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Critical temperatures and pressures of caprolactam, dimethyl sulfoxide, 1,4-dimethylpiperazine, and 2,6-dimethylpiperazine
Fluid Phase Equilibria 473 (2018) 32e36
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Critical temperatures and pressures of caprolactam, dimethyl sulfoxide, 1,4-dimethylpiperazine, and 2,6-dimethylpiperazine Eugene D. Nikitin*, Alexander P. Popov Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, Amundsen Street, 107a, 620016 Ekaterinburg, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 March 2018 Received in revised form 24 May 2018 Accepted 25 May 2018 Available online 26 May 2018
The critical temperatures and pressures of caprolactam (CASRN 105-60-2), dimethyl sulfoxide (CASRN 67-68-5), 1,4-dimethylpiperazine (CASRN 106-58-1), and 2,6-dimethylpiperazine (CASRN 108-49-6) have been measured by the pulse-heating technique applicable to thermally unstable compounds. Experimental critical constants have been compared with those calculated using the group contribution methods of Wilson and Jasperson, Marrero and Gani, Hukkerikar and co-workers. The critical properties of dimethyl sulfoxide measured in this work have also been compared with the results of computer simulation by Vahid and Maginn. © 2018 Published by Elsevier B.V.
Keywords: Critical properties Thermally unstable compounds Measurement Pulse-heating method Estimation
1. Introduction This paper presents the critical temperatures and pressures of four compounds of industrial importance: caprolactam (the Chemical Abstracts Registry Number is 105e60-2), dimethyl sulfoxide (DMSO, CASRN 67-68-5), 1,4-dimethylpiperazine (CASRN 106-58-1), and 2,6-dimethylpiperazine (CASRN 108-49-6). Caprolactam is an intermediate primarily used in the production of Nylon 6 fibers and resins. About 6.5 billion kilograms of caprolactam are produced annually [1]. Dimethyl sulfoxide (DMSO) is widely employed as a solvent and reaction medium. Piperazine and many of its derivatives have important pharmacological properties. Piperazines are also used in manufacture of resins, plastics, pesticides and other materials. All the compounds studied in this work decompose at their critical points. Extensive decomposition of caprolactam above 550 K during the vapor pressure measurements was observed by Steele et al. [2] while the critical temperature of caprolactam is about 800 K according to our experiments. DMSO is not a very stable compound as well; it decomposes at about its normal boiling point (Tnb ¼ 462:5 K). The onset temperature of the decomposition
* Corresponding author. E-mail addresses: [email protected] (A.P. Popov).
(E.D.
https://doi.org/10.1016/j.fluid.2018.05.029 0378-3812/© 2018 Published by Elsevier B.V.
Nikitin),
[email protected]
of pure DMSO was 468 K in the experiments of Lam et al. [3]. Using an accelerating rate calorimeter, Yang et al. [4] found that the onset temperature was 472.55 K. The critical temperature of DMSO can be roughly estimated using the Guldberg rule: Tc ¼ 1:5Tnb ¼ 693 K, so that one may expect that DMSO will be very unstable at the critical point. Piperazine decomposes at the critical point; nevertheless, Steele et al. [5] and VonNiederhausern et al. [6] could measure the critical properties of this compound using special methods. It is reasonable to suggest that dimethylpiperazines are unstable at the critical points too. The critical properties are equilibrium ones, and, strictly speaking, the critical point of an unstable compound is the critical point of a mixture of its decomposition products at the condition of chemical equilibrium. However, instead of using the critical point of this mixture, most investigators require the point which this compound would have if it were stable and no decomposition occurred. It is the definition that we shall use further. Such a critical point is not attainable in the course of a quasi-static process and in this meaning it is hypothetical. So we want to emphasize once more: by the critical point of an unstable compound, we shall mean a hypothetical critical point which the compound would have if no decomposition occurred. In practice, the critical properties of an unstable compound can be measured directly because chemical decomposition occurs with a finite rate. To do this, one can quickly heat a sample of the compound under study up to the critical temperature and perform all
E.D. Nikitin, A.P. Popov / Fluid Phase Equilibria 473 (2018) 32e36
33
2.2. Method
developed by us in the early nineties, and by now the critical properties of about 250 compounds, most of which are thermally unstable, have been measured. Most of these data have been collected in a recent review (Part 12 [19]) and the previous parts of this series of publications. The pulse-heating technique has been described in detail in previous papers [14e18]. The method is based on the phenomenon of the superheat of liquids [20,21] and consists in measuring the pressure dependence of the temperature of the attainable superheat (the line of the attainable superheat) with the help of a thin wire probe heated by electric current pulses. The critical point is the end point on both the vapor-liquid equilibrium line and the line of the attainable superheat. The duration of the heating pulses is short enough - from 0.03 to 1.0 ms e to limit decomposition of thermally unstable compounds in order to measure the critical properties. The line of the attainable superheat of DMSO at a duration of the heating pulse of 0.06 ms is shown in Fig. 1. The last point on this kind of a line corresponds to the apparent values of the critical pressure and temperature. If a compound under study is thermally unstable at the critical point, the apparent critical pressure and temperature of it may depend on the duration of a heating pulse. In this