J . Phys. Chem. 1991, 95, 938-940
938
Chain-Length Dependence of the Melting Point Difference between Hydrogenated and Deuterated Crystalline n-Alkanes Douglas L. Dorset, Electron Diffraction Department, Medical Foundation of Buffalo, Inc., 73 High St., Buffalo, New York 14203
Herbert L. Strauss, and Robert C. Snyder* Department of Chemistry, University of California, Berkeley, California 94720 (Received: July 20, 1990)
The melting point difference between a hydrogenated n-alkane and its deuterated counterpart is found to be dependent on the length of the n-alkane. The melting point difference increases in going to longer chains. For chains ranging in length from methane to polyethylene, the difference is to a good approximation linearly related to the melting point. The observed relation AT,,, = 6T, can be accounted for on the basis of the principle of corresponding states. The value of 6 obtained from a plot of AT,,, vs T , agrees well with the value of S reported earlier from an analysis of vapor pressure data for CH4 and
CD,.
Introduction
We report here our finding that there is a significant chainlength dependence of the melting point difference between hydrogenated and deuterated crystalline n-alkanes. The existence of an isotope effect on the melting point has long been known, having been reported in the earliest literature describing the synthesis and physical properties of completely deuterated molecules, such as of benzene.' The phenomenon had received little attention, however, until it was implicated by Stehling et aL2 as a possible cause, through selective partitioning, of isotopic clustering during the crystallization of mixtures of hydrogenated and deuterated polymethylene chains. These authors reported significant isotope melting point differences for hexatriacontane and for polyethylene. Since then, however, it appears that no additional melting point data have been reported on crystalline n-alkanes shorter than Cj2. Interest in the possibility of isotopic clustering has increased with the concurrent increase in the use of binary isotopic mixtures to "label" hydrocarbon chain systems for the measurement of their physical properties by techniques such as neutron scattering and NMR and vibrational spectroscopy. Neutron scattering studies have in fact revealed that isotopic segregation occurs in a number of systems consisting of amorphous mixtures of hydrogenated and deuterated chain^.^-^ This phenomenon had been predicted by Buckingham and Hentschel,6 who first demonstrated that the upper critical solution temperature (UCST) for isotopic mixtures of polymers can have a sufficiently high value to effect a separation. These authors showed that the UCST, which derives from the small difference in the volume between the hydrogenated and deuterated chains, has a value that is proportional to the degree of polymerization. Thus, isotopic segregation can occur only for mixtures of chains that have high molecular weights. Current debate no longer is focused on the possibility of the phenomenon, but rather on how general it Our own interest in the melting point isotope effect for n-alkanes developed from studies on the slow microphase separation that can occur in crystalline solid solutions of two n-alkanes of different chain lengths. In such cases, we have found that the replacement ( I ) Ingold, C. K.; Raisin, C. G.; Wilson, C. L.J . Chem. SOC.1936, 915. (2) Stehling, F. C.; Ergos, E . ; Mandelkern, L. Macromolecules 1971, 4 ,
672. (3) Bates, F. S.;Fetters, L. J.; Wignall, G. D. Macromolecules 1988, 21, 1086. (4) Bates, F. S.;Wignall, G. D.; Kochler, W. C . Phys. Reo. Leu. 1985.55, 2425. (5) Bates, F. S.;Wignall, G. D.Phys. Reo. Left. 1986, 57, 1429. (6) Buckingham, A. D.; Hentschel, H. G. E. J . Polym. Sci.: Polym. Phys. Ed. 1980, 18, 853. ( 7 ) Yang, H.; Stein, R. S.;Han, C. C.; Bauer, B. J.; Kramer, E. J. Po/ym. Commun. 1986, 21, 132.
