Molecular Dynamics Studies on Liquid-Phase Dynamics and

Article pubs.acs.org/JPCB

Molecular Dynamics Studies on Liquid-Phase Dynamics and Structures of Four Different Fluoropropenes and Their Binary Mixtures with R‑32 and CO2 Gabriele Raabe* Institut für Thermodynamik, Technische Universität Braunschweig, Hans-Sommer-Straße 5, 38106 Braunschweig, Germany ABSTRACT: Fluoropropenes such as R-1234yf or R-1234ze(E) have attracted attention as low GWP (global warming potential) refrigerants, both as pure compounds but also to an increasing extent as components in refrigerant blends. In our earlier work [Raabe, G.; Maginn, E. J. J. Phys. Chem. B 2010, 114, 10133−10142 and Raabe, G. J. Phys. Chem. B 2012, 116, 5744−5751], we have introduced a transferable force field for different fluoropropene compounds. This molecular model has already been applied for predictive molecular simulation studies on the vapor− liquid phase equilibria in binary mixtures of the tetrafluoropropenes R-1234yf or R1234ze(E) with the difluoromethane R-32 and CO2. In this work we present molecular dynamics simulations on the liquid phase properties of the pure fluoropropenes R-1234yf, R-1234ze, R-1234ze(E), and R-1216 and their binary mixtures with CO2 and R-32. Our study covers temperatures from 273 to 313 K, pressures up to 3.5 MPa, and different mixture compositions. We provide predictions on the densities and transport properties of the pure compounds and the binary mixtures to complement experimental data. Additionally, we have analyzed radial and spatial distribution functions in the systems to gain insight into their microscopic structures and preferred interaction sites.

1. INTRODUCTION Hydrofluoroolefins (HFOs) such as 2,3,3,3-tetrafluoro-1propene (R-1234yf) and trans-1,3,3,3-tetrafluoro-1-propene (R-1234ze(E)) have been proposed as new class of refrigerants with low global warming potential (GWP).1 However, the fluoropropenes usually have smaller volumetric cooling capacities than conventional hydrofluorocarbon (HFC) refrigerants,2 and they are all, with the exception of hexafluoropropene, R-1216, flammable. Thus, blends of fluoropropenes with other refrigerants are considered as a practical choice to yield working fluids with reduced flammabilities and/or higher volumetric refrigerant capacities compared to the pure HFOs. Mixtures of R-1234yf or R-1234ze(E) with difluoromethane R32 for instance have been proposed as alternative refrigerant blends to replace R-410A in domestic heat pump or air conditioning systems.3,4 Mixtures of fluoropropenes with CO2 have recently attracted attention as a ternary mixture of CO2, the tetrafluoroethane R-134a and R-1234ze(E) (called R-445A) is discussed as alternative refrigerant for mobile air conditioning (MAC) systems.5 Mixtures of the tetrafluoropropenes R1234yf, cis- or trans-R-1234ze with CO2 are also proposed as blowing or foaming agents.6,7 Then again, the hexafluoropropene, R-1216, is an important intermediate in the fluorochemical industry. Thus, information on the thermophysical properties of CO2 + R-1216 mixtures is useful for the development of supercritical solvation processes with CO2 as stripping agent.8 The exploration of potential applications of mixtures of fluoropropenes with R-32 or CO2 requires a detailed © 2013 American Chemical Society

knowledge of their thermophysical properties, but respective experimental studies are rarely found in free literature. Experimental information is only available for the isochoric heat capacities of R-1234ze(E) + CO2 mixtures,9 the thermal conductivity of R-1234ze(E) + R-32,10 PVTx data in systems of the CO2 + R-1234yf,11 and saturated densities for R-1234yf + R-32.12 Experimental studies of vapor−liquid equilibria (VLE) only comprise mixtures of R-1234yf or R-1234ze(E) with R32,13,14 and R-1216 + CO2.8 Molecular simulations allow for predictions on thermophysical properties of possible mixtures to complement experimental data, provided that adequate molecular models for the pure compounds exist. In our earlier work,15−17 we have introduced a transferable force field for fluoropropenes comprising compounds such as R-1234yf, R-1216, and both the trans- and cis-1,3,3,3- tetrafluoro-1-propene, i.e. R1234ze(E) and R-1234ze. The force field model has already been applied in simulation studies on the VLE and liquid-phase properties of the pure compounds, and to yield predictions on the VLE of binary mixtures of R-1234yf and R-1234ze(E) with CO2 and R-3218 and for the ternary blend R-445A.19 In this contribution, we employ the force field model for fluoropropenes for molecular dynamics simulations on the liquid-phase properties of R-1234yf, R-1234ze(E), R-1234ze, and R-1216 and their binary mixtures with R-32 and CO2. We Received: September 20, 2013 Revised: November 11, 2013 Published: December 11, 2013 240

dx.doi.org/10.1021/jp409408k | J. Phys. Chem. B 2014, 118, 240−254

The Journal of Physical Chemistry B

Article

Figure 1. Structures of the compounds studied in this work: 2,3,3,3-tetrafluoro-1-propene (R-1234yf), trans-1,3,3,3-tetrafluoro-1-propene (R1234ze(E)), 1,1,2,3,3,3-hexafluoropropene (R-1216), cis-1,3,3,3-tetrafluoro-1-propene (R-1234ze), difluoromethane (R-32), and carbon dioxide (CO2). Also shown is the nomenclature for the different Lennard-Jones (LJ) atom types used in their molecular modeling.

exactly three bonds (1−4 interactions) are scaled by a factor of 1/2 and 1/1.2, respectively, whereas full LJ and electrostatic interactions are considered between atoms separated by more than three bonds. Our molecular model for fluoropropenes is a transferable force field with regard to both the intramolecular terms and the LJ parameters. The partial charges though were calculated for all compounds individually from ab initio simulations for isolated molecules by the ESP approach with the CHELPG fitting scheme (HF/6-31G* level of theory).21 More details on the parametrization of the molecular model for fluoropropenes are given in our earlier work,16,17 with a complete list of force field parameters provided in the Supporting Information of ref 17. In our earlier work18 we have introduced a fully flexible all atoms force field model for R-32 that reproduces the VLE of the pure compound in good agreement with REFPROP calculations. Our simulation studies in ref 18 on phase equilibria in a binary mixture of R-32 with R-1234yf and R1234ze(E) have shown that our molecular modeling yields reliable predictions for the VLE in these systems as the simulated data agree well with experimental data.13,14 For carbon dioxide, we have employed the TraPPE model by Potoff and Siepmann, 22 for which the calculation of intermolecular interaction is also based on LJ site and fixed partial charges on the three atomic sites, although the TraPPE force field models CO2 as a rigid molecule. In our recent work,18 we have also already employed the combination of the TraPPE CO2 model and our fluoropropenes force field for predictive simulation studies on the VLE of the binary systems CO2 + R-1234yf, and CO2 + R-1234ze(E). All LJ parameters for interactions between unlike atoms, both in studies on pure compounds as well as for the simulation of mixtures, are obtained from the Lorentz−Berthelot combining rule, i.e

provide predictions on the liquid densities and viscosities, which are compared with correlations by REFPROP 9.1,20 where possible. The different numbers and locations of the fluorine atoms in the fluoropropenes result in different charge distributions across the molecules, which in turn are expected to influence the nature of their interactions with other compounds. Thus, to gain insight into preferred interaction sites and the resulting local ordering, we have also analyzed spatial and radial distribution functions, for both the pure fluoropropenes and their mixtures with R-32 and CO2.

