Prediction of Vapor–Liquid Coexistence Properties and Critical Points

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Prediction of Vapor−Liquid Coexistence Properties and Critical Points of Polychlorinated Biphenyls from Monte Carlo Simulations with the TraPPE−EH Force Field Evgenii O. Fetisov† and J. Ilja Siepmann*,†,‡ †

Department of Chemistry and Chemical Theory Center, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455, United States ‡ Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Avenue SE, Minneapolis, Minnesota 55455, United States S Supporting Information *

ABSTRACT: Gibbs ensemble Monte Carlo simulations using the explicit-hydrogen version of the transferable potentials for phase equilibria (TraPPE−EH) force field were carried out to predict the vapor−liquid coexistence and critical properties of biphenyl, monochlorinated biphenyls, and of 16 polychlorinated biphenyls. The predictions are in very good agreement with the limited experimental data. Transferring the TraPPE−EH Lennard-Jones parameters from benzene to construct biphenyl yields predicted critical properties and normal boiling temperature with an average deviation of less than 1 %. The saturated vapor pressures for biphenyl, 2-chorobiphenyl, and 4-chlorobiphenyl fall within 10 % of the experimental data. Overall, the critical temperatures increase nearly linearly with the number of chlorine substituents and are correlated with the dipole moment for the monochlorinated isomers. In contrast, 4,4′-dichlorobiphenyl, the most elongated compound, exhibits the highest critical temperature among the disubstituted biphenyls.

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INTRODUCTION Polychlorinated biphenyls (PCBs) exist in 209 congeners, C12H10−nCln (with 1 ≤ n ≤ 10), and represent an important class of organic compounds with some technological benefits but very high toxicity. The U.S. Environmental Protection Agency lists them as persistent organic pollutants, compounds that resist biological, photolytic, and chemical degradation.1 Moreover, their destruction can lead to extremely toxic dibenzofurans and dibenzoxins through partial oxidation. Owing to the PCB’s relatively high melting points (ranging from 298 K for 3-chlorobiphenyl to 579 K for decachlorobiphenyl2), information on their fluid phase equilibria is sparse, whereas experimental data are plentiful for aqueous solubilities and Henry’s law constants and octanol−water partition coefficients.2 Phillips et al.3 used quantum mechanical continuunm solvation models to predict the Henry’s law constants in water for all 209 congeners. The transferable potentials for phase equilibria (TraPPE) family of force fields has recently been extended to include the explicit-hydrogen (EH) description of benzene, aromatics with heteroatoms, and substituted benzenes.4,5 The transferability of its parameters is exploited in this work to construct models for biphenyl and mono- and polychlorinated biphenyls. The TraPPE−EH models are used for Monte Carlo (MC) simulations to compute the vapor−liquid coexistence curve (VLCC) and critical properties of these important compounds. © XXXX American Chemical Society

Although biphenyl and PCBs are not chemically stable at their critical temperatures, knowledge of the critical parameters is important as input for equation-of-state modeling of chemical processes.6,7 The remainder of this article is organized as follows: Next, the force field and simulations details are provided; thereafter, the predicted VLCC and critical properties are discussed and compared to the available experimental data, followed by concluding remarks.

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COMPUTATIONAL METHODS Force Field. The TraPPE−EH force field4,5 uses LennardJones (LJ) and Coulomb potentials to represent the nonbonded interactions ⎡⎛ ⎞12 ⎛ ⎞6 ⎤ qiqj σij σij u(rij) = 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ 4πε0rij ⎣⎝ ij ⎠

(1)

where rij, εij, σij, qi, qj, and ε0 are the distance between interaction sites i and j, the LJ well depth, the LJ diameter, the partial charges on interaction sites i and j, and the permittivity Special Issue: Modeling and Simulation of Real Systems Received: May 25, 2014 Accepted: July 10, 2014

