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Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2-pentanone, 1-octene or ethylbenzene via molecular simulation
ARTICLE IN PRESS MLQ-07520; No of Pages 6 Journal of Molecular Liquids xxx (2017) xxx–xxx
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Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2-pentanone, 1-octene or ethylbenzene via molecular simulation Michael T. Huber, John M. Stubbs* Department of Chemistry and Physics, University of New England, 11 Hills Beach Road, Biddeford, ME 04005, United States
A R T I C L E
I N F O
Article history: Received 8 February 2017 Received in revised form 14 June 2017 Accepted 15 June 2017 Available online xxxx Keywords: Supercritical carbon dioxide Vapor-liquid equilibrium Pressure-composition diagram Monte Carlo simulation
A B S T R A C T Pressure-composition phase diagrams were determined for binary systems of CO2 + 1-pentanol, CO2 + 2-pentanone, CO2 + 1-octene, and CO2 + ethylbenzene at 308.15, 328.15, and 348.15 K. Monte Carlo molecular simulations in the Gibbs ensemble allowed coexistence compositions to be determined as a function of pressure. Good agreement to experimental data is achieved and is improved upon consideration of the 2 K over prediction of the pure CO2 critical temperature. The solvation structure with CO2 is also examined. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluids have become increasingly important for their potential uses in a variety of settings including separations and reaction media [1,2] as well as pharmaceutical particle formation [3]. In particular, supercritical carbon dioxide (sc-CO2 ) has been studied extensively due to its comparatively mild critical point of 304.14 K, 7.3843 MPa, and 0.4682 g cm −3 [4]. Solvent properties of sc-CO2 are readily tunable through pressure or temperature changes or addition of a cosolvent [5,6], however the applicability is limited in part due to lack of knowledge of phase behavior, particularly at elevated pressures. One route to predicting the phase behavior of systems of interest includes molecular simulation which allows multiphase and solubility equilibria to be studied [7]. Previously, we have studied the influence of CO2 on the solubility of four organic solutes in poly(ethylene glycol) [8] where the solutes covered a range of structures and polarities. Many previous studies have shown that molecular simulation is able to successfully be applied to binary phase behavior involving supercritical fluids, e.g. [9–11]. In this work we determine the binary phase behavior between sc-CO2 and four organic molecules illustrated in Fig. 1 – ethylbenzene (EB), 1-octene (OCT), 2-pentanone (PNE) and 1-pentanol (PTL) – in order to explore the ability of
* Corresponding author. E-mail address: [email protected] (J.M. Stubbs).
molecular simulation to predict the properties of arbitrary systems not included in the development of the molecular models and, where possible, determine level of agreement with experimental values. The choice of solutes was made on the basis of representing polar protic (PTL) and polar aprotic (PNE) as well as non-polar flexible (OCT) and rigid (EB) structures for molecules of comparable composition (EB and OCT, PNE and PTL) and comparable strength of intermolecular interactions as represented approximately by normal boiling point values (409.3 K for EB and 411 K for PTL [12]). 2. Methods 2.1. Molecular models All molecules were represented with the transferable potentials for phase equilibria - united atom (TraPPE-UA) force field of Siepmann and coworkers [13–16] which treats carbon atoms and their bonded hydrogens as single pseudoatom interaction sites. Generally, this force field employs rigid bond lengths, flexible bond angle bending and dihedral rotations for intramolecular interactions of sites separated by up to 3 bonds. For more distant intramolecular sites or sites on different molecules, intermolecular interactions are considered and are made up of the Lennard-Jones 12-6 potential for dispersion and repulsion as well as the Coulombic potential. Electrostatic interactions were represented through partial charge sites on each atom in CO2 , the ketone carbon and oxygen sites in PNE, and
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Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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Fig. 1. Structural representation of the four organic solutes investigated in this study.
