Parameterization Approach for a Systematic Extension of the

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Parameterization Approach for a Systematic Extension of the Hydrofluoroolefin Force Field to Fluorinated Butenes and Hydrochlorofluoroolefin Compounds Gabriele Raabe* Institut für Thermodynamik, Technische Universität Braunschweig, Hans-Sommer-Straße 5, Braunschweig, 38106, Germany

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S Supporting Information *

ABSTRACT: We here present a correlation to estimate the required Lennard-Jones (LJ) parameters for the modeling of the fluorine atom type in our force field for hydrofluoroolefins (HFOs). This shall enable a consistent parametrization for HFO compounds with any number of bonded fluorine atoms. Additionally, we provide new LJ parameters for the chlorine atom type, optimized by fine-tuning agreement with recent experimental data for the hydrochlorofluoroolefins (HCFOs) trans-1-chloro-3,3,3-trifluoropropene (HCFO-1233zd(E)) and 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf). Both the introduced correlation and the reoptimized chlorine parameter shall form the basis for a systematic extension of the HFO force fieldoriginally developed for fluorinated propenesto fluorinated butenes and HCFO compounds. The parametrization approach is tested by Gibbs Ensemble Monte Carlo simulations on the vapor−liquid equilibria of 3,3,3-trifluoro-1-propene (HFO-1243zf), cis- and trans-1,1,1,4,4,4-hexafluorobutene (HFO-1336mzz(Z/E)), HCFO-1233zd(E), HCFO-1233xf, and cis1-chloro-2,3,3,3-tetrafluoropropene (HCFO-1224yd(Z)). We here provide simulation results for the vapor pressures, saturated densities, and heats of vaporization of these compounds, as well as estimates for their critical properties and normal boiling points in comparison with reference data.

1. INTRODUCTION Along with the introduction of propene-based hydrofluoroolefins (HFO) such as 2,3,3,3-tetrafluoro-1-propene (HFO1234yf) or 1,3,3,3-tetrafluoro-1-propene (HFO-1234ze(E/Z)) as fourth generation of refrigerants with low global warming potential (GWP), HFO compounds based on fluorinated butenes as well as hydrochlorofluoroolefins (HCFO) are discussed also as alternative “low-GWP” working fluids for different applications. cis-1,1,1,4,4,4-Hexafluoro-2-butene HFO-1336mzz(Z) for instance was introduced as a working fluid for high temperature heat pumps (HTHP) and Organic Rankine Cycles.1 In recent patents2−4 further fluorinated butenes such as 2,3,3,4,4,4-hexafluoro-1-butene (HFO1336yf), 1,3,3,4,4,4-hexafluoro-1-butene (HFO-1336ze), or 2,4,4,4-tetrafluoro-1-butene (HFO-1354mfy) were launched as new working fluids, for instance as heat transfer fluids in mixtures with other HFO compounds or HFC (hydrofluorocarbon) refrigerants. The HCFO compound trans-1chloro-3,3,3-trifluoropropene HCFO-1233zd(E) is mainly discussed as a refrigerant for chiller applications.5 AGC Asahi Glass6 introduced the cis-chloro-2,3,3,3-tetrafluoropropene HCFO-1224yd(Z) as displacement for 1,1,1,3,3-pentafluoropropane R-245fa (GWP = 8823]), and also the 2-chloro3,3,3-trifluoropropene HCFO-1233xf is already being studied as a working fluid.7 © XXXX American Chemical Society

As for all newly proposed HFO/HCFO compounds, one faces the problem that experimental data for the thermophysical properties of these fluorinated butenes and HCFOs are rare, though this information is required to evaluate their performance in potential technical applications. In our earlier work,8,9 we introduced a transferable force field for HFO compounds based on fluoropropenes that allows for a reliable prediction/reproduction of their thermophysical properties. The molecular model was already applied for simulation studies on the fluorinated butenes cis- and transHFO-1336mzz.10 However, we have observed in our earlier studies9 that the transferability of the Lennard-Jones (LJ) parameters for the fluorine atom types used in the HFO force field depends on the number of fluorine atoms in the molecule. Whereas the original parametrization of the fluorine atoms yielded good results for the tetrafluoro- compounds, we needed to derive modified parameters for one of the fluorine atom types for the “heavier” HFO-compounds cis-1,2,3,3,3pentafluoropropene (HFO-1225ye(Z)) and 1,1,2,3,3,3-hexaSpecial Issue: Hans Hasse Received: June 21, 2019 Accepted: July 30, 2019

A

DOI: 10.1021/acs.jced.9b00588 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

