J. Phys. Chem. B 2006, 110, 13195-13202
13195
Phase Equilibria in Carbon Dioxide Expanded Solvents: Experiments and Molecular Simulations Yao Houndonougbo,† Hong Jin,†,| Bhuma Rajagopalan,†,| Kean Wong,†,| Krzysztof Kuczera,‡,§ Bala Subramaniam,†,| and Brian Laird*,†,‡ Center for EnVironmentally Beneficial Catalysis, UniVersity of Kansas, Lawrence Kansas 66047, Department of Chemistry, UniVersity of Kansas, Lawrence, Kansas 66045, Department of Molecular Biosciences, UniVersity of Kansas, Lawrence, Kansas 66045, and Chemical and Petroleum Engineering, UniVersity of Kansas, Lawrence, Kansas 66045 ReceiVed: March 14, 2006; In Final Form: May 1, 2006
We present complementary molecular simulations and experimental results of phase equilibria for carbon dioxide expanded acetonitrile, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. The volume expansion measurements were done using a high-pressure Jerguson view cell. Molecular simulations were performed using the Gibbs ensemble Monte Carlo method. Calculations in the canonical ensemble (NVT) were performed to determine the coexistence curve of the pure solvent systems. Binary mixtures were simulated in the isobaric-isothermal distribution (NPT). Predictions of vapor-liquid equilibria of the pure components agree well with experimental data. The simulations accurately reproduced experimental data on saturated liquid and vapor densities for carbon dioxide, methanol, ethanol, acetone, acetic acid, toluene, and 1-octene. In all carbon dioxide expanded liquids (CXL’s) studied, the molecular simulation results for the volume expansion of these binary mixtures were found to be as good as, and in many cases superior to, predictions based on the Peng-Robinson equation of state, demonstrating the utility of molecular simulation in the prediction of CXL phase equilibria.
1. Introduction Solvent usage has been linked to waste generation and associated environmental and economic burdens. In addition to creating liquid wastes that must be properly handled and disposed off, conventional solvents readily evaporate. The solvent emissions have been linked to adverse environmental effects such as poor air quality, human illness, and global climate change. During the past decade, many research groups have been active at finding alternate media for performing catalysis. CO2, water, CO2 expanded liquids (CXLs), and room-temperature ionic liquids (RTILs) have received much attention as benign media. The application of supercritical CO2 (scCO2) as a benign medium in catalytic chemistry and reaction engineering satisfies several green chemistry and engineering principles such as pollution prevention, lower toxicity, and use of an “abundantly available” resource with no increase in environmental burden. However, the reaction benefits are often marginal with scCO2. In many cases, scCO2-based reactions are limited by inadequate solubilities of preferred homogeneous catalysts. Additionally, CO2 is nonpolar, which usually results in relatively low reaction rates. Furthermore, high process pressures (hundreds of bars) are required. The combination of high pressures and low reaction rates increase energy consumption and reactor volumes, both of which adversely affect process economics and nullify the environmental advantages. In contrast, the use of * To whom correspondence should be addressed. E-mail:
[email protected]. † Center for Environmentally Beneficial Catalysis. ‡ Department of Chemistry. § Department of Molecular Biosciences. | Chemical and Petroleum Engineering.
organic solvents offers important reaction benefits. For example, solvents are typically chosen with dielectric properties that help solubilize preferred homogeneous catalysts and favor the desired reaction. However, the concerns with conventional organic solvents are toxicity and environmentally deleterious vapor emissions that may also form explosive mixtures with air. In recent years, investigations at the Center for Environmentally Beneficial Catalysis laboratories and elsewhere1-14 have clearly demonstrated how a relatively new class of solvents are promising alternative media for performing catalytic reactions. A CXL is a mixed solvent composed of CO2 condensed into an organic solvent. By varying the CO2, a continuum of liquid media ranging from the neat organic solvent to scCO2 is generated, the properties of which can be adjusted by tuning the operating pressure; e.g., a large amount of CO2 favors gas solubility and the presence of polar organic solvents enhances metal catalyst solubility. CEBC researchers have recently demonstrated that CXLs are optimal solvent media for a variety of homogeneous catalytic oxidations,15 hydroformylation,16 and solid acid-catalyzed reactions.17 Reaction advantages include higher gas miscibility compared to organic solvents at ambient conditions, enhanced transport rates due to the properties of dense CO2, and between 1 and 2 orders of magnitude greater TOFs (turnover frequency) than in neat organic solvent or scCO2. Environmental and economic advantages include substantial (up to 80 vol %) replacement of organic solvents with environmentally benign dense-phase CO2 and milder process pressures (tens of bars) compared to scCO2 (hundreds of bars). Thus, CXLs have emerged as important components in the optimization of catalytic systems. Moreover, the possibility of controlling CO2 pressure in CO2 expanded organic solvents