the hydroxyl hydrogen, oxygen and its bonded CH2 group in PTL. All parameters in the force field have been developed to reproduce single-component vapor-liquid equilibria and critical properties and parameters of identical functional groups (e.g. −CH2 −CH3 ) are consistent across molecules. Whereas CO2 and the aromatic ring of EB are kept rigid, the remaining molecules or parts of molecules are conformationally flexible. 2.2. Simulation details Simulations were carried out in the NPT Gibbs ensemble [17–19] with translational, rotational, and coupled-decoupled configurational bias Monte Carlo (CBMC) regrowth moves [20–23] to sample configuration space together with CBMC particle-exchange moves to equilibrate chemical potential and volume change moves to equilibrate pressure. Temperature values of 308.15 K, 328.15 K, and 348.15 K were studied each over a range of pressure values starting at 1 MPa and increasing in 1 MPa increments (i.e. 1, 2, 3, . . . MPa) until the upper critical solution pressure was exceeded. NCO2 + Nsolute = 700 total molecules were used with either 400 + 300, 500 + 200, or 600 + 100 employed depending upon the lever rule and which composition would yield a sufficiently large liquid box size of at least twice the non-bonded interaction cutoff, taken to be 12 Å. Analytical tail corrections were used beyond the cutoff distance, and long-range Coulombic interactions were determined with an Ewald summation with Kmax = 6, j × L = 5, and tin-foil boundary conditions [24]. At least 105 and 1.5 × 106 Monte Carlo cycles were used for equilibration and production, respectively, where 1 Monte Carlo cycle consists of Nmolecules = 700 Monte Carlo moves. Statistical uncertainties were estimated by dividing the simulation data into five blocks and determining the averages and standard errors of mean between block average data [24]. 3. Results and discussion 3.1. Phase equilibria Pressure-composition phase diagram results for EB + CO2 are shown in Fig. 2. As the temperature increases, compositions of the EB-rich phase are shifted to higher pressures, and it can be inferred that the location of the upper critical solution pressure (UCSP) increases. Though in qualitative agreement with experimental trends, compared to experimental results [25] at the same temperatures (308.15 K and 328.15 K), it is evident the simulation results over predict the amount of CO2 in the EB-rich liquid phase, or equivalently are shifted to approximately 1–3 MPa lower pressures. This is likely due in part to the differences between the model
Fig. 2. EB + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at a) 308.15, b) 328.15, and c) 348.15 K, respectively; error bars are smaller than the symbol size. Filled symbols indicate experimental results with black circles at 308 K, blue right triangles at 318 K, red squares at 328 K [25], black inverse triangles at 313.2 K and green triangles at 353.2 K [26]. A close up of the CO2 -rich region for all results is shown in d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and experimental critical points – the CO2 model, which estimates the critical point as 306.2 K, 7.77 MPa, and 0.4649 g cm −3 [13], over predicts the critical temperature by 0.6% (2 K) – so that the simulation results are more appropriately compared to experimental data at slightly lower temperatures. In fact, there is good agreement between the simulation results at 328.15 K and the experimental data at 318 K particularly at higher pressures. In Fig. 2d, trends in the solubility of EB in CO2 are well reproduced by the simulation results both in terms of the increasing amount of organic compound in CO2 as temperature increases as well as the presence of a maximum value of xCO2 . However, simulation results in general appear shifted to higher solubilities of EB, i.e. lower xCO2 which is an indication that the cross-interactions between molecule types are slightly over predicted; alternatively, this may be due to the model’s over prediction of the vapor pressure of EB [14]. Fig. 3 shows the pressure-composition results for OCT + CO2 . Showing a very similar temperature dependence as EB + CO2 , the simulation results are also in good agreement with the 333.15 K experimental data [27]. Although the 328.15 K OCT-rich phase simulation results are shifted to noticeably lower pressures than the 333.15 K experimental points, this is in part due to the temperature difference as well as the higher critical temperature of the CO2 ; the over prediction of the vapor pressure of OCT [14] may also play a role. Simulation results for PNE + CO2 in Fig. 4 show the same phase diagram shapes and temperature dependencies as those in Figs. 2 and 3. These results are in good agreement with available experimental data [28], considering the uniform 5 K temperature difference, and though the experimental data extend to higher pressures than the simulation results this is due to the difficulty in carrying out multiphase simulations too close to the critical point where fluctuations and finite size effects prevent reliable property estimation. The final set of phase diagrams, for PTL, are shown in Fig. 5, which also includes several experimental data sets for temperatures at or close to the simulation values. All simulation results reproduce trends in the experimental data; additionally, comparison to
Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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Fig. 3. OCT + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at 308.15, 328.15, and 348.15 K, respectively; error bars are smaller than the symbol size. Filled red circles indicate experimental results at 333.15 K [27]. A close up of the CO2 -rich region for all results is shown in b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
experimental points at temperatures slightly below those of the simulations show good agreement particularly at higher pressures. For example, in Fig. 5c simulation results at 348.15 K closely match experimental data around the UCSP taken at 343.2 K [29] and 343.7 K [31] while at lower pressures the simulations over predict the amount of CO2 in the liquid phase; similarly, in Fig. 5b the simulation results at 328.15 K compare favorably to experimental data at 325.9 K [30] near the UCSP but are also shifted to higher xCO2 values at lower pressures. Turning to the predominantly CO2 vapor-like phase in Fig. 5d, there is essentially quantitative agreement between simulation results and comparable experimental values, though at 348.15 K the simulations over predict the amount of PTL slightly for pressures below 6 MPa. Better agreement to the experimental vapor pressure for PTL [15] compared to EB (vide supra) may account for the excellent agreement for vapor-like phase composition values shown here. For reference, saturated coexistence densities of both vapor-like and liquid-like phases for all simulated systems in this work are provided in Table 1. 3.2. Structural analysis The radial distribution function, g(r), is a means to understanding condensed phase structure [24]. Defined as the number of sites of one type in a radial shell centered on another site relative to a completely homogeneous distribution, it can readily depict the solvation
Fig. 4. PNE + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at 308.15, 328.15, and 348.15 K, respectively; error bars are smaller than the symbol size. Filled symbols indicate experimental results with black circles at 313.15 K, red squares at 333.15 K, and green inverse triangles at 353.15 K [28]. A close up of the CO2 -rich region for all results is shown in b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. PTL + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at a) 308.15, b) 328.15, and c) 348.15 K, respectively; unless shown, error bars are smaller than the symbol size. Filled symbols indicate experimental results with black circles at 313.2 K, green crosses at 343.2 K [29] black inverse triangles at 314.6 K, red squares at 325.9 K blue right triangles at 337.4 K [30], red triangles at 333.1 K, and green left triangles at 343.7 K [31]. A close up of the CO2 -rich region for all results is shown in d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
environment and relative amount of rigidity in solvation interactions. Shown in Fig. 6a and b are center-of-mass (COM) g(r) graphs for CO2 around CO2 as well as CO2 around EB at 328.15 K and 1, 4 and 8 MPa. In all cases the first peak for CO2 around itself occurs at around 4 Å. For the liquid phase in Fig. 6a, there is also a broad second peak around 8 Å; as pressure increases, the first peak decreases while the second increases, as does the minimum between peaks. This shift is consistent with a shift towards a less defined, more supercritical fluid-like structure such as that seen in Fig. 6b. There is a similar shift in the CO2 around EB peaks in the liquid phase. The solvation structure of CO2 around PTL, as depicted in Fig. 6c and d, is not much different which shows the same pressure-induced structural changes. Differences between CO2 around EB compared to PTL are primarily due to the smaller size of PTL which allows their COMs to approach more closely. The g(r) curves can be integrated along with the bulk density values to yield number integrals, N(r), which give the number of sites of a particular type within a radius r of another site. Fig. 7 shows the corresponding N(r) curves from the g(r) depicted in Fig. 6. Similar to what we have reported previously [8], the number of CO2 molecules around each other is initially larger than the number around either EB or PTL due to the smaller size of CO2 . Subsequently for the vaporlike phases (Fig. 7b and d) there is a cross-over point after which the number of CO2 molecules around either EB or PTL exceeds the number around itself; for EB this occurs at around 5.7 Å and for PTL between 5.0 and 5.4 Å. On the other hand for the liquid phases the number of CO2 molecules around themselves either matches the number around EB or PTL, or exceeds it by as many as two molecules for PTL at 8 MPa. For EB the highest value is closer to an excess of 1 molecule of CO2 around itself. This is despite there being a much higher xCO2 for EB, however it is consistent with a microheterogeneous view (i.e. CO2 -rich and CO2 -poor regions) of the liquid environment for PTL due to its ability to form hydrogen-bonded
Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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Table 1 Coexistence densities; subscripts indicate uncertainty in the final digit. EB
308.15 K
P/MPa
qv /g cm −3
ql /g cm −3
qv /g cm −3
ql /g cm −3
qv /g cm −3
ql /g cm −3
1 2 3 4 5 6 7 8 9
0.018171 0.038004 0.060163 0.08551 0.11561 0.15353
0.84871 0.85331 0.85801 0.86292 0.86546 0.85687
0.017312 0.035362 0.055033 0.076715 0.10121 0.12863 0.16182 0.2021
0.82942 0.83131 0.83391 0.83562 0.83682 0.83555 0.8251 0.7963
0.016773 0.033611 0.051414 0.070844 0.092085 0.11471 0.14023 0.16951 0.20154
0.81051 0.81142 0.81183 0.81241 0.81274 0.81004 0.80707 0.80197 0.7814
OCT
308.15 K −3
P/MPa
qv /g cm
1 2 3 4 5 6 7 8 9 10
0.018151 0.037933 0.060113 0.085527 0.11571
PNE
308.15 K −3
P/MPa
qv /g cm
1 2 3 4 5 6 7 8 9 10
0.018161 0.038002 0.060036 0.085735 0.11591
PTL
308.15 K −3
P/MPa
qv /g cm
1 2 3 4 5 6 7 8 9 10 11 12 13
0.017941 0.037661 0.059644 0.084864 0.11461 0.15201 0.2071
328.15 K
348.15 K
328.15 K ql /g cm
−3
0.72112 0.73271 0.74601 0.76127 0.77715
qv /g cm
−3
0.017161 0.035342 0.055065 0.076854 0.10142 0.12962 0.16292
348.15 K ql /g cm
−3
0.70051 0.70781 0.71523 0.72282 0.73052 0.73663 0.74045
328.15 K ql /g cm
−3
0.80241 0.81792 0.83211 0.84503 0.85235
qv /g cm
−3
0.017231 0.035384 0.055085 0.077076 0.10161 0.12953 0.16322 0.20678
ql /g cm
0.80973 0.81681 0.82572 0.83282 0.84162 0.84963 0.8462
qv /g cm
−3
0.016771 0.034782 0.054291 0.075746 0.099753 0.12682 0.15872 0.19744 0.24963 0.568
aggregates analogous to other alcohols, e.g. [32–34]. Analogous g(r) and N(r) curves for OCT and PNE are not significantly different from those of EB after accounting for variations in density and xCO2 . 4. Conclusions Pressure-composition phase diagrams for CO2 and several different organic molecules were readily predicted by Monte Carlo
ql /g cm −3
0.016561 0.033441 0.051425 0.070915 0.09221 0.11542 0.14103 0.17085 0.20613 0.2522
0.68121 0.68581 0.69001 0.69432 0.69811 0.70173 0.70392 0.70436 0.7011 0.6914
348.15 K ql /g cm
−3
0.77782 0.78732 0.79612 0.80343 0.80882 0.81135 0.8081 0.7993
328.15 K −3
qv /g cm −3
qv /g cm −3
ql /g cm −3
0.016643 0.033503 0.051614 0.071189 0.09262 0.11591 0.14185 0.17278 0.20799 0.2552
0.75471 0.76101 0.76643 0.77083 0.77432 0.77566 0.77556 0.7732 0.7642 0.7523
348.15 K ql /g cm
−3
0.79151 0.79602 0.80112 0.80551 0.81002 0.81412 0.81693 0.81837 0.8171 0.7875
qv /g cm −3
ql /g cm −3
0.015831 0.032481 0.050193 0.069265 0.089817 0.11231 0.13721 0.16461 0.19642 0.23285 0.2791 0.3333 0.441
0.77411 0.77661 0.77922 0.78243 0.78514 0.78704 0.78912 0.79053 0.7891 0.7891 0.7843 0.7762 0.7524
molecular simulation. Without any experimental data as input, good agreement with available experimental data was achieved, where deviations, when present, can be attributed to the slight over prediction of the CO2 model’s critical temperature and organic compound’s vapor pressure. Based on these results, provided that molecular force field parameters are available this approach can be applied to other systems of interest and reasonable agreement with experimental data can be anticipated. Structural analysis
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and J.I. Siepmann for discussion, and the University of Minnesota Supercomputing Institute where the calculations were partially carried out. References
Fig. 6. Center-of-mass radial distribution functions for CO2 around CO2 (solid lines) and CO2 around the second component (dashed lines) at 328.15 K. Black, red and green indicate pressures of 1, 4 and 8 MPa, respectively. a) EB liquid phase; b) EB vapor-like phase; c) PTL liquid phase; d) PTL vapor-like phase. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
indicates a shift from a liquid-like to supercritical fluid-like solvation environment as pressure increases.
Acknowledgments The authors wish to thank the Maine Space Grant Consortium Undergraduate Scholarship Program and the University of New England’s College of Arts and Sciences Dean’s office for support, J. Bellan
Fig. 7. Number integrals corresponding to radial distribution functions in Fig. 6. Line styles as in Fig. 6.