fluoropropene (HFO-1216) with five and six fluorine atoms, respectively. This modified parameter was then also used for modeling HFO-1336mzz,10 which also contains six fluorine atoms, though the LJ ε value was thereby assigned to a different fluorine atom type. This procedure has been admittedly somehow arbitrary and raises the question how the fluorine parameters shall be assigned to further fluorinated butene compounds with varying numbers of the different fluorine atom types. Another unsolved problem regarding the transferability of the LJ parameters of the HFO force field is the modeling of 3,3,3-trifluoro-1-propene (HFO-1243zf). For this compound we needed to introduce a new hydrogen atom type to achieve a good agreement between molecular simulation results and experimental data for the vapor pressure.8 Unfortunately, more recent experimental data11 show that the force field yields too high saturated liquid densities; thus, a revision of the force field modeling for this compound is also desirable. Therefore, one aim of this work is to derive a consistent parametrization that enables studies on HFO compounds with any number of bonded fluorine atoms. This shall form the basis for a systematic extension of the HFO force field to fluorinated butenes and also HCFO compounds. The HFO force field was also already extended to the HCFO compounds cis- and trans-1-chloro-3,3,3-trifluoropropene (HCFO-1233zd(E/Z)).10 Thereby the Lennard-Jones parameters for the chlorine atom type Cl were derived from fine-tuning the agreement with the then available vapor−liquid equilibria (VLE) data for this compound.12 When we now tested the HCFO force field for the compound 2-chloro-3,3,3trifluoropropene (HCFO-1233xf), an isomer of HCFO1233zd(E/Z), we found that the force field describes HCFO-1233xf as having too high a boiling point. A further objective of this work is therefore the reoptimization of the LJ parameters for the chlorine atom type, based on a larger data set, that is, new experimental data for both HCFO-1233zd(E)13−15 and HCFO-1233xf.15,16 The new parametrization of the HFO/HCFO force field is then tested by predictive simulation studies on the vapor−liquid equilibria of cis-1chloro-2,3,3,3-tetrafluoropropene HCFO-1224yd(Z).

Figure 1. Structures of the compounds studied in this work: 3,3,3trifluoro-1-propene (HFO-1243zf), cis- and trans-1,1,1,4,4,4-hexafluorobutene (HFO-1336mzz(Z/E)), trans-1-chloro-3,3,3-trifluoropropene (HCFO-1233zd(E)), 2-chloro-3,3,3-trifluoropropene (HCFO-1233xf), and cis-1-chloro-2,3,3,3-tetrafluoropropene (HCFO-1224yd(Z)). Also given is the nomenclature for the different Lennard-Jones atom types, that is, CT and CM for the single and double bonded carbon, HC for the hydrogen bonded to a carbon with no electron-withdrawing substituents, H1 for a hydrogen bonded to the same carbon as one fluorine or chlorine atom, F for the generalized fluorine atom type and Cl for the chlorine. For HCFO1233xf and -1224yd(Z) also the numbering of the atoms is provided to assign the partial charges according to Table 2.

derived for all compounds individually from ab initio simulations, the Lennard-Jones (LJ) parameters for the defined atom types of the force field are transferable and were adjusted to reproduce experimental data of selected HFO compounds. The intramolecular potential energy due to changes in the molecular geometry is calculated based on harmonic terms for bond stretching and angle bending, a cosine term for rotations of the dihedral angles, and by nonbonded interactions (LJ and electrostatic) between atoms separated by more than three bonds. Nonbonded LJ and electrostatic interactions between atoms in the same molecule separated by exactly three bonds (1−4 interactions) are scaled by a factor of 1/2 and 1/1.2, respectively. The equilibrium bond lengths, bond angles and dihedral angles as well as the associated force constants of the intramolecular potential terms in eq 1 were also derived from ab initio simulations, though they were determined in such a way that they are transferable between different HFO/HCFO compounds as well. A summary of the force field parameters of the HFO/HCFO model is given in ref 17. Simulation studies on HCFO-1233xf requires the parametrization of the CT−CM−Cl angle bending term and of the Cl−CM−CT−F torsion term, as these angles are not present in the compounds covered by the force field up to now. As described in detail in ref 17, parameters for intramolecular potential terms are derived by ab initio simulations on the BYLYP18,19/DGDZVP20 level of theory using Gaussian.21 Initially, the nominal bond angle and phase angle of the dihedral were determined from the energy minimized structure, then the force constants were derived by scanning the degree of freedom in small intervals. The resulting parameters for these intramolecular terms are given in Table 1, the ab initio results are provided in the Supporting Information. For the simulation studies of the HCFO compounds 1233xf and 1224yd(Z), also partial charges need to be determined. In the parametrization protocol of the HFO/HCFO force field this is done by performing ab initio simulations on isolated molecules at the HF/6-31G* level of theory, again using

2. COMPUTATIONAL METHODS Molecular Modeling. Force Field Model. The structures of the HFO/HCFO working fluids covered in this work are shown in Figure 1, together with the nomenclature for the different Lennard-Jones atom types used for their modeling. The functional form of the HFO force field is given by Uconf =

∑

kr(r − r0)2 +

bonds

+

∑

∑

kθ(θ − θ0)2

angles

kχ [1 + cos(nχ − δ)]

ÄÅ É | l ÅÅi y12 i y6ÑÑÑ o qiqj o o o Å ÑÑ σ σ o o j z j z 1 ij ij Å o o j z j z Å Ñ j z j z Å Ñ + ∑∑m ε − + 4 } j z j z Ñ ijÅ o o j z j z Å Ñ o o j z j z Å Ñ πε r r r 4 o ij { Ñ 0 ij o Åk ij { i j>1 o o k Å Ñ ÑÖ n ÅÇ ~ dihedral

(1)

A detailed description of the molecular model and its parametrization is given in our previous work;8,17 thus, only a short summary is provided here. The calculation of intermolecular (nonbonded) interactions is based on site− site terms with Lennard-Jones centers and fixed partial charges on the atomic sites. Whereas the partial charges are always B



