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Molecular Modeling of the Vapor-Liquid Equilibrium Properties of the Alternative Refrigerant 2,3,3,3-Tetrafluoro-1-propene (HFO-1234yf) Gabriele Raabe* and Edward J. Maginn Department of Chemical and Biomolecular Engineering, University of Notre Dame, 182 Fitzpatrick Hall, Notre Dame, Indiana 46556-5637
ABSTRACT The European Union legislation 2006/40/EC results in a phase-out of the presently used tetrafluoroethane refrigerant R134a from automotive heating ventilation and air conditioning systems. This necessitates the adoption of alternative refrigerants, and 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf) is currently regarded as the most promising alternative refrigerant. However, the lack of experimental data hampers independent studies on its performance in technical applications. We have developed a force field for HFO-1234yf that enables reliable predictions of its thermophysical properties via molecular simulation. The simulation results complement experimental data and provide a molecular-level perspective of the fluid behavior. In this letter we present the force field and its validation using Gibbs ensemble simulations on its vapor liquid equilibria. SECTION Statistical Mechanics, Thermodynamics, Medium Effects
I
field for molecular simulation studies of HFO-1234yf and the results of our simulation studies on its vapor-liquid-phase equilibria. More details on the force field development as well as a complete parameter set and simulation results for different fluoropropenes will be given in another publication.14
n order to reduce the overall emission of greenhouse gases, the European Union (EU) legislation 2006/40/EC1 bans the use of refrigerants in automotive heating ventilation and air conditioning (HVAC) systems that have global warming potentials (GWPs) higher than 150. Thus, the phaseout of the presently used tetrafluoroethane refrigerant R134a from January 2011 on necessitates the adoption of alternative refrigerants that comply with the guidelines of the EU. Therefore, refrigerant suppliers are working on the development of alternative refrigerants that allow a near drop-in replacement of R134a. Currently, the most promising alternative refrigerants are fluoropropenes, with 2,3,3,3-tetrafluoro-1-propene (HFO-1234yf) being particularly attractive to car manufacturers.2,3 Understanding and controlling the performance of HVAC systems with these new refrigerants requires a detailed knowledge of the thermodynamic and transport properties of the working fluids. Unfortunately, only little information on the thermophysical properties of fluoropropenes is available. In the recent years, molecular simulation studies have emerged as an important complement to experiment to obtain reliable thermodynamic and transport properties.4 A number of force fields for refrigerants are available in the literature, but these force fields mainly comprise models for either fluoromethanes, fluoroethanes, or fluoroethenes.5-10 To our best knowledge, until now there are no molecular models available for fluorinated propenes. Thus, our intention is to develop a transferable force field that covers different kinds of fluoropropenes that are currently proposed as refrigerants, either as pure compounds or as a component in a lowGWP refrigerant mixture.11-13 In this letter we present a force
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The molecular model in this work has been developed in the framework of the AMBER force field15 with its functional form given by X X kr ðr -r0 Þ2 þ kθ ðθ -θ0 Þ2 UConf ¼ bonds
þ
X
angles
kχ ½1 þ cosðnχ -δÞ
dihedral
8 2 9 !12 !6 3 = XX< σ σ q q 1 ij ij i j 5þ 4εij 4 ð1Þ þ : 4πε0 rij ; rij rij i j>i Therein, the calculation of intermolecular interactions is based on site-site terms with Lennard-Jones (LJ) interaction centers on the atomic sites and additional fixed partial charges to model the electrostatic interactions. The intramolecular potential energy is described by harmonic terms for bond stretching and angle bending, a cosine series to include energies arising from internal rotations of the dihedral angles, Received Date: September 29, 2009 Accepted Date: October 27, 2009 Published on Web Date: November 06, 2009