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Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2-pentanone, 1-octene or ethylbenzene via molecular simulation Michael T. Huber, John M. Stubbs* Department of Chemistry and Physics, University of New England, 11 Hills Beach Road, Biddeford, ME 04005, United States
A R T I C L E
I N F O
Article history: Received 8 February 2017 Received in revised form 14 June 2017 Accepted 15 June 2017 Available online xxxx Keywords: Supercritical carbon dioxide Vapor-liquid equilibrium Pressure-composition diagram Monte Carlo simulation
A B S T R A C T Pressure-composition phase diagrams were determined for binary systems of CO2 + 1-pentanol, CO2 + 2-pentanone, CO2 + 1-octene, and CO2 + ethylbenzene at 308.15, 328.15, and 348.15 K. Monte Carlo molecular simulations in the Gibbs ensemble allowed coexistence compositions to be determined as a function of pressure. Good agreement to experimental data is achieved and is improved upon consideration of the 2 K over prediction of the pure CO2 critical temperature. The solvation structure with CO2 is also examined. © 2017 Elsevier B.V. All rights reserved.
1. Introduction Supercritical fluids have become increasingly important for their potential uses in a variety of settings including separations and reaction media [1,2] as well as pharmaceutical particle formation [3]. In particular, supercritical carbon dioxide (sc-CO2 ) has been studied extensively due to its comparatively mild critical point of 304.14 K, 7.3843 MPa, and 0.4682 g cm −3 [4]. Solvent properties of sc-CO2 are readily tunable through pressure or temperature changes or addition of a cosolvent [5,6], however the applicability is limited in part due to lack of knowledge of phase behavior, particularly at elevated pressures. One route to predicting the phase behavior of systems of interest includes molecular simulation which allows multiphase and solubility equilibria to be studied [7]. Previously, we have studied the influence of CO2 on the solubility of four organic solutes in poly(ethylene glycol) [8] where the solutes covered a range of structures and polarities. Many previous studies have shown that molecular simulation is able to successfully be applied to binary phase behavior involving supercritical fluids, e.g. [9–11]. In this work we determine the binary phase behavior between sc-CO2 and four organic molecules illustrated in Fig. 1 – ethylbenzene (EB), 1-octene (OCT), 2-pentanone (PNE) and 1-pentanol (PTL) – in order to explore the ability of
* Corresponding author. E-mail address: [email protected] (J.M. Stubbs).
molecular simulation to predict the properties of arbitrary systems not included in the development of the molecular models and, where possible, determine level of agreement with experimental values. The choice of solutes was made on the basis of representing polar protic (PTL) and polar aprotic (PNE) as well as non-polar flexible (OCT) and rigid (EB) structures for molecules of comparable composition (EB and OCT, PNE and PTL) and comparable strength of intermolecular interactions as represented approximately by normal boiling point values (409.3 K for EB and 411 K for PTL [12]). 2. Methods 2.1. Molecular models All molecules were represented with the transferable potentials for phase equilibria - united atom (TraPPE-UA) force field of Siepmann and coworkers [13–16] which treats carbon atoms and their bonded hydrogens as single pseudoatom interaction sites. Generally, this force field employs rigid bond lengths, flexible bond angle bending and dihedral rotations for intramolecular interactions of sites separated by up to 3 bonds. For more distant intramolecular sites or sites on different molecules, intermolecular interactions are considered and are made up of the Lennard-Jones 12-6 potential for dispersion and repulsion as well as the Coulombic potential. Electrostatic interactions were represented through partial charge sites on each atom in CO2 , the ketone carbon and oxygen sites in PNE, and
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Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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Fig. 1. Structural representation of the four organic solutes investigated in this study.