situation, the measured values of the critical pressure pm c and critical temperature Tcm are determined by the extrapolation of the apparent critical property vs the duration of a heating pulse curve to a zero heating time. In this work, the durations of heating pulses were 0.035, 0.06, 0.11, 0.22, 0.46, and 0.85 ms; the probe lengths were 1, 2, and 3 cm; and three or four samples of each compound were employed. Although each of the compounds studied decompose at their critical points, no obvious dependence of the apparent critical temperature and pressure on the durations of the heating pulses was observed. It is likely that the molar fractions of decomposition products formed during a heating pulse were so small that they did not significantly affect the critical properties. Thus, the measured values of the critical temperature Tcm and pressure pm c were determined by averaging the apparent critical parameters over all the heating times, probe lengths, and samples. It has been found that for both stable and unstable compounds m these measured values of the critical properties pm c and Tc are a bit smaller than the true critical values. The true critical pressure pc and temperature Tc are calculated by the following equations:
The pulse-heating method used for the measurement of the critical temperatures and pressures of the compounds studied was
m pc ¼ pm c po ; Tc ¼ Tc t0 ;
the necessary measurements before considerable decomposition of the material occurs. Several methods applicable to the measurement of the critical properties of thermally unstable compounds have been developed [7e18]. These methods limit decomposition in the course of measuring the critical properties. In reality, the critical properties of a system (the compound under study þ a small amount of decomposition products) are measured using these techniques. Some of these methods rely on ascertaining the dependence of the apparent critical properties on residence time. This dependence arises due to the decomposition of a compound under study. The longer the residence time, the larger the molar fraction of decomposition products grows. The critical properties of a pure, non-decomposed compound are determined by the extrapolation of the apparent critical property vs residence time curve to zero residence time. A knowledge of the critical properties of a compound, even if it is unstable at the critical point, enables estimation of its thermodynamic and transport properties because the critical constants are used as inputs in many correlations based on the law of corresponding states. It is clear, of course, that these correlations work only in the region of stability of an unstable compound. To reduce the decomposition of the compounds studied in this work in the course of measuring the critical properties, the measurements have been performed by the pulse-heating method with ultralow residence times [14e18]. 2. Experimental 2.1. Material Samples of the compounds investigated in this work were purchased from Sigma-Aldrich and used without any additional purification. The purities and Chemical Abstract Service Registry Numbers (CASRN) of the samples are listed in Table 1. Before and after measuring the critical properties of DMSO, IR spectra of the sample were obtained using a Nicolet 6700 FT-IR spectrometer. Both spectra were completely identical.
(1)
Table 1 Purities of compounds used in critical point measurement (Sigma-Aldrich, GC, supplier's certificates of analysis). CASRNa
Purity (mol. fraction)
Caprolactam
105-60-2
0.9999
Dimethyl sulfoxide
67-68-5
0.999
1,4-Dimethylpiperazine
106-58-1
0.999
2,6-Dimethylpiperazine
108-49-6
0.998
Compound
a
Structural formula
Chemical abstracts service registry number.
Fig. 1. Temperature of the attainable superheat of DMSO (-) against the pressure; B, m critical point; pm c and Tc are the measured values of the critical pressure and temperature. The time from the beginning of a heating pulse to the moment of boiling-up is 0.06 ms.
34
E.D. Nikitin, A.P. Popov / Fluid Phase Equilibria 473 (2018) 32e36
where 1=p0 and 1=t0 are correction factors. The method of calculation of the correction factors was given elsewhere [18,22]. The values of the correction factors mainly depend on a similarity parameter of a compound under study: the acentric factor or the Filippov parameter [23]:
A ¼ 100
pvp ðTr ¼ 0:625Þ ; pc
boiling point of 1,4-dimethylpiperazine, we took the average of the temperatures obtained by Arony and Le Fevre [31] and Lanum and Morris [32]. For 2,6-dimethylpiperazine, we found only one value of the normal boiling temperature given by Sigma-Aldrich [33]. Then the Filippov parameters, the correction factors, and the critical parameters were calculated, which were then used in a second iteration. Usually two iterations were enough because the correction factors and the Filippov parameter weakly depend on one another. As shown by Tables 2 and 3, the correction factors 1=p0 and 1=t0 range from 1.025 to 1.037 and from 1.003 to 1.004, respectively. That is, the correction procedure increases the critical pressure by about 2.5e3.7% and the critical temperature by 0.3 or 0.4%. There may be a doubt about the reliability of the calculation of the correction factors and the critical properties of 2,6dimethylpiperazine because, as noted above, we found in the literature only one value of the normal boiling point. Here one should bear in mind that the influence of the variation of the normal boiling point on the critical properties is weak. If the normal boiling temperature of 2,6-dimethylpiperazine is changed by 10%, the critical temperature and critical pressure are changed by only 0.16% and 1.8%, respectively. These are smaller than the uncertainties of the measurement, so the uncertainty in Tnb is adequately encompassed by the uncertainties in the critical measurements.