10.1021/jp061592w CCC: $33.50 © 2006 American Chemical Society Published on Web 06/15/2006
13196 J. Phys. Chem. B, Vol. 110, No. 26, 2006 gives an alternative to temperature-controlled crystallizations by avoiding slowness of the temperature loop, cooling, and heat transfer.18 To rationally exploit CXLs, a complete knowledge of the phase equilibria involving CO2/organic solvent mixtures is required. Of particular interest are the vapor-liquid equilibria (VLE) properties for each of the pure components and the multicomponent including binary mixtures. Determination of vapor-liquid properties based on experimental data is the most reliable. Many experiments have focused on phase equilibria in carbon dioxide expanded solvents, including binary mixtures of CO2 with acetonitrile, acetone, acetic acid, ethanol, methanol, and toluene.19-25 However, binary VLE data are not available in the literature for many solvent/CO2 pairs, often necessitating time-consuming experiments. It would be useful to have a reliable predictive tool in such cases. For chemical engineering applications, vapor-liquid equilibria are typically estimated with an empirical equation of state (EOS) such as the Peng-Robinson (PR) EOS.26 The PREOS is a simple two-parameter van der Waals (vdW) type cubic EOS.27 Equations of state are derived based on pure component properties. To apply them to mixtures, mixing rules for the parameters are required. Because there is no exact statistical mechanics solution for properties of dense fluids based on their intermolecular potentials, the mixing rules used in EOS calculations are empirical26 and must be optimized specifically for each mixture by using experimental data. This has resulted in a large set of mixing rules proposed in the literature. For complex systems, complicated mixing rules are often needed for reliable predictions. A promising alternative to EOS models is molecular simulation. Recent improvements in computing power and algorithms combined with the availability of force fields have allowed the calculation of VLE properties using molecular simulation. Several methods, such as Gibbs ensemble Monte Carlo (GEMC),23,28-30 histogram reweighting,31,32 and Gibbs-Duhem integration,33,34 have been proposed to simulate phase equilibria. In molecular simulations, a reliable molecular potential is indispensable for obtaining an accurate prediction of properties. Molecular potential parameters are optimized by using pure system experimental information, and mixture potential parameters are then determined by using a combining rule. A large variety of molecular models for pure fluids is available in the literature. Some were optimized to accurately model the vaporliquid equilibria properties. We have chosen to use in the present work, when available, simple molecular potentials reported in the literature that were shown to accurately model VLE of pure substances. The mixtures are then simulated by using the Lorentz-Berthlot combining rules.35 We demonstrated recently how molecular simulation techniques and simple force fields available in the literature can be used to predict the VLE in CO2 expanded acetonitrile.36 In this paper, we extend our simulation work to the study of phase equilibria in several organic CXL binaries such as CO2 and acetone, methanol, ethanol, acetic acid, toluene, and 1-octene. For these calculations, the Gibbs ensemble Monte Carlo (GEMC) method23,28-30 was used. To validate the choice of our molecular potential, we first performed simulations within canonical ensemble (NVT) to calculate the vapor-liquid equilibria (VLE) curves for the pure component systems. Then, the isobaric-isothermal ensemble (NPT) was used to simulate phase equilibrium properties of binary mixtures. The vaporliquid equilibrium property of interest for the CXLs studied is the volume expansion of the solvent by CO2 at temperature T
Houndonougbo et al. and pressure P that is defined by
V(T, P) V0(T, P0)
(1)