2. FORCE FIELD MODELS The structures of all compounds studied in this work, and the nomenclature for the different Lennard-Jones (LJ) atom types that were used in their molecular modeling are shown in Figure 1. In our force field model for fluoropropenes, the potential energy is expressed by the following standard functional form UConf =

∑

kr(r − r0)2 +

bonds

+

∑

∑

kθ(θ − θ0)2

angles

kχ [1 + cos(nχ − δ)]

dihedral

+

⎧ ⎪

12 ⎫ ⎛ σ ⎞6 ⎤ qq ⎪ σij ⎞ ⎟⎟ − ⎜⎜ ij ⎟⎟ ⎥ + 1 i j ⎬ ⎥ r 4πε0 rij ⎪ ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠ ⎭

⎡⎛

∑ ∑ ⎨4εij⎢⎢⎜⎜ i

j>i

⎪ ⎩

(1)

Therein, the intermolecular potential energy is calculated as the sum of LJ and electrostatic interactions between the atomic sites with fixed partial charges. The intramolecular contribution to the potential energy is modeled by harmonic terms for bond stretching and angle bending, and a cosine term to account for internal torsions. Nonbonded LJ and electrostatic interactions between atoms of the same molecule that are separated by 241


The Journal of Physical Chemistry B εij =

εiiεjj ,

σij =

Article

σii + σjj

(2) 2 Thus, no interaction parameters were used in the simulation studies on the mixtures, and therefore all our simulations represent pure predictions.

3. SIMULATION DETAILS The molecular dynamics simulations in the liquid phase were performed using the DL_POLY simulation package.23 The cubic boxes consisted of N = 270 molecules for the studies on the pure HFOs, N = 400 molecules in the mixtures, and N = 500 and 600 for simulations on pure R-32 and CO2, respectively. The simulation studies on mixtures comprised mole fractions of CO2 or R-32 of x1 = 0.0, 0.2, 0.4, 0.6, 0.8, and 1.0. Periodic boundary conditions were applied, and the cutoff radius varied between 14 and 15 Å, depending on the resulting size of the simulation box. Standard long-range corrections to the LJ energy and pressure were applied for all potentials by employing usual tail corrections.24 The Ewald25 sum was used to deal with the electrostatic interactions. To derive averaged densities and energy contributions, we first performed simulations in the Nosé−Hoover26,27 NpT ensemble with coupling constants of τT = 0.1 ps and τp = 1.0 ps. The trajectories were integrated by the velocity Verlet algorithm24 with a time step of Δt = 0.0005 ps. The systems were equilibrated for 2.5 ns, followed by a production run of 2.5 ns. Ensemble averages for the densities were then derived from the ensemble average of the system volume V and the molar mass of the mixture M by ρ N ·M = ⟨V ⟩·NA kg·m−3 (3)

Figure 2. Averaged autocorrelation functions over the three independent off-diagonal tensor elements of the viscous pressure tensor pαβ (red line) in the system R-32 + R-1234yf at 273 K and 1 MPa with xR‑32 = 0.6. The resulting instantaneous value of the shear viscosity from the Green−Kubo24 method as function of correlation time is shown as a blue line.

We have additionally studied the transport and structural properties of the pure HFO compounds and their mixtures with R-32 and CO2 by MD simulations in the Nosé−Hoover− NVT ensemble with a time step of Δt = 0.0005 ps and a coupling constant of τT = 0.5 ps. The systems were again equilibrated for 1 ns at the average densities obtained from the NpT-simulations. In the following NVT-production runs of 10 ns, we saved the positions every 0.025 ps and the pressure tensors every 0.0025 ps for further analysis. The shear viscosities were computed by the Green−Kubo24 method of integrating the averaged autocorrelation functions over three independent off-diagonal tensor elements of the viscous pressure tensor pαβ η=

V 3k bT

∫0

instance pure R-1234ze at 270 K, it was required to increase the correlation time to up to 10 ps. We have also studied the self-diffusion coefficients D of the pure fluoropropenes compounds, which were derived from the Einstein relation24 as the mean-square displacement along the trajectory of a particle D = lim

t →∞

(5)

which were then averaged over all particles in the system. Standard deviations of all ensemble averages were determined by dividing the production runs into 10 blocks and applying standard block average technique.24 We have additionally studied the liquid structures of the systems by radial (RDFs) and spatial (SDFs) distribution functions, which were determined by analyzing the system trajectory with the TRAVIS package.28 All contour surfaces of the SDFs were then visualized by the software package gOpenMol.29

∞

[⟨pxy (0) ·pxy (t )⟩ + ⟨pxz (0) ·pxz (t )⟩

+ ⟨pyz (0) ·pyz (t )⟩]dt

⟨|r(t ) − r(0)|2 ⟩ 6t

(4)

For most state points and mixtures we found a correlation time of 5 ps to be sufficient to yield well-converging results for the viscosity. Figure 2 exemplarily shows a plot of the averaged autocorrelation function (red line) of the off-diagonal tensor elements over correlation time in the mixture R-32 + R-1234yf (273 K, 1 MPa, xR‑32 = 0.6). Also shown is the instantaneous value of the viscosity as function of the correlation time (blue line) derived from integrating the function above. This depiction illustrates that the resulting value for the viscosity is from 4 ps on well converged to the value ηi = 0.172 mPas (block average). However, to obtain converged results for systems with higher viscosity at lower temperatures, for

4. RESULTS AND DISCUSSION 4.1. Pure Fluoropropene Compounds. Liquid Densities and Transport Properties. In Table 1 we have summarized the simulation results for the densities, viscosities, and diffusion coefficients in the liquid phase of the pure fluoropropenes (cis-) R-1234ze, (trans-) R-1234ze(E), R-1234yf, and R-1216 at different temperatures and pressures. Figure 3 shows the molar densities of the fluoropropenes as function of temperature in 242



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Table 1. Liquid Density ρ, Shear Viscosity η, and SelfDiffusion Coefficient D of Different Fluoropropene Compounds from MD Simulation Studies in This Worka ρ (kg m−3)

T (K)

p (MPa)

270.00 273.15 273.15 290.00 298.15 300.00 313.15 313.15

2.0 1.0 3.5 2.0 2.0 2.0 2.0 3.5

1309.2 1300.7 1306.2 1257.1 1237.4 1229.1 1194.0 1197.9

270.0 273.15 273.15 280.0 290.0 300.0 310.0 313.15

2.0 1.0 3.5 2.0 2.0 2.0 2.0 3.5

1279.5 1267.0 1275.5 1249.6 1210.3 1175.7 1150.5 1144.8

273.15 273.15 313.15

1.0 3.5 3.5

1187.3 1196.9 1059.3

273.15 273.15 273.15 280.0 290.0 300 313.15

1.0 2 3.5 2.0 2.0 2.0 3.5

1436.8 1443.6 1449.8 1416.5 1368.5 1330.9 1285.8

η (mPa s)

R-1234ze ± 18.4 0.366 ± 17.7 0.348 ± 17.1 0.361 0.295 ± 19.3 ± 22.8 0.255 ± 20.6 0.249 ± 21.9 0.219 ± 21.5 0.234 R-1234ze(E) ± 20.7 0.300 ± 19.2 0.271 ± 18.2 0.278 ± 22.7 0.260 ± 24.2 0.221 0.199 ± 26.2 ± 285 0.176 ± 25.5 0.173 R-1234yf ± 23.2 0.204 ± 20.3 0.206 ± 27.7 0.136 R-1216 ± 26.1 0.236 ± 25.4 0.254 ± 23.0 0.256 ± 30.3 0.233 ± 30.6 0.197 ± 33.9 0.178 ± 32.7 0.158

D (10−9 m2 s−1)