0022-365419 112095-0938$02.50/0
TABLE I: Melting Points of Hydrogenated md Deuterated n-Alkmes, Polyethylene, Cyclododecrne, and Benzene comwund sourcd TmSa K AT-* I 2 3 2 3 2 3 2 4 2 5 2 6 2 5 2 6 2 7 2 6 2 3 2
90.7b 89.86 143.6 142.4 177.8 175.8 216.8 214.4 244.0 241.4 291.2 287.2 304.8 300.8 3 10.4 306.4 324.0 319.8 339.2 334.8 342.6 338.6 349.6 345.6 -410 -405 334.3 332.6 278.6f 279.9f
0.89b
1.15 1.87 2.46 2.48 4.01 4.1 1 3.88 4.32 4.27 4.22p 3.93d 4.8Y 1.7 -1.3f
OOur measured values unless otherwise indicated. Reference 8. Triple point temperatures. Includes measurement from ref 10. dlncludes measurements from refs 2 and 9. eAverage of values reported in refs 2 and 9. fReference 1. ESources of samples: 1, Fisher (Pittsburgh, PA); 2, MSD (Montreal, Quebec); 3, Wiley (Columbus, OH);4, Fluka (Hauppauge, NY); 5, Aldrich (Milwaukee, W1); 6, Supelco (Bellefonte, PA); 7, Eastman (Rochester. NY).
of one of the components by its deuterated analogue produces an asymmetry in phase behavior: that is, the systems CHn/CDdand CDn/CHdare not equivalent. For the C3O/c36 system, as will be reported elsewhere, the difference is dramatic, and this led us to examine the relation between the isotope melting point difference and the chain length of n-alkanes. Isotopic Melting Point
Data
Table I lists the melting points and melting point differences for some hydrogenated and deuterated n-alkanes and for polyethylene, cyclododecane, and benzene. The saturated hydrocarbon 0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 2, 1991 939
Melting Points of Crystalline n-Alkanes
1 Figure 1. Plot of the isotope melting point difference, AT, = 7+" - p,, against 7", for some n-alkanes and polyethylene. The data used are listed in Table 1. The n-alkanes may be identified by their number of carbons, indicated on the right side of the figure.
values listed are from our own measurements, except for methane* and melt-crystallized p~lyethylene.~,~ The methane values are triple-point temperatures. For polyethylene, we used the average of the two measurements previously r e p ~ r t e d . ~Earlier ,~ values reported for n-C362*9 and n-C3210 have been combined with our own. We have also included our own values for cyclododecane and the literature values for benzene.' For our measurements, we used a Mettler TA3300 differential scanning calorimeter. The heating rate was 1.0 OC/min. A temperature scale for the n-alkanes was established by leastsquares fitting the DSC peak melting points to the most accurate bulk melting point values reported for the protonated n-alkanes."J2
Discussion The melting point of a given crystalline hydrogenated n-alkane is consistently greater than that of the corresponding deuterated n-alkane, that is, the melting point difference, defined AT,
P', - Pm
is always positive. In Figure 1, AT,,, is plotted against P',,and a nearly linear relation is found. The data points fall near the least-squares straight line drawn through the origin. To account for the effects of isotopes on thermodynamic quantities, two rather different approaches have been used. The by-far most analyzed quantity has been vapor pressure. An analysis of the melting isotope effect is a natural extension of that for the vapor pressure isotope effect (VPIE), which requires a comparison of the liquid VPIE with that of the solid. The two approaches may be distinguished in terms of their starting points-the principle of corresponding states in one case and shifts in vibrational frequencies in the other." The two are, of course, not fundamentally different, since in either case a complete consideration must take into account the difference in (8) Colwell, J . H.; Gill. E. K.; Morrison, J . A. J . Chem. Phys. 1963, 39, 635. (9) English, A. D.;Smith, P.; Axelson, D. E. Polymer 1985, 26, 1523. (IO) Ungar, G.; Keller, A. Colloid Polym. Sci. 1979, 257, 90. ( I I ) Weast. R. C., Ed. CRC Handbook of Chemistry and Physics, 60th ed.; CRC Press: Boca Raton, FL, 1981; p C-81. (12) Broadhurst, M. G. J . Res. Nut. Bur. Standards 1962, 66A, 241. (13) Jancso. G.; Van Hook,W. A. Chem. Rev. 1974, 74, 689.