where V represents the total volume of the liquid phase at temperature T and P, and V0 is the total volume of the pure solvent at the same temperature and atmospheric pressure. The resulting molecular models for binary mixtures are compared to our experimental data for liquid-phase volume expansion. Furthermore, our results from molecular simulations are compared to those from the Peng-Robinson equation of state. The remainder of this article is organized as follows. In the next three sections, experimental, simulation, and modeling methods are described in detail. Simulations are compared to experiments and to PR-EOS calculation results in the fifth section. The conclusion of our work is given in the sixth section. 2. Experimental Method The volumetric expansion studies by CO2 were performed following the method by Ming et al.37 First, the organic solvent was loaded in a high-pressure Jurgeson view cell rated to withstand 400 bar at 100 °C. While the temperature was maintained constant at the desired value, the volume of the expanded liquid phase, as a result of CO2 addition, was measured at each equilibrated pressure. The increase in volume of liquid phase relative to the volume of the organic liquid loaded initially was thus plotted with pressure. 3. Simulation Details and Models The Gibbs ensemble Monte Carlo (GEMC) method23,28-30 was used to perform the pure-component and binary mixture simulations. Calculations within the canonical ensemble (NVT) were performed to determine the coexistence curve of the purecomponent systems. A total of N ) 512 molecules was used in all pure-component simulations. Binary mixtures were simulated in the isobaric-isothermal ensemble (NPT), with a total of N ) 600 molecules placed in the two simulation boxes. Calculations with a larger number of molecules for the NVT and NPT ensembles point to negligible system size effects. All the GEMC simulations were equilibrated for more than 5 × 104 Monte Carlo cycles (N trial moves per cycle), and results were collected for an additional 105 MC cycles. The acceptance ratio of moves for each simulation were 1% volume exchange, 19% swap moves, 40% particle displacement, and 40% rigid rotations. Nonbonded interactions for all molecules studied in this work are represented by pairwise additive Lennard-Jones (LJ) 12-6 potentials and Coulombic interactions of partial charges
U(rij) ) 4ij
[( ) ( ) ] σij rij
12
-
σij rij
6
+
qiqj 4π0rij
(2)
where rij, ij, σ, qi, and qj are the separation, LJ well depth, LJ size, and partial charges, respectively, for interacting atoms i and j. We used the united-atom representation in which CHx groups (with 0 e x e 4) are represented as a single interaction site that is located at the position of the carbon atom. Unlike interaction parameters were calculated by using LorentzBerthelot combining rules.35 For all simulations, an Ewald sum with tinfoil boundary conditions (κL ) 5.6 and Kmax ) 5) was used to calculate the long-range electrostatic interactions.35 Lennard-Jones nonbonded interactions were truncated at L ) 10 Å, and standard longrange corrections were employed.38
Phase Equilibria in Carbon Dioxide Expanded Solvents
J. Phys. Chem. B, Vol. 110, No. 26, 2006 13197
TABLE 1: Parameters for Nonbonded Interactions (refs 39-44)
TABLE 2: Equilibrium Bond Angles and Force Constants (refs 41-44)
molecule
atom/group
/kb (K)
σ (Å)
q (e)
molecule
bend
angle (deg)
kθ/kb (K rad2)
carbon dioxide
C O CH3 C N CH3 O H CH3 CH2 O H CH3 C O CH3 C O(dC) O(-H) H CH3 CH(aro) C(aro) CH3 CH2(-C) CH CH2(dC)
28.129 80.507 90.6 105 48.8 98 93 0 98 46 93 0 98 40.0 79 98 41.0 79 93 0 98 50.5 21.0 98 46 47.0 85.0
2.757 3.033 3.8 3.0 3.4 3.75 3.02 0 3.75 3.95 3.02 0 3.75 3.82 3.05 3.75 3.90 3.05 3.02 0 3.75 3.695 3.88 3.75 3.95 3.73 3.675
0.6512 -0.3256 0.269 0.129 -0.398 0.265 -0.7 0.435 0 0.265 -0.7 0.435 0 0.424 -0.424 0.12 0.42 -0.45 -0.46 0.37 0 0 0 0 0 0 0
methanol ethanol
CH3-O-H CH3-CH2-O CH2-O-H CH3-C-CH3 CH3-CdO CH3-CdO CH3-C-O O-CdO C-O-H CH3-C-CH CH-C-CH CH-CH-CH CH3-CH2-CH2 CH2-CH2-CH2 CH2dCH2-CH2
108.5 109.47 108.5 117.2 121.4 126 111.4 123 107 120 120 120 114 114 119.7
55400 50400 55400 62500 62500 40300 35300 40300 17600 rigid rigid rigid 62500 62500 70420
acetonitrile methanol ethanol
acetone acetic acid
toluene 1-octene
The intramolecular interactions were treated in the following way: the bond length between two neighboring pseudo-atoms was fixed. A harmonic potential was used to control bond angle bending
Ubend )
k0 (θ - θ0)2 2
(3)
where θ is the actual bending angle, θ0 is the equilibrium bending angle, and k0 is the force constant. The dihedral rotations were controlled by a cosine series