± ± ± ± ± ± ± ±

0.024 0.028 0.022 0.026 0.019 0.016 0.009 0.019

2.61 2.78 2.63 3.51 3.76 4.24 4.84 4.65

± ± ± ± ± ± ± ±

0.21 0.14 0.12 0.18 0.21 0.33 0.24 0.19

± ± ± ± ± ± ± ±

0.027 0.020 0.024 0.013 0.020 0.014 0.005 0.004

3.13 3.17 3.19 3.51 4.33 4.81 5.55 5.78

± ± ± ± ± ± ± ±

0.16 0.13 0.16 0.23 0.48 0.23 0.35 0.38

± 0.017 ± 0.015 ± 0.010

4.45 ± 0.18 4.32 ± 0.31 7.93 ± 0.45

± ± ± ± ± ± ±

3.65 3.51 3.53 3.94 4.69 5.41 6.39

0.019 0.023 0.010 0.029 0.015 0.012 0.011

± ± ± ± ± ± ±

Figure 3. Molar densities of different fluoropropenes as function of temperature from MD simulation studies: R1234ze (right-facing crossed triangle, blue), R-1234ze(E) (open crossed circle, red), R1234yf (open crossed square, green), and R-1216 (down crossed triangle, purple) at p = 2 MPa. Also shown are calculated densities by REFPROP for R-1234ze(E) (, red), R-1234yf (, green) and R1216 (, purple), as well as experimental data for R-1234ze(E). (open dotted circle,30 filled circle, black31), R-1234yf (open dotted square,32 filled square, gray,33 filled square, black34), R-1216 (open down dotted triangle,35 down triangle, gray33) and R-1234ze (open right-facing dotted triangle,36 dashed connecting line added to guide the eyes; exp. data connected by dash−dot line are saturated liquid densities).

0.23 0.25 0.19 0.21 0.31 0.17 0.39

which we have summarized in Table 2. The dipole moments of the different compounds arrange in order μR‑1234ze > μR‑1234yf > μR‑1234ze(E) > μR‑1216. As expected, the cis-isomere R-1234ze with the highest dipole moment has the highest molar densities, whereas the lowest molar densities of R-1216 are originated by its comparatively small dipole moment. However, the molar densities of the two tetrafluoropropenes R-1234ze(E) and R1234yf do not scale with their dipole moments. In Table 3, we have exemplarily compared the contribution of Lennard-Jones (vdW) and electrostatic interactions to the configurational energy of the four fluoropropenes at 273 K and 3.5 MPa. The comparison clearly shows that the main contribution to the interaction potential arise from Coulombic interactions, which also differ significantly between the different fluoropropenes, whereas the van der Waals interactions are relatively similar. Surprisingly the highest Coulombic interactions occur in the trans-R-1234ze(E) despite its smaller dipole moment compared to cis-R-1234ze and R-1234yf. Thus, for this compound, Coulombic interaction can not only result from dipole−dipole interactions, but have to be caused by higher multipole interactions. In Table 2 we also provide the elements Qxx, Qyy, Qzz and Qxy of the traceless quadrupole tensor of the fluoropropenes derived from the ab initio simulations on isolated molecules. To enable a comparison between the molecular quadrupole moments of the different fluoropropenes, we have employed an empirical equation proposed by Eubank39 to estimate effective molecular quadrupole moments of nonsymmetric molecules from the diagonal elements of their traceless quadrupole tensor 2 2 2 Q eff = (Q xx + Q yy2 + Q zz2 ) (6) 3

a

Additional simulation results for R-1234yf shown in Figures 3 and 4 are given in our earlier work.16

comparison with experimental data30−37 and calculations by REFPROP 9.1 where available. The depiction indicates that the MD studies yield reliable predictions for the densities of the fluoropropenes R-1234ze(E), R-1234yf, and R-1216 as the simulation results are in general in good agreement with both experiment and REFPROP calculations. Only for R-1234ze(E), the simulations tend to overestimate the liquid density, with deviations from REFPROP calculations of max 2% at 270 K. Experimental data for the densities of the cis-isomere R-1234ze are rare and only comprise saturated densities and liquid-phase densities at T ≥ 300 K.36,37 The comparison of the simulation results of R-1234ze and experimental data at T = (300−313) K suggests that the force field also allows for reliable predictions for the densities of this compound. The hexafluoropropene with its molar mass of 150.02 g mol−1 has clearly higher mass densities than the tetrafluoropropenes with their molar mass of 114.04 g mol−1. However, Figure 3 illustrates that R-1216 exhibits the smallest molar densities of all fluoropropenes studied here, with ρR‑1234ze > ρR‑1234ze(E) > ρR‑1234yf > ρR‑1216. In our earlier work,16,17 we have determined the electrostatic potentials of isolated molecules of the different compound from ab initio simulations (using Gaussian38) to derive the partial charges for the molecular modeling of the fluoropropenes. These simulations also yielded information of the dipole moments of the different compounds, 243



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Table 2. Dipole Moment μ and Traceless Quadrupole Moment Qij of Different HFO Molecules from ab Initio Simulations on Isolated Molecules (EPS/CHELPG Fitting Scheme, HF/6-31G* Level of Theory, Using Gaussian38), and Estimated Effective Quadrupole Moments from eq 6 HFO

μ (D)

Qxx (DÅ)

Qyy (DÅ)

Qzz (DÅ)

Qxy (DÅ)

Qeff (DÅ)

R-1234ze R-1234ze(E) R-1234yf R-1216 R-32

3.54 1.31 2.57 1.02 2.24

0.2692 −2.8813 1.2458 −0.2813 −2.0531

1.4439 3.0509 0.0185 −1.2414 1.1002

−1.7131 −0.1696 −1.2643 1.5227 0.9529

−2.9004 1.2070 2.3149 0.4336 0.0005

1.84 3.43 2.10 1.62 2.05

Apart from the viscosity correlations used in REFPROP there are others viscosity models available in the literature for R1234yf41−43 and for R-1234ze(E)43 which, however, are not discussed here. The calculated viscosities for R-1234ze(E) and R-1234yf by the extended corresponding-state models (ECS)44 in REFPROP tend to overestimate the experimental data by Cousins and Laesecke. However, the larger deviations between calculation and experiment at lower temperatures shown in Figure 4 are mainly due to the different pressures for which the viscosities were determined. The MD simulation results for the viscosities of R-1234yf and R-1234ze(E) are in general in good agreement with the REFPROP calculations; however, for R1234ze(E) the simulation yields increasingly too high viscosities with decreasing temperatures. For R-1234yf, the simulated viscosities are lower than the results from REFPROP calculations, and with this in better agreement with the experimental data. The viscosity modeling of R-1216 in REFPROP is also based on the ECS approach, and it is purely predictive due to the lack of experimental data.20 The ECS model estimates generally lower viscosities than our MD studies. The predicted temperature dependency of the R-1216 viscosities from REFPROP is similar to that of R-1234ze(E), and it yields a more pronounced decrease of the viscosity with increasing temperature as for R-1234yf. Also shown are viscosities for the cis-R1234ze from MD simulations, but no ECS correlations or experimental data for comparison are available for this compound. However, the viscosities of the three tetrafluoropropenes arrange in the order ηR‑1234ze > ηR‑1234ze(E) > ηR‑1234yf, which is consistent with the order of their molar densities. Accordingly, the diffusion coefficients rank DR‑1234yf > DR‑1234ze(E) > DR‑1234ze (see Table 1). In their comparison of the experimental viscosities of R1234yf and R-1234ze(E), Cousins and Leasecke have stated that the viscosities of the two compounds do not scale with their dipole moments and suggested that the charge distribution across the entire molecules have to be taken into account to evaluate their polarities. This supports our argument that the higher molar density and therefore higher viscosity of the R-1234ze(E) compared to that of R-1234yf despite its lower dipole moment is caused by its high quadrupolar moment. As expected, the cis-isomer R-1234ze with the highest dipole moment exhibits the highest shear viscosities. The higher viscosity of the less polar R-1216 compared to that of R1234yf originates in its higher molar mass. Structural Properties. The varying locations of fluorine in the different fluoropropene compounds result in significant different charge distributions which in turn affect the thermophysical properties as discussed before, although it can be expected that it also significantly influences the local ordering in the liquids. To gain insight into the resulting