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Correlation for the LJ Parameters of the Flourine Atom Type. The HFO force field generally distinguishes between two different fluorine atom types, that is, the FCM atom type for the fluorine bonded to the sp2 CM carbon, and FCT for the fluorine in the CF3 group, bonded to the sp3 CT carbon atom type. Both fluorine atom types are described by the same value for the ε parameter (0.23617 kJ mol−1) but different σ parameters (2.9 and 2.94 Å, respectively). For the modeling of the heavier fluoropropene compounds HFO-1216 and -1225ye(Z) we derived modified values for the ε and σ parameter of the FCM atom type (0.2184 kJ mol−1,2.92 Å),9 and this ε value was also assigned to the FCT atom type in the modeling of HFO-1336mzz(E/Z).10 To derive a correlation for the fluorine LJ parameters, we omit this differentiation of different fluorine atom types and only use the generalized type F. We have then determined the average values for the fluorine ε and σ parameters used so far in the successful modeling of the different HFO/HCFO compounds HFO-1243zf, 1234yf, -1234ze(E), -1234ze(Z), -1216, -1225ye(Z), -1336mzz(E/Z), and HCFO-1233zd(E/Z)). From this, it can be observed that the required ε value decreases with increasing molar mass M of the HFO/HCFO compound. We also intend to model all hydrogen atoms in HFO-1243zf by the HC (σHC = 2.65 Å) atom type, that is, to omit the use of the HC1 atom type (σHC = 1.85 Å) that we especially introduced for this compound in the early stage of the force field development.8 Therefore, a higher ε value for the fluorine atoms in HFO-1243zf is then required to reproduce both experimental vapor pressure and liquid densities. Taking this into account, the function εF =

Table 1. Additionally Required Force Field Parameters for HCFO-1233xf angle

kθ (kJ mol−1 rad−2)

CT−CM−Cl dihedral

376.2 kχ

n

δ (deg)

2.094

3

0

Cl−CM−CT−F

θ0 (deg) 113.8

Gaussian. The partial charges are therein derived by the ESP approach with the CHELPG fitting scheme.22 The partial charges of HCFO-1233xf and -1224yd(Z) are summarized in Table 2. For HCFO-1233zd(E) as well as for the HFO compounds studied here, the partial charges are the same as in our earlier work.8,10 Table 2. Partial Charges of the HCFO Compounds Studied in This Work HCFO-1233xf

HCFO-1224yd(Z)

no.

type

q (e)

type

q (e)

1 2 3 4 5 6 7 8 9

CM CM CT HC HC Cl F F F

−0.20911 −0.07335 0.71582 0.16136 0.16136 −0.07658 −0.22650 −0.22650 −0.22650

CM CM CT H1 Cl F F F F

−0.15595 0.19698 0.54568 0.18643 −0.04479 −0.15997 −0.18946 −0.18946 −0.18946

Table 3. Revised GEMC Simulation Results for the Vapor Pressure p, Saturated Liquid Density ρL and Saturated Vapor Density ρV and Heats of Vaporization ΔHvap of HFO-1243zf, HFO-1336mzz(Z), and HFO-1336mzz(E) Using Fluorine LJ Parameters Derived from the Correlation Given by eq 2 T

p

u(p)

ρL

u(ρL) −3

K

MPa

MPa

kg m

283.15 303.15 313.15 333.15 343.15 353.15

0.368 0.664 0.908 1.536 1.894 2.245

0.018 0.025 0.037 0.067 0.037 0.048

1025.5 963.2 931.2 857.2 803.2 721.4

313.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15

0.125 0.235 0.374 0.440 0.576 0.718 0.911 1.1610 1.420

0.006 0.010 0.018 0.017 0.017 0.046 0.014 0.024 0.048

1332.2 1267.7 1242.82 1202.9 1169.9 1125.1 1086.8 1045.0 992.2

303.15 313.15 323.15 333.15 343.15 353.15 363.15

0.219 0.300 0.400 0.574 0.736 0.937 1.252

0.010 0.013 0.019 0.017 0.026 0.019 0.024

1308.1 1273.4 1234.5 1200.2 1152.5 1109.4 1064.5

kg m

−3

HFO-1243zf 2.7 2.0 3.4 1.9 2.8 7.4 HFO-1336mzz(Z) 2.1 2.4 3.5 3.0 2.7 4.0 3.2 4.3 8.6 HFO-1336mzz(E) 3.1 2.1 3.9 3.2 4.4 3.4 4.0 C

ρV

u(ρV) −3

kg m

kg m

−3

ΔHvap −1

kJ mol

u(ΔHvap) kJ mol−1

16.9 30.3 42.2 75.7 96.8 118.0

0.9 1.6 2.3 2.3 3.5 6.3

19.76 17.95 16.87 14.25 12.80 11.01

0.07 0.10 0.06 0.15 0.12 0.22

8.1 15.3 24.9 28.4 37.6 46.9 60.9 78.8 102.2

0.3 0.8 1.4 1.3 1.3 1.2 1.5 2.1 5.4

28.12 26.25 25.13 24.13 22.88 21.61 20.34 18.96 17.01

0.05 0.11 0.07 0.06 0.09 0.09 0.06 0.11 0.11

15.4 20.8 27.7 39.8 51.7 66.1 92.8

0.8 1.0 1.5 1.3 2.2 1.8 2.9

25.04 24.17 22.90 21.72 20.41 19.09 17.35

0.08 0.08 0.07 0.06 0.08 0.10 0.07



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f(M) for all compounds can be described by an exponential decay according to εF/kJ mol−1 = 0.21751 + 0.50204 e−M /35.02266