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cutoff for the Ewald summation was set to approximately 40 % of the average box length to reduce the computational cost. The volume and swap move probabilities were adjusted to yield approximately one accepted move of each type per MC cycle (where one MC cycle consists of N = 200 moves).18 The configurational-bias MC algorithm19 was used for particle transfer moves. For biphenyl, the simulations were extended to fairly low reduced temperatures were sampling of particle transfers of complete biphenyl molecules becomes very challenging. Thus, in addition to these complete particle transfers, two benzene impurity molecules were added to the system, thereby increasing the sampling efficiency by allowing for particle transfers of benzene and for identity switch transfers where a benzene molecule in one phase is converted to biphenyl and the reverse transformation (from biphenyl to benzene) is executed in the other phase (i.e., the biphenyl transfer rate is boosted by dividing it into two steps).20,21 The remaining move probabilities were divided equally between the translational, rotational and conformational moves where the latter involve only rotations around the C1−C1′ bond. The maximum displacements for these moves were adjusted to yield acceptance probabilities of 50 %. For every temperature, eight independent simulation runs were performed that consisted of 45 000 MC cycles for equilibration and of at least 40 000 MC cycles for production. The data from the eight independent runs were used to estimate the statistical uncertainties (standard errors of the mean). The vapor−liquid coexistence densities at near-critical temperatures were determined from density histograms;22 the critical temperature, Tc, and critical density, ρc, were computed using the density scaling law and the law of rectilinear diameter, respectively, with the scaling exponent, β, set to 0.326.23−25 The critical pressure was estimated by fitting the saturated vapor pressures from the near-critical temperatures to the Antoine equation,26 and the normal boiling point was determined from fits of the saturated vapor pressures near this temperature to the Clausius−Clapeyron equation.26 Numerical values of the VLCC properties (liquid density, ρliq, vapor density, ρgas, saturated vapor pressure, psat, and heat of vaporization, ΔHvap) are provided in Table S22 in the Supporting Information.

of vacuum, respectively. Because of the significant extent of charge density delocalization in aromatic compounds, the TraPPE−EH force field utilizes transferable Lennard-Jones parameters for ring atoms and substituents, whereas the partial charges are specific to a given compound. In the development of the TraPPE−EH force field,4,5 benzene and chlorobenzene were among the compounds used for the parametrization. The TraPPE−EH LJ parameters used for the chlorinated biphenyls are listed in Table 1. The Lorentz-Berthelot combining rules are used to determine LJ parameters for unlike interactions.8 Table 1. TraPPE−EH Lennard-Jones Parameters for Chlorinated Benzenes and Biphenyls atom type

ε/kB [K]

σ [Å]

C(aro)C(aro)X(aro) HC(aro) ClC(aro)

30.7 25.45 149

3.60 2.36 3.42

The TraPPE-EH force field treats aromatic rings and the directly connected atoms as rigid entities. In this work, the phenyl rings were also treated as rigid but were allowed to rotate with respect to each other around the C1−C1′ bond of the biphenyls. The molecular structures and rotational barriers of all compounds were determined from gas-phase optimized geometries and torsional scans based on electronic structure calculations at the M06-2X/6-311+G(d,p) level of theory9 and basis set10 (see Tables S1 to S21 in the Supporting Information). The high degree of charge density delocalization in aromatic compounds results in nontransferability of the partial charges used to represent the electron density. Therefore, the atom-centered partial charges for the biphenyl compounds were computed using the CM5 charge model11 for the gas-phase optimized structures embedded in the SM8 continuum solvation model12 with 1-octanol as the universal solvent for the TraPPE−EH development.4,5 Use of the continuum solvent allows incorporation of some of the polarization effects present in condensed phases, and 1-octanol is an appropriate reference solvent with an intermediate dielectric constant. The partial atomic charges for each compound are provided in Tables S1 to S20 in the Supporting Information. Simulation Details. Configurational-bias MC simulations in the Gibbs ensemble13,14 were performed to compute the single-component vapor−liquid coexistence curves (VLCCs). The simulated systems contained 200 molecules. A spherical potential truncation at 14 Å and analytical tail corrections for energy and pressure were used for the LJ interactions.15,16 The Ewald summation technique16,17 was used to compute Coulomb interactions. Gibbs ensemble simulations13,14 for VLCCs utilize two periodically replicated simulation boxes that are in thermodynamic contact but without a direct interface: conventional MC moves (translational, rotational, and conformational moves applied to individual molecules) are used to reach thermal equilibrium, volume exchange and particle swap moves between the boxes are performed to equilibrate the pressure and chemical potential. In the present simulations, the liquid box had linear dimensions larger 30 Å, and the total volume of the system was adjusted during the equilibration period so that, on average, approximately 20 to 40 molecules could be found in the vapor phase.18 Since the linear dimension of the vapor box can be quite large at low reduced temperatures, the direct space

