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J. Phys. Chem. 1991,95,9000-9007
Heat Capacities of Parafflns and Polyethylene Yimin Jin and Bernhard Wunderlich* Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996- 1600, and Division of Chemistry, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6197 (Received: February 27, 1991; In Final Form: April 29, 1991)
The heat capacities of the homologous series of paraffins from n-propane to polyethylene in the solid state are analyzed by use of the advanced thermal analysis system (ATHAS) developed for linear macromolecules. While the skeletal heat capacity contributions linked to the intramolecular vibrations follow a simple functional relationship with the number of chain atoms [el= 519 - 3508/n2], one detects for the heat capacities linked to the intermolecular vibrations a clear odd/even fluctuation [OJodd= 158 - 116.7/dn; 03- = 158 - 103.6/dn]. All prior measured data are included in the analysis in addition to new data on n-hexatriacontane (C36H74),n-tetratetracontane (C4Hm), and n-pentacontane (CmHIo2).Similarly, the heat capacities in the liquid state can be generated within a precision of *1.7% (rms error), using empirical contributions from the CH2 and CH3 groups [CpCH2= 17.33 + 0.04551c CpcH3= 30.41 + 0.01479‘33. With heat capacities of the solid and liquid known, the transitions and thermal functions H,S,and G can be derived and extrapolated to paraffins not measured. For all homologues a large increase in heat capacity beyond that expected from the contributions of vibrations is observed 50-100 K below the fusion temperature. This increase in heat capacity is shown to be in line with the gradual increase in conformational disorder proven by polyethylene crystal simulation using supercomputers.
I. Introduction Heat capacities of linear macromolecules have been a topic of longstanding interest in our laboratory.’ A major attempt was made to correlate all measured heat capacities by establishing a critically reviewed data bank.2 Next, the heat capacities of the solid3c and liquid5 states were interpreted in terms of their molecular motion. The analysis was aided by the simplicity of linear molecules. The limits of this analysis were outlined in a prior publication.6 In this paper, the feasibility of this analysis for shorter, linear molecules is explored by comparison of the heat capacities of polyethylene and paraffins. Literature data for analysis included the following paraffins: n-propane to n-octan-eicosane (C20H42),10 n-tetraeicosane (C24H50),’’ npentacosane (C25HS2!r11 n-hexacosane (C26HM),” n-dotnacontane (C32HM),l1 and n-tntriacontane (C33H68).10 In addition, new data are presented for the temperature range from 130 to 430 K for n-hexatriacontane (C36H74), n-tetratetracontane (C,H,), and n-pentacontane (C5OH102) that have become recently available in pure form. Overall, the above analysis reveals that data for all normal paraffins can be represented by the above analysis with a precision of fl .O%, which is similar to that of most experimental determinations. At temperatures closer to the melting temperature an increase in heat capacity beyond that of the vibrational contribution becomes obvious. lt will be suggested that this increase is caused by a gradual increase in conformational disorder, a state defined earlier as a “condis crystal”.” Condis crystals of over 100 substances of large and small molecules were identified based on their thermal properties, structure, and molecular motion.I4 ( I ) Wunderlich, B.; Dole, M. J . Polym. Sci. 1957, 21, 201. (2) The ATHAS Data Bank 1980 Gaur, U.; Lau, S.-F.; Shu, H.-C.; Wunderlich, B. B.; Mehta, A.; Wunderlich, B. J. Phys. Chem. Ref.Data 1981, IO, 89. 119: 1001; 1982, 1 1 , 313, 1065; 1983, 12, 29, 65, 91. Update 1990: Varma-Nair, M.; Wunderlich, B. J. Phys. Chem. Ref.Data 1991, 20, 349. (3) Cheban. Yu.V.; Lau, S.-F.; Wunderlich, B. Colloid Polym. Sci. 1982, 260, 9. (4) Lau. S.-F.;Wunderlich, B. J. Therm. AMI. 1983. 28, 59. (5) Loufakis, K.;Wunderlich, B. J. Phys. Chem. 1988, 92, 4205. ( 6 ) Bu, H.S.;Cheng, S. Z. D.; Wunderlich, B. J . Phys. Chem. 1987, 91, 4179. (7) Kemp. J. D.; Egan, C. J. J . Am. Chem. Soc. 1938, 60, 1521. (8) Aston, J. G.; Messerly, G. H. J. Am. Chem. Soc. 1940, 62, 1917. (9) Messerly,J. F.; Guthrie, G. B.; Todd, S. S.;Finke, H. L. J . Chem. Eng. Data 1967, 12, 338. (IO) Parks, G. S.; Huffman, H. M.; Thomas, S . B. J . Am. Chem. SOC. 1930, 52, 1032.
( I I ) Parks, G. S.; Moore, G. E.;Renquist, M. L.; Naylor, B. F.; McClaine, L. A.; Fujii, P. S.; Hatton, J. A. J. Am. Chem. Soc. 1949, 71, 3386. (12) Andon, R. J. L.; Martin, J. F. J . Chem. Thermodyn. 1976.8, 1159. ( I 3) Wunderlich, B.; Mdler, M.; Grebowicz, J. Adu. Polym. Sci. 1984, 60/4l, 1.