the external and internal frequencies between the liquid and the solid phases. In the present case, the principle of corresponding states conveniently serves as a basis for accounting for the linear relation between AT,,, and T,. In its simplest form, however, this principle is seldom found applicable to the crystalline state because crystal structures tend to be extremely diverse. The nonpolar, homogeneous character of the crystalline n-alkanes makes an application feasible for the system at hand. At temperatures well below the melting point, the crystalline packing arrangements for the series are similar: the chains pack parallel in lamellae; there are only two possible subcell arrangements, orthorhombic or triclinic, and these arrangements are nearly alike in stability and density." Most important, the state of the crystalline n-alkanes just below the melting point is similar. Detailed infrared studies on the hexagonal phase, the phase that is assumed by the odd-numbered n-alkanes CII-C45as the melting point is approached, indicate that just below T , the chains are conformationally disordered in some degree.I4 Recent studies on Csoand Cw, whose crystal structures do not change to the hexagonal form but remain orthorhombic up to the melting point, also indicate a degree of premelting conformational disorder that is in line with that found for the hexagonal phase." These observations, combined with the results the present study, suggest that the state of n-alkane chains in the solid at the melting point is similar for all chain lengths. The molecular packing in a hydrogenated n-alkane crystal can be assumed to be essentially identical with that in the deuterated crystal,16 the major difference being that the unit cell of the deuterated crystal is slightly smaller due to reduced vibrational amplitudes. This near identity led Grigor and Steele" to use the principle of corresponding states as a basis for estimating the triple-point temperature difference between CH4 and CD4. A corresponding states derivation of the relation between T,,, and AT, begins by expressing the reduced temperature in molecular units. For an n-alkane having n carbons, we have then P,= kBT/cn (2) where t, is the depth of the well associated with the intermolecular potential for the chain in the crystal and kBis Boltzmann's constant.'* At the melting point, the principle of corresponding states indicates that the reduced temperatures associated with the hydrogenated and deuterated n-alkanes of chain length n are equal. Thus
pH,,, = PDm,n so that from eq 2 we have
(3)
= pm,n/tDn which, with eq 1, may be rewritten
(4)
P'm.n/CHn
ATm,n = [(eH, - cDn)/tDnI 7 H m . n (5) As we have indicated, the value of the well depth, en, is dependent on the length of the chain. The fractional change in c, in going from the hydrogenated to the deuterated chain is, however, independent of chain length if chain-end effects are ignored, since all the methylene groups are essentially equivalent. The fractional change in t, is 6, which we define 6 = (tH, - C D n ) / € D n (6) which combined with eq 5 gives
AT,,, = @,,, (7) Thus, we find, in agreement with experiment, that T,,, is proportional to the melting point, T,, and not to n, the number of carbon atoms. From the slope of the least-squares straight line (14) Maroncelli, M.; Qi, S. P.; Strauss. H.L.; Snyder, R.G. J . Am. Chcm. SOC.1982,104,6237; Maroncelli, M.; Strauss, H.L.; Snyder, R.G. J. Chem. Phys. 1985.82, 281 1. ( I 5) Kim, Y.; Strauss, H. L.; Snyder, R.G. J. Phys. Gem. 1989,93,7520. (16) A quantitative verification of the identical crystal structures for analogous compounds will be presented in a future publication. (17) Grigor, A. F.; Steele, W. A. J . Chem. Phys. 1968, 48. 1038. (18) de Boer, J. Physica 1948, 14, 139.
J . Phys. Chem. 1991,95, 940-945
940
drawn in Figure 1, we find 6 0.0122,a value that compares well with the value 0.0095 obtained by Grigor and Steele” from their analysis of vapor pressure data for CH4and CD4. We note that a smaller slope, 0.0103,is obtained from data for n-alkanes shorter than 11 carbons, reflecting the fact that the AT,,,versus p,,,plot has a slight positive curvature. In view of the extreme range of molecular weights represented in Figure 1, the observed, nearly linear relation between AT,,, and p,,, seems remarkable, and.it must be accountable, as we have noted, to the close chemical and structural similarities within the homologous series. Conversely then, different packing structures and chemically different molecules would be expected to lead to values of 6 that are significantly different from the value found for the n-alkanes. Cyclododecane has a close chemical similarity to the n-alkanes. This chain is, however, locked into a ringlike conformation that necessarily leads to a quite different type crystal packing.19 Melting point measurements on hydrogenated and deuterated cyclododecane (Table I) give 6 = 0,0051. This value is about half that found for the n-alkanes. In the cyclododecane ring, the methylene groups point somewhat “inward” and thus tend to make contact with other methylenes in the same ring. This reduces intermolecular interaction between hydrogens, so it is reasonable that the changes in 6 are smaller than for linear alkanes. Benzene presents a more radical departure from the linear alkanes. For this molecule (Table I), 6 = -0.0046,that is, the melting point of the C6D6is higher than that of C6H6.’ Benzene differs from the n-alkanes in two significant ways: the liquid solidifies to an ordered crystal, unlike that for either the linear alkanes or cyclododecane; the C-H bonds are directed toward the (19) Dunitz, J. D.; Shearer, H. M. M. Helu. Chim. Acta 1960, 43, 18.
