Adiabatic Calorimetry of Organic Salts Tetra-n-hexylammonium Perchlorate BY JOHN T. S. ANDREWS AND JOHN E. GORDON Liquid Crystal Institute and Department of Chemistry, Kent State University, Kent, Ohio 44242 ReceirJed 2 1 st Augu.st, 197 1 We have measured the heat capacity of a zone refined sample of tetra-ii-hexyla~nmoniuiii per- chlorate (99.94 % pure, by analysis of the fusion curve). Values of the transition temperatures, enthalpies and entropies are : fusion 379.18 K, 16 350 J mol-I, 43.10 J K-I mol-I ; transition (1) 367.51, 2658, 7.24 ; transition (2) 355.91, 5839, 16.42; transition (3) 333.57, 22 990, 68.93. We interpret fusion and transition (3) as being due, respectively, to ioiiic melting (break down of the lattice) and " melting " of the hexyl groups. Transitions (1) and (2) are explained by re-orientation of the perclilorate anions. The melting points of quaternary ammonium salts are usually rather low, when compared with most ionic materials.This property has led to their investigation as possible media for organic reactions, especially those involving materials unstable at elevated temperatures. The low fusion temperatures, which are easily accessible, have also encouraged study of the physico-chemical properties of these material^,'-^ particularly from the viewpoint of their fusion mechanisms. For these purposes salts with very poorly nucleophilic anions (ClO;, BF,) and consequent chemical stability in the melt, are of greatest importance. Tetra-n-hexylammoniuin perchlorate, (C6Hl 3)4NC104, although not the lowest melting of these materials, also shows solid state polymorphism.One of us (J. E. G.) has observed three phase transitions by microscopic and differential thermal tech- niques,G but was unable to investigate them fully. Since then, Janz and co-workers have included this material in a study of several quaternary ammonium salts, using dilatometry, differential scanning calorimetry, and other techniques in an attempt to understand the thermodynamics of the fusion pro~ess.~ A precise determination of the heat capacity of this material, together with the enthalpy and entropy increments associated with the transitions, would provide a basis for a better understanding of these processes. In addition, we were curious as to the comparison of the adiabatic equilibrium results with those obtained by differential scanning calorimetry.This latter technique is in widespread use, yet iis limitations are not universally understood. Tetrahexylamnionium perchlorate is particularly suitable for this investigation as it is very stable and may be zone refined easily. We were able to achieve relatively high purity (using zone refining and calorimetric techniques) which has not been done in previous work with molten quaternary ammonium salts. EX PER1 M ENT AL MATERIAL The sample of tetra-n-hexylammonium perchlorate was prepared by the reaction of the iodide with perchtoric acid in aqueous ethanol solution, followed by two re-precipitations in 546J . T . S . ANDREWS AND J . E, GORDON 547 the presence of excess perchloric acid. The material was recrystallized once from ethanol+ water and twice from ethyl acetate+diethyl ether and then was dried thoroughly under vacuum.The product contained less than 10 p.p.m. of iodine (the analysis was performed by Galbraith Laboratories, Knoxville, Tenn.). The h e white crystals were zone rebed in evacuated Pyrex tubes until all solid zones were singly crystalline (after about 100 passes). The sample was loaded into the calorimeter by fusion through a Pyrex frit under vacuum, and the calorimeter sealed (gold gasketlknife edge) under a small pressure of helium (to assist in the attainment of equilibrium). CALORIMETRY A silver calorimeter fitted with a screw closure and an adiabatic vacuum thermostat were employed in the heat capacity measurements. Both the calorimeter and the thermostat were very similar to apparatus described by We~trurn,~ except that four channels of auto- matic control were employed (one for each of the top, middle, and bottom portions of the adiabatic shield, and one for the guard shield which surrounded the adiabatic shield), and that an automatic a.c.resistance bridge was used for the temperature measurements. A full description of the apparatus will be presented elsewhere. All measurements of mass, temperature,8 and electrical energy were refered to calibrations performed by the National Bureau of Standards. The results of measurements on a standard sample of synthetic sapphire indicate an overall accuracy of about 0.1 %, while the experimental precision is somewhat better than this. RESULTS The experimental heat capacity measurements are presented in table 1.These values are expressed on a molal basis (sample mass in vacuo 39.7329 g, C24H52NC104 = 454.1373 g mol-l, density 0.913 g ml-l 3, taking the ice point as 273.15 K. The results have been corrected for " curvature ", and for the (small) differences in addenda (helium, gold) to the calorimeter when run empty and with sample. These data are illustrated in fig. 1. No difficulties were encountered during the measure- ments, except that very long equilibration times were encountered in the transition regions. In fusion, for example, equilibrium was reached only two to three days after an energy addition. Equilibration times in crystal I were also long (about half a day). The purity of the sample