Utorsion ) c0 + c1[1 + cos(φ + f1)] + c2[1 - cos(2φ)] + c3[1 + cos(3φ)] (4) where f1, φ, and ci are the phase factor, the dihedral angle, and the ith expansion coefficient, respectively. The detailed molecular model of each molecule used in the present work is presented below. Carbon Dioxide. Carbon dioxide molecules were represented by rigid three-site models with Lennard-Jones sites and partial charges located at the atomic positions (see eq 2). The EPM2 potential parameters (see Table 1) developed by Harris and Yung39 and optimized for VLE were used. The CdO bond length was fixed at 1.149 Å. Acetonitrile. For acetonitrile, the rigid three-site model from the work of Hirata40 were used. The nonbonded interaction parameters are listed in Table 1. The bond lengths for acetonitrile molecule were fixed at 1.46 and 1.17 Å for CH3-C and C≡N bonds, respectively. Acetone. The united-atom version of the transferable potential for phase equilibra (TraPPE-UA) force field41 were employed for acetone. The CH3 groups were replaced by pseudo-atoms that were located at the position of the carbons. The pairwise additive Lennard-Jones and Coulombic interactions parameters used are presented in Table 1. The fixed bond length employed by TraPPE-UA force field for acetone are 1.52 and 1.229 Å for CH3-C and CdO bonds, respectively. The values employed
acetone acetic acid
toluene 1-octene
for the harmonic bending potential (eq 3) parameters for CH3C-CH3 and CH3-CdO angles in acetone molecule can be found in Table 2. Methanol. The TraPPE-UA force field developed for alcohols42 was used to model the methanol molecule. In the TraPPEUA, the methyl group was treated as a pseudo-atom located at the site of the carbon, whereas the hydroxyl oxygen and hydrogen were modeled explicitly. Parameters for the nonbonded interactions described by eq 2 are listed in Table 1. The CH3-O bond length was fixed at 1.43 Å and the O-H bond was kept at a 0.945 Å value. Table 2 displays eq 3 parameters used for methanol CH3-O-H angle bending. Ethanol. As in the case of methanol, the ethanol molecule was described by the united atom transferable potential for phase equilibria of alcohols.42 The methyl and ethylene groups were represented by pseudo-atoms placed at their carbon sites, and the hydroxyl oxygen and hydrogen were modeled explicitly. Nonbonded and angle parameters are listed in Tables 1 and 2, respectively. The CH3-CH2-O-H dihedral angle was controlled by eq 4, and the coefficient values are in Table 3. Acetic Acid. Simulations of acetic acid were performed by using the optimized molecular force field for vapor-liquid equilibrium for carboxylic acids proposed by Kamath et al.43 The methyl group of the acetic acid molecule was replaced by a pseudo-atom centered at the carbon, and the rest of the molecule was represented explicitly. The bond lengths were fixed at 1.52 Å for CH3-C, 1.214 Å for CdO, 1.364 Å for C-O, and 0.97 Å for O-H. The parameters of the nonbonded potential governed by eq 2 are listed in Table 1; Table 2 contains the angle bending coefficients for the acetic acid model. The motion of the dihedral angles about the carboxyl group in acetic acid was controlled by eq 4, and the parameters can be found in Table 3. Toluene. The TraPPE-UA force field for alkylbenzenes44 was used to model toluene. The methyl (CH3) group and methine (CH) group of the aromatic ring were replaced by pseudo-atoms located at the carbon sites. The toluene molecule was assumed rigid and planar. The bond lengths were fixed by using values of 1.54 and 1.40 Å for the carbon-carbon single bond and for aromatic rings, respectively. Lennard-Jones and Coulombic interactions parameters used for the toluene molecule can be found in Table 1. The intramolecular interactions were described by harmonic bond angle bending (eq 3) and dihedral (eq 4) potentials; the values of their parameters are listed in Tables 2 and 3. 1-Octene. As in the case of toluene, the 1-octene molecule was modeled using the TraPPE-UA force field for alkenes.44 The CH3, CH2, and CH groups were represented by their
13198 J. Phys. Chem. B, Vol. 110, No. 26, 2006
Houndonougbo et al.
TABLE 3: Torsional Parameters (refs 42-44) molecule
dihedral
f1 (deg)
c0/kb (K)
c1/kb (K)
c2/kb (K)
c3/kb (K)
ethanol acetic acid
CH3-CH2-O-H CH3-C-O-H OdC-O-H CH3-CH2-CH2-CH2 CH2-CH2-CH2-CH2 CH2dCH2-CH2-CH2
0 0 180 0 0 0
0 0 0 0 0 688.5
209.82 630.0 630.0 355.03 355.03 86.36
-29.17 1562.4 1562.4 -68.19 -68.19 -109.77
187.93 0 0 791.32 791.32 -282.24
1-octene
corresponding pseudo-atoms located at the carbon atom center. The bond lengths were fixed at 1.54 Å for CH3-CH2 and CH2CH2 bonds. The fixed bond length value for CH2dCH was 1.33 Å. The nonbonded parameters for 1-octene molecule are listed in Table 1. The intramolecular motions were described by eq 3 for bond angles and eq 4 for dihedral angles. The parameters of these intramolecular interactions can be found in Tables 2 and 3. 4. Peng-Robinson Equation of State We have compared the volume expansion results of our molecular simulations to those calculated by using the PengRobinson equation of state
P)
a(T) RT - 2 V - b V + 2bV - b2
(5)
where T, P, R, and V are the temperature, pressure, the ideal gas constant, and molar volume, respectively. For a component i, parameters a and b are given by
ai ) 0.457235
[ ( x )]
(RTci)2 1 + ki 1 Pci
bi ) 0.077796
T Tci
RTci Pci
ki ) 0.37464 + 1.54226