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Hypothetical Thermodynamic Properties: the Boiling and Critical 2 Temperatures of Polyethylene and Polytetrafluoroethylene

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Hypothetical Thermodynamic Properties: the Boiling and Critical 2 Temperatures of Polyethylene and Polytetrafluoroethylene BATCH: je3a28 USER: cmh69 DIV: @xyv04/data1/CLS_pj/GRP_je/JOB_i03/DIV_je030211u DATE: March 31, 2004 1 Hypothetical Thermodynamic Properties: The Boiling and Critical 2 Temperatures of Polyethylene and Polytetrafluoroethylene 3 James S. Chickos* 4 Department of Chemistry and Biochemistry, University of MissourisSt. Louis, St. Louis, Missouri 63121 5 6 The normal (p ) 101.325 kPa) boiling-temperature behavior of a homologous series, TB, as a function of 7 the number of repeat units, N, is fit by a hyperbolic function whose limiting value asymptotically 8 approaches TB(∞) ) (1217 ( 246) K for series related to polyethylene and approximately TB(∞) ) 915 K 9 for those related to polytetrafluoroethylene. Normal boiling temperatures have been fit to the function 10 TB ) TB(∞)[1-1/(aBN +bB)] where aB and bB are constants characteristic of the series investigated. Similar 11 behavior is observed for the critical temperature, TC. As the number of repeat units, N, approaches infinity, 12 TB and TC are found to converge. This provides an indirect method of determining TC(∞). Combined with 13 a few other experimentally determined critical temperatures, the TC of an entire series can be predicted. 14 Consistent with the convergence of TB and TC, the limiting critical pressure, PC(∞), is found to approach 15 1 atm as N approaches infinity. The vaporization enthalpy and entropy at the boiling temperature, g g 16 ∆l Hm(TB) and ∆l Sm(TB), used initially to suggest hyperbolic behavior of TB, show complex behavior with 17 increasing N. This behavior is discussed in terms of a simple mathematical model proposed previously. 18 19 Introduction temperature approaches a finite limiting value, TB(∞). The 54 numerical values of the constants, c and d, determined 55 20 Hypothetical thermodynamic properties have been shown experimentally, result in a value TB(∞) ) 1078 K. The 56 21 to provide information useful in the evaluation of thermo- vaporization enthalpies at the normal boiling temperature 57 22 chemical properties. For example, subcooled vaporization g (∆l Hm(TB)), the critical temperature (TC), and critical 58 23 enthalpies evaluated at T ) 298.15 K have been used to pressure (PC) were also found to approach finite limits as 59 24 validate sublimation enthalpies of solids;1 the distribution the size of the molecule increases.7 Equation 1 was empiri- 60 25 of polyaromatic hydrocarbons between the gas and par- cally derived by Kreglewski and Zwolinski7 using results 61 26 ticulate phase has been found to be proportional to the of Kurata and Isida8 on hole theory treatment of n-paraffin 62 27 hypothetical subcooled liquid vapor pressure.2 Melting tem- liquids. Kurata and Isida found that the effective length 63 28 peratures of compounds that decompose before reaching of a carbon skeleton should be proportional to the two- 64 29 the liquid state can be evaluated from solubility measure- thirds power of the number of carbon atoms when M > 5. 65 30 ments and used to obtain estimates of fusion enthalpies; 31 these values can be used subsequently in various other ) ∞ - -d 2/3 TB(M) TB( ) ce M (1) 32 thermodynamic cycles.3 33 Most textbooks describing the physical properties of This paper reports a mathematical relationship empiri- 66 34 organic compounds point out that a homologous series cally derived from Gibbs’ equation that suggests that 67 35 shows regular increases in both normal melting and boiling boiling temperatures of homologous series related to poly- 68 36 temperatures as the size of the molecule increases. It has ethylene and polyperfluoroethylene may asymptotically 69 37 been shown, previously, that the melting temperature of approach finite limits. Application of a model and the 70 38 the n-alkanes does not increase indefinitely but asymptotic- corresponding protocol recently used to predict the melting 71 39 ally approaches a limiting value, T ) 411 K, as character- temperatures of homologous series is also applied to their 72 4,5 40 ized by the melting temperature of polyethylene. In this boiling temperature and critical temperature and pres- 73 41 article, the question of whether the normal boiling tem- sure.4 The limiting temperatures obtained are remarkably 74 42 perature of a homologous series, TB, increases indefinitely similar to those previously derived. The results support the 75 43 or whether it too asymptotically approaches a limiting previous model that suggested that boiling temperature, 76 44 value is discussed. vaporization enthalpy at the boiling temperature, and the 77 45 The increase in the normal boiling temperature of a critical temperature and pressure of polymers are finite. 