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DOI: 10.1021/jz900070h |J. Phys. Chem. Lett. 2010, 1, 93–96
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Scheme 1. Structure, Atom Types, and Partial Charges of HFO1234yf
Table 1. Force Field Parameters for HFO-1234yf force bond CMdCM
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kr (kJ 3 mol-1 3 Å-2) 2831.69
r0 (Å) 1.331
CM-CT
1328.84
1.511
CT-FCT
1544.61
1.353
CM-HC
1627.07
1.086
CM-FCM
1864.73
1.330
angle
and by nonbonded interactions between atoms separated by at least three bonds. Nonbonded LJ and electrostatic interactions between atoms separated by exactly three bonds (1-4 interactions) are scaled by a factor of 1/2 and 1/1.2, respectively. All LJ parameters for unlike atoms are obtained from the Lorentz-Berthelot combining rule. The parameters for the intramolecular terms and the partial charges of our force field were derived from ab initio simulations, whereas the LJ parameters were adjusted to finetune agreement with experimental data for model compounds and different fluoropropenes. More details on the parametrization of the molecular model will be provided in an expansive paper covering a transferable force field for different fluoropropenes.14 Our set of force field parameters for HFO-1234yf as shown in Scheme 1 is summarized in Table 1. The force field for HFO-1234yf has been tested by performing Gibbs ensemble simulations of its vapor liquid equilibrium, and the results will be discussed in detail in the following section. In addition, we provide molecular dynamics simulation results on the liquid structure of HFO1234yf by radial distribution functions (RDFs). The vapor-liquid coexistence curve (VLCC) of HFO1234yf is shown in Figure 1. Figure 2 illustrates a comparison of simulated vapor pressures with experimental results.16,17 These figures illustrate that our simulation results reproduce very well the experimental data for the vapor pressures and saturated densities of HFO-1234yf over the entire coexistence range. All simulated densities and vapor pressures agree with the experimental data within the error bars of the simulations. The good reproduction of both the VLCC and vapor pressure curve results in an excellent estimate of the critical point. Our predicted critical temperature of 366.4 K agrees with the averaged experimental value16,17 of 367.9 K to within 0.4%, and our estimated critical pressure of 3.376 MPa lies in the range of the experimental data by Hulse17 (3.26 MPa) and Tanaka and Higashi16 (3.382 MPa). Our estimated critical density (469.8 kg 3 m-3) slightly underestimates the experimental value16 of 478 kg 3 m-3 by 1.7%; however, all estimated critical data agree with experiment within the range of uncertainties of the estimates. Our simulation results yield an estimate of the normal boiling point of (243.3 ( 3.5) K that is also in excellent agreement with the interpolated experimental result17 of 243.8 K. Unfortunately, no experimental data are available for the heats of vaporization of HFO-1234yf. Tanaka and Higashi calculated the heats of vaporization (ΔHvap) by a Clausius-
force constant
kθ (kJ 3 mol-1 3 rad-2)
θ0 (deg)
HC-CMdCM
152.09
120.6 107.5
FCT-CT-FCT
367.61
CM-CT-FCT
313.17
111.3
HC-CM-HC
122.63
118.7 122.6
CMdCM-FCM
211.38
FCM-CM-CT
319.57
112.5
CMdCM-CT
209.70
124.1
dihedral X-CMdCM-X
kχ (kJ 3 mol-1)
n
δ (deg)
27.84
2
180
FCM-CM-CT-FCT
1.0445
3
0
CMdCM-CT-FCT
0.5951
3
180
ε (kJ 3 mol-1)
σ (Å)
CM
0.41000
3.40
CT
0.31091
3.40
FCM FCT
0.23617 0.23617
2.90 2.94
HC
0.06570
2.65
atom type
Figure 1. Comparison between experimental data for the saturated densities of HFO-1234yf and Gibbs ensemble simulation results obtained in this work.
Clapeyron equation based on their experimental vapor pressure curve, which they correlated by a Wagner-type equation. Figure 3 compares our simulation results to their estimated values of ΔHvap. Our simulated heats of vaporization slightly
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DOI: 10.1021/jz900070h |J. Phys. Chem. Lett. 2010, 1, 93–96
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Figure 4. RDF for HFO-1234yf in the liquid phase at 298.15 K and 1 MPa.