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RESULTS AND DISCUSSION As a first step, the VLCC properties of biphenyl were calculated since there are sufficient experimental data available to allow for an assessment of the accuracy of the TraPPE−EH force field. Figure 1 shows a comparison of the predicted VLCC along with experimental data.27,28 Although the predicted data do not match perfectly the experimental data in the near-critical region, it should be noted that those experiments were done at very high temperatures where decomposition is unavoidable. Moreover, the critical properties (Tc = 763 ± 3 K and ρc = 315 ± 4 kg/m3) are very close to the recommended experimental values (773 ± 3 K and 310 ± 10 kg/m3, respectively).29 A Clausius-Clayperon plot of the saturated vapor pressures for biphenyl is shown in Figure 2. The predicted vapor pressures for T ≤ 625 K are very close to the low-temperature experimental values (with a mean unsigned deviation of 3%). As a result, the predicted normal boiling point (Tb = 530 ± 2 K) is in close agreement with the experimental value (528.4 K).27 In addition, the TraPPE−EH model yields pc = 3400 ± 30 kPa in excellent agreement with the recommended B

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The temperature dependence of the heats of vaporization for biphenyl is illustrated in Figure 3. The predicted ΔHvap values

Figure 1. Vapor−liquid coexistence curve for biphenyl (red squares), 2-chlorobiphenyl (magenta diamonds), 3-chlorobiphenyl (purple down triangles), and 4-chlorobiphenyl (cyan circles). Open and filled symbols and the solid lines show the computed coexistence densities (error bars are smaller than the symbol size), the estimated critical point, and the scaling law fit, respectively. Blue left and green right triangles depict the experimental data for biphenyl by Chirico et al.27 and Ellard and Yanko,28 respectively.

Figure 3. Temperature dependence of the heats of vaporization for biphenyl. Red squares (uncertainties are smaller than the symbol size) and blue up triangles show the values computed for the TraPPE−EH force field with a calorimetric approach and obtained from experimental vapor pressures via application of the Cox and Clapeyron equations.27

determined using a calorimetric approach (i.e., from the internal energy difference and the pressure−volume term) are somewhat larger than the low-temperature ΔHvap data obtained from application of the Cox and Clapeyron equations to measured saturated vapor pressures (T ≤ 560 K).27 Chirico et al.27 also used extrapolations from the Cox equation to estimate ΔHvap values for 580 K ≤ T ≤ 700 K. For elevated temperatures (above 650 K), the predicted ΔHvap values fall below the extrapolation of the experimental data. The application of the Cox and Clapeyron equations appears to underestimate the temperature dependence of ΔHvap and the extrapolation does not yield a vanishing ΔHvap as Tc is approached. Overall, the accuracy of the predicted VLCC data obtained for biphenyl without refitting of any of the force field parameters demonstrates the transferability of the TraPPE− EH force field from benzene to biphenyl. In conjunction with the prior assessment of the transferability of the parameter for the chlorine substituent (fitted to chlorobenzene and validated for the three dichlorobenzene isomers, two trichlorobenzene isomers, and hexachlorobenzene),5 the TraPPE−EH force field can be used for predictions of the VLCC properties of PCBs with high confidence. For monochlorinated congeners of biphenyl, experimental data are much more scarce and only experimental vapor pressures for 2-chlorobiphenyl and 4-chlorobiphenyl31 and the normal boiling point for 3-chlorobiphenyl32 are available. For the remaining congeners, only (sublimation) vapor pressures at very low temperatures estimated from gas−liquid chromatographic methods are available, but computing these retention indices is beyond the scope of the present paper. The predicted values of the saturated vapor pressure for 2- and 4chlorobiphenyl are compared in Figure 2 to extrapolated values obtained from the August equation with parameters fitted to vapor pressures at temperatures below 525 K.31 The TraPPE− EH reproduces the relative differences between the 2- and 4isomers quite well and the predicted normal boiling points of 553 ± 3 K and 560 ± 3 K are in good agreement with the