(2)
where pvp is the vapor pressure, Tr ¼ T=Tc is the reduced temperature. To calculate the Filippov parameters and the critical properties, m we used an iteration method. For the first iteration, pm c and Tc were used as the critical constants. The vapor pressure of caprolactam at a reduced temperature Tr ¼ 0:625 was estimated using an equation obtained by Steele et al. [2]; the normal boiling temperature of caprolactam was taken according to the measurements by Steele and co-workers too: Tnb ¼ 543:962 K. For the other compounds, the pressure at a reduced temperature Tr ¼ 0:625 was calculated by an equation suggested by Filippov [23]:
log10
P* T* T* T* 1 0:3252 þ 0:40529 ¼ 3:9726 log10 þ pvp T T T (3)
Here P* and T* are the pressure and temperature characteristic of a compound. The values of P* and T* were calculated from Eq. (3) m using pm c , Tc , and the normal boiling point Tnb (see Table 2). The normal boiling temperature Tnb of DMSO was estimated by averaging over several literature sources [24e30]. For the normal
2.3. Uncertainties The uncertainties of the critical properties measured by the pulse-heating method were discussed in detail elsewhere [17,18,34]. For compounds like the ones measured here with
Table 2 Normal boiling temperatures Tnb , correction factors 1=t0 , and critical temperatures Tc of compounds studied and piperazine: experimental values and comparison with predictive methods. Compound
Tnb /K
1=t0
Tс /K Exptl
Caprolactam Dimethyl sulfoxide 1,4-Dimethylpiperazine 2,6-Dimethylpiperazine Piperazine a b c d e f g
543.96 462.5 403.89 435.2 421.74
1.004 1.003 1.004 1.003
a
801 ± 8 718 ± 7a 606 ± 6a 646 ± 6a 661 ± 1b 656.3 ± 2.0c
WJd
MGe
H-swf
H-sg
878.80 719.6 591.0 636.8 643.6
770.70 729.0 691.0 705.8 686.5
747.41 729.0 625.4 654.0 634.3
747.41 729.0 625.4 654.0 634.3
This work. The relative expanded uncertainty Ur ðTc Þ ¼ 0:01 with 0.95 level of confidence. Experimental data by Steele et al. [5]. Experimental data by VonNiederhausern et al. [6]. The method of Wilson and Jasperson as presented by Poling et al. [36]. The method of Marrero and Gani [37]. The method of Hukkerikar et al. [38], step-wise regression procedure. The method of Hukkerikar et al. [38], simultaneous regression procedure.
Table 3 Acentric factors u, correction factors 1=p0 , and critical pressures pc /MPa of compounds studied and piperazine: experimental values and comparison with predictive methods. Compound Caprolactam Dimethyl sulfoxide 1,4-Dimethylpiperazine 2,6-Dimethylpiperazine Piperazine a b c d e f g
u 0.504 0.311 0.334 0.386
1=p0 1.037 1.025 1.036 1.026
Exptl a
4.66 ± 0.14 5.13 ± 0.15a 3.73 ± 0.11a 3.80 ± 0.11a 5.80b 5.42 ± 0.11c
This work. The relative expanded uncertainty Ur ðpc Þ ¼ 0:03 with 0.95 level of confidence. Experimental data by Steele et al. [5]. Experimental data by VonNiederhausern et al. [6]. The method of Wilson and Jasperson as presented by Poling et al. [36]. The method of Marrero and Gani [37]. The method of Hukkerikar et al. [38], step-wise regression procedure. The method of Hukkerikar et al. [38], simultaneous regression procedure.
WJd
MGe
H-swf
H-sg
5.487 7.162 3.451 3.719 5.463
4.786 5.650 3.567 3.849 5.616
5.294 5.533 3.887 4.141 5.736
4.972 5.641 3.647 3.986 5.701
E.D. Nikitin, A.P. Popov / Fluid Phase Equilibria 473 (2018) 32e36
comparatively low molar mass, low acentric factors (u < 1), and little hydrogen bonding, the uncertainties are dpc ¼ 0:03pc , dTc ¼ 0:01Tc , where Tc is the absolute temperature. These uncertainties are the combined expanded uncertainties at the 95% level of confidence. 3. Results and discussion The experimental critical temperatures and pressures of the compounds studied in this work are given in Tables 2 and 3 For comparison, these tables also contain the critical temperature and pressure of piperazine measured by both Steele et al. [5] and VonNiederhausern et al. [6]. As mentioned above, Steele et al. [2] measured the vapor pressure of caprolactam in the temperature range from 349.982 to 567.668 K. They estimated the critical temperature of caprolactam by the Ambrose method [35] and determined the critical pressure using the Wagner vapor-pressure equation for the fitting procedure. They obtained the following values: Tc ¼ 806 K and pc ¼ 4:8 MPa; these values lie within the limits of the uncertainties of our measurements. The critical constants for four compounds and piperazine were also calculated using the group contribution methods of Wilson and Jasperson (WJ) [36], Marrero and Gani (MG) [37], and Hukkerikar et al. [38]. Other group contribution methods were not used because they could not account for the functional groups found in DMSO. Tables 2 and 3 show that the critical temperature of DMSO is predicted very well with errors of 0.22% (the WJ method) and 1.53% (the MG, H-sw, and H-s methods). However, the critical pressure of DMSO is not predicted well; all the methods used noticeably overestimate