was determined by " fractional fusion " (table 2).' The slope of a plot of the reciprocal of the fraction melted against the melting temp- erature gave a sample purity of 99.94 %.Table 3 summarizes the enthalpy determinations for the transition regions. Transition enthalpies and entropies were obtained by integrating the difference between the experimental heat capacity curves and a " lattice '' obtained by judicious extrapolation of the heat capacity observed above and below the transition temperatures. The lowest temperature transition (3) differed from the others in that several weeks were required to obtain the equilibrium form after cooling through the transition (shown both by positive temperature drifts and by the spread of the transition energy values).This corresponds to the difficulty reported by Janz et aI. for tetra-n-amyl- ammonium thiocyanate. We encountered no difficulty with the other transitions reported here, but it should be remembered that our cooling rates were less than those used by Janz. The transition enthalpy reported for transition (3), accordingly, is that observed after the sample had remained below the transition for several weeks. The other values in table 3 reflect lesser equilibration times. DISCUSSION ictrahexylainmonium perchlorate) have been reported by Janz and his associates. The fusion thermodynamics of several quaternary ammonium salts (including548 ADIABATIC CALORIMETRY OF ORGANIC SALTS These workers used differential scanning calorimetry and assigned uncertainties of k 0.5 K to the reported transition temperatures and 3.3 % to the transition enthalpies.Table 4 reproduces their reported values together with those found by adiabatic calorimetry in this research. The two sets of values are not entirely consistent and those temperatures found in the equilibrium measurements are lower. We suggest that this discrepancy is to be expected because of the sluggish transitions which we observed in this material. Apparently the elevated scanning calorimetric temperatures are the result of overheating. Differences in sample purity may also account for these discrepancies. TRANSITION (3) A N D FUSION Janz et aL2 have suggested that the melting of quaternary ammonium salts may be considered as two processes which are essentially separate. They are positional melting, or break up of the crystal lattice which should be comparable to the melting of the alkali halides, and configurational melting of the alkyl chains attached to the ammonium ion which should be comparable to the melting of the n-paraffins.Fur- ther, these authors suggest that the entropy change for this Configurational melting should be calculable as R In a, where SZ is the number of configurations available to PERCHLOR A T E ~ ? ~ . TABLE 1 .-EXPERIMENTAL HEAT CAPACITY DETERMINATIONS OF TETRA-n-HEXYLAMMONIUM C P l 306.98 777.0 314.08 802.5 323.87 855.7 331.11 1716 335.48 2795 341.44 928.7 349.69 964.4 355.75 2427 361.74 977.3 369.01 1317 375.61 1244 379.07 7.527E4 382.17 1454 T/K J mol-1 K-1 series I series I1 374.40 924.2 377.07 1057 378.67 4643 379.05 3.549E4 379.12 8.674E4 379.15 1.592E5 379.17 1.506E5 379.31 6916 380.47 986.2 382.52 989.1 384.58 992.5 386.62 995.5 CPl T / K J mol-* K-1 series I11 357.68 1031 359.24 972.3 360.97 976.4 362.83 984.3 364.68 994.2 366.51 1015 367.51 1.397E4 368.56 954.7 370.49 906.0 372.44 907.1 374.39 915.8 376.32 944.4 377.79 1074 AHf A 380.12 1082 series IV 339.87 917.9 341.52 925.7 343.30 934.7 345.21 952.2 347.11 954.9 349.01 962.4 350.88 973.6 352.75 986.3 354.50 1002 355.61 3592 C P I T/K J mol- 1 K- 1 355.91 8.892E5 356.22 3374 357.34 1028 358.99 967.1 360.67 971.0 series V 300.52 752.6 304.35 766.6 308.28 781.9 312.31 798.5 316.29 816.0 320.21 835.4 324.14 856.2 328.07 879.5 331.79 1372 333.57 5.931E5 333.58 2.974E5 333.69 3.478E4 335.54 1378 338.28 916.0 340.23 919.8 AH run A 354.68 996.1 360.44 972.4 A H run B AH2 A AH1 A CP I AH run C AH;- B 380.66 987.0 series VI 369.23 904.1 370.16 896.4 371.08 888.8 series V1I series VIII AH run D AH run E AH run F AH run G 382.22 988.9 series IX T/K J mol-1 K-1 AHf C AH3 A AH2 B AH1 B AHf D AH3 B AH2 C AH, C series X AH3 C a A, B, C, etc.are the identification of the enthalpy determinations; b temperature scale, I.P.T.S., 1948.J . T. S . ANDREWS AND J . E . GORDON 549 the chains through gauche-trans kinking (a " kink-block " proce~s).~ For tetra-n- amyl- and tetra-n-hexyl-ammonium ions, respectively, these authors calculated the configurational entropy changes to be about 71 and 96 J K-l mol-l. The experi- mental results for tetra-n-amylammonium thiocyanate agreed well with this prediction.It seems likely, however, that the two processes are intermixed for tetrahexyl- ammonium perchlorate. The melting entropy, 43.10 J K-1 mol-', is considerably greater than that found for alkali halides (for example, 25 J K-l mol-1 for KBr),l0 whilst the entropy of transition (3) (68.93 J K-l mol-l) is less than that predicted by the " kink-block " model, 96 J K-' mol-l. The sum of the experimental entropies for fusion and transition (3) (112.03 J K-l mol-l) is, however, close to the sum of I I I I I I I I I ,' I I I I I I I I 80C. I I I I I I I I I I I I 1 i 1 1 I I I I C 'I A 300 340 T/K 380 FIG. 1 .-Heat capacity of tetra-n-hexylamnionium perchlorate. A, 333.57 ; B, 355.91 ; C, 367.51 ; D, 379.18. TABLE 2.