Table 3. Contribution to the Configuration Energy of Different Fluoropropenes from vdW and Coulombic Interactions in the Liquid Phase at 273 K, 3.5 MPa HFO R-1234yf R-1234ze(E) R-1234ze R-1216

Evdw (kJ mol−1)

Ecoul (kJ mol−1)

−13.65 −14.53 −14.76 −13.89

−103.13 −154.13 −150.75 −87.78

± ± ± ±

0.16 0.18 0.18 0.18

± ± ± ±

0.16 0.19 0.20 0.17

The calculated effective quadrupole moments of the four fluoropropenes are also given in Table 2, and indicate that R1234ze(E) exhibits a quadrupole moment significantly higher than those of the other compounds. Thus, it can be summarized that the high molar densities of the cis- and trans-R-1234ze compounds are due to high Coulombic interactions that result from dipolar interactions for R1234ze, but quadrupolar interactions for R-1234ze(E). Simulation results for the viscosities of the four fluoropropenes at 2 MPa are depict in Figure 4, together with recent experimental data by Cousins and Laesecke40 for R-1234ze(E) and R-1234yf at saturated liquid conditions, and calculated viscosities by REFPROP for these compounds and R-1216.

Figure 4. MD simulation results for the viscosities of different pure fluoropropenes at different temperatures and 2 MPa: R1234ze (open right-facing crossed triangle, blue), R-1234ze(E) (open crossed circle, red), R-1234yf (open crossed square, green), and R-1216 (open down crossed triangle, purple). Also shown are calculated viscosities at p = 2 MPa by REFPROP for R-1234ze(E) (, red), R-1234yf (, green) and R-1216 (purple), and recent experimental data from Cousins and Laesecke40 for the viscosity of R1234ze(E) (filled circle, gray) and R1234yf (filled square, gray) at saturated liquid conditions. Also shown as dashed line (  ) is a polynomial fit to the MD simulation results for R-1234ze to guide the eyes. 244



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Figure 5. Spatial distribution function (SDF) of the different fluorine atoms around the HFO molecules in the pure fluoropropenes (a) R-1216, (b) R-1234yf, (c) R-1234ze, and (d) R-1234ze(E) at 273 K and 1 MPa. Green surfaces indicate locations of FCT atoms, yellow mash surface, areas of higher concentration of FCM atoms bonded to the outer CM atom, and orange mash surfaces, those of FCM atoms bonded to the central CM atom (only in R-1216, and R-1234yf). All surfaces represent 1.7 times of the average density. To simplify the mapping of the different fluorine atoms to their regions of higher population, the corresponding atoms are marked by rings in the same color.

microscopic structure in the different pure fluoropropenes compounds, we have analyzed the arrangement of the different fluorine atoms around the HFO molecules by spatial distribution functions (SDFs). Figure 5 illustrates the surfaces of higher fluorine populations (1.7 times the average density) around (a) R-1216, (b) R-1234yf, (c) R-1234ze, and (d) R1234ze(E) molecules at 273 K and 1 MPa. Shown as green surfaces are populations of the FCT atoms of the CF3-group that arrange in ring structures around the molecules with the radius of the ring being normal to the CT−CM−CM plane. Areas in front of fluorine atoms are always omitted by the FCT atoms. Thus, due to varying distributions of the fluorine atoms in the different compounds, diverse forms for the surfaces of enhanced FCT populations result. The FCM fluorine atoms that are bonded to the central CM atom in R-1216 and R-1234yf accumulate in areas similar to those of the FCT atoms, as shown by the orange regions that encompass the green surfaces. For the R-1234yf compound, FCM atoms also locate to a great extent in the region facing the CH2 end group. The FCM atoms that are bonded to the outer CM atom in R-1216, R-1234ze, and R-1234ze(E) are also mainly located in a ring structure around the CT−CM−CMplane. For R-1216 and R-1234ze(E) an extended area of higher population of FCM atoms exists in front of the CF3-end group,

whereas this region is a much less favorable location for FCM atoms in the cis-R1234ze. For this compound, the FCM atoms migrate away from the CF3 group toward the region between the two hydrogen atoms, where also a higher concentration of FCT fluorines can be observed. Although enhanced concentrations of fluorine atoms in the vicinity of the hydrogen atoms can be observed for all tetrafluoropropenes, the areas directly facing the H-atoms always show low fluorine concentrations. In general, the highest relative population densities for FCT atoms vary from 2.1 to 2.4, whereas they are between 2.4 and 2.9 for the FCM populations. These comparable low population densities of fluorines in the vicinity of hydrogen atoms do not suggest significant hydrogen-bonding interactions. This is consistent with our findings from the analysis of different hydrogen− fluorine-RDFs for R-1234yf, R-1234ze, and R-1234ze(E) in our earlier work17 and for R-1234yf by Skarmoutsos and Hunt.45 Thus, the general assumption that fluorines attached to carbons do not act as H-bond acceptors45 is also true for the tetrafluoropropenes studied here. 4.2. Binary Mixtures of Fluoropropenes with R-32. Densities and Viscosities. We have studies the liquid-phase properties of binary mixtures of the fluoropropenes R-1234ze, R-1234ze(E), and R-1234yf or R-1216 and R-32 at T = 273 K, 245



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Table 4. Liquid Densities ρ in Binary Mixtures of R-32 (1) and Different Fluoropropenes (2) from MD Simulation Studies in This Work R-32

+ R-1234ze

+ R-1234ze(E)

+ R-1234yf

+ R-1216

T (K)

p (MPa)

x1 (mol mol−1)

ρ (kg m−3)

ρ (kg m−3)

ρ (kg m−3)

ρ (kg m−3)

273.15

1.0

273.15

3.5

313.15

3.5

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0

1300.7 1268.8 1238.2 1195.8 1139.9 1069.2 1306.2 1277.1 1242.6 1202.3 1145.0 1075.9 1197.9 1163.2 1123.3 1066.5 994.7 903.5

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

17.7 20.2 19.2 21.7 24.4 17.9 17.1 18.8 19.7 20.4 24.2 18.2 21.5 23.1 23.5 27.8 31.8 30.3

1267.0 1243.1 1213.7 1182.7 1133.0

± ± ± ± ±

19.2 19.7 21.1 23.3 23.9

1185.7 1170.9 1145.5 1122.2 1098.3

± ± ± ± ±

20.7 20.8 22.0 23.5 23.5

1436.8 1397.2 1339.9 1283.0 1202.8

± ± ± ± ±

26.1 24.0 27.0 26.3 27.2

1275.6 1252.5 1221.7 1188.1 1145.3

± ± ± ± ±

18.2 20.2 20.8 23.1 22.9

1196.9 1174.4 1160.5 1133.4 1110.7

± ± ± ± ±

20.3 21.3 20.7 24.7 22.4

1449.8 1405.3 1361.6 1290.7 1207.0

± ± ± ± ±

23.0 22.2 27.0 24.3 28.6

1144.8 1119.6 1082.8 1038.6 975.6

± ± ± ± ±

25.5 26.6 29.0 31.2 34.2

1059.3 1027.5 1001.2 965.0 951.9

± ± ± ± ±

27.7 28.9 28.9 35.1 39.2

1285.8 1238.0 1179.2 1100.6 1016.4

± ± ± ± ±

32.7 33.3 35.8 36.3 37.11

Table 5. Shear Viscosities η in Binary Liquid Mixtures of R-32 (1) and Different Fluoropropenes (2) from MD Simulation Studies in This Work R-32