The liquid heat capacities of all paraffins will be shown to follow a simple addition scheme that can be linked to the more detailed analysis of the data on polyethylene that cover a temperature range from 260 to 600 K.5 With basic data on the heat capacity known, the equilibrium transitions and thermodynamic functions enthalpy, H,entropy, S, and Gibbs function, G, could be established and interpreted as a function of chain length. 11. Experimental Section Samples. The three newly analyzed n-paraffins were obtained from Aldrich Chemical Co., Inc., Milwaukee, WI. The purities are 98%, 99%, and 99+% for n-hexatricontane, n-tetratetracontane, and n-pentacontane, respectively. Calorimetry. A commercial Thermal Analysis 2100 system from TA Instruments Inc. (former DuPont Co., Instrument Systems Division) with a 912 dual sample DSC and DSC autosampler were used for heat capacity measurements of all samples. Experimental details and analysis were given in detail in previous p a p e r ~ . l ~ *A’ ~single-run heat capacity measurement technique was used for the measurements.” The error was < I % for high-temperature data (350-750 K) and 11 start negative and show a maximum before they join the middle range, quite similar to the polyethylene case.35 These deviations are mirrored in changes in the corresponding 8 values with temperature and suggest the limits of the approximate skeletal frequency spectrum. For applicability of the model the 8 values should be independent of temperature. Any improvement of the frequency spectrum must at present rely, however, on additional fitting of experimental data. For evaluation of the thermodynamic functions at higher temperatures these somewhat larger percentage errors are tolerable since the absolute values of heat capacity are small (see Figures 3 and 7 ) . The systematic deviation at higher temperatures is not a limitation to the model which is based on the assumption that all heat capacity is caused by vibration. Instead, it links to similar effects seen in polyethylene, first observed in 1962p6 and finally resolved r e ~ e n t l y . ~The ~ , increase ~~ in experimental heat capacity beyond that caused by vibrational motion has been linked to conformational disorder introduced into the crystal before any phase transition (see Figures 4 and 6). For polyethylene this deviation occurs first somewhat below room temperature.22 Similar first deviations can be estimated to be about 110 K for pentane, 120 K for heptane, 150 K for decane, 200 K for hexadodecane, and 260 K for pentacontane. Typical deviations of all data from a smooth curve are f20 K. The deviations in heat capacity can exceed 20% for the longer paraffins at the transition temperature (see Figure 6 ) . An integration of C J T yields an excess entropy ranging from 1.4 J/(K mol) for decane to 8.7 J/(K mol) for hexacosane. Although these excess entropies are only a few percent of the total entropies of transition [118 J/(K mol) for decane and 279 J / ( K mol) for hexacosane], the motion is im(34) Wunderlich. B.; Jones, L. D. J. Macromol. Sci. 1969, 8 3 , 67. (35) Grebowicz, J.; Suzuki, H.; Wunderlich, B. Polymer 1985, 26, 5 1 I . (36) Wunderlich, B. J. Chem. Phys. 1962. 37, 1207.
portant for the understanding of chain diffusion, crystal annealing, and lamellar deformation. Conformational disorder has for a long time been linked with many of the transitions of paraffins at temperatures below melting. Of particular interest is the transition to a hexagonal phase which was originally thought to be a "rotor phase"37 but could be shown more recently by analysis of the transition entropies to be conformationally disordered condis c r y ~ t a l ) . ' ~The J ~ present work shows that some of the motion in the hexagonal phase is already possible below the transition temperature. A similar conclusion was reached by measurement of the fraction of gauche conformation by infrared analysis.38 Even paraffins that show no hexagonal phase have a measurable gauche concentration below the melting point. Recent supercomputer simulation of crystals of polyethylene or paraffins gave information on the concentration and lifetimes of the gauche defect^.^^,^^ The calorimetry is in accord with these recent observations. Depending on chain length, some 50-100 K below the melting temperature a measurable concentration of gauche conformations with lifetimes of 1-10 ps occur. The concentration increases with temperature and can in certain paraffins lead to a transition to a hexagonal condis phase with a much higher concentration of gauche conformation, so that the anisotropy of the polymer chain is lost. The link between the hexagonal phase of the n-paraffins and that of polyethylene a t elevated pressure has been discussed e1~ewhere.I~ Enthalpy, Entropy, and Free Enthalpy. With heat capacities either known or predictable for all n-paraffins, it is possible to establish the complete thermodynamic functions as soon as all transition parameters are determined. Extensive discussions of the transitions are available in the literat~re'~3~J' and have formed the basis of the understanding of the melting of p0lyethylene,9~ including a theory-based prediction of the equilibrium melting temperature.40 From the present work complete tables for enthalpy, entropy, and free enthalpy have been computed from propane (C3H8) to triacontane (C30H62)and for some longer paraffins up to pentacontane (C34H70, C3sH72, C36H74,CMHs2, C43H88,C4Hg0, and CSOHlO2).It would take too much space to display all data. A typical graph is shown as Figure 9 for pentacontane. Data tables for any of the n-paraffins, as well as polyethylene and the other more than 100 polymers that are part of the ATHAS Data Bank, can be requested from the authors. Acknowledgment. This work was supported by the Division of Materials Research, National Science Foundation, Polymers Program, Grant DMR 881 841 2, and the Division of Materials Sciences, Office of Basic Energy Sciences, U.S.Department of Energy, under Contract DE-AC05-840R21400 with Martin Marietta Energy Systems, Inc. Registry No. C36H74r 630-06-8; CuHw,7098-22-8; CSOHIo2, 659640-3; polyethylene, 9002-88-4; methyl, 2229-07-4; methylene, 2465-56-7. (37) Muller, A. Proc. R. SOC.London 1932, A138, 514. (38) Snyder, R. G.;Straws, H. L.; Kim, Y. Bull. Am. Phys. Soc. 1989, 34 (3). 853. (39) Wunderlich, B. Macromolecular Physics; Academic: New York, 1 9 8 0 Vol. 3. (40) Wunderlich, B.; Czornyj, G. Macromolecules 1977, 10, 906.