(2)

−1

where M is the molar mass in g mol . For the σ value, the optimal averaged values are σF = 2.93 Å for HFO/HCFO based on propenes σF = 2.92 Å for HFO/HCFO based on butenes

To test the applicability of the correlation, we only consider the compounds HFO-1243zf and HFO-1336mzz(E/Z), for which the transferability of the fluorine parameters did not work or has been somehow arbitrary. For these compounds, the correlation yields HFO‐1243zf (M = 96.051 g mol−1): εF = 0.24984 kJ mol−1, σF = 2.93 Å HFO‐1336mzz(Z/E)(M = 164.06 g mol−1): εF = 0.22215 kJ mol−1, σF = 2.92 Å

For the compounds HFO-1234yf, -1234ze(E), -1234ze(Z), -1216, and -1225yd(Z), for which the force field was already successfully employed, the force field parameters shall remain unchanged. Thus, it is not the goal of this work to change the parametrization of the force field in general, but to provide an approach to enable its application for larger HFO compounds based on butenes with a higher number of bonded fluorine atoms, as well as for the systematic extension of the molecular model to HCFO compounds. Optimization of the LJ Parameters of the Chlorine Atom Type. The new chlorine LJ parameters are established by finetuning agreement with experimental VLE data for the HCFO compounds 1233zd(E)13−15 and 1233xf,15,16 which comprise the same number of fluorine atoms, that is, have the same molar mass of M = 130.5 g mol−1. According to the correlation introduced in the previous section, we use the following fluorine parameters

Figure 2. Gibbs ensemble (GEMC) simulation results for the vapor pressure (upper diagram) and VLCC (bottom diagram) of HFO1243zf (crossed triangles, gray and green); HFO-1336mzz(E) (crossed circles, blue and gray); and HFO-1336mzz(Z) (crossed squares, red and gray) in comparison with calculations using REFPROP23 for HFO-1243zf (green line) and HFO-1336mzz(Z) (red line) and experimental data for HFO-1336mzz(E) by Tanaka et al.31,32 Colored symbols represent simulation results obtained in this work by employing the correlation proposed in eq 2, the gray symbols show simulation results from our previous work8−10 using the original parametrization.

HCFO‐1233zd(E)/ −1233xf: εF = 0.22960 kJ mol−1, σF = 2.93Å

For the optimization of Lennard-Jones parameters εCl and σCl, we employed the robust Nelder−Mead23 algorithm and use an objective function that considers normalized root-meansquare deviations for vapor pressures and saturated densities. This optimization yields εCl = 1.09086 kJ mol−1,

HCFO compounds to establish and validate the optimized chlorine LJ parameters. The cutoff radius for the LennardJones interactions was set to 12 Å, and standard long-range corrections to the energy and pressure were applied.17,26 The cutoff radius for the electrostatic interactions was adjusted to half the box length, and the Ewald sum technique26,27 was employed. The simulations were equilibrated for 200 000 cycles, and the production runs consisted of 400 000 cycles. Each cycle comprised N attempted moves, that is, (0.2−0.5)% volume moves, (29.5−49.5)% interbox molecular transfer moves (rotational-bias and configurational-bias), and (50−65)% intrabox moves (molecule regrowth, translation of, and rotation around, the center-of-mass). The ratios of the different moves were manually adjusted, depending on the system and state point studied, to ensure that the equilibrium conditions are satisfied. Equilibration was monitored by verifying that the

σCl = 3.525Å

These new optimized chlorine parameters are then validated by predictive simulation studies on HCFO-1224yd(Z). For this compound with a molar mass of M = 148.48 g mol−1, eq 2 gives HCFO‐1224yd(Z):

εF = 0.22475 kJ mol−1, σF = 2.93 Å

Simulation Details. Vapor−liquid equilibria of the pure compounds were calculated via Monte Carlo Gibbs ensemble24 (GEMC) simulations in the NVT-ensemble using the simulation code TOWHEE.25 The systems consisted of N = 256 molecules for the HFO compounds to test the correlation for the fluorine LJ parameters, and N = 432 molecules for the D



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Table 4. Revised Estimated Critical Properties and Normal Boiling Points of the HFO Compounds Studied in this Work Using the Modified Fluorine LJ Parameters from the Correlation Given in Eq 2 in Comparison with Experimental Data where Availablea Tc, sim HFO-1243zf HFO1336mzz(Z) HFO1336mzz(E)

u(Tc, sim)

K

K

372.2 375.5 440.4 438 405.1 401.6

3.1 4.5 7.1 6.7 6.0 5.6

Tc,exp

ρc.sim

K

kg m

376.93b 444.42d−444.5e 403.37f

ρc.exp

u(ρc.sim)

−3

416.3 421.9 497.3 491.3 515.6 513

−3

−3

pc,sim

u(pc,sim)

kg m

kg m

MPa

MPa

8.5 39.6 19.8 20.0 18.4 17.0

414.26c

3.42 3.56 2.89 2.7 3.07 2.92

1.1 1.1 0.49 0.56 0.77 0.64

471d−507e 515.3f

pc, exp

Tb,sim

MPa 3.517b 2.895e−2.901d 2.7664f

u(Tb,sim) Tb,exp

K

K

247.9 250.1 306.8 305.5 282.9 278.8

9.6 4.3 4.0 5.7 6.7 6.3

K 247.7c 306.6

a

Given in italics are results by the original parameterization8,10. bHigashi et al.11 cRyo Akasaka29 dTakana et al.33 eTanaka et al.34 fTanaka et al.32