it, especially the WJ method, with an error of 39.6%. The critical pressure of caprolactam is overestimated by the predictive methods too, but the critical temperature is both over- and underestimated. The critical properties of 1,4-dimethylpiperazine and 2,6-dimethylpiperazine are predicted by these groupcontribution methods with an accuracy ranging from 2.48e14.0% for the critical temperature, and 7.48e8.97% for the critical pressure. It is important that all the critical property predictive methods used in this study give the right trend for the isomers of dimethylpiperazine. The critical pressure of 2,6dimethylpiperazine is greater than that of 1,4-dimethylpiperazine, and the critical temperature of 2,6-dimethylpiperazine is higher than that of 1,4-dimethylpiperazine. This correlates with the fact that the normal boiling point of 2,6-dimethylpiperazine is greater than that of 1,4-dimethylpiperazine. It is interesting to compare the critical properties of isomers of dimethylpiperazine to those of piperazine. As mentioned above, the critical constants of piperazine were measured by Steele et al. [5] and VonNiederhausern et al. [6]. Table 2 shows that the critical temperature and pressure of piperazine are higher than those of 1,4-dimethylpiperazine and 2,6-dimethylpiperazine although usually the critical temperature increases and the critical pressure decreases with an increase in molar mass within a homologous series. However, this rule does not always work. For instance, among compounds containing nitrogen, the critical temperature of pyrrolidine is higher than that of 1-methylpyrrolidine, the critical temperature of benzenamine is higher than that of 4methylbenzenamine, and so on [19,39]. We calculated the critical properties of piperazine by the same group contribution methods we used for the other compounds. In the Wilson and Jasperson method, the normal boiling point is used to estimate both the critical temperature and the critical pressure. The normal boiling temperature of piperazine was taken as the average of the values obtained by Steele et al. [5] and VonNiederhausern et al. [6]. The Wilson and Jasperson method predicts that piperazine has the highest critical temperature, followed by 2,6-dimethylpiperazine,
35
then 1,4-dimethylpiperazine, which is in full agreement with the experimental data. However, the Marrero and Gani method, which is exclusively based on the structure of molecules, predicts a lower Tc for piperazine than for the isomers of dimethylpiperazine. The revised method of Marrero and Gani published by Hukkerikar et al. [38] predicts that the critical temperature of piperazine lies between those of 1,4-dimethylpiperazine and 2,6dimethylpiperazine. Vahid and Maginn, using a combination of molecular simulation and PCIP-SAFT equation of state modeling, computed the vapor pressure and the density on the vapor-liquid coexistence curve of pure DMSO [40]. At our request, they estimated the critical properties of DMSO. From their SAFT equation of state, they found Tc ¼ 730 K and pc ¼ 10.25 MPa. In their opinion, better estimates could be obtained using density function theory with rectilinear diameter extrapolation, which gave Tc ¼ 720 K and pc ¼ 5.7 MPa with an uncertainty of about 5% [41]. This last estimate of the critical temperature practically coincides with our experimental value, though the critical pressure obtained by them is higher than that measured by us. 4. Conclusion The critical temperatures and pressures of caprolactam, dimethyl sulfoxide, 1,4-, and 2,6-dimethylpiperazines have been measured. A knowledge of the critical properties of compounds enables estimation of their thermodynamic and transport properties because the critical parameters are used as inputs in many correlations based on the law of corresponding states. The critical properties of these compounds have also been estimated by the group contribution methods of Wilson and Jasperson (WJ), Marrero and Gani (MG), Hukkerikar and co-workers in two variants (H-sw and H-s). The critical temperature of DMSO was well predicted by all the methods used, but they noticeably overestimate the critical pressure. The critical pressure of caprolactam is overestimated by the predictive methods too while the critical temperature of this compound is both overestimated and underestimated; the MG method gives the best results for both the critical pressure and temperature of caprolactam. For 1,4-dimethylpiperazine, the critical temperature is best estimated by the WJ method and the critical pressure is best determined by the H-sw one. For 2,6dimethylpiperazine, the H-sw and H-s methods give the best results for the critical temperature, and the MG method provides the best estimation of the critical pressure. For DMSO, computer simulation gives a critical temperature that is very close to the experimental one (the error is 0.28%) but the critical pressure differs from the experimental one by 11.1%. Acknowledgements The study was supported by the Complex Program for Basic Research of the Ural Branch of the Russian Academy of Sciences N 18-2-2-13. The authors are grateful to Drs. E.J. Maginn and A. Vahid for sending their estimates of the critical properties of DMSO. List of symbols A p T