-FRACTIONAL MELTING OF TETRA-n-HEXYLAMMONIUM PERCHLORATE * TIK C,/J mol-1 K-1 AT/K TAHIJ mol-1 1 If TfinsllK 378.67 4643 0.670 2920 5.59 379.01 379.05 3.549E4 0.095 6206 2.63 379.10 379.12 8.674E4 0.039 9 567 1.71 379.14 379.15 1.592E5 0.021 12 954 1.26 379.16 379.17 1.506E5 0.01 1 14 603 1.12 379.17 triple point of sample 1 .oo 379.177 triple point of pure material 0.00 379.21 9 mole fraction of impurity 0.0006 * data from fusion series I1550 ADIABATIC CALORIMETRY OF ORGANIC SALTS TABLE 3 .-ENTHALPY INCREMENTS OF FUSION AND TRANSITION OF TETRA-n-HEXYLAMMONIUM PERCHLOR ATE source fusion r I1 I11 V VII vrir transition (1) I 111 V VIII JX transition (2) I I V V VIII JX transition (3) I V VIII IX X XI no.of runs 3 9 5 3 1 2 2 6 2 2 1 2 7 3 1 1 3 7 1 1 1 1 T1 /K 372.22 373.00 373.42 371.41 371.60 371 3 2 357.72 361 -90 361.37 359.44 366.47 353.75 351.82 354.18 355.10 352.17 328.44 326.12 327.56 323.03 323.02 325.36 T21K 385.19 381.49 381.08 381.69 381.87 381.19 372.26 371.47 371.41 371.30 371.10 365.76 359.84 361.37 359.43 359.50 337.26 339.26 339.36 338.30 338.33 340.47 28 681 24 070 23 457 25 891 25 887 25 476 average lattice AHf 16 422 11 693 12 220 14 006 6 859 average lattice AH1 17 572 13 392 12 819 9 993 12 982 average 1 a tt ice AH2 30 612 34 196 33 425 36 169 36 139 36 205 value 1 at t ice AH3 J mol-1 26 140" 25401 * 25 572 25 581 25 571 25 573 25 574&4 h 9 225 16 349 H371- H361 I 1 mol-1 12 090 0 12 145 12 211 12 205 12 198 12 20558 b 9 547 2 658 H361- 113491 J mol-1 17 516 17 262 * 17 524 17 515 17 520 17 519k4 11 680 5 839 H339- H325 J mol-1 35 205 C 34 931 C 35 324 35 130C 35 060 c 35 165c 35 324 12 332 22 992 a Excluded from the average as drift correction uncertain ; b precision index is twice the standard deviation of the mean ; c excluded because of non-equilibrium behaviour.J .T . S . ANDREWS AND J . E . GORDON 55 1 that predicted by the two models (121 J K-l inol-l). We suggest that the configur- ational entropy is acquired in two steps : the greater portion in transition (3) (68.93 J K-l mol-I), and most of the remainder in fusion. The alkyl chains are probably extended and overlapping in the low temperature phase,' and some configurations of the kinked chains may be unobtainable until the lattice breaks up ; the difference be- tween the observed entropy sum for fusion and transition (3) and that predicted by the models may be due to the maintenance of some structure in the melt immediately above fusion.TABLE 4.-TRANSITION PARAMETERS FOR TETR A-11-HEXYLAMMONIUM PERCHLORATE fusion transition ( 1 ) transition (2) transition (3) Temperature uncertainty this work ref. (3) Tt/K 379.18 383 AHf/J niol-' 16 350 18 000 ASf/J mol-' K--' 43.10 48 Tl /K AH,/J mol-' AS,/J mol-' K-' T2 /K AH,/J molt' AS2/J mol-l K-1 T3 /K AH,/J inol-l A&/J mol-' K-l 367.51 7.24 355.91 16.42 333.57 68.93 2 658 5 839 22 990 369 2 500 358 5 900 16 335 23 000 69 6.3 & 0.01 K (this work), 0.5 K (ref. (3)). Enthalpy uncertainty & 0.1 "/o (this work), k 3 % (Eef. (3)). TRANSITIONS ( 1 ) A N D (2) We believe that the entropy increments for these two transitions are adequately explained in terms of the rotational disorder of the perchlorate ions.Guthrie and McCullough l 2 have shown that the transition entropies of plastic crystals (in which the molecules rotate in a restricted manner in the solid state) accord well with those calculated by considering possible orientations of the molecules in the different phases. Furthermore, Newns and Staveley have demonstrated that transitions in ionic materials involving polyatomic ions may similarly be explained in many cases. Guthrie and McCullough suggest that possible orientations will match symmetry elements of both molecule (or ion) and crystal lattice. If the perchlorate ion is considered as a tetrahedron in a cubic environment (the high temperature phase of ammonium perchlorate is cubic) l4 there are four sets of such orientations.These are illustrated in fig. 2, and the corresponding symmetry elements are listed in table 5. They may be designated T, (two distinguishable orientations), DZd (6), C,, (8), and C,, (12). The entropy due to the orientational configuration of the ion is R In N (where N is the number of distinguishable orientations available to the ion), and the change of orientational entropy on passing from one phase to another is R In N,/Nl. If the major contribution to the entropy of transition comes from the orientational changes, then transitional entropies may be calculated for various combinations of the sets of orientations, and the results compared with the experimental values. The work of Newns and Staveley suggests that this procedure is of value, and that entropy contributions due to volume increments may be ignored.Two transition schemes are suggested by the experimental results, and they are summarized in table 6. Both schemes correctly predict the entropy of transition (2),552 ADIABATIC CALORIMETRY OF ORGANIC SALTS but are rather low in their predictions of the entropy of transition (1). Scheme 2, however, is more nearly correct for transition (I) and the sum of the entropies of transitions (1) and (2) ( R In 17.3) is much closer to that predicted by scheme 2 ( R In 16) than that predicted by scheme 1 ( R In 14.5). Scheme 1 utilises all the sets of orient- ations, while scheme 2 arbitrarily excludes the 12 C2v orientations. Furthermore, scheme 2 requires that only one of the two possible Td orientations be used in phase 111, so that this phase is ordered in scheme 2, but disordered according to scheme 1.We feel that the choice between these two schemes may not be made on the basis of the thermodynamic data alone. Both schemes lead to reasonably accurate pre- dictions for the entropies of transitions 1 and 2, particularly since the effect of volume increments has not been considered (although we expect this to be It is conceivable that the C,, orientations might be excluded in this material, due to steric set c 3 v C Z U FTG. 2.