Table 5. GEMC Simulation Results for the Vapor Pressure p, Saturated Liquid Density ρL and Saturated Vapor Density ρV and Heats of Vaporization ΔHvap of the Chlorinated Compounds HCFO-1233zd(E) and HCFO-1233xf with New Cl Parameters T

p

ρL

u(p)

−3

K

MPa

MPa

kg m

273.15 298.15 303.15 323.15 353.15 373.15 383.15

0.0478 0.139 0.155 0.313 0.723 1.138 1.359

0.003 0.003 0.005 0.004 0.006 0.010 0.004

1328.9 1269.1 1253.7 1202.8 1113.7 1046.4 992.4

300.0 320.0 340.0 350.0 360.0 370.0 380.0 390.0 400

0.143 0.272 0.489 0.635 0.813 1.037 1.292 1.580 1.949

0.003 0.003 0.007 0.008 0.006 0.014 0.015 0.018 0.019

1243.9 1191.0 1136.6 1105.7 1074.0 1041.1 1007.4 965.2 923.4

kg m

with

τ=1−

T Tc

u(ρV) −3

kg m

−3

ΔHvap −1

u(ΔHvap) kJ mol−1

kg m

kJ mol

2.8 7.7 8.4 16.6 37.8 60.4 72.2

0.2 0.2 0.3 0.3 0.4 0.8 0.4

27.85 26.05 25.66 24.14 21.34 19.17 17.74

0.02 0.02 0.03 0.02 0.02 0.05 0.04

7.9 14.5 25.9 33.5 42.9 55.4 70.6 87.9 113.4

0.2 0.2 0.5 0.5 0.4 1.0 1.2 1.5 2.0

25.32 23.83 22.14 21.25 20.25 19.15 17.97 16.63 15.13

0.04 0.03 0.03 0.02 0.02 0.02 0.03 0.03 0.06

3. RESULTS AND DISCUSSION Simulation Results for HFO-1243zf, -1336mzz(Z), and -1336mzz(E) Based on the New Correlation for Fluorine LJ Parameters. The GEMC simulation results for the compounds HFO-1243zf, -1336mzz(Z), and -1336mzz(E) employing the correlation from eq 2 to determine the LennardJones parameters of their fluorine atoms are summarized in Table 3. Figure 2 shows a comparison of the simulation results for the vapor pressure and vapor−liquid coexistence curve (VLCC) of the three HFO compounds with reference data. For the sake of clarity, no experimental data for HFO-1243zf and -1336mzz(Z) are used as reference in Figure 2, but only calculations by REFPROP28 employing accurate Helmholtz equations of state (EOS) for these compounds.29,30 For HFO1336mzz(E), for which no reference EOS is available yet, experimental data by Tanaka et al.31,32 are shown for comparison. Figure 2 well illustrates that the correlation for the fluorine LJ parameters provides quite similar results (colored symbols) as the original parametrization (shown by gray symbols). For HFO-1336mzz(E), the correlation yields an improved reproduction of the vapor pressures, whereas the saturated liquid densities now tend to overestimate the experimental data. For HFO-1336mzz(Z) though, the new LJ fluorine

(3)

and the law of rectilinear diameters ρL − ρ V = ρc + Bτ 2

−3

HCFO-1233zd(E) 1.2 0.7 1.0 0.9 1.4 2.1 1.8 HCFO-1233xf 1.0 0.8 1.1 1.2 1.1 1.7 1.8 2.1 2.3

simulated chemical potentials in both phases agreed within their error bars. Standard deviations of all ensemble averages for the vapor pressure, saturated densities, and heats of vaporization were determined by the standard block average technique.17,26 To estimate the critical properties of the different compounds, we employed the TOWHEE utility routine “fitcoex”. Therein, the simulation results at subcritical conditions are fitted to the scaling law26 ρ L − ρ V = Aτ β

ρV

u(ρL)

(4)

using an Ising exponent of β = 0.32. The routine also provides estimates of the normal boiling point and of the critical pressure by extrapolating the simulation results for the vapor pressure using the Clausius−Clapeyron equation. The stated errors of the critical properties and normal boiling point are those given by the fitcoex routine, and they take into account both the uncertainties of the simulated properties as input data, and the errors of the fitting procedure. E