+ R-1234ze −1

T (K)

p (MPa)

x1 (mol mol )

273.15

1.0

273.15

3.5

313.15

3.5

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4 0.6 0.8 1.0

η (mPa s ) 0.348 0.298 0.263 0.237 0.188 0.152 0.361 0.305 0.257 0.229 0.182 0.163 0.234 0.200 0.161 0.143 0.127 0.093

± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ± ±

+ R-1234ze(E) η (mPa s )

0.028 0.022 0.020 0.028 0.027 0.012 0.022 0.019 0.015 0.025 0.027 0.009 0.019 0.012 0.019 0.017 0.014 0.006

p = (1 and 3.5) MPa and at 313.15 K/3.5 MPa. Simulation results for the liquid densities and viscosities are given in Tables 4 and 5. Figure 6 shows simulation results for the liquid densities of the four binary mixtures with different compositions at 273 K and 1 MPa. Also shown are calculated densities ρ(xR‑32) for the mixtures R-32 + R1234yf, R-32 + R1234ze(E), and R-32 + R-1216 from REFPROP. The correlation of mixture properties in REFPROP requires the fitting of binary mixing parameters. For the binary systems R-32 + R-1234yf and R-32 + R-1234ze(E) these mixture parameters are experimentally based values. For the mixture R-32 + R1216, for which no experimental data are available, an estimation scheme is used in REFPROP to approximate the interaction parameters.20

+ R-1234yf η (mPa s)

+ R-1216 η (mPa s)

0.271 0.252 0.227 0.204 0.173

± ± ± ± ±

0.020 0.014 0.010 0.012 0.012

0.204 0.189 0.179 0.169 0.151

± ± ± ± ±

0.017 0.012 0.012 0.015 0.019

0.236 0.218 0.208 0.190 0.172

± ± ± ± ±

0.017 0.013 0.012 0.008 0.020

0.278 0.256 0.228 0.206 0.182

± ± ± ± ±

0.024 0.019 0.027 0.021 0.011

0.206 0.197 0.189 0.173 0.166

± ± ± ± ±

0.015 0.010 0.018 0.008 0.017

0.255 0.226 0.216 0.186 0.177

± ± ± ± ±

0.001 0.017 0.014 0.027 0.021

0.173 0.159 0.140 0.131 0.108

± ± ± ± ±

0.004 0.014 0.011 0.005 0.012

0.136 0.122 0.114 0.101 0.104

± ± ± ± ±

0.010 0.012 0.007 0.011 0.011

0.158 0.142 0.129 0.112 0.107

± ± ± ± ±

0.011 0.010 0.011 0.005 0.011

For the binary mixture R-32 + R-1234yf, the predicted densities from our MD studies agree with the REFPROP correlations within the error bars of the simulations. As discussed above, our molecular model for R-1234ze(E) tends to overestimate its liquid densities. Thus, the simulated densities of the mixture R-32 + R-1234ze(E) are up to 1.9% higher than the REFPROP values. However, taking into account that the MD simulation results are purely predictive, this is still a good agreement. For the binary mixture R-32 + R-1216 both the MD simulation studies and the REFPROP correlations are predictive. With averaged deviations of 1.9% (max 3.6%) between them, both predictions for the mixture densities are in fair agreement. However, the MD simulations yield higher values and a less pronounced decrease of the densities with 246



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Figure 6. Liquid densities from MD simulation studies for the binary mixture R-32 + R1234ze (open right-facing crossed triangle; blue dotted line added to guide the eyes), R-32 + R-1234ze(E) (open crossed circle, red), R-32 + R-1234yf (open crossed square, green), and R32 + R-1216 (open down crossed triangle, purple) at 273 K and p = 1 MPa. Also shown are calculated densities by REFPROP for R-32 + R-1234ze(E) (, red), R-32 + R-1234yf (, green) and R-32 + R1216 (, purple).

increasing R-32 composition. No correlations for comparison are available for the mixture R-32 + R-1234ze. The viscosities η(xR‑32) of the mixtures at 273 K and 1 MPa are depicted in Figure 7, again together with REFPROP Figure 8. Center-of-Mass (CoM) RDFs in the binary mixtures R-32 + R1234ze (, blue), R-32 + R1234ze(E) (, red), R-32 + R-1234yf (, green) and R-32 + R-1216 (, purple) at 273 K and 3.5 MPa and xR‑32 = 0.4. (a) RDF of R-32 around the HFO molecules, (b) RDF of R-32 around other R-32 molecules; also shown is the corresponding RDF in the pure fluid (  ) at the same state point. (c) CoMRDFs of HFO molecules around other HFO molecules. Shown as dashed lines in the same color are the RDFs in the pure fluoropropenes at the same state point.

increasing xR‑32, and only marginal negative deviation from linearity (shown as dashed line). A similar behavior could be expected at least for the mixtures R-32 + R-1234yf and R-32 +R-1234ze(E) as the compounds R-1234yf and R-1234ze(E) shall offer comparable properties to R-134a. For the mixture R32 + R1234e(E), REFPROP predicts a moderate negative deviation from a linear decay, but it is more pronounced for the mixture R-32 + R-1234yf. For these two mixtures, the MD simulation results are in good agreement with the REFPROP calculations within the range of their uncertainties, though it seems that the simulated viscosities follow a linear trend (shown as dashed lines). For the mixture R-32 + R-1216, REFPROP again describes a pronounced negative deviation of η(xR‑32) from linearity, whereas the data from MD simulations predict a linear decay of the viscosity with increasing xR‑32 (dashed line). This results in considerable deviations between REFPROP calculations and molecular simulation results for this binary mixture. For the system R-32 + R-1234ze, for which no REFPROP correlations are available, the MD simulations again predict a nearly linear course of η(xR‑32). However the simulation results for the viscosities are, in general, subject to notable uncertainties and therefore do not allow for a reliable

Figure 7. Liquid viscosities from MD simulation studies for the binary mixture R-32 + R1234ze ((open right-facing crossed triangle, blue), R32 + R-1234ze(E) (open crossed circle, red), R-32 + R-1234yf (open crossed square, green), and R32 + R-1216(open down crossed triangle, purple) at 273 K and p = 1 MPa. Also shown are calculated viscosities by REFPROP for R-32 + R-1234ze(E) (, red), R-32 + R-1234yf (, green) and R-32 + R-1216 (, purple).

calculations where possible. For the sake of comparison, we have also calculated the viscosities η(xR‑32) of the mixture R-32 + R134a by REFPROP at the same state point, which is shown as inserted depiction in Figure 8. For this system, an equation of mixture is available in REFPROP, which is based on a multitude of experimental data for different thermodynamic properties of the mixture.46 For R-32 + R-134a, REFPROP correlation yields a nearly linear decay of the viscosity with 247



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Figure 9. Spatial distribution functions (SDF) in the binary mixtures (a) R-1216 + R-32, (b) R-1234yf + R-32, (c) R-1234ze + R-32, and (d) R1234ze(E) + R-32 at 273K and 3.5 MPa, with xR‑32 = 0.4. Green surfaces indicate locations of FCT atoms, yellow and orange surfaces that of FCM atoms of the HFO molecules (bonded to outer or middle CM atoms, respectively), cyan contours represent cumulative populations of FR‑32. White solid surfaces are areas of higher population of HR‑32 around the HFO, white mash and pink surfaces are the HFO hydrogens around R-32 (bonded to outer or middle CM atoms, respectively). All surfaces represent 1.5 times the average density.