-Sets of distinguishable orientations of a tetrahedron in a cubic environment. TABLE 5.-sYMMETKY ELEMENTS FOR A TETRAHEDRON IN A CUBIC! LATTICE coinciding symmetry elements tetrahedron cubic lattice distinguishable orientations T l (4) 3-fold axis (4) %fold axis 2 (3) 2-fold axis (6) mirror plane (3) 4-fold axis (6) diagonal mirror plane D2d c30 c 2 u (1) 2-fold axis (2) 2-fold axis (1) 4-fold axis (2) 2-fold axis (6) mirror plane (2) (4) (I) 3-fold axis (1 1 (3) mirror plane (3) (1) 2-fold axis (1) (2) mirror plane (1) (1 1 vertical mirror plane diagonal mirror plane 3-fold axis diagonal mirror plane 2-fold axis horizontal mirror plane vertical mirror plane 6 8 12J .T. S. ANDREWS AND J . E. GORDON 553 hindrance from the " melted " hexyl chains. We would expect that the disorder of phase 111 implied by scheme 1 should be resolved by a transition to an ordered phase at some lower temperature. We found no evidence for any such transition (by differential thermal analysis) down to liquid nitrogen temperatures, but this does not exclude the possibility that ordering might take place as part of the processes leading to transition (3) or at temperatures below the limit of our d.t.a.scan. TABLE 6.-TRANSTTION SCHEMES FOR TETRA-n-HEXYLAMMONIUM PERCHLORATE phase orientation sets total number of orientations entropy/J mol-* K-1 scheme 1 111 T d 2 transition (2) R In (16/2) 17.29 transition (1) R In (28/16) 4.65 I1 Td + D 2 d + C S v 16 I T d + D 2 d + C3u+ c2v 28 scheme 2 I11 one of Td (ordered) 1 I1 both T d + D z d 8 I Td + D 2 d + c3u 16 transition (2) R In (S/l) 17.29 transition (1) R In (16/8) 5.76 experiment transition (2) R In 7.2 16.42 transition (1) R In 2.4 7.24 CONCLUSION The general model proposed by Janz is reasonable.The melting of these materials may be compared, on the one hand, to the positional melting of ionic materials, and, on the other, to the configurational melting of the n-paraffins. However, we believe that the two processes are intermixed in this material due to the rather long hexyl chains. Transitions (1) and (2) may be accounted for by considering the orientational entropy of the perchlorate ion. The equilibrium data obtained in this research agree quite well with those ob- tained by differential scanning calorimetry. The transition temperatures found here are somewhat lower than those from d.s.c. measurements, probably due to over- heating of the sample in the d.s.c. work. ADDENDUM We are grateful to a referee for drawing our attention to an alternative interpretation of our results.He pointed out that the sum of the entropies of transitions (I), (2) and (3) (93 J K-l mol-l) is close to that predicted by the kink-block model for the configurational melting of the hexyl groups on the cation (96 J K-l mol-l), and he suggested that the break up of the lattice and the rotational disordering of the anion occur together in the fusion transition. We think that 24 J K-l mol-l is a reasonable approximation to the entropy of the lattice break up, as the fusion entropies of potassium bromide and potassium perchlorate are very similar (25 and 23 J K-l mo1-1 respective1y),l0 and the presence of a transition ( N R In 18 at 572.7 K) l5 in potassium perchlorate implies that the perchlorate ion is disordered in the solid phase of this material.The entropy of fusion of tetrahexylammonium perchlorate is 43.10 J K-' mo1-1 so that this alternative explanation assigns about 19 J K-' mol-' to the554 entropy of the rotational disordering of the perchlorate ion in this material. This is about R In 10, less than the full entropy of restricted rotational disorder of a tetrahedron in a cubic lattice (R In 28), which implies either that full disorder is not attained i n the liquid phase, or that the ion is partially disordered in the solid phase, This entropy " deficit " is rather large, and we do not think that this alternative inter- pretation is likely. In addition, it fails to account for the observed entropies of transitions (1) and (2), which are in close agreement with those expected from the restricted rotation of the tetrahedral anion.ADIABATIC CALORIMETRY OF ORGANIC SALTS We thank Professors R. C. Fort, Jr., V. D. Neff, E. F. Westrum, Jr., and C. A. Wulff for their helpful comments. The Air Force Office of Scientific Research is to be thanked for generous support. Acknowledgement is also made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this research. J. E. Gordon, TechniquesandMethods of Organic and OrganometaNic Chemistry, Vol. 1, ed. D. B. Denny (Marcel Dekker, New York, 1969), p. 51. T. G. Coker, B. Wunderlich and G . J. Janz, Trans. Fnraday Soc., 1969, 65, 3361. T. G. Coker, J. Ambrose and G. J. Janz, J . Anzer. Chem. Soc., 1970,92, 5293. J .Levkov, W. Kohr and R. A. Mackay, J . Phys. Chem., 1971,75, 2066. A. R. Ubbelohde, Melting and Crystal Structure (Oxford University