Filippov's similarity parameter pressure temperature
Greek symbols 1=p0 correction factor for the critical pressure 1=t0 correction factor for the critical temperature
36
Subscripts c nb vp r
E.D. Nikitin, A.P. Popov / Fluid Phase Equilibria 473 (2018) 32e36
critical state normal boiling vapor reduced value
Superscript m measured value References [1] J. Ritz, H. Fuchs, H. Kieczka, W.C. Moran, Caprolactam, Ullmann's Encyclopedia of Industrial Chemistry, Wiley-VCH, Weinheim, 2005, https://doi.org/10.1002/ 14356007.a05_031.pub2. [2] W.V. Steele, R.D. Chirico, S.E. Knipmeyer, A. Nguyen, J. Chem. Eng. Data 47 (2002) 689e699. [3] T.T. Lam, T. Vickery, L. Tuma, J. Therm. Anal. Calorim. 85 (2006) 25e30. [4] X.-W. Yang, X.-Y. Zhang, Z.-Ch Guo, W.-Sh Bai, L. Hao, H.-Y. Wei, Thermochim. Acta 559 (2013) 76e81. [5] W.V. Steele, R.D. Chirico, S.E. Knipmeyer, A. Nguyen, N.K. Smith, J. Chem. Eng. Data 42 (1997) 1037e1052. [6] D.M. VonNiederhausern, G.M. Wilson, N.F. Giles, J. Chem. Eng. Data 51 (2006) 1986e1989. [7] E.D. Nikitin, High Temp. 36 (1998) 305e318. [8] D. Ambrose, D.G. Grant, Trans. Faraday Soc. 53 (1957) 771e778. [9] L.C. Roess, J. Inst. Pet. Technol. 22 (1936) 665. [10] A.S. Teja, M. Gude, D.J. Rosenthal, Fluid Phase Equil. 52 (1989) 193e200. [11] L.C. Wilson, W.V. Wilding, H.L. Wilson, G.V. Wilson, J. Chem. Eng. Data 40 (1995) 765e768. [12] D.M. VonNiederhausern, G.M. Wilson, N.F. Giles, J. Chem. Eng. Data 45 (2000) 157e160. [13] W.V. Steele, R.D. Chirico, S.E. Knipmeyer, A. Nguyen, J. Chem. Thermodyn. 23 (1991) 957e977. [14] E.D. Nikitin, P.A. Pavlov, P.V. Skripov, J. Chem. Thermodyn. 25 (1993) 869e880. [15] E.D. Nikitin, P.A. Pavlov, A.P. Popov, Fluid Phase Equil. 149 (1998) 223e232. [16] E.D. Nikitin, P.A. Pavlov, M.G. Skutin, Fluid Phase Equil. 161 (1999) 119e134. [17] E.D. Nikitin, A.P. Popov, YuG. Yatluk, V.A. Simakina, J. Chem. Eng. Data 55 (2010) 178e183. [18] E.D. Nikitin, P.A. Pavlov, Method GSSSD ME 163e2010. Method of
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Fluid Phase Equilibria j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / fl u i d
Critical temperatures and pressures of caprolactam, dimethyl sulfoxide, 1,4-dimethylpiperazine, and 2,6-dimethylpiperazine Eugene D. Nikitin*, Alexander P. Popov Institute of Thermal Physics, Ural Branch of the Russian Academy of Sciences, Amundsen Street, 107a, 620016 Ekaterinburg, Russia
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 March 2018 Received in revised form 24 May 2018 Accepted 25 May 2018 Available online 26 May 2018
The critical temperatures and pressures of caprolactam (CASRN 105-60-2), dimethyl sulfoxide (CASRN 67-68-5), 1,4-dimethylpiperazine (CASRN 106-58-1), and 2,6-dimethylpiperazine (CASRN 108-49-6) have been measured by the pulse-heating technique applicable to thermally unstable compounds. Experimental critical constants have been compared with those calculated using the group contribution methods of Wilson and Jasperson, Marrero and Gani, Hukkerikar and co-workers. The critical properties of dimethyl sulfoxide measured in this work have also been compared with the results of computer simulation by Vahid and Maginn. © 2018 Published by Elsevier B.V.
Keywords: Critical properties Thermally unstable compounds Measurement Pulse-heating method Estimation
1. Introduction This paper presents the critical temperatures and pressures of four compounds of industrial importance: caprolactam (the Chemical Abstracts Registry Number is 105e60-2), dimethyl sulfoxide (DMSO, CASRN 67-68-5), 1,4-dimethylpiperazine (CASRN 106-58-1), and 2,6-dimethylpiperazine (CASRN 108-49-6). Caprolactam is an intermediate primarily used in the production of Nylon 6 fibers and resins. About 6.5 billion kilograms of caprolactam are produced annually [1]. Dimethyl sulfoxide (DMSO) is widely employed as a solvent and reaction medium. Piperazine and many of its derivatives have important pharmacological properties. Piperazines are also used in manufacture of resins, plastics, pesticides and other materials. All the compounds studied in this work decompose at their critical points. Extensive decomposition of caprolactam above 550 K during the vapor pressure measurements was observed by Steele et al. [2] while the critical temperature of caprolactam is about 800 K according to our experiments. DMSO is not a very stable compound as well; it decomposes at about its normal boiling point (Tnb ¼ 462:5 K). The onset temperature of the decomposition
* Corresponding author. E-mail addresses: [email protected] (A.P. Popov).
(E.D.
https://doi.org/10.1016/j.fluid.2018.05.029 0378-3812/© 2018 Published by Elsevier B.V.