R-32 molecules prefer to form clusters in mixture with fluoropropenes. Figure 8c) shows the CoM-RDFs of different fluoropropenes in mixture with R-32 compared to the pure HFO liquid at the same state point. The position (5.4−5.7 Å) and also the form of the first peak are similar in the mixture and the pure fluid, but the heights of the first maximum is reduced in the mixture. This indicates that the presence of R-32 molecules perturbs the local structure in the fluoropropenes. This is most pronounced for the mixture R-32 + R-1234ze, which also exhibits the highest maximum in the R-32−HFO-RDF. This hints at stronger interactions of R-32 with R-1234ze than with the other fluoropropenes studied here. Support for this conclusion follows from the analysis of the spatial distribution functions of both R-32 molecules around fluoropropenes and of the different fluoropropenes around R-32, shown in Figure 9. Again the SDFs were analyzed for mixtures with xR‑32 = 0.4 at 273 K and 3.5 MPa. All surfaces depicted in Figure 9 represent 1.5 times of the average density. We also analyzed the distribution of the different HFO fluorine atoms around the fluoropropenes as shown in Figure 6 for the pure compounds. However, although the FCM and FCT atoms are still located in the same regions around the fluoropropenes as in the pure fluid, their population densities are reduced to (1.4 to 1.5) times of the average value, and thus are not shown in Figure 9. The only exception is the mixture R-32 + R-1234ze(E) in which a higher concentration of the FCM fluorine around the R-1234ze(E) can still be found (yellow mashed contour). Apart from this are the regions of higher concentrations of HFO fluorines in the

conclusion as to what extent the mixture viscosities deviate from curve linearity. Structural Properties. To gain insight into the microscopic structure of R-32 + HFO mixtures and preferred interaction sites between R-32 and the different fluoropropenes, we have analyzed both radial and spatial distribution functions. We therefore have exemplarily considered mixtures with mole fraction of xR‑32 = 0.4 at 273 K and 3.5 MPa. Figure 8a) shows the RDFs of the center of mass (CoM) of R-32 around the CoM of the different fluoropropene compounds. The first peaks indicate attractive interactions between tetrafluoropropenes and R-32 at about 4.9 Å, whereas the peak is shifted to higher distances of about 5.2 A for the R-32 + R-1216 mixture. The R-32 + R-1234ze mixture exhibits the highest maximum (1.8), whereas the peak in the R-32 + R-1216 is notably lower (1.6). The peaks in mixtures of R-32 with R-1234yf and R1234ze(E) are very similar in their height (1.7) and shape. In general, the first maxima in the R-32 + HFO mixtures are neither very high nor sharp and therefore do not suggest hydrogen-bonding interactions. The R-32−R-32 CoM-RDFs in mixtures with different fluoropropenes in comparison with the pure R-32 are depicted in Figure 8b). All systems exhibit first maximum at about 4.4 A, but their heights vary between 2.0 for the mixture R-32 +R1234ze and 2.3 for the system R-32 + R-1216. With this, the peaks of R-32−R-32-RDFs in binary mixtures with fluoropropenes are notably higher than in the pure R-32 liquid (1.8), and also higher than the R-32−HFO-RDFs. This suggests that the 248



Article

Table 6. Liquid Densities ρ in Binary Mixtures of CO2 (1) and Different Fluoropropenes (2) from MD Simulation Studies in This Work CO2

+ R-1234ze

+ R-1234ze(E)

+ R-1234yf

+ R-1216

T (K)

p (MPa)

x1 (mol mol−1)

ρ (kg m−3)

ρ (kg m−3)

ρ (kg m−3)

ρ (kg m−3)

273.15

3.5

313.15

3.5

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4

1306.2 1269.7 1226.1 1163.2 1073.8 932.6 1197.9 1157.7 1094.7

± ± ± ± ± ± ± ± ±

17.1 18.3 19.9 21.3 25.7 23.4 21.5 22.9 26.5

1275.6 1241.2 1197.3 1140.2 1059.7

± ± ± ± ±

18.2 19.4 21.4 23.3 26.4

1144.8 ± 25.5 1100.8 ± 26.2 1038.9 ± 31.9

1196.9 1164.1 1128.7 1082.3 1022.9

± ± ± ± ±

20.3 21.1 22.8 25.4 27.6

1059.3 ± 27.7 1010.8 ± 31.0 942.3 ± 34.9

1449.8 1393.6 1327.1 1240.7 1113.2

± ± ± ± ±

23.0 23.7 25.5 26.6 30.2

1285.8 ± 32.7 1204.1 ± 34.7 1111.3 ± 37.1

Table 7. Shear Viscosities η in Binary Liquid Mixtures of CO2 (1) and Different Fluoropropenes (2) from MD Simulation Studies in This Work CO2

+ R-1234ze

+ R-1234ze(E)

+ R-1234yf

+ R-1216

T (K)

p (MPa)

x1 (mol mol−1)

η (mPa s)

η (mPa s)

η (mPa s)

η (mPa s)

273.15

3.5

313.15

3.5

0 0.2 0.4 0.6 0.8 1.0 0 0.2 0.4

0.361 0.306 0.272 0.218 0.160 0.105 0.234 0.194 0.160

± ± ± ± ± ± ± ± ±

0.022 0.024 0.014 0.023 0.017 0.008 0.019 0.017 0.020

pure fluoropropenes now in the mixtures populated by the fluorine atoms of R-32 (cyan surfaces). Interestingly, the highest population density of FR‑32 around HFO molecules (2.7) occurs in the mixture R-32 + R-1216. This might be due to the fact that the fluorine atoms there concentrate in a relatively limited area parallel to the CT−CM−CM plane of the R-1216 molecules, whereas for all other mixtures the regions of higher FR‑32 concentrations are more expanded. The widest extension of the region of higher FR‑32 population can be found around the R-1234ze molecule. Areas of higher concentration of the R-32 hydrogens around the fluoropropenes are mainly caused by the location of the FR‑32 atoms (see white surfaces behind the cyan contours around R-1216, R-1234ze, and R-1234ze(E)). In addition to this, higher HR‑32 concentrations exist in the vicinity of the FCM fluorine atoms of R-1216 and R-1234yf and R-1234ze(E). The most extended region of a higher HR‑32 population can again be found around R-1234ze, but here in the vicinity of the FCT fluorine atoms of the −CF3 end group. It is also noteworthy how differently the fluoropropenes arrange around the R-32 molecules. As might be expected, a higher population of the HFO hydrogens can be found in the vicinity of the R-32 fluorines. The extension of the regions and also the highest density that can be found there arrange in the order R-1234ze > R-1234yf > R-1234ze(E). The white surfaces around R-32 in the mixtures the cis- and trans-R1234ze correspond to the population of the H1 hydrogen bonded to the outer CM atom. In the mixture of R-32 + R-1234ze, also the HC atoms bonded to the middle CM atom accumulate in the same region around R-32 as shown by the pink embedded surface. For R-32 + R-1234ze(E) though, the population density of this hydrogen around R-32 is much lower and therefore not shown in Figure 8d). In the vicinity of the R-32