Press, London, 1965). J. E. Gordon, J . Amer. Chem. Soc., 1965, 87,4347 and unpublished observations. J. C . Trowbridge and E. F. Westrum, Jr., J. Phys. Chem., 1963, 67, 2381. E. F. Westrum, Jr., G. T. Furukawa and J. P. McCullough, in Experimental Thermoa'yimmics, Vol. 1, ed. J. P. McCullough and D. W. Scott (Butterworths, London, 1968). S. Blasenberg and W. Pechhold, Rheofogica Acta, 1967, 6, 174. lo G . J. Janz, Molten Salts Handbook (Academic Press, New York, 1967). l 1 A. Zalkin, Acta Cryst., 1957, 10, 557. l2 G. B. Guthrie and J. P. McCullough, J. Phys. Chem. Solids, 1961, 18, 53. l 3 D. M. Newns and L. A. K. Staveley, Chem. Rev., 1966, 66, 267.l4 M. Stammler, R. Bruenner, W. Schmidt and D. Orcutt, Adu. X-ray Cryst., 1965, 9, 170. F. D. Rossini, D. D. Wagman, W. H. Evans, S. Levine and 1. Jaffe, Selected Values of Chemical Thermodynamic Properties, Nat. Bur. Stand. Circ. 500 (US. Government Printing Office. Washington, D.C., 1952).Adiabatic Calorimetry of Organic SaltsTetra-n-hexylammonium PerchlorateBY JOHN T. S. ANDREWS AND JOHN E. GORDONLiquid Crystal Institute and Department of Chemistry,Kent State University, Kent, Ohio 44242ReceirJed 2 1 st Augu.st, 197 1We have measured the heat capacity of a zone refined sample of tetra-ii-hexyla~nmoniuiii per-chlorate (99.94 % pure, by analysis of the fusion curve). Values of the transition temperatures,enthalpies and entropies are : fusion 379.18 K, 16 350 J mol-I, 43.10 J K-I mol-I ; transition (1)367.51, 2658, 7.24 ; transition (2) 355.91, 5839, 16.42; transition (3) 333.57, 22 990, 68.93.Weinterpret fusion and transition (3) as being due, respectively, to ioiiic melting (break down of thelattice) and " melting " of the hexyl groups. Transitions (1) and (2) are explained by re-orientationof the perclilorate anions.The melting points of quaternary ammonium salts are usually rather low, whencompared with most ionic materials. This property has led to their investigation aspossible media for organic reactions, especially those involving materials unstable atelevated temperatures. The low fusion temperatures, which are easily accessible,have also encouraged study of the physico-chemical properties of these material^,'-^particularly from the viewpoint of their fusion mechanisms.For these purposessalts with very poorly nucleophilic anions (ClO;, BF,) and consequent chemicalstability in the melt, are of greatest importance.Tetra-n-hexylammoniuin perchlorate, (C6Hl 3)4NC104, although not the lowestmelting of these materials, also shows solid state polymorphism. One of us (J. E. G.)has observed three phase transitions by microscopic and differential thermal tech-niques,G but was unable to investigate them fully. Since then, Janz and co-workershave included this material in a study of several quaternary ammonium salts, usingdilatometry, differential scanning calorimetry, and other techniques in an attempt tounderstand the thermodynamics of the fusion pro~ess.~A precise determination of the heat capacity of this material, together with theenthalpy and entropy increments associated with the transitions, would provide abasis for a better understanding of these processes.In addition, we were curiousas to the comparison of the adiabatic equilibrium results with those obtained bydifferential scanning calorimetry. This latter technique is in widespread use, yet iislimitations are not universally understood. Tetrahexylamnionium perchlorate isparticularly suitable for this investigation as it is very stable and may be zone refinedeasily. We were able to achieve relatively high purity (using zone refining andcalorimetric techniques) which has not been done in previous work with moltenquaternary ammonium salts.EX PER1 M ENT ALMATERIALThe sample of tetra-n-hexylammonium perchlorate was prepared by the reaction of theiodide with perchtoric acid in aqueous ethanol solution, followed by two re-precipitations in54J .T . S . ANDREWS AND J . E, GORDON 547the presence of excess perchloric acid. The material was recrystallized once from ethanol+water and twice from ethyl acetate+diethyl ether and then was dried thoroughly undervacuum. The product contained less than 10 p.p.m. of iodine (the analysis was performed byGalbraith Laboratories, Knoxville, Tenn.). The h e white crystals were zone rebed inevacuated Pyrex tubes until all solid zones were singly crystalline (after about 100 passes).The sample was loaded into the calorimeter by fusion through a Pyrex frit under vacuum, andthe calorimeter sealed (gold gasketlknife edge) under a small pressure of helium (to assist inthe attainment of equilibrium).CALORIMETRYA silver calorimeter fitted with a screw closure and an adiabatic vacuum thermostat wereemployed in the heat capacity measurements.Both the calorimeter and the thermostatwere very similar to apparatus described by We~trurn,~ except that four channels of auto-matic control were employed (one for each of the top, middle, and bottom portions of theadiabatic shield, and one for the guard shield which surrounded the adiabatic shield), andthat an automatic a.c. resistance bridge was used for the temperature measurements. A fulldescription of the apparatus will be presented elsewhere.All measurements of mass,temperature,8 and electrical energy were refered to calibrations performed by the NationalBureau of Standards. The results of measurements on a standard sample of syntheticsapphire