consideration of the relations between vapor pressures, activity coefficients, and activity coefficient ratios indicates

a rationale for selecting derivatives and stationary phases; derivative formation should tend to lower cohesive energy in order to increase solute vapor pressures. (The concept of a dual-character molecule is useful for selecting derivatizing agents.) The stationary phase should differ in nature from either the derivative or the parent hydroxyl compounds. Thus, a liquid phase with a high solubility parameter can be advantageous, e.g., the fluoroesterTCNP system. Alternatively, the selective interaction feature may be emphasized as with PFP derivatives with DBTCP or TXP solvents where orientation entropies for isomers are important (see Table V or Table VI, T;".~ values).

Acknowledgment. We thank Mr. Walter G. Taschek of the Army Research and Development Center for his help with the initial thermodynamic calculations. We also thank the University of Wisconsin and the National Science Foundation for support of this project. Supplementary Material Available: Tables I and 11, listing values for solutes with solvents of this study, and Table Id, listing vapor pressure data at 80 "C, with second virial coefficients, density data, and expansion coefficients (3 pages). Ordering information is available on any current masthead page.

Oxide Salt Reactlons in Matrix Isolatlon. Infrared Spectrum of the Ti,+C0,2- Triple Ion in Argon Matrices Shelle J. David and Bruce S. Ault' Department of Chemistry, Unlverslty of Clnclnnatl, Clnclnnatl, Ohlo 45221 (Recelved: February 22, 1982; I n Flnal Form: Ju& 19, 1982)

The salt/molecule reaction technique, which has been employed in the past to carry out halide ion transfer and anion formation in argon matrices, has been extended to oxide salt reactions. The codeposition of TlzO with samples of Ar/C02 and its isotopic counterparts gave rise to a series of product bands which have been assigned to the C032-anion in the T12+C032-triple ion. A lowering of the symmetry of the carbonate anion from D a h to probably (2%was observed, as a consequence of the T1+ cations. The antisymmetric C-0 stretching mode of the CO2-anion was split by 185 cm-', to 1506 and 1311 cm-', similar to the splitting observed for the COS2-anion in alkali carbonate melts. In addition, the spectra were in good agreement with those of the alkali-metalcarbonates in nitrogen matrices, formed through direct vaporization of the salt. Attempts to carry out analogous reactions with the alkali-metal oxides, MzO, were unsuccessful due to the decomposition during the vaporization process. The results here establish that oxide transfer to a suitable acceptor from T120 can take place, to isolate oxyanions of interest.

Introduction The salt/molecule reaction technique has been used numerous times in conjunction with matrix isolation for the formation of unusual halide-containing anions in inert matrices.'" In this technique, an alkali halide salt molecule, often CsF, is vaporized and codeposited with a suitable halide acceptor diluted in argon. Halide anion transfer occurs, and the product anion is trapped in an ion pair with the alkali-metal cation. The extension of this technique to gas-phase reactions of oxide salts would be (1) Ault, B. S. J. Phys. Chem. 1979,83, 837. (2) Auk, B. S. Inorg. Chem. 1979, 18, 3339. (3) Ault, B. S.; Andrews, L. J. Chem. Phys. 1975, 63, 2466. (4) Ault, B. S. J . Phys. Chem. 1980, 84, 3448.

of the interest as well, and a range of unusual oxyanions might be formed in this manner. Vaporization of oxide salts is much more difficult than that of the halide-containing salts as a consequence of the much greater lattice energy. The group 2A oxides, such as CaO, require extremely high temperatures and then decompose upon vaporization.s Conflicting reports alternately suggest that the alkali oxide salts, M20, can or cannot be vaporized without d e c o m p ~ s i t i o n .However, ~~~ (5) Klabunde, K. "Chemistryof Free Atoms and Particles";Academic Press: New York, 1980. (6) Brewer, L.; Margrave, J. L. USAEC, National Science Foundation, UCRL-1864, 1952. (7) Klemm, W.; Scharf, N. J. 2.Anorg. Allg. Chem. 1960, 303, 263.

QQ22-3654l82I2086-4618$Q1.25lQ 0 1982 American Chemical Society

Gas-chromatographic study of the solution thermodynamics of

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