Figure 2. Comparison between experimental vapor pressures and Gibbs ensemble simulation results obtained in this work (symbols as in Figure 1).
systems consisting of 256 molecules. The Ewald sum technique was employed to deal with the electrostatic interactions with a cutoff radius adjusted to half the box length. The cutoff radius for the LJ interactions was set to 12 Å, and standard long-range corrections to the energy and pressure were applied. The simulations were equilibrated for 50 000100 000 cycles, followed by production runs of 100 000 cycles. Each cycle consisted of 256 attempted moves, such as a volume move, translation of the center-of-mass, rotation about the center-of-mass, and a configurational-bias exchange move between the boxes. The probabilities of the different moves were manually adjusted for each temperature to ensure that the equilibrium conditions were satisfied. The pressures were calculated via the pressure virial equation. The heats of vaporization (ΔHvap) were determined using the energy (E) and density (F) of the liquid and vapor phase and the vapor pressure (ps): 1 V L V 1 ð2Þ ΔHvap ¼ E -E þ ps V - L F F
Figure 3. Comparison between estimated heats of vaporization16 of HFO-1234yf and Gibbs ensemble simulation results obtained in this work (symbols as in Figure 1).
overestimate the calculations by Tanaka and Higashi, but fall within 1 kJ 3 mol-1 of their estimates. Fluorinated hydrocarbons are known to exhibit hydrogen bonding,5 so it can be expected that the thermophysical properties of HFO-1234yf are affected by some local ordering. To gain insight into the intermolecular hydrogen bonding, we analyzed the local structure of HFO-1234yf in the liquid phase at 298.15 K and 1 MPa by RDFs. Figure 4 shows the RDFs of the fluorines around the HC hydrogens. There are three distinctive peaks representing the location of the FCT fluorine of the CF3 group around the HC hydrogens. The first peak at a short distance of 0.26 nm clearly indicates hydrogen bonding interactions between the FCT fluorine and the HC hydrogen. This also results in a deviation from Trouton's rule as our simulation results at 244 K give a standard entropy of vaporization of 89.84 J 3 mol-1 3 K-1. Surprisingly, no hydrogen bonding is formed by the FCM fluorine in HFO-1234yf, with the FCM-HC RDF showing no distinctive peaks. The VLCC of HFO-1234yf was calculated via Monte Carlo Gibbs ensemble using the simulation code TOWHEE,18 with
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where the superscripts designate the simulation boxes, i.e., the saturated liquid and vapor phase. Standard deviations of all ensemble averages were determined by dividing the production runs into 10 blocks. The critical properties of HFO-1234yf were estimated by fitting the simulation results at subcritical conditions to the scaling law T ð3Þ FL -FV ¼ Aτβ with τ ¼ 1 TC and the law of rectilinear diameters FL þ FV ¼ Fc þ Bτ 2
ð4Þ
by employing the TOWHEE utility routine fitcoex.18 We assumed that the model obeys the Ising exponent β = 0.32. The critical pressure and normal boiling point were estimated by extrapolating the vapor pressure curve using the Clausius-Clapeyron equation. We have additionally performed molecular dynamics simulations in the liquid phase using the DL_POLY simulation
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package.19 The cubic boxes consisted of N = 216 molecules and similar simulation settings were applied as in the GEMC simulations. The system was equilibrated for 2.5 ns in the Nose-Hoover NpT ensemble followed by a production run of 2.5 ns, from which RDFs were computed. We have presented a force field for molecular simulation studies of HFO-1234yf. The performance of the force field has been tested by GEMC simulation studies on its vapor-liquid phase equilibria properties. The simulated VLCC and vapor pressure curve of HFO-1234yf agree within their error bars with recent experimental data. This also results in an excellent reproduction of the critical point and the normal boiling point. The simulated heats of vaporization fall within 1 kJ 3 mol-1 of the estimates by Tanaka and Higashi. The analysis of hydrogen bonding interactions by RDFs reveals that intermolecular hydrogen bonds are only formed between the FCT fluorines of the -CF3 end group and the HC hydrogens, whereas the FCM fluorine in HFO-1234yf is not involved in hydrogen bonding interactions. Motivated by our excellent results for the VLE properties of HFO-1234yf, we are currently studying a wide range of its thermophysical and transport properties by molecular dynamics simulations. These results from molecular dynamics studies will be the subject of a following publication, as well as the complete set of parameters and molecular simulation results for other fluoropropenes.
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SUPPORTING INFORMATION AVAILABLE Numerical results for the saturated densities, vapor pressures, and heats of vaporization from GEMC simulations. This material is available free of charge via the Internet at http://pubs.acs.org.