indicate an overall accuracy of about 0.1 %, while the experimental precision issomewhat better than this.RESULTSThe experimental heat capacity measurements are presented in table 1. Thesevalues are expressed on a molal basis (sample mass in vacuo 39.7329 g, C24H52NC104= 454.1373 g mol-l, density 0.913 g ml-l 3, taking the ice point as 273.15 K. Theresults have been corrected for " curvature ", and for the (small) differences inaddenda (helium, gold) to the calorimeter when run empty and with sample.Thesedata are illustrated in fig. 1. No difficulties were encountered during the measure-ments, except that very long equilibration times were encountered in the transitionregions. In fusion, for example, equilibrium was reached only two to three days afteran energy addition. Equilibration times in crystal I were also long (about half a day).The purity of the sample was determined by " fractional fusion " (table 2).'The slope of a plot of the reciprocal of the fraction melted against the melting temp-erature gave a sample purity of 99.94 %.Table 3 summarizes the enthalpy determinations for the transition regions.Transition enthalpies and entropies were obtained by integrating the differencebetween the experimental heat capacity curves and a " lattice '' obtained by judiciousextrapolation of the heat capacity observed above and below the transitiontemperatures.The lowest temperature transition (3) differed from the others in that several weekswere required to obtain the equilibrium form after cooling through the transition(shown both by positive temperature drifts and by the spread of the transition energyvalues). This corresponds to the difficulty reported by Janz et aI.for tetra-n-amyl-ammonium thiocyanate. We encountered no difficulty with the other transitionsreported here, but it should be remembered that our cooling rates were less than thoseused by Janz. The transition enthalpy reported for transition (3), accordingly, isthat observed after the sample had remained below the transition for several weeks.The other values in table 3 reflect lesser equilibration times.DISCUSSIONictrahexylainmonium perchlorate) have been reported by Janz and his associates.The fusion thermodynamics of several quaternary ammonium salts (includin548 ADIABATIC CALORIMETRY OF ORGANIC SALTSThese workers used differential scanning calorimetry and assigned uncertainties ofk 0.5 K to the reported transition temperatures and 3.3 % to the transition enthalpies.Table 4 reproduces their reported values together with those found by adiabaticcalorimetry in this research.The two sets of values are not entirely consistent andthose temperatures found in the equilibrium measurements are lower. We suggestthat this discrepancy is to be expected because of the sluggish transitions which weobserved in this material.Apparently the elevated scanning calorimetric temperaturesare the result of overheating. Differences in sample purity may also account forthese discrepancies.TRANSITION (3) A N D FUSIONJanz et aL2 have suggested that the melting of quaternary ammonium salts may beconsidered as two processes which are essentially separate. They are positionalmelting, or break up of the crystal lattice which should be comparable to the meltingof the alkali halides, and configurational melting of the alkyl chains attached to theammonium ion which should be comparable to the melting of the n-paraffins. Fur-ther, these authors suggest that the entropy change for this Configurational meltingshould be calculable as R In a, where SZ is the number of configurations available toPERCHLOR A T E ~ ? ~ .TABLE 1 .-EXPERIMENTAL HEAT CAPACITY DETERMINATIONS OF TETRA-n-HEXYLAMMONIUMC P l306.98 777.0314.08 802.5323.87 855.7331.11 1716335.48 2795341.44 928.7349.69 964.4355.75 2427361.74 977.3369.01 1317375.61 1244379.07 7.527E4382.17 1454T/K J mol-1 K-1series Iseries I1374.40 924.2377.07 1057378.67 4643379.05 3.549E4379.12 8.674E4379.15 1.592E5379.17 1.506E5379.31 6916380.47 986.2382.52 989.1384.58 992.5386.62 995.5CPl T / K J mol-* K-1series I11357.68 1031359.24 972.3360.97 976.4362.83 984.3364.68 994.2366.51 1015367.51 1.397E4368.56 954.7370.49 906.0372.44 907.1374.39 915.8376.32 944.4377.79 1074AHf A380.12 1082series IV339.87 917.9341.52 925.7343.30 934.7345.21 952.2347.11 954.9349.01 962.4350.88 973.6352.75 986.3354.50 1002355.61 3592C P IT/K J mol- 1 K- 1355.91 8.892E5356.22 3374357.34 1028358.99 967.1360.67 971.0series V300.52 752.6304.35 766.6308.28 781.9312.31 798.5316.29 816.0320.21 835.4324.14 856.2328.07 879.5331.79 1372333.57 5.931E5333.58 2.974E5333.69 3.478E4335.54 1378338.28 916.0340.23 919.8AH run A354.68 996.1360.44 972.4A H run BAH2 AAH1 ACP IAH run CAH;- B380.66 987.0series VI369.23 904.1370.16 896.4371.08 888.8series V1Iseries VIIIAH run DAH run EAH run FAH run G382.22 988.9series IXT/K J mol-1 K-1AHf CAH3 AAH2 BAH1 BAHf DAH3 BAH2 CAH, Cseries XAH3 Ca A, B, C, etc.are the identification of the enthalpy determinations; b temperature scale, I.P.T.S.,1948J . T. S . ANDREWS AND J . E . GORDON 549the chains through gauche-trans kinking (a " kink-block " proce~s).