Nikitin),
[email protected]
of pure DMSO was 468 K in the experiments of Lam et al. [3]. Using an accelerating rate calorimeter, Yang et al. [4] found that the onset temperature was 472.55 K. The critical temperature of DMSO can be roughly estimated using the Guldberg rule: Tc ¼ 1:5Tnb ¼ 693 K, so that one may expect that DMSO will be very unstable at the critical point. Piperazine decomposes at the critical point; nevertheless, Steele et al. [5] and VonNiederhausern et al. [6] could measure the critical properties of this compound using special methods. It is reasonable to suggest that dimethylpiperazines are unstable at the critical points too. The critical properties are equilibrium ones, and, strictly speaking, the critical point of an unstable compound is the critical point of a mixture of its decomposition products at the condition of chemical equilibrium. However, instead of using the critical point of this mixture, most investigators require the point which this compound would have if it were stable and no decomposition occurred. It is the definition that we shall use further. Such a critical point is not attainable in the course of a quasi-static process and in this meaning it is hypothetical. So we want to emphasize once more: by the critical point of an unstable compound, we shall mean a hypothetical critical point which the compound would have if no decomposition occurred. In practice, the critical properties of an unstable compound can be measured directly because chemical decomposition occurs with a finite rate. To do this, one can quickly heat a sample of the compound under study up to the critical temperature and perform all
E.D. Nikitin, A.P. Popov / Fluid Phase Equilibria 473 (2018) 32e36
33
2.2. Method
developed by us in the early nineties, and by now the critical properties of about 250 compounds, most of which are thermally unstable, have been measured. Most of these data have been collected in a recent review (Part 12 [19]) and the previous parts of this series of publications. The pulse-heating technique has been described in detail in previous papers [14e18]. The method is based on the phenomenon of the superheat of liquids [20,21] and consists in measuring the pressure dependence of the temperature of the attainable superheat (the line of the attainable superheat) with the help of a thin wire probe heated by electric current pulses. The critical point is the end point on both the vapor-liquid equilibrium line and the line of the attainable superheat. The duration of the heating pulses is short enough - from 0.03 to 1.0 ms e to limit decomposition of thermally unstable compounds in order to measure the critical properties. The line of the attainable superheat of DMSO at a duration of the heating pulse of 0.06 ms is shown in Fig. 1. The last point on this kind of a line corresponds to the apparent values of the critical pressure and temperature. If a compound under study is thermally unstable at the critical point, the apparent critical pressure and temperature of it may depend on the duration of a heating pulse. In this situation, the measured values of the critical pressure pm c and critical temperature Tcm are determined by the extrapolation of the apparent critical property vs the duration of a heating pulse curve to a zero heating time. In this work, the durations of heating pulses were 0.035, 0.06, 0.11, 0.22, 0.46, and 0.85 ms; the probe lengths were 1, 2, and 3 cm; and three or four samples of each compound were employed. Although each of the compounds studied decompose at their critical points, no obvious dependence of the apparent critical temperature and pressure on the durations of the heating pulses was observed. It is likely that the molar fractions of decomposition products formed during a heating pulse were so small that they did not significantly affect the critical properties. Thus, the measured values of the critical temperature Tcm and pressure pm c were determined by averaging the apparent critical parameters over all the heating times, probe lengths, and samples. It has been found that for both stable and unstable compounds m these measured values of the critical properties pm c and Tc are a bit smaller than the true critical values. The true critical pressure pc and temperature Tc are calculated by the following equations:
The pulse-heating method used for the measurement of the critical temperatures and pressures of the compounds studied was
m pc ¼ pm c po ; Tc ¼ Tc t0 ;
the necessary measurements before considerable decomposition of the material occurs. Several methods applicable to the measurement of the critical properties of thermally unstable compounds have been developed [7e18]. These methods limit decomposition in the course of measuring the critical properties. In reality, the critical properties of a system (the compound under study þ a small amount of decomposition products) are measured using these techniques. Some of these methods rely on ascertaining the dependence of the apparent critical properties on residence time. This dependence arises due to the decomposition of a compound under study. The longer the residence time, the larger the molar fraction of decomposition products grows. The critical properties of a pure, non-decomposed compound are determined by the extrapolation of the apparent critical property vs residence time curve to zero residence time. A knowledge of the critical properties of a compound, even if it is unstable at the critical point, enables estimation of its thermodynamic and transport properties because the critical constants are used as inputs in many correlations based on the law of corresponding states. It is clear, of course, that these correlations work only in the region of stability of an unstable compound. To reduce the decomposition of the compounds studied in this work in the course of measuring the critical properties, the measurements have been performed by the pulse-heating method with ultralow residence times [14e18]. 2. Experimental 2.1. Material Samples of the compounds investigated in this work were purchased from Sigma-Aldrich and used without any additional purification. The purities and Chemical Abstract Service Registry Numbers (CASRN) of the samples are listed in Table 1. Before and after measuring the critical properties of DMSO, IR spectra of the sample were obtained using a Nicolet 6700 FT-IR spectrometer. Both spectra were completely identical.
(1)
Table 1 Purities of compounds used in critical point measurement (Sigma-Aldrich, GC, supplier's certificates of analysis). CASRNa
Purity (mol. fraction)
Caprolactam
105-60-2
0.9999
Dimethyl sulfoxide
67-68-5
0.999
1,4-Dimethylpiperazine
106-58-1
0.999
2,6-Dimethylpiperazine
108-49-6
0.998
Compound
a
Structural formula
Chemical abstracts service registry number.
Fig. 1. Temperature of the attainable superheat of DMSO (-) against the pressure; B, m critical point; pm c and Tc are the measured values of the critical pressure and temperature. The time from the beginning of a heating pulse to the moment of boiling-up is 0.06 ms.
34
E.D. Nikitin, A.P. Popov / Fluid Phase Equilibria 473 (2018) 32e36
where 1=p0 and 1=t0 are correction factors. The method of calculation of the correction factors was given elsewhere [18,22]. The values of the correction factors mainly depend on a similarity parameter of a compound under study: the acentric factor or the Filippov parameter [23]:
A ¼ 100
pvp ðTr ¼ 0:625Þ ; pc
boiling point of 1,4-dimethylpiperazine, we took the average of the temperatures obtained by Arony and Le Fevre [31] and Lanum and Morris [32]. For 2,6-dimethylpiperazine, we found only one value of the normal boiling temperature given by Sigma-Aldrich [33]. Then the Filippov parameters, the correction factors, and the critical parameters were calculated, which were then used in a second iteration. Usually two iterations were enough because the correction factors and the Filippov parameter weakly depend on one another. As shown by Tables 2 and 3, the correction factors 1=p0 and 1=t0 range from 1.025 to 1.037 and from 1.003 to 1.004, respectively. That is, the correction procedure increases the critical pressure by about 2.5e3.7% and the critical temperature by 0.3 or 0.4%. There may be a doubt about the reliability of the calculation of the correction factors and the critical properties of 2,6dimethylpiperazine because, as noted above, we found in the literature only one value of the normal boiling point. Here one should bear in mind that the influence of the variation of the normal boiling point on the critical properties is weak. If the normal boiling temperature of 2,6-dimethylpiperazine is changed by 10%, the critical temperature and critical pressure are changed by only 0.16% and 1.8%, respectively. These are smaller than the uncertainties of the measurement, so the uncertainty in Tnb is adequately encompassed by the uncertainties in the critical measurements.