0.278 0.245 0.223 0.190 0.146

± ± ± ± ±

0.024 0.014 0.029 0.004 0.019

0.173 ± 0.004 0.146 ± 0.006 0.129 ± 0.015

0.206 0.186 0.169 0.148 0.130

± ± ± ± ±

0.015 0.015 0.017 0.015 0.014

0.136 ± 0.010 0.111 ± 0.008 0.092 ± 0.008

0.255 0.214 0.192 0.167 0.137

± ± ± ± ±

0.001 0.016 0.015 0.015 0.016

0.158 ± 0.011 0.124 ± 0.009 0.106 ± 0.009

hydrogens, also small regions with a higher concentration of HFO-fluorine atoms exist. For R-1234yf and R-1234ze(E) this area is a favorable location for the FCM atoms, whereas for R1234ze, the FCT atoms are located there. 4.3. Binary Mixtures of Fluoropropenes with CO2. Densities and Viscosities. In general we intended to study the liquid-phase properties of binary mixtures of the fluoropropenes R-1234ze, R-1234ze(E), R-1234yf, or R-1216 and CO2 at the same temperatures, pressures, and compositions as we considered their binary mixtures with R-32. However, due to the VLE region at lower pressures or higher CO 2 concentrations, we had to limit our studies to p = 3.5 MPa and only performed simulations for xCO2 = 0.2 and 0.4 at 313.15 K/3.5 MPa. The simulation results for the liquid densities and viscosities are given in Tables 6 and 7 and are depicted in Figures 10 and 11. Also shown there are REFPROP calculations for the densities ρ(xCO2) and viscosities η(xCO2) in the mixtures CO2 + R1234yf, CO2 + R-1234ze(E) and CO2 + R-1216. The excellent agreement between REFPROP calculations and MD simulation results for the mixture densities of CO2 + R1234yf and CO2 + R-1234ze(E) could be expected as the binary mixing parameters in REFPROP were fitted to our molecular simulation results18 for the VLE properties in these systems. With averaged deviation of 0.84%, good agreement between MD simulations and REFPROP can also be found for the mixture CO2 + R-1216, for which the parameters in REFPROP are experimentally based, whereas the simulation studies are purely predictive. However, the simulation studies generally yield lower mixture densities for the CO2 + R1216 mixture than REFPROP. Again, no correlation is available for the mixture CO2 + R-1234ze for comparison with our simulation results. 249



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Structural Properties. We have again determined both radial and spatial distribution functions for the binary mixtures of CO2 + HFO at 273 K and 3.5 MPa and mole fraction of xCO2 = 0.4, i.e. at the same conditions as in our studies with R-32. Figure 12a) shows the CoM-RDFs of CO2 molecules around

Figure 10. Liquid densities from MD simulation studies for the binary mixture CO2 + R1234ze (open right-facing crossed triangle, blue, dotted line added to guide the eyes), CO2 + R-1234ze(E) (open crossed circle, red), CO2 + R-1234yf (open crossed square, green), and CO2 + R-1216 (open down crossed triangle, purple) at 273 K and p = 3.5 MPa, in comparison with calculated densities by REFPROP for CO2 + R-1234ze(E) (, red), CO2 + R-1234yf (, green) and CO2 + R-1216 (, purple).

Figure 12. Center-of-mass (CoM) RDFs in the binary mixtures CO2 + R1234ze (, blue), CO2 + R1234ze(E) (, red), CO2 + R1234yf (, green), and CO2 + R-1216 (, purple) at 273 K and 3.5 MPa and xCO2 = 0.4: (a) RDF of CO2 around the HFO molecules, (b) RDF of CO2 around other CO2 molecules, also shown is the corresponding RDF in the pure fluid (  ) at the same state point. (c) CoMRDFs of HFO molecules around other HFO molecules. Shown as dashed lines in the same color are the RDFs in the pure fluoropropenes at the same state point.

Figure 11. Liquid viscosities from MD simulation studies for the binary mixture CO2 + R1234ze (open right-facing crossed triangle, blue), CO2 + R-1234ze(E) (open crossed circle, red), CO2 + R-1234yf (open crossed square, green), and CO2 + R-1216 (open down crossed triangle, purple) at 273 K and p = 3.5 MPa. Also shown are calculated viscosities by REFPROP for CO2 + R-1234ze(E) (, red), CO2 + R1234yf (, green) and CO2 + R-1216 (, purple).

the CoM of the different fluoropropenes. The first peaks of the CO2−HFO RDFs can be found at smaller distances (4.5−4.8 A) compared to the corresponding R-32−HFO mixtures. The first peak in the mixture CO2+ R-1234ze is with 1.5 notably smaller than that of R-32−R-1234ze, whereas the maximum of the RDF of CO2 around R-1216 is with 1.8, clearly higher than that of R-32. Again, the comparable small first mixima in the mixtures CO2 + R1234yf, CO2 + R-1234ze(E), and CO2+ R1234ze do not suggest hydrogen-bonding interactions with the HFO hydrogens and CO2 oxygen atom. The CO2−CO2 CoM-RDFs in mixtures with different fluoropropenes are shown in Figure 12b). All mixtures exhibit a first maximum at about 4.0 A, with very similar peak heights in the order of 2.1. As before in the R-32−HFO mixtures, the peaks of CO2−CO2−RDFs in binary mixtures with fluoropropenes are higher than in the pure fluid (1.83), and also notably

For all CO2 + HFO mixtures studied here, the REFPROP calculations give a nearly linear decay of the viscosity with increasing xCO2. Only for the mixture viscosity of CO2 + R-1234ze(E) at 273 K, REFPROP predicts a positive deviation from linearity (shown as red dashed line). The MD simulation results for the mixture viscosities in CO2 + R1234yf, CO2 + R1234ze(E), and CO2+ R-1216 generally agree well with the REFPROP calculations within the range of their uncertainties. For CO2 + R-1234ze, the MD results also yield a nearly linear decay of η(xCO2) (blue dashed line) with the tendency to positive deviations from linearity. This is consistent with the predicted behavior from MD studies and REFPROP for the mixture CO2 + R-1234ze(E). 250



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Figure 13. Spatial distribution functions (SDF) in the binary mixtures (a) R-1216 + CO2, (b) R-1234yf + CO2, (c) R-1234ze + CO2 and (d) R1234ze(E) + R-32 at 273 K and 3.5 MPa, with xCO2 = 0.4 . Green surfaces indicate locations of FCT atoms, yellow and orange surfaces that of FCM atoms of the HFO molecules (bonded to outer or middle CM atoms, respectively). Red mashed contours represent cumulative populations of OCO2. White and pink mashed surfaces are areas of higher population of HFO hydrogens around CO2 (bonded to outer or middle CM atoms, respectively). All surfaces represent 1.5 times the average density.

higher than the CO2−HFO-RDFs. This is comparable to the observation made by Zhang and Siepmann47 in their study on ternary mixtures of CO2, n-alkanes, and perfluoroalkane. Comparing CO2−CO2, CO2−CHx, and CO2−CFx RDFs, they found the highest peaks in RDFs for the like CO2−CO2 pairs, from which they concluded that the smaller CO2 molecules tend to cluster. Thus, a similar conclusion can be drawn for mixtures of CO2 and fluoropropenes, and also for R32 + HFO mixtures, as discussed above. As before in mixtures with R-32, we have also compared the CoM-RDFs of different fluoropropenes in mixtures with CO2 compared to the pure HFO liquid. The depiction in Figure 12c) illustrates that, again, the form of the first peak in the mixture remains similar to that in the pure fluid but that their heights are reduced. The reduction is ∼0.08, similar for all CO2 + HFO mixtures, and slightly more pronounced than in mixtures with R-32 (0.04−0.07). This suggests that CO2 perturbs the local structure in the fluoropropenes slightly more than the presence of R-32 molecules. As the CoM-RDFs only provide a coarse and averaged picture of the interactions between CO2 and HFO molecules, we have again investigated the specific interaction sides and resulting local ordering in the mixtures by SDFs. As shown in Figure 13, we have analyzed the SDFs of CO2 and other HFO molecules around the fluoropropene molecules, and of the different fluoropropene atoms around CO2. As in our studies on R-32 mixtures and on the CoM-RDFs before, we have considered mixtures with xCO2 = 0.4 at 273 K and 3.5 MPa.