~ For tetra-n-amyl- and tetra-n-hexyl-ammonium ions, respectively, these authors calculated theconfigurational entropy changes to be about 71 and 96 J K-l mol-l. The experi-mental results for tetra-n-amylammonium thiocyanate agreed well with this prediction.It seems likely, however, that the two processes are intermixed for tetrahexyl-ammonium perchlorate. The melting entropy, 43.10 J K-1 mol-', is considerablygreater than that found for alkali halides (for example, 25 J K-l mol-1 for KBr),l0whilst the entropy of transition (3) (68.93 J K-l mol-l) is less than that predictedby the " kink-block " model, 96 J K-' mol-l.The sum of the experimental entropiesfor fusion and transition (3) (112.03 J K-l mol-l) is, however, close to the sum ofIIIIIIIII ,' IIIIII II80C.IIIIIIIIIIII1i11IIIIC 'I A300 340T/K380FIG. 1 .-Heat capacity of tetra-n-hexylamnionium perchlorate. A, 333.57 ; B, 355.91 ; C, 367.51 ;D, 379.18.TABLE 2.-FRACTIONAL MELTING OF TETRA-n-HEXYLAMMONIUM PERCHLORATE *TIK C,/J mol-1 K-1 AT/K TAHIJ mol-1 1 If TfinsllK378.67 4643 0.670 2920 5.59 379.01379.05 3.549E4 0.095 6206 2.63 379.10379.12 8.674E4 0.039 9 567 1.71 379.14379.15 1.592E5 0.021 12 954 1.26 379.16379.17 1.506E5 0.01 1 14 603 1.12 379.17triple point of sample 1 .oo 379.177triple point of pure material 0.00 379.21 9mole fraction of impurity 0.0006* data from fusion series I550 ADIABATIC CALORIMETRY OF ORGANIC SALTSTABLE 3 .-ENTHALPY INCREMENTS OF FUSION AND TRANSITION OF TETRA-n-HEXYLAMMONIUMPERCHLOR ATEsourcefusionrI1I11VVII vrirtransition (1)I111VVIIIJXtransition (2)II VVVIIIJXtransition (3)IVVIIIIXXXIno. of runs3953122622127311371111T1 /K372.22373.00373.42371.41371.60371 3 2357.72361 -90361.37359.44366.47353.75351.82354.18355.10352.17328.44326.12327.56323.03323.02325.36T21K385.19381.49381.08381.69381.87381.19372.26371.47371.41371.30371.10365.76359.84361.37359.43359.50337.26339.26339.36338.30338.33340.4728 68124 07023 45725 89125 88725 476averagelatticeAHf16 42211 69312 22014 0066 859averagelatticeAH117 57213 39212 8199 99312 982average1 a tt iceAH230 61234 19633 42536 16936 13936 205value1 at t iceAH3J mol-126 140"25401 *25 57225 58125 57125 57325 574&4 h9 22516 349H371- H361 I1 mol-112 090 012 14512 21112 20512 19812 20558 b9 5472 658H361- 113491J mol-117 51617 262 *17 52417 51517 52017 519k411 6805 839H339- H325 J mol-135 205 C34 931 C35 32435 130C35 060 c35 165c35 32412 33222 992a Excluded from the average as drift correction uncertain ; b precision index is twice the standarddeviation of the mean ; c excluded because of non-equilibrium behaviourJ .T . S . ANDREWS AND J . E . GORDON 55 1that predicted by the two models (121 J K-l inol-l). We suggest that the configur-ational entropy is acquired in two steps : the greater portion in transition (3) (68.93 JK-l mol-I), and most of the remainder in fusion. The alkyl chains are probablyextended and overlapping in the low temperature phase,' and some configurations ofthe kinked chains may be unobtainable until the lattice breaks up ; the difference be-tween the observed entropy sum for fusion and transition (3) and that predicted by themodels may be due to the maintenance of some structure in the melt immediately abovefusion.TABLE 4.-TRANSITION PARAMETERS FOR TETR A-11-HEXYLAMMONIUM PERCHLORATEfusiontransition ( 1 )transition (2)transition (3)Temperature uncertaintythis work ref.(3)Tt/K 379.18 383AHf/J niol-' 16 350 18 000ASf/J mol-' K--' 43.10 48Tl /KAH,/J mol-'AS,/J mol-' K-'T2 /KAH,/J molt'AS2/J mol-l K-1T3 /KAH,/J inol-lA&/J mol-' K-l367.517.24355.9116.42333.5768.932 6585 83922 9903692 5003585 9001633523 000696.3& 0.01 K (this work), 0.5 K (ref. (3)). Enthalpy uncertainty& 0.1 "/o (this work), k 3 % (Eef. (3)).TRANSITIONS ( 1 ) A N D (2)We believe that the entropy increments for these two transitions are adequatelyexplained in terms of the rotational disorder of the perchlorate ions.Guthrie andMcCullough l 2 have shown that the transition entropies of plastic crystals (in whichthe molecules rotate in a restricted manner in the solid state) accord well with thosecalculated by considering possible orientations of the molecules in the differentphases. Furthermore, Newns and Staveley have demonstrated that transitions inionic materials involving polyatomic ions may similarly be explained in many cases.Guthrie and McCullough suggest that possible orientations will match symmetryelements of both molecule (or ion) and crystal lattice. If the perchlorate ion isconsidered as a tetrahedron in a cubic environment (the high temperature phase ofammonium perchlorate is cubic) l4 there are four sets of such orientations.Theseare illustrated in fig. 2, and the corresponding symmetry elements are listed in table 5.They may be designated T, (two distinguishable orientations), DZd (6), C,, (8), andC,, (12). The entropy due to the orientational configuration of the ion is R In N(where N is the number of distinguishable orientations available to the ion), and thechange of orientational entropy on passing from one phase to another is R In N,/Nl.If the major contribution to the entropy of transition comes from the orientationalchanges, then transitional entropies may be calculated for various combinations of thesets of orientations, and the results compared with the experimental values. Thework of Newns and Staveley suggests that this procedure is of value, and that entropycontributions due to volume increments may be ignored.Two transition schemes are suggested by the experimental results, and they aresummarized in table 6.Both schemes correctly predict the entropy of transition (2)552 ADIABATIC CALORIMETRY OF ORGANIC SALTSbut are rather low in their predictions of the entropy of transition (1). Scheme 