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AUTHOR INFORMATION Corresponding Author: (17)
*To whom correspondence should be addressed; on leave from the Institut f€ ur Thermodynamik, Technische Universit€ at Braunschweig, Germany. Tel.: þ49 531 391 2628. E-mail:
[email protected].
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ACKNOWLEDGMENT G.R. gratefully acknowledges funding by a Deutsche Forschungsgemeinschaft research fellowship (RA 946/21). We thank Dr. K. Tanaka and Dr. R. Singh, Honeywell, Int., for sharing their experimental information with us. We acknowledge Notre Dame's Center for Research Computing for providing the computing resources used in this work.
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Maginn, E. J. Transforming Molecular Simulation into a Mainstream Chemical Engineering Tool. Chem. Eng. Prog. 2009, 105, 9. Potter, S. C.; Tildesley, D. J.; Bugess, A. N.; Rogers, S. C. A Transferable Potential Model for the Liquid-vapour Equilibria of Fluoromethanes. Mol. Phys. 1997, 92, 825–833. Lisal, M.; Vacek, V. Molecular Dynamic Simulations of Fluorinated Ethanes. Mol. Phys. 1996, 87, 167–187. Fermeglia, M.; Ferrone, M.; Pricl, S. Development of an AllAtoms Force Field from Ab Initio Calculations for Alternative Refrigerants. Fluid Phase Equilib. 2003, 210, 105–116. Stoll, J.; Vrabec, J.; Hasse, H. A Set of Molecular Models for Halogenated Hydrocarbons. J. Chem. Phys. 2003, 119, 11396– 11407. Peguin, R. P. S.; Kamath, G.; Potoff, J. J.; da Rocha, S. R. P. AllAtom Force Field for the Prediction of Vapor-Liquid Equilibria and Interfacial Properties of HFA134a. J. Phys. Chem. B 2009, 113, 178–187. Kelkar, M. S.; Shiflett, M. B.; Yokozeki, A.; Maginn, E. J. Development of Force Fields for Hydrofluorocarbons. Presented at the AIChE Annual Meeting, Philadelphia, PA, November 16-21, 2008. E. I. Du Pont de Nemours & Co. Patent WO 2007/126414 A2, 2007. Honeywell International, Inc. Patent US 2008/0308763 A1, 2008. Ineos Fluor Holdings, Ltd. Patent US 2009/0158771 A1, 2009. Raabe, G; Maginn E. J. A Transferable Force Field for Fluoropropenes. To be submitted for publication. Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Gould, I. R.; Merz, K. M. Jr.; Ferguson, D. M.; Spellmeyer, D. C.; Fox, T.; Caldwell, J. W.; Kollmann, P. A. A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules. J. Am. Chem. Soc. 1995, 117, 5179–5197. Tanaka, K.; Higashi, Y. Thermophysical Properties of HFO1234yf. Presented at the Third IIR Conference on Thermophysical Properties and Transfer Processes of Refrigerants, Boulder, CO, June 23-26, 2009. Hulse, R.; Singh, R.; Pham, H. Physical Properties of HFO1234yf. Presented at the Third IIR Conference on Thermophysical Properties and Transfer Processes of Refrigerants, Boulder, CO, June 23-26, 2009. MCCCS Towhee Simulation Package. http://towhee.sourceforge.net Smith, W.; Forester, T. R. The DL_POLY Molecular Simulation Package. http://www.cse.clrc.ac.uk/msi/software/DL_POLY.
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Directive 2006/40/EC of the European Parliament and of the Council of 17 May 2006 relating to emissions from airconditioning systems in motor vehicles and amending Council Directive 70/156/EEC. Official Journal of the European Union, L161/12, 2006. Spatz, M.; Minor, B. HFO-1234yf, a Low GWP Refrigerant for MAC. Presented at the VDA Alternative Refrigerant Winter Meeting, Saalfelden, Austria, Febraury 13-14, 2008. Ikegami, T.; Aoki, K.; Lijima, K. New Refrigerant Evaluation results. Presented at the VDA Alternative Refrigerant Winter Meeting, Saalfelden, Austria, February 13-14, 2008.
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