Figure 2. Clausius-Clayperon plot for biphenyl (red squares), 2chlorobiphenyl (magenta diamonds), 3-chlorobiphenyl (purple down triangles), and 4-chlorobiphenyl (cyan circles). The open and filled symbols show the computed saturated vapor pressures and estimated critical pressures, respectively. The open and filled blue left triangles depict the experimental data for biphenyl by Chirico et al.27 and the critical pressure of biphenyl recommended by Tsonopoulos and Ambrose.29 The solid magenta and cyan lines show extrapolations to lower temperatures of the computed data for 2-chlorobiphenyl, and 4chlorobiphenyl, and the dashed purple and orange lines show extrapolations to higher temperatures of the corresponding experimental data by Geidarov et al.31

experimental value of 3380 ± 100 kPa.29 Here it should be noted that very accurate vapor pressures are also obtained for other compounds using the TraPPE−EH force field4,5,30 because the explicit hydrogen sites yield an improved representation of the molecular shape and, hence, allow one to obtain both accurate entropies of transfer and accurate enthalpies of transfer, whereas united-atom models with interaction sites on the carbon postitions have to compromise. C

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Table 2. Critical Properties, Boiling Temperatures, and CM5 Dipole Moments of Monochlorinated Biphenyl Isomers Tc

ρc

pc

Tb

μ

compound

method

K

kg/m3

kPa

K

D

2-chlorobiphenyl

TraPPE-EH Geidarov et al.31 Joback and Reid33 Lydersen34 TraPPE-EH Gomberg and Bachman32 Joback and Reid33 Lydersen34 TraPPE-EH Geidarov et al.31 Joback and Reid33 Lydersen34

789 ± 2

355 ± 3

3300 ± 200

553 ± 3 553 ± 5

1.79

784 774 806 ± 2

344 ± 4

3300 ± 300

558 ± 4 557−558

2.24

791 781 803 ± 3

345 ± 4

3300 ± 300

560 ± 3 560 ± 4

2.26

3-chlorobiphenyl

4-chlorobiphenyl

794 784

Table 3. Critical Properties and CM5 Dipole Moments of Di-, Tri-, Tetra-, Penta-, and Decachlorinated Biphenyl Congeners compound

ρc

Tc

compound

K

2,2′-dichlorobiphenyl 2,3-dichlorobiphenyl 2,3′-dichlorobiphenyl 2,4-dichlorobiphenyl 2,4′-dichlorobiphenyl 2,5-dichlorobiphenyl 2,6-dichlorobiphenyl 3,3′-dichlorobiphenyl 3,4-dichlorobiphenyl 3,4′-dichlorobiphenyl 3,5-dichlorobiphenyl 4,4′-dichlorobiphenyl 3,4,4′-trichlorobiphenyl 3,3′,4,4′-tetrachlorobiphenyl 3,3′,4,4′,5-pentachlorobiphenyl decachlorobiphenyl