(2)
where pvp is the vapor pressure, Tr ¼ T=Tc is the reduced temperature. To calculate the Filippov parameters and the critical properties, m we used an iteration method. For the first iteration, pm c and Tc were used as the critical constants. The vapor pressure of caprolactam at a reduced temperature Tr ¼ 0:625 was estimated using an equation obtained by Steele et al. [2]; the normal boiling temperature of caprolactam was taken according to the measurements by Steele and co-workers too: Tnb ¼ 543:962 K. For the other compounds, the pressure at a reduced temperature Tr ¼ 0:625 was calculated by an equation suggested by Filippov [23]:
log10
P* T* T* T* 1 0:3252 þ 0:40529 ¼ 3:9726 log10 þ pvp T T T (3)
Here P* and T* are the pressure and temperature characteristic of a compound. The values of P* and T* were calculated from Eq. (3) m using pm c , Tc , and the normal boiling point Tnb (see Table 2). The normal boiling temperature Tnb of DMSO was estimated by averaging over several literature sources [24e30]. For the normal
2.3. Uncertainties The uncertainties of the critical properties measured by the pulse-heating method were discussed in detail elsewhere [17,18,34]. For compounds like the ones measured here with
Table 2 Normal boiling temperatures Tnb , correction factors 1=t0 , and critical temperatures Tc of compounds studied and piperazine: experimental values and comparison with predictive methods. Compound
Tnb /K
1=t0
Tс /K Exptl
Caprolactam Dimethyl sulfoxide 1,4-Dimethylpiperazine 2,6-Dimethylpiperazine Piperazine a b c d e f g
543.96 462.5 403.89 435.2 421.74
1.004 1.003 1.004 1.003
a
801 ± 8 718 ± 7a 606 ± 6a 646 ± 6a 661 ± 1b 656.3 ± 2.0c
WJd
MGe
H-swf
H-sg
878.80 719.6 591.0 636.8 643.6
770.70 729.0 691.0 705.8 686.5
747.41 729.0 625.4 654.0 634.3
747.41 729.0 625.4 654.0 634.3
This work. The relative expanded uncertainty Ur ðTc Þ ¼ 0:01 with 0.95 level of confidence. Experimental data by Steele et al. [5]. Experimental data by VonNiederhausern et al. [6]. The method of Wilson and Jasperson as presented by Poling et al. [36]. The method of Marrero and Gani [37]. The method of Hukkerikar et al. [38], step-wise regression procedure. The method of Hukkerikar et al. [38], simultaneous regression procedure.
Table 3 Acentric factors u, correction factors 1=p0 , and critical pressures pc /MPa of compounds studied and piperazine: experimental values and comparison with predictive methods. Compound Caprolactam Dimethyl sulfoxide 1,4-Dimethylpiperazine 2,6-Dimethylpiperazine Piperazine a b c d e f g
u 0.504 0.311 0.334 0.386
1=p0 1.037 1.025 1.036 1.026
Exptl a
4.66 ± 0.14 5.13 ± 0.15a 3.73 ± 0.11a 3.80 ± 0.11a 5.80b 5.42 ± 0.11c
This work. The relative expanded uncertainty Ur ðpc Þ ¼ 0:03 with 0.95 level of confidence. Experimental data by Steele et al. [5]. Experimental data by VonNiederhausern et al. [6]. The method of Wilson and Jasperson as presented by Poling et al. [36]. The method of Marrero and Gani [37]. The method of Hukkerikar et al. [38], step-wise regression procedure. The method of Hukkerikar et al. [38], simultaneous regression procedure.