2,however, is more nearly correct for transition (I) and the sum of the entropies oftransitions (1) and (2) ( R In 17.3) is much closer to that predicted by scheme 2 ( R In 16)than that predicted by scheme 1 ( R In 14.5). Scheme 1 utilises all the sets of orient-ations, while scheme 2 arbitrarily excludes the 12 C2v orientations.Furthermore,scheme 2 requires that only one of the two possible Td orientations be used in phase111, so that this phase is ordered in scheme 2, but disordered according to scheme 1.We feel that the choice between these two schemes may not be made on the basisof the thermodynamic data alone. Both schemes lead to reasonably accurate pre-dictions for the entropies of transitions 1 and 2, particularly since the effect of volumeincrements has not been considered (although we expect this to be It isconceivable that the C,, orientations might be excluded in this material, due to stericsetc 3 v C Z UFTG. 2.-Sets of distinguishable orientations of a tetrahedron in a cubic environment.TABLE 5.-sYMMETKY ELEMENTS FOR A TETRAHEDRON IN A CUBIC! LATTICEcoinciding symmetry elementstetrahedron cubic latticedistinguishableorientationsT l (4) 3-fold axis (4) %fold axis 2(3) 2-fold axis(6) mirror plane(3) 4-fold axis(6) diagonal mirror planeD2dc30c 2 u(1) 2-fold axis(2) 2-fold axis(1) 4-fold axis(2) 2-fold axis(6) mirror plane (2)(4)(I) 3-fold axis (1 1(3) mirror plane (3)(1) 2-fold axis (1)(2) mirror plane (1)(1 1vertical mirror planediagonal mirror plane3-fold axisdiagonal mirror plane2-fold axishorizontal mirror planevertical mirror plane681J .T. S. ANDREWS AND J . E. GORDON 553hindrance from the " melted " hexyl chains. We would expect that the disorder ofphase 111 implied by scheme 1 should be resolved by a transition to an ordered phaseat some lower temperature. We found no evidence for any such transition (bydifferential thermal analysis) down to liquid nitrogen temperatures, but this does notexclude the possibility that ordering might take place as part of the processes leadingto transition (3) or at temperatures below the limit of our d.t.a.scan.TABLE 6.-TRANSTTION SCHEMES FOR TETRA-n-HEXYLAMMONIUM PERCHLORATEphase orientation setstotal number oforientations entropy/J mol-* K-1scheme 1111 T d 2transition (2) R In (16/2) 17.29transition (1) R In (28/16) 4.65I1 Td + D 2 d + C S v 16I T d + D 2 d + C3u+ c2v 28scheme 2I11 one of Td (ordered) 1I1 both T d + D z d 8I Td + D 2 d + c3u 16transition (2) R In (S/l) 17.29transition (1) R In (16/8) 5.76experimenttransition (2) R In 7.2 16.42transition (1) R In 2.4 7.24CONCLUSIONThe general model proposed by Janz is reasonable.The melting of these materialsmay be compared, on the one hand, to the positional melting of ionic materials, and,on the other, to the configurational melting of the n-paraffins. However, we believethat the two processes are intermixed in this material due to the rather long hexylchains. Transitions (1) and (2) may be accounted for by considering the orientationalentropy of the perchlorate ion.The equilibrium data obtained in this research agree quite well with those ob-tained by differential scanning calorimetry. The transition temperatures found hereare somewhat lower than those from d.s.c. measurements, probably due to over-heating of the sample in the d.s.c.work.ADDENDUMWe are grateful to a referee for drawing our attention to an alternative interpretation of ourresults. He pointed out that the sum of the entropies of transitions (I), (2) and (3) (93 J K-lmol-l) is close to that predicted by the kink-block model for the configurational melting ofthe hexyl groups on the cation (96 J K-l mol-l), and he suggested that the break up of thelattice and the rotational disordering of the anion occur together in the fusion transition.We think that 24 J K-l mol-l is a reasonable approximation to the entropy of the latticebreak up, as the fusion entropies of potassium bromide and potassium perchlorate are verysimilar (25 and 23 J K-l mo1-1 respective1y),l0 and the presence of a transition ( N R In 18 at572.7 K) l5 in potassium perchlorate implies that the perchlorate ion is disordered in thesolid phase of this material.The entropy of fusion of tetrahexylammonium perchlorate is43.10 J K-' mo1-1 so that this alternative explanation assigns about 19 J K-' mol-' to th554entropy of the rotational disordering of the perchlorate ion in this material. This is aboutR In 10, less than the full entropy of restricted rotational disorder of a tetrahedron in acubic lattice (R In 28), which implies either that full disorder is not attained i n the liquidphase, or that the ion is partially disordered in the solid phase,This entropy " deficit " is rather large, and we do not think that this alternative inter-pretation is likely. In addition, it fails to account for the observed entropies of transitions(1) and (2), which are in close agreement with those expected from the restricted rotation ofthe tetrahedral anion.ADIABATIC CALORIMETRY OF ORGANIC SALTSWe thank Professors R. C. Fort, Jr., V. D. Neff, E. F. Westrum, Jr., and C. A.Wulff for their helpful comments. The Air Force Office of Scientific Research isto be thanked for generous support. Acknowledgement is also made to the donorsof the Petroleum Research Fund, administered by the American Chemical Society,for partial support of this research.J. E. 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