837 ± 4 832 ± 4 826 ± 3 823 ± 4 837 ± 5 840 ± 3 834 ± 3 825 ± 3 834 ± 3 843 ± 4 838 ± 3 844 ± 4 879 ± 3 907 ± 4 933 ± 5 1166 ± 8

kg/m 379 384 391 379 374 396 392 377 380 383 390 376 398 421 421 554

corresponding experimental values31 of 553 ± 5 K and 560 ± 4 K, respectively. However, it should be noted that further extrapolation of the experimental data to higher temperatures indicates deviations at T ≥ 600 K for 4-chlorobiphenyl, whereas the extrapolations of the predicted and measured data for 2chlorobiphenyl closely trace each other (see Figure 2). The predicted normal boiling point of 3-chlorobiphenyl also agrees well with the available experimental data. The predicted critical properties for the three isomers along with Tc estimates from popular group contribution methods33,34 are summarized in Table 2. Both the TraPPE−EH force field and the group contribution methods indicate a slightly lower Tc for 2chlorobiphenyl than the other two isomers whose Tc values agree to within their statistical uncertainties. For the monochlorinated biphenyls, the trend in Tc reflects the differences in the molecular dipole moments computed from the CM5 partial charges. The VLCCs were also computed for all 12 dichlorobiphenyl isomers, the most toxic isomers1 with three, four, and five chlorine substituents, and fully chlorinated biphenyl. The critical properties for these compounds are summarized in in Table 3 and the numerical VLCC data are provided in Table S22 in the Supporting Information. The Tc values for the dichlorinated biphenyls fall between 823 and 844 K, that is, on average about 35 K higher than for the monochlorinated

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

μ

pc 3

5 6 7 6 3 6 5 4 4 7 3 4 7 9 10 8

kPa 3200 3500 3200 3000 3100 3000 3300 3200 3200 3500 3400 3400 2900 2800 2500 2700

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

D 200 200 300 300 200 400 200 200 200 300 200 300 500 400 400 600

1.50 3.01 2.72 2.21 3.28 0.66 1.17 1.28 3.53 2.02 2.65 0.00 1.83 1.09 1.80 0.00

congeners. For the dichlorinated biphenyls, the trends in Tc are not well correlated by their molecular dipole moments, and indeed 4,4′-dichlorobiphenyl, the isomer with the smallest dipole moment but the most elongated shape, exhibits the highest Tc. As illustrated for selected PCBs in Figure 4, the addition of chlorine subsitutents leads to increases in the orthobaric liquid and critical densities and to an upward shift of the VLCCs. The dependence of the critical temperature on the number of chlorine atoms is presented in Figure 5. The Tc values overall increase linearly with increasing number of the substituents (the slope is about 39 K per chlorine), but with considerable spread among isomers. The number of possible isomers is largest for penta- and hexachlorobiphenyl and computing the VLCC properties and critical points for all 209 congeners is beyond the scope of the present work. However, when needed, the approach discussed here can be readily used to obtain the critical properties of any congener with a good accuracy.

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CONCLUSIONS Using the explicit-hydrogen version of the transferable potentials for phase equilibria (TraPPE−EH) force field, VLCC properties and critical points of mono- and 16 polychlorinated biphenyls along with biphenyl itself have been determined. Comparison with the very limited experD

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field and CHE-1152998 for work on PCBs) is gratefully acknowledged. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS

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REFERENCES

Computer resources were provided by the Minnesota Supercomputing Institute.