?r electrons of adjacent molecules and thus the interactions are quite different from the hydrogen-hydrogen interactions that occur between saturated molecules. We will briefly comment on the second approach to explaining isotope effects. If all modes are approximated by harmonic oscillators, the difference between the vapor pressures of the different isotomers13 and therefore between the melting points is given approximately by
AT,,, = A / F - B / T
(8)
where A =u
x
[(uilH’
- uiCH’) - (u,ID’ - uiCD’)],
hui
< kT
low frequencies
B = -b high frequencies
[(uilH
- qcH)- (uilD - u i C D ) ] , hv, > kT
where 1 and c refer to the liquid and crystalline states. The constants a and b involve the enthalpy of the transition, and the low-frequency sum includes the translation-rotation lattice modes. For the n-alkanes, the B term alone would give a linear correlation with n, since each methylene group adds equally to the sum. The observed nonlinearity must result from the A term and the effects of disorder. The latter is not explicitly taken account of in these formulas.
Acknowledgment. We gratefully acknowledge support of this work by the National Science Foundation Polymers Program, Grants DMR 86-10783(to the Medical Foundation of Buffalo) and DMR 87-01586(to the University of California, Berkeley) and by the National Institutes of Health, Grant G M 27690 (to the University of California, Berkeley).
Molecular Dynamics of Initial Events In the Thermal Degradation of Polymers Marc R. Nyden* Center for Fire Research, National Institute of Standards and Technology, Gaithersburg, Maryland 20899
and Donald W. Noid Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 (Received: January 15, 1990; In Final Form: April 27, 1990)
Computer simulations, based on molecular dynamics, were used to investigate the kinetic stability of model polymers as a function of temperature, secondary structure, and molecular weight. The rate constants for random &ion of the carbomrbon bonds were obtained from simulations starting from both planar zigzag and coiled conformations. The coiled polymers were found to be more stable than planar zigzag polymers with the same primary structure. The computer-generated rates correlated reasonably well with the functional predictions of the Rice, Ramsperger, and Kassel theory of unimolecular reactivity; however, deviations were observed for some of the short-chained polymers. Computer movies revealed pronounced coiling in the vicinity of dissociating bonds. This behavior was examined in light of proposed mechanisms for intramolecular hydrogen transfer.
Introduction The thermal degradation of polymers proceeds through a complex sequence of reactions which frequently culminate in the formation of toxic and otherwise undesirable products.’-3 A complete theory of this process would enable scientists to exert a measure of control over degradation pathways and the resulting product distributions. However, despite the considerable attention which has been directed to this matter, a detailed understanding of the thermal degradation process has not yet been achieved. One of the obstacles which has slowed the pace of progress in this area is that the initial stages of the thermal degradation process ‘Author to whom correspondence should be addressed.
are dominated by reactions involving free radicals and other unstable intermediates. These initial reactions cannot be isolated in experiments so that the measured properties are actually global averages involving a number of distinct reaction types.).‘ Furthermore, the reactions of interest are unimolecular in nature and tend to be extremely fast, proceeding from start to finish in picosecond time scales. This makes experimental measurements (1) Paabo, M.; Levin, B. C. Fire Mails. 1978. 11, 55. (2) Madorsky, S. L. Thermal Degradation of Organic Polymers; Interscience: New York, 1964; p 94. (3) Mita, A. In Aspects of Degradation and Stabilization of Polymers; Jellinek, H. H. G., Ed.; Elsevier Scientific: Amsterdam, 1978; p 248. (4) Inaba, A.; Kashiwagi, T. Macromolecules 1986, 19, 2412.
0022-3654/91 /2095-0940$02.50/0 0 1991 American Chemical Society