Thus, for the sake of comparability with the analysis of the R-32 mixtures, all surfaces shown in Figure 13 again represent 1.5 times the average density. In general, the regions with enhanced relative densities of CO2 oxygen atoms around the fluoropropene molecules (red mashed surfaces) are more widely extended than the corresponding areas of R-32 fluorines in the R-32 + HFO mixtures. This might explain why CO2 molecules perturb the local structure around the HFO molecules more than in R-32. The highest relative density (2.1) of CO2 molecules around fluoropropenes can be found in the mixture CO2 + R-1216. This, together with the highest peak for this system in the CoM-RDFs in Figure 12a), suggests that CO2 molecules slightly prefer to surround the perfluoropropene rather than the tetrafluoropropenes. Again, this is consistent with the conclusion by Zhang and Siepmann, who observed that the vicinity of the perfluoroalkanes is a slightly more favorable location for CO2 molecules compared to that of n-alkanes. We have also analyzed the distribution of the different HFO fluorine atoms around the CO2 molecules. In general, regions of higher concentrations of fluorine atoms of the HFO can be found as rings equatorial to the O−C−O axis, although the population densities vary for the different fluoropropenes. Population densities of >1.5 times the average value can only be observed for the FCM fluorines of R-1234yf and R-1234ze(E), shown as an orange surface in Figure 13b) and a yellow mash contour in Figure 13d), respectively. Regions with higher concentrations of the HFO hydrogens exist in front of the CO2 251



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Figure 14. Diffusivity of R-32 and CO2 in mixtures with different fluoropropenes at 273 K and 3.5 MPa. (a) Diffusion coefficient of R-32 in mixtures with R-1234yf (open crossed square, green), R-1234ze(E) (open crossed circle, red), R-1234ze (open crossed triangle, right facing, blue), and R1216 (open crossed down triangle, purple). b) Diffusion coefficient of CO2 in mixtures with R-1234yf (open crossed square, green), R-1234ze(E) (open crossed circle, red), R-1234ze (open crossed triangle, right facing, blue), and R-1216 (open crossed down triangle, purple). Also shown as lines are linear fits of the MD simulation results.

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CONCLUSION We have presented molecular dynamics simulations on the densities, viscosities and diffusion coefficients for the pure liquid fluoropropenes R-1234yf, R-1234ze(E), R-1234ze, and R-1216 at temperatures from T = (273 to 313) K under pressures up to 3.5 MPa. Comparison with experimental data and REFPROP calculations indicates that our molecular models for fluoropropenes yield reliable predictions for their thermophysical properties. We have additionally compared the dipole and effective quadrupole moments of the different fluoropropenes derived from ab initio simulations. This suggests that the relative high densities and viscosities of cisand trans-R-1234ze compared to those of R-1234yf result from stronger Coulombic interactions that are due to a high dipole moment for R-1234ze, but a high quadrupole moment for R1234ze(E). The different charge distributions in the fluoropropenes are due to the different number and locations of the fluorine atoms in the molecules, which in turn also change the local ordering in the liquids. This was illustrated by our analysis of the SDFs of different fluorine atoms around the HFO molecules. We have also performed MD simulation studies on binary mixtures of the fluoropropenes with CO2 and R-32 to provide information on their liquid densities and viscosities for which experimental data are scarce. A comparison with predictions by REFPROP for the mixtures of R-32 and CO2 with R-1234yf, R1234ze(E), and R-1216 show again a generally good agreement between molecular simulation and correlation results. To gain insight into the microscopic structures and the nature of interaction between fluoropropenes and R-32 or CO2 in the liquid mixtures, we have analyzed both radial and spatial distribution functions at the state point T = 273 K and p = 3.5 MPa with xCO2/xR‑32 = 0.4 as an illustrative example. The higher peaks of R-32−R-32 and CO2−CO2 in the binary mixtures compared to those of the pure liquids suggest that both components prefer to form clusters in mixtures with fluoropropenes. The comparison of the CoM-RDF and SDFs for the different R-32 + HFO mixtures indicates stronger

oxygens, shown as mashed contours with hemispherical shape in Figure 13b−d). Similar to the observations in its mixture with R-32, both hydrogens (white and pink surface) of the cisisomer exhibit population densities of >1.5 times around the CO2 molecules, whereas for R-1234ze(E) only the outer H1 atom shows a relative higher concentration in the vicinity of the CO2 oxygens. For the mixture studies here, maximal population densities of HFO hydrogens around CO2 do not exceed values of 1.9 times the average value, which again do not suggest pronounced hydrogen-bonding interactions. 4.4. Diffusivity of CO2 and R-32 in Binary Mixtures with Fluoropropenes. At the same state point T = 273 K and p = 3.5 MPa at which we have analyzed the local structures of the mixtures, we have additionally studied the diffusivity of CO2 and R-32 in different fluoropropenes. The diffusion coefficients as functions of composition in mixtures of R-32 + HFO and CO2 + HFO are depicted in Figure 14 a) and b), respectively. It is particularly noticeable that the diffusivity of CO2 in mixtures with different fluoropropenes differ more than that of R-32. This is most pronounced by comparing their diffusivities in R1234yf and R-1216. Whereas at a mole fraction of x1 = 0.4 the diffusion coefficient of R-32 in the two HFOs only differs by ∼13%, the diffusion coefficient of CO2 in R-1234yf is more than twice the value of that of DCO2 in R-1216. For both R-32 and CO2 their diffusivities in the cis- and trans-isomer of R1234ze are always similar, with a higher diffusion coefficient in R-1234ze(E). In general, R-32 exhibits the lowest diffusivity in mixtures with R-1234ze, whereas CO2 has the smallest diffusion coefficients in mixtures with R-1216. This is consistent with our finding from the structural analysis that the attractive interactions between R-32 and R-1234ze are stronger than with the other fluoropropenes. CO2 on the other side exhibits the strongest attractive interactions with the perfluoropropene R1216 that causes its reduced mobility in these mixtures. 252



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interactions of R-32 with R-1234ze than with the other fluoropropenes studied here. CO2 on the other side prefers to surround the perfluoropropene R-1216 rather than the tetrafluoropropenes. This is also supported by the analysis of the diffusion coefficients of R-32 and CO2 in the different fluoropropenes, as R-32 exhibits the lowest diffusivity in mixtures with R-1234ze, whereas CO2 exhibits the lowest diffusivity in mixtures with R-1216. In general, both the peak heights in the CO2/R-32 + HFO RDFs, and the relative population densities in the SDFs are relatively small. Thus, no evidence was found for pronounced hydrogen-bonding interactions between the R-32 and HFO fluorines and hydrogens or the CO2 oxygen and the HFO hydrogens.

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AUTHOR INFORMATION

Corresponding Author

*Telephone: +49 531 391 2628. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Dr. Ryo Akasaka, Kyushu Sangyo University, and Dr. Katsuyuki Tanaka, Nihon University, for sharing their experimental information for R-1234ze with us before publishing.

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REFERENCES

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