(1) Environmental Protection Agency. Polychlorinated Biphenyls. www.epa.gov/pcb (accessed 2007). (2) Shiu, W. Y.; Mackay, D. A critical review of aqueous solubilities, vapor pressures, Henry’s law constants, and octanol−water partition coefficients of the polychlorinated biphenyls. J. Phys. Chem. Ref. Data 1986, 15, 911−929. (3) Phillips, K. L.; Sandler, S. I.; Greene, R. W.; Di Toro, D. M. Quantum mechanical predictions of the Henry’s law constants and their temperature dependence for the 209 polychlorinated biphenyl congeners. Environ. Sci. Technol. 2008, 42, 8412−8418. (4) Rai, N.; Siepmann, J. I. Transferable potentials for phase equilibria. 9. Explicit-hydrogen description of benzene and fivemembered and six-membered heterocyclic aromatic compounds. J. Phys. Chem. B 2007, 111, 10790−10799. (5) Rai, N.; Siepmann, J. I. Transferable potentials for phase equilibria. 10. Explicit-hydrogen description of substituted benzenes and polycyclic aromatic compounds. J. Phys. Chem. B 2012, 117, 273− 288. (6) Prausnitz, J. M.; Lichtenthaler, R. N.; de Azvedo, E. G. Molecular Thermodynamics of Fluid Phase Equilibria, 3rd ed.; Prentice Hall: Englewood Cliffs, NJ, 1998. (7) Sandler, S. I. Chemical and Engineering Thermodynamics; Wiley: New York, 1989. (8) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, A. Intermolecular Forces: Their Origin and Determination; Pergamon Press: Oxford, UK, 1987. (9) Zhao, Y.; Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: Two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 2008, 120, 215−241. (10) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. Selfconsistent molecular orbital methods. XX. A basis set for correlated wave functions. J. Chem. Phys. 1980, 72, 650−654. (11) Marenich, A. V.; Jerome, S. V.; Cramer, C. J.; Truhlar, D. G. Charge Model 5: An extension of Hirshfeld population analysis for the accurate description of molecular interactions in gaseous and condensed phases. J. Chem. Theory Comput. 2012, 8, 527−541. (12) Marenich, A. V.; Olson, R. M.; Kelly, C. P.; Cramer, C. J.; Truhlar, D. G. Self-consistent reaction field model for aqueous and nonaqueous solutions based on accurate polarized partial charges. J. Chem. Theory Comput. 2007, 3, 2011−2033. (13) Panagiotopoulos, A. Z. Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble. Mol. Phys. 1987, 61, 37−41. (14) Panagiotopoulos, A. Z.; Quirke, N.; Stapleton, M.; Tildesley, D. J. Phase equilibria by simulation in the Gibbs ensemble Alternative derivation, generalization and application to mixture and membrane equilibria. Mol. Phys. 1988, 63, 527−545. (15) Wood, W. W.; Parker, F. R. Monte Carlo equation of state of molecules interacting with the Lennard-Jones potential. I. A supercritical isotherm at about twice the critical temperature. J. Chem. Phys. 1957, 27, 720−733. (16) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids; Oxford University Press: New York, 1987. (17) Ewald, P. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 1921, 64, 253−287.

Figure 4. Vapor−liquid coexistence curves for 2,2′-dichlorobiphenyl (blue circles), 4,4′-dichlorobiphenyl (red squares), 3,4,4′-trichlorobiphenyl (cyan up triangles), 3,3′,4,4′-tetrachlorobiphenyl (magenta left triangles), 3,3′,4,4′,5-pentachlorobiphenyl (green right triangles), and decachlorobiphenyl (purple down triangles). Open and filled symbols and the solid lines show the computed coexistence densities (error bars are smaller than the symbol size), the estimated critical point, and the scaling law fit, respectively.

Figure 5. Dependence of the critical temperatures of PCB congeners as a function of the number of chlorine substituents. The dashed line shows an unweighted linear fit.

imental data indicates that the TraPPE−EH force field is able to reproduce experimental critical values within 1 % and vapor pressures within 10 %. The predicted critical properties will be useful to benchmark group contribution methods and as input parameters for equation of state modeling.

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ASSOCIATED CONTENT

S Supporting Information *

Coordinates and CM5 charges for all molecules along with the numerical VLCC data (22 tables). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

Financial support from the National Science Foundation (CBET-1159837 for development of the TraPPE−EH force E

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