78 46 homologous series decreases with increasing size, requiring 47 the use of nonlinear expressions to fit experimental data. Sources of Data 79 48 Both third-order polynomials and exponential functions The boiling-temperature data used in this study were 80 6,7 49 have been previously used to model this property. The obtained from a variety of sources. The major sources of 81 50 polynomial expressions increase with increasing repeat data for each series reported are cited in the supplementary 82 51 unit, and therefore the boiling temperature is unbound. tables. Boiling temperatures for a few individual com- 83 52 The exponential expression, eq 1, predicts that, as the pounds have been obtained from some of the commercial 84 53 number of carbon atoms M approaches infinity, the boiling chemical catalogs and handbooks. Vaporization enthalpies 85 used in this study at the boiling temperature, T ) TB, are 86 * To whom correspondence may be addressed. E-mail: [email protected]. those from the API 44-TRC Handbook.9 Boiling tempera- 87 10.1021/je030211u CCC: $27.50 © xxxx American Chemical Society Published on Web 00/00/0000 PAGE EST: 8.7 BATCH: je3a28 USER: cmh69 DIV: @xyv04/data1/CLS_pj/GRP_je/JOB_i03/DIV_je030211u DATE: March 31, 2004 B Journal of Chemical and Engineering Data listed in Table 1. Since Gibbs’ energy of vaporization at 123 equilibrium conditions (TB, p ) 101.325 kPa) is zero, 124 g g ∆l Sm(TB) may be replaced by ∆l Hm(TB)/TB in the equa- 125 tions presented in Table 1. Solving for TB results in eq 2 126 where m and C represent the slopes and intercepts of the 127 lines in Figure 1. The slopes (m) and intercepts (C) are 128 listed in Table 1. Equation 2 is the equation of a hyper- 129 g bola that asymptotically approaches m as ∆l Hm(TB) ap- 130 proaches infinity. The slopes obtained from the equations 131 in Figure 1 are different but similar in magnitude as are 132 the intercepts; the intercepts are also large. If the vapor- 133 ization enthalpy of an increasing chain is boundless, then 134 the average of the slopes reported in Table 1 suggest a 135 limiting boiling temperature, TB(∞) ≈ 3000 K. This is 136 discussed in more detail below. 137 ) g g - TB m∆l Hm(TB)/(∆l Hm(TB) C) (2) If the normal boiling temperature, TB, of a homologous 138 series is truly modeled by a hyperbolic function, as sug- 139 gested by eq 2, and similar to what has been observed with 140 melting temperature,4 then a plot of the function 1/[1 - 141 g Figure 1. A plot of the ∆l Hm(TB) measured at T ) TB vs the TB(N)/TB(∞)] against the number of repeat units of the 142 g ) b ∆l Sm(TB) also calculated at T TB of , the n-alkanes (C3 to C20); homologous series, N, where TB(N) represents the normal 143 2 9 , n-alkylcyclopentanes (C7 to C21); , and n-alkylcyclohexanes boiling temperature of each member of the series, should 144 (C8 to C24). The lines drawn through the data were obtained by a result in a straight line.4 For series that converge to 145 linear regression analysis. All the data were used for the n- “polyethylene”, N represents the number of methylene 146 alkanes; the triangle and square clearly off each respective line groups. Initial calculations using TB(∞) ) 3000 K resulted 147 represents the value for ethylcyclopentane (C7) and ethylcyclo- in nonlinear plots; however, allowing TB(∞) to vary resulted 148 hexane (C8), and each was not included in the regression analysis. The equations for each line are reproduced in Table 1. in the representative plots shown in Figure 2. The linear 149 relationship observed between N and 1/[1 - TB(N)/TB(∞)] 150 for the compounds plotted in Figure 2 (and for all the 151 88 tures for the n-alkanes are available from C1 to C100. Many compounds of Table 2) provided analytical expressions that 152 89 of these are values that have been extrapolated from a could be solved for T in terms of T (∞), N, and two 153 90 variety of different mathematical relationships and are B B parameters, a and b , the slope and intercept of the plots 154 91 estimated. Experimental values for boiling temperature B B 9,10 in Figure 2, respectively. Solving for TB in terms of TB(∞), 155 92 and vaporization enthalpy up to n-C20 have been used. N, a , and b results in eq 3 156 93 Recommended critical properties were used when avail- B B 94 able.11 Values from other sources were used to verify some T ) T (∞)(1 - 1/(a N + b )) (3) 95 of the data. Data for many of the same compounds can be B B B B 96 found in the various compendia cited in the Supporting Experimental boiling-temperature data were then fit to 157 97 Information. Boiling temperature values differ depending this expression by a nonlinear least-squares program. Input 158 98 on the source; qualitatively, the same conclusions were parameters included T and N, the normal boiling tem- 159 99 reached regardless of the source.
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