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parameters from eq 2 result in a better description of the VLLC. The revised simulation results for the saturated liquid densities of HFO-1243zf are now in good agreement with the reference data, whereas the original parametrization based on the introduction of the HC1 atom type largely overestimated the experimental values. However, the new parametrization tends to produce too high vapor pressures. This results in lower estimates for the critical temperature and critical pressure as shown by the comparison of estimated critical data and normal boiling points of the HFO compounds with experimental data in Table 4. Though the new parametrization yields improved estimates for the critical density and normal boiling point of HFO-1234zf. For HFO- 1336mzz(Z), the new GEMC simulation results provide a better prediction of the critical temperature Tc, critical pressure pc, and normal boiling point Tb compared to the original parametrization. Reference data33,34 for the critical density ρc of HFO1336mzz(Z) vary largely, though the estimated value from the GEMC simulation falls well in the range of the reference data. For HFO1336mzz(E), the new correlation for the fluorine LJ parameters results in a higher value for Tc than the original parameter; it now also overestimated the experimental value by 0.4%. This also results in too high predictions for pc, whereas the estimate for the critical density of HFO-1336mzz(E) agrees very well with the experimental value. Simulations Results for HCFO Compounds Based on the New Optimized Chlorine LJ Parameter. Table 5 comprises GEMC simulation results for the HCFO compounds 1233zd(E) and 1233xf, which are based on fluorine LJ parameters determined by the correlation from eq 2 and new LJ parameters for the chlorine atom type, optimized to finetune agreement with experimental VLE data for these compounds. The depiction of the simulation results for the vapor pressure and VLCC in comparison with calculations by REFPROP based on reference EOS35,36 in Figure 3 illustrates that the new parametrization allows for an equally good description of the VLE properties of both HCFO compounds. Whereas a tendency to underestimate the vapor pressure data of HCFO-1233xf at lower temperatures can be observed, the revised simulation results tend to yield too high vapor pressures for HCFO-1233zd(E) with increasing temperatures. The simulation results for the VLCC of both compounds show good agreement with the reference data, and also very similar results for HCFO-1233zd(E) obtained by the new and original parametrization. The new chlorine parameters were then validated by predictive GEMC simulation studies on HCFO-1224yd(Z). The simulation results for the VLE are given in Table 6. As this compound comprises one more bonded fluorine atom than HCFO-1233, this simulation study also tests the applicability of the correlation for the fluorine LJ parameters. Figure 4 attests the good agreement of the simulation results for the vapor pressure and the saturated densities with calculations using the reference EOS by Akasaka et al.37 In Table 7 we compare estimates for the critical properties and the normal boiling point of the HCFO compounds with experimental or other reference data. The new parametrization yields a lower Tc for HCFO-1233zd(E) compared to the description by the original parameters, but improved estimates for both, the critical pressure and density. For HCFO-1233xf, the estimates for the critical temperature and density agree very well with the reference data within the range of their uncertainties, whereas the critical pressure pc as well as the

Figure 3. Gibbs ensemble (GEMC) simulation results for the vapor pressure (upper diagram) and VLCC (bottom diagram) for the HCFO compounds 1233zd(E) (crossed diamond, blue and gray) and 1233xf (crossed triangle, purple) in comparison with calculations using REFPROP23 shown as solid lines in the corresponding colors. For HCFO-1233zd(E), the colored symbols represent simulation results obtained in this work by employing the correlation proposed in eq 2 and the optimized chlorine LJ parameter, the gray symbols show simulation results from our previous work10 using the original parametrization.

normal boiling point are overestimated, though there are some uncertainties regarding the reference data for the critical pressure of HFO-1233xf as the value determined by the preliminary equation of state36 differs significantly from the estimate by Zhang et al.16 For HCFO-1224yd(Z) the predicted critical temperature and normal boiling point overestimate the reference data by about 3 K, whereas the estimated critical density is by ≈3% too low. However, these are encouraging results in light of the fact that the simulation studies for this compound are purely predictive.

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CONCLUSION We have introduced a correlation to determine the LJ parameters of the fluorine atom type of HFO compounds with varying number of bonded fluorine atoms. We thereby omit distinguishing between the FCT and FCM atom type as in our previous work, and only use a generalized atom type F. F



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Table 6. Predictive GEMC Simulation Results for the Vapor Pressure p, Saturated Liquid Density ρL, and Saturated Vapor Density ρV, and Heats of Vaporization ΔHvap of HCFO-1224yd(Z) T

p

ρL

u(p)

ρV

u(ρL) −3

K

MPa

MPa

kg m

300.0 320.0 340.0 350.0 360.0 370.0 380.0 390.0 400.0

0.144 0.290 0.503 0.645 0.844 1.058 1.330 1.620 1.987

0.002 0.007 0.005 0.008 0.007 0.007 0.016 0.011 0.014

1364.6 1307.8 1243.3 1209.2 1176.3 1137.1 1093.7 1047.9 998.7

kg m

−3

−3

kg m

HCFO-1224yd(Z) 0.7 1.5 0.9 1.3 1.5 1.3 2.4 1.8 2.5

ΔHvap

u(ρV) −3

9.0 17.7 30.0 38.4 50.8 64.6 82.3 103.0 131.8

u(ΔHvap)

−1

kg m

kJ mol

0.2 0.4 0.3 1.0 0.6 0.6 1.4 1.1 2.0

25.59 23.95 22.30 21.37 20.31 19.14 17.84 16.48 14.89

kJ mol−1 0.04 0.10 0.03 0.02 0.03 0.02 0.02 0.03 0.04

Figure 4. Purely predictive Gibbs ensemble (GEMC) simulation results for the vapor pressure (left diagram) and VLCC (right diagram) of HCFO-1244yd(Z) obtained in this work in comparison with calculations (line) using REFPROP23 based on the reference EOS by Akasaka et al.37

Table 7. Estimated Critical Properties and Normal Boiling Points of the HCFO Compounds Studied in This Work in Comparison with Experimental Data where Availablea Tc, sim HCFO-1233zd(E) HCFO-1233xf HCFO-1224yd(Z)

u(Tc, sim)