the hydroxyl hydrogen, oxygen and its bonded CH2 group in PTL. All parameters in the force field have been developed to reproduce single-component vapor-liquid equilibria and critical properties and parameters of identical functional groups (e.g. −CH2 −CH3 ) are consistent across molecules. Whereas CO2 and the aromatic ring of EB are kept rigid, the remaining molecules or parts of molecules are conformationally flexible. 2.2. Simulation details Simulations were carried out in the NPT Gibbs ensemble [17–19] with translational, rotational, and coupled-decoupled configurational bias Monte Carlo (CBMC) regrowth moves [20–23] to sample configuration space together with CBMC particle-exchange moves to equilibrate chemical potential and volume change moves to equilibrate pressure. Temperature values of 308.15 K, 328.15 K, and 348.15 K were studied each over a range of pressure values starting at 1 MPa and increasing in 1 MPa increments (i.e. 1, 2, 3, . . . MPa) until the upper critical solution pressure was exceeded. NCO2 + Nsolute = 700 total molecules were used with either 400 + 300, 500 + 200, or 600 + 100 employed depending upon the lever rule and which composition would yield a sufficiently large liquid box size of at least twice the non-bonded interaction cutoff, taken to be 12 Å. Analytical tail corrections were used beyond the cutoff distance, and long-range Coulombic interactions were determined with an Ewald summation with Kmax = 6, j × L = 5, and tin-foil boundary conditions [24]. At least 105 and 1.5 × 106 Monte Carlo cycles were used for equilibration and production, respectively, where 1 Monte Carlo cycle consists of Nmolecules = 700 Monte Carlo moves. Statistical uncertainties were estimated by dividing the simulation data into five blocks and determining the averages and standard errors of mean between block average data [24]. 3. Results and discussion 3.1. Phase equilibria Pressure-composition phase diagram results for EB + CO2 are shown in Fig. 2. As the temperature increases, compositions of the EB-rich phase are shifted to higher pressures, and it can be inferred that the location of the upper critical solution pressure (UCSP) increases. Though in qualitative agreement with experimental trends, compared to experimental results [25] at the same temperatures (308.15 K and 328.15 K), it is evident the simulation results over predict the amount of CO2 in the EB-rich liquid phase, or equivalently are shifted to approximately 1–3 MPa lower pressures. This is likely due in part to the differences between the model
Fig. 2. EB + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at a) 308.15, b) 328.15, and c) 348.15 K, respectively; error bars are smaller than the symbol size. Filled symbols indicate experimental results with black circles at 308 K, blue right triangles at 318 K, red squares at 328 K [25], black inverse triangles at 313.2 K and green triangles at 353.2 K [26]. A close up of the CO2 -rich region for all results is shown in d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
and experimental critical points – the CO2 model, which estimates the critical point as 306.2 K, 7.77 MPa, and 0.4649 g cm −3 [13], over predicts the critical temperature by 0.6% (2 K) – so that the simulation results are more appropriately compared to experimental data at slightly lower temperatures. In fact, there is good agreement between the simulation results at 328.15 K and the experimental data at 318 K particularly at higher pressures. In Fig. 2d, trends in the solubility of EB in CO2 are well reproduced by the simulation results both in terms of the increasing amount of organic compound in CO2 as temperature increases as well as the presence of a maximum value of xCO2 . However, simulation results in general appear shifted to higher solubilities of EB, i.e. lower xCO2 which is an indication that the cross-interactions between molecule types are slightly over predicted; alternatively, this may be due to the model’s over prediction of the vapor pressure of EB [14]. Fig. 3 shows the pressure-composition results for OCT + CO2 . Showing a very similar temperature dependence as EB + CO2 , the simulation results are also in good agreement with the 333.15 K experimental data [27]. Although the 328.15 K OCT-rich phase simulation results are shifted to noticeably lower pressures than the 333.15 K experimental points, this is in part due to the temperature difference as well as the higher critical temperature of the CO2 ; the over prediction of the vapor pressure of OCT [14] may also play a role. Simulation results for PNE + CO2 in Fig. 4 show the same phase diagram shapes and temperature dependencies as those in Figs. 2 and 3. These results are in good agreement with available experimental data [28], considering the uniform 5 K temperature difference, and though the experimental data extend to higher pressures than the simulation results this is due to the difficulty in carrying out multiphase simulations too close to the critical point where fluctuations and finite size effects prevent reliable property estimation. The final set of phase diagrams, for PTL, are shown in Fig. 5, which also includes several experimental data sets for temperatures at or close to the simulation values. All simulation results reproduce trends in the experimental data; additionally, comparison to
Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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Fig. 3. OCT + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at 308.15, 328.15, and 348.15 K, respectively; error bars are smaller than the symbol size. Filled red circles indicate experimental results at 333.15 K [27]. A close up of the CO2 -rich region for all results is shown in b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
experimental points at temperatures slightly below those of the simulations show good agreement particularly at higher pressures. For example, in Fig. 5c simulation results at 348.15 K closely match experimental data around the UCSP taken at 343.2 K [29] and 343.7 K [31] while at lower pressures the simulations over predict the amount of CO2 in the liquid phase; similarly, in Fig. 5b the simulation results at 328.15 K compare favorably to experimental data at 325.9 K [30] near the UCSP but are also shifted to higher xCO2 values at lower pressures. Turning to the predominantly CO2 vapor-like phase in Fig. 5d, there is essentially quantitative agreement between simulation results and comparable experimental values, though at 348.15 K the simulations over predict the amount of PTL slightly for pressures below 6 MPa. Better agreement to the experimental vapor pressure for PTL [15] compared to EB (vide supra) may account for the excellent agreement for vapor-like phase composition values shown here. For reference, saturated coexistence densities of both vapor-like and liquid-like phases for all simulated systems in this work are provided in Table 1. 3.2. Structural analysis The radial distribution function, g(r), is a means to understanding condensed phase structure [24]. Defined as the number of sites of one type in a radial shell centered on another site relative to a completely homogeneous distribution, it can readily depict the solvation
Fig. 4. PNE + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at 308.15, 328.15, and 348.15 K, respectively; error bars are smaller than the symbol size. Filled symbols indicate experimental results with black circles at 313.15 K, red squares at 333.15 K, and green inverse triangles at 353.15 K [28]. A close up of the CO2 -rich region for all results is shown in b). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 5. PTL + CO2 pressure-composition phase diagrams. Black, red and green open diamonds indicate simulation results at a) 308.15, b) 328.15, and c) 348.15 K, respectively; unless shown, error bars are smaller than the symbol size. Filled symbols indicate experimental results with black circles at 313.2 K, green crosses at 343.2 K [29] black inverse triangles at 314.6 K, red squares at 325.9 K blue right triangles at 337.4 K [30], red triangles at 333.1 K, and green left triangles at 343.7 K [31]. A close up of the CO2 -rich region for all results is shown in d). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
environment and relative amount of rigidity in solvation interactions. Shown in Fig. 6a and b are center-of-mass (COM) g(r) graphs for CO2 around CO2 as well as CO2 around EB at 328.15 K and 1, 4 and 8 MPa. In all cases the first peak for CO2 around itself occurs at around 4 Å. For the liquid phase in Fig. 6a, there is also a broad second peak around 8 Å; as pressure increases, the first peak decreases while the second increases, as does the minimum between peaks. This shift is consistent with a shift towards a less defined, more supercritical fluid-like structure such as that seen in Fig. 6b. There is a similar shift in the CO2 around EB peaks in the liquid phase. The solvation structure of CO2 around PTL, as depicted in Fig. 6c and d, is not much different which shows the same pressure-induced structural changes. Differences between CO2 around EB compared to PTL are primarily due to the smaller size of PTL which allows their COMs to approach more closely. The g(r) curves can be integrated along with the bulk density values to yield number integrals, N(r), which give the number of sites of a particular type within a radius r of another site. Fig. 7 shows the corresponding N(r) curves from the g(r) depicted in Fig. 6. Similar to what we have reported previously [8], the number of CO2 molecules around each other is initially larger than the number around either EB or PTL due to the smaller size of CO2 . Subsequently for the vaporlike phases (Fig. 7b and d) there is a cross-over point after which the number of CO2 molecules around either EB or PTL exceeds the number around itself; for EB this occurs at around 5.7 Å and for PTL between 5.0 and 5.4 Å. On the other hand for the liquid phases the number of CO2 molecules around themselves either matches the number around EB or PTL, or exceeds it by as many as two molecules for PTL at 8 MPa. For EB the highest value is closer to an excess of 1 molecule of CO2 around itself. This is despite there being a much higher xCO2 for EB, however it is consistent with a microheterogeneous view (i.e. CO2 -rich and CO2 -poor regions) of the liquid environment for PTL due to its ability to form hydrogen-bonded
Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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Table 1 Coexistence densities; subscripts indicate uncertainty in the final digit. EB
308.15 K
P/MPa
qv /g cm −3
ql /g cm −3
qv /g cm −3
ql /g cm −3
qv /g cm −3
ql /g cm −3
1 2 3 4 5 6 7 8 9
0.018171 0.038004 0.060163 0.08551 0.11561 0.15353
0.84871 0.85331 0.85801 0.86292 0.86546 0.85687
0.017312 0.035362 0.055033 0.076715 0.10121 0.12863 0.16182 0.2021
0.82942 0.83131 0.83391 0.83562 0.83682 0.83555 0.8251 0.7963
0.016773 0.033611 0.051414 0.070844 0.092085 0.11471 0.14023 0.16951 0.20154
0.81051 0.81142 0.81183 0.81241 0.81274 0.81004 0.80707 0.80197 0.7814
OCT
308.15 K −3
P/MPa
qv /g cm
1 2 3 4 5 6 7 8 9 10
0.018151 0.037933 0.060113 0.085527 0.11571
PNE
308.15 K −3
P/MPa
qv /g cm
1 2 3 4 5 6 7 8 9 10
0.018161 0.038002 0.060036 0.085735 0.11591
PTL
308.15 K −3
P/MPa
qv /g cm
1 2 3 4 5 6 7 8 9 10 11 12 13
0.017941 0.037661 0.059644 0.084864 0.11461 0.15201 0.2071
328.15 K
348.15 K
328.15 K ql /g cm
−3
0.72112 0.73271 0.74601 0.76127 0.77715
qv /g cm
−3
0.017161 0.035342 0.055065 0.076854 0.10142 0.12962 0.16292
348.15 K ql /g cm
−3
0.70051 0.70781 0.71523 0.72282 0.73052 0.73663 0.74045
328.15 K ql /g cm
−3
0.80241 0.81792 0.83211 0.84503 0.85235
qv /g cm
−3
0.017231 0.035384 0.055085 0.077076 0.10161 0.12953 0.16322 0.20678
ql /g cm
0.80973 0.81681 0.82572 0.83282 0.84162 0.84963 0.8462
qv /g cm
−3
0.016771 0.034782 0.054291 0.075746 0.099753 0.12682 0.15872 0.19744 0.24963 0.568
aggregates analogous to other alcohols, e.g. [32–34]. Analogous g(r) and N(r) curves for OCT and PNE are not significantly different from those of EB after accounting for variations in density and xCO2 . 4. Conclusions Pressure-composition phase diagrams for CO2 and several different organic molecules were readily predicted by Monte Carlo
ql /g cm −3
0.016561 0.033441 0.051425 0.070915 0.09221 0.11542 0.14103 0.17085 0.20613 0.2522
0.68121 0.68581 0.69001 0.69432 0.69811 0.70173 0.70392 0.70436 0.7011 0.6914
348.15 K ql /g cm
−3
0.77782 0.78732 0.79612 0.80343 0.80882 0.81135 0.8081 0.7993
328.15 K −3
qv /g cm −3
qv /g cm −3
ql /g cm −3
0.016643 0.033503 0.051614 0.071189 0.09262 0.11591 0.14185 0.17278 0.20799 0.2552
0.75471 0.76101 0.76643 0.77083 0.77432 0.77566 0.77556 0.7732 0.7642 0.7523
348.15 K ql /g cm
−3
0.79151 0.79602 0.80112 0.80551 0.81002 0.81412 0.81693 0.81837 0.8171 0.7875
qv /g cm −3
ql /g cm −3
0.015831 0.032481 0.050193 0.069265 0.089817 0.11231 0.13721 0.16461 0.19642 0.23285 0.2791 0.3333 0.441
0.77411 0.77661 0.77922 0.78243 0.78514 0.78704 0.78912 0.79053 0.7891 0.7891 0.7843 0.7762 0.7524
molecular simulation. Without any experimental data as input, good agreement with available experimental data was achieved, where deviations, when present, can be attributed to the slight over prediction of the CO2 model’s critical temperature and organic compound’s vapor pressure. Based on these results, provided that molecular force field parameters are available this approach can be applied to other systems of interest and reasonable agreement with experimental data can be anticipated. Structural analysis
Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074
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and J.I. Siepmann for discussion, and the University of Minnesota Supercomputing Institute where the calculations were partially carried out. References
Fig. 6. Center-of-mass radial distribution functions for CO2 around CO2 (solid lines) and CO2 around the second component (dashed lines) at 328.15 K. Black, red and green indicate pressures of 1, 4 and 8 MPa, respectively. a) EB liquid phase; b) EB vapor-like phase; c) PTL liquid phase; d) PTL vapor-like phase. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
indicates a shift from a liquid-like to supercritical fluid-like solvation environment as pressure increases.
Acknowledgments The authors wish to thank the Maine Space Grant Consortium Undergraduate Scholarship Program and the University of New England’s College of Arts and Sciences Dean’s office for support, J. Bellan
Fig. 7. Number integrals corresponding to radial distribution functions in Fig. 6. Line styles as in Fig. 6.
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Please cite this article as: M. Huber, J. Stubbs, Prediction of binary phase behavior for supercritical carbon dioxide + 1-pentanol, 2pentanone, 1-octene or ethylbenzene via molecular simulation, Journal of Molecular Liquids (2017), http://dx.doi.org/10.1016/j.molliq. 2017.06.074