WJd
MGe
H-swf
H-sg
5.487 7.162 3.451 3.719 5.463
4.786 5.650 3.567 3.849 5.616
5.294 5.533 3.887 4.141 5.736
4.972 5.641 3.647 3.986 5.701
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comparatively low molar mass, low acentric factors (u < 1), and little hydrogen bonding, the uncertainties are dpc ¼ 0:03pc , dTc ¼ 0:01Tc , where Tc is the absolute temperature. These uncertainties are the combined expanded uncertainties at the 95% level of confidence. 3. Results and discussion The experimental critical temperatures and pressures of the compounds studied in this work are given in Tables 2 and 3 For comparison, these tables also contain the critical temperature and pressure of piperazine measured by both Steele et al. [5] and VonNiederhausern et al. [6]. As mentioned above, Steele et al. [2] measured the vapor pressure of caprolactam in the temperature range from 349.982 to 567.668 K. They estimated the critical temperature of caprolactam by the Ambrose method [35] and determined the critical pressure using the Wagner vapor-pressure equation for the fitting procedure. They obtained the following values: Tc ¼ 806 K and pc ¼ 4:8 MPa; these values lie within the limits of the uncertainties of our measurements. The critical constants for four compounds and piperazine were also calculated using the group contribution methods of Wilson and Jasperson (WJ) [36], Marrero and Gani (MG) [37], and Hukkerikar et al. [38]. Other group contribution methods were not used because they could not account for the functional groups found in DMSO. Tables 2 and 3 show that the critical temperature of DMSO is predicted very well with errors of 0.22% (the WJ method) and 1.53% (the MG, H-sw, and H-s methods). However, the critical pressure of DMSO is not predicted well; all the methods used noticeably overestimate it, especially the WJ method, with an error of 39.6%. The critical pressure of caprolactam is overestimated by the predictive methods too, but the critical temperature is both over- and underestimated. The critical properties of 1,4-dimethylpiperazine and 2,6-dimethylpiperazine are predicted by these groupcontribution methods with an accuracy ranging from 2.48e14.0% for the critical temperature, and 7.48e8.97% for the critical pressure. It is important that all the critical property predictive methods used in this study give the right trend for the isomers of dimethylpiperazine. The critical pressure of 2,6dimethylpiperazine is greater than that of 1,4-dimethylpiperazine, and the critical temperature of 2,6-dimethylpiperazine is higher than that of 1,4-dimethylpiperazine. This correlates with the fact that the normal boiling point of 2,6-dimethylpiperazine is greater than that of 1,4-dimethylpiperazine. It is interesting to compare the critical properties of isomers of dimethylpiperazine to those of piperazine. As mentioned above, the critical constants of piperazine were measured by Steele et al. [5] and VonNiederhausern et al. [6]. Table 2 shows that the critical temperature and pressure of piperazine are higher than those of 1,4-dimethylpiperazine and 2,6-dimethylpiperazine although usually the critical temperature increases and the critical pressure decreases with an increase in molar mass within a homologous series. However, this rule does not always work. For instance, among compounds containing nitrogen, the critical temperature of pyrrolidine is higher than that of 1-methylpyrrolidine, the critical temperature of benzenamine is higher than that of 4methylbenzenamine, and so on [19,39]. We calculated the critical properties of piperazine by the same group contribution methods we used for the other compounds. In the Wilson and Jasperson method, the normal boiling point is used to estimate both the critical temperature and the critical pressure. The normal boiling temperature of piperazine was taken as the average of the values obtained by Steele et al. [5] and VonNiederhausern et al. [6]. The Wilson and Jasperson method predicts that piperazine has the highest critical temperature, followed by 2,6-dimethylpiperazine,
35
then 1,4-dimethylpiperazine, which is in full agreement with the experimental data. However, the Marrero and Gani method, which is exclusively based on the structure of molecules, predicts a lower Tc for piperazine than for the isomers of dimethylpiperazine. The revised method of Marrero and Gani published by Hukkerikar et al. [38] predicts that the critical temperature of piperazine lies between those of 1,4-dimethylpiperazine and 2,6dimethylpiperazine. Vahid and Maginn, using a combination of molecular simulation and PCIP-SAFT equation of state modeling, computed the vapor pressure and the density on the vapor-liquid coexistence curve of pure DMSO [40]. At our request, they estimated the critical properties of DMSO. From their SAFT equation of state, they found Tc ¼ 730 K and pc ¼ 10.25 MPa. In their opinion, better estimates could be obtained using density function theory with rectilinear diameter extrapolation, which gave Tc ¼ 720 K and pc ¼ 5.7 MPa with an uncertainty of about 5% [41]. This last estimate of the critical temperature practically coincides with our experimental value, though the critical pressure obtained by them is higher than that measured by us. 4. Conclusion The critical temperatures and pressures of caprolactam, dimethyl sulfoxide, 1,4-, and 2,6-dimethylpiperazines have been measured. A knowledge of the critical properties of compounds enables estimation of their thermodynamic and transport properties because the critical parameters are used as inputs in many correlations based on the law of corresponding states. The critical properties of these compounds have also been estimated by the group contribution methods of Wilson and Jasperson (WJ), Marrero and Gani (MG), Hukkerikar and co-workers in two variants (H-sw and H-s). The critical temperature of DMSO was well predicted by all the methods used, but they noticeably overestimate the critical pressure. The critical pressure of caprolactam is overestimated by the predictive methods too while the critical temperature of this compound is both overestimated and underestimated; the MG method gives the best results for both the critical pressure and temperature of caprolactam. For 1,4-dimethylpiperazine, the critical temperature is best estimated by the WJ method and the critical pressure is best determined by the H-sw one. For 2,6dimethylpiperazine, the H-sw and H-s methods give the best results for the critical temperature, and the MG method provides the best estimation of the critical pressure. For DMSO, computer simulation gives a critical temperature that is very close to the experimental one (the error is 0.28%) but the critical pressure differs from the experimental one by 11.1%. Acknowledgements The study was supported by the Complex Program for Basic Research of the Ural Branch of the Russian Academy of Sciences N 18-2-2-13. The authors are grateful to Drs. E.J. Maginn and A. Vahid for sending their estimates of the critical properties of DMSO. List of symbols A p T
Filippov's similarity parameter pressure temperature
Greek symbols 1=p0 correction factor for the critical pressure 1=t0 correction factor for the critical temperature
36
Subscripts c nb vp r
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critical state normal boiling vapor reduced value
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