Tc,exp

K

K

K

436.8 440.8 438.3 431.3

1.7 1.9 2.8 1.7

438.7b−439.6c 439.98d 428.7f−429.2g

ρc.sim kg m

−3

477.8 475.6 472.0 516.0

ρc.exp

u(ρc.sim) kg m

−3

kg m

−3

480.2c

4.0 4.0 6.0 5.0

476.0e 530g−535f

pc,sim

u(pc,sim)

pc, exp

MPa

MPa

MPa

K

K

K

3.62 3.90 3.86 3.61

0.6 0.43 0.21 0.21

3.624c−3.772b

288.4 290.9 290.6 290.8

5.9 3.5 1.0 1.6

291.4c

3.32d−3.62g 3.32f−3.38g

Tb,sim

u(Tb,sim)

Tb,exp

285.69e 287.6f

a

For HCFO-1233zd(E) also results10 from the original parameterization are given in italics. bHulse et al.12 cMondejar et al.14 dZhang et al.,16 estimated from experimental vapor pressure data. eRyo Akasaka36 fAkaska et al.37 gFukushima et al.38

We have tested the correlation by determining fluorine parameters for the HFO compounds -1243zf, -1336mzz(E), and -1336mzz(Z), for which the transferability of the fluorine parameters did not work or has been somehow arbitrary in our previous work. We performed GEMC simulations for these compounds and found generally good agreement between the simulation results for the VLE properties based on this correlation and the original parametrization. To some extent the correlation even yields an improved reproduction of reference data. By employing this correlation, we are able to forego the use of the atom type HC1, specially introduced for HFO-1243zf. Thus, the presented correlation for fluorine LJ parameters enables a consistent modeling of all HFO

compounds independent of the number of bonded fluorine atoms. Furthermore we have reoptimized the Lennard-Jones parameter for the chlorine atom type by fine-tuning agreement with recent experimental VLE data for HCFO-1233zd(E) and -1233xf. The parametrization of the bonded fluorine atoms in these compounds was thereby based on the correlation introduced in this work. The new parametrizationwith regard to both the fluorine and chlorine atom typewas then tested by predictive simulation studies on the HCFO compound 1224yd(Z), which contains one bonded fluorine more than HCFO-1233zd(E) and -1233xf. The good reproduction of the reference VLE data of this compound by G



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of hydrofluoroolefins, Hydrochlorofluoro-olefins, and their blends. HVACR Res. 2014, 20, 2203−220. (8) Raabe, G.; Maginn, E. J. Molecular modeling of the vapor-liquid equilibrium properties of the alternative refrigerant 2,3,3,3-tetrafluoro1-propene HFO-1234yf. J. Phys. Chem. Lett. 2010, 1, 93−96. (9) Raabe, G. Molecular Modeling of Fluoropropene Refrigerants. J. Phys. Chem. B 2012, 116, 5744−5751. (10) Raabe, G. Molecular Simulation Studies on the Vapor-LiquidEquilibria of the cis- and trans-HCFO-1233zd, and the cis- and transHFO-1336mzz. J. Chem. Eng. Data 2015, 60 (8), 2412−2419. (11) Higashi, Y.; Shirai, C.; Akasaka, R. Measurement of pρT properties, vapor pressures, saturated densities, and critical parameters for R1243zf. Proceedings of the 19th Symposium on Thermophysical Properties, NIST: Boulder, CO, USA, 2015. (12) Hulse, R. J.; Basu, R. S.; Singh, R. R.; Thomas, R. H. P. Physical properties of HCFO-1233zd(E). J. Chem. Eng. Data 2012, 57, 3581− 3586. (13) Di Nicola, G.; Fedele, L.; Brown, J. S.; et al. Saturated Pressure Measurement of trans-1-Chloro-3,3,3-trifluoroprop-1-ene (R1233zd(E)). J. Chem. Eng. Data 2017, 62, 2496−2500. (14) Mondejar, M. E.; McLinden, M. O.; Lemmon, E. W. Thermodynamic Properties of Trans-1-chloro-3,3,3-trifluoropropene (R1233zd(E)): Vapor Pressure, p-rho-T Data, Speed of Sound Measurements and Equation of State. J. Chem. Eng. Data 2015, 60, 2477−2489. (15) Tanaka, K. Vapor Pressure and Saturated Liquid Density of HCFO-1233zd(E) and HCFO-1233xf. Trans JSRAE 2016, 33, 105− 111. (16) Zhang, W.; Yang, Z.; Lu, J.; Lu, J. Vapor Pressure of 2-Chloro3,3,3-Trifluoropropene (HCFO-1233xf)). J. Chem. Eng. Data 2013, 58, 2307−2310. (17) Raabe, G. Molecular Simulation Studies on Thermophysical Properties - with Application to Working Fluids; Springer Series on Molecular Modeling and Simulation: Applications and Perspectives Springer, 2017. (18) Becke, A. D. Density-functional thermochemistry.III. The role of exact exchange. J. Chem. Phys. 1993, 98, 5648−5652. (19) Lee, D.; Yang, W.; Parr, R. G. Development of the ColleSalvetti correlation-energy formula into a functional of the electron density. Phys. Rev. B: Condens. Matter Mater. Phys. 1988, 37, 785−789. (20) Godbout, N.; Salahub, D. R.; Andzelm, J.; Wimmer, E. Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I, Boron through neon, optimization technique and validation. Can. J. Chem. 1992, 70, 560−571. (21) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A., Jr.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Salvador, P.; Dannenberg, J. J.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; AlLaham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. et al. Gaussian 98, revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998. (22) Breneman, C. M.; Wiberg, K. B. Determining Atom-Centered Monopoles from Molecular Electrostatic Potentials. The Need for High Sampling Density in Formamide Conformational Analysis. J. Comput. Chem. 1990, 11, 361−373. (23) Nelder, J. A.; Mead, R. A Simplex Method for Function Minimization. Comput. J. 1965, 7, 308−313. (24) Panagiotopoulos, A. Z. Direct determination of phase coexistence properties of fluids by Monte Carlo simulation in a new ensemble. Mol. Phys. 1987, 61, 813−826. (25) Martin, M. G. MCCCS Towhee: a tool for Monte Carlo molecular simulation. Mol. Simul. 2013, 39, 1212−1222 MCCCS

the molecular simulation results demonstrates the applicability of the correlation for the fluorine LJ parameters also for HCFO compounds. With this, we are able to provide an approach that enables the extension of the HFO force field to butene-based HFO compounds with varying number of bonded fluorine atoms, as well as to HCFO compounds.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.9b00588. Results from ab initio simulations for scanning the CT− CM−Cl bending angle and the Cl−CM−CT−F dihedral angle in HCFO-1233xf, together with a depiction of the torsion profile (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel.: +49 531 391 2628. E-mail: [email protected]. ORCID

Gabriele Raabe: 0000-0003-2758-9460 Funding

This research was funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - RA946/3−1 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author would like to thank Andreas Mecklenfeld of her group at TU Braunschweig for providing the Nelder−Mead algorithm for the optimization of the LJ parameters for the chlorine atom type Cl. All simulations were performed on the HPC compute server Phoenix of the TU Braunschweig.

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DEDICATION When I changed my field of research from experimental studies to molecular simulation, the work of Hans Hasse, linking successfully molecular simulations and technical applications, became a great inspiration to me. Later I had the privilege that Hans accepted to be one of the reviewers in my habilitation procedure. I would like to thank Hans Hasse for his role in my development. Happy Birthday Hans, and I wish you many more years of productive scholarship, health, and happiness.

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REFERENCES

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Towhee: (accessed July 2017 to downlaod version 7.2.0) http:// Towhee.sourceforge.net . (26) Frenkel, D.; Smit, B. Understanding Molecular Simulation; Academic Press, 1996. (27) Ewald, P. P. Die Berechnung optischer und elektrostatischer Gitterpotentiale. Ann. Phys. 1921, 369, 253. (28) Lemmon, E. W.; Huber, M. L.; McLinden, M. O. REFPROP, Reference Fluid Thermodynamic and Transport Properties. NIST Standard Reference Database 23, version 10.0; NIST, 2019. (29) Akasaka, R. Recent trends in the development of Helmholtz energy equations of state and their application to 3,3,3-trifluoropro-1ene (R-1243zf). STBE 2016, 22, 1136−1144. (30) Akasaka, R.; Lemmon, E. W.; A Helmholtz energy equation of state for cis-1,1,1,4,4,4-hexafluoro-2-butene (R-1336mzz(Z)); ACRA 2016 - 8th Asian Conference on Refrigeration and Air-Conditioning, Taipei, Taiwan, 2016. (31) Tanaka, K.; Ishikawa, J.; Kontomaris, K. K. p T Property of HFO-1336mzz(E) (trans-1,1,1,4,4,4-Hexafluoro-2-butene). J. Chem. Eng. Data 2017, 62, 2450−2453. (32) Tanaka, K.; Ishikawa, J.; Kontomaris, K. K. Thermodynamic properties of HFO-1336mzz(E) (trans-1,1,1,4,4,4-hexafluoro-2-butene) at saturation conditions. Int. J. Refrig. 2017, 82, 283−287. (33) Tanaka, K.; Akasaka, R.; Sakaue, E.; Ishikawa, J.; Kontomaris, K. K. Thermodynamic Properties of cis-1,1,1,4,4,4-Hexafluoro-2butene (HFO-1336mzz(Z)): Measurement of the pρT Property and Determinations of Vapor Pressure, Saturated Liquid and Vapor Densities, and Critical Parameters. J. Chem. Eng. Data 2016, 61, 2467−2473. (34) Tanaka, K.; Akasaka, R.; Sakaue, E.; Ishikawa, J.; Kontomaris, K. K. Measurement of the Critical Parameters for cis-1,1,1,4,4,4Hexafluoro-2-butene. J. Chem. Eng. Data 2017, 62, 1135−1138. (35) Akasaka, R.; Fukushima, M.; Lemmon, E. W. A Helmholtz Energy Equation of State for cis-1-chloro-2,3,3,3-tetraflouropropene. 21st European Conference on Thermophysical Properties, Graz, Austria, 2017. (36) Akasaka, R. A preliminary Equation of State for HCFO-1233xf, Personal communication, 2016. (37) Akasaka, R.; Fukushima, M.; Lemmon, E. W. A Helmholtz Energy Equation of State for R-1224yd(Z). 21st European Conference on Thermophysical Properties, Graz, Austria, 2017. (38) Fukushima, M.; Hayamizu, H.; Hashimoto, M.; Thermodynamik Properties of Low-GWO Refrigerant for Centrifugal Chiller. International Refrigeration and Air Conditioning Conference; Perdue, USA, 2016.

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Parameterization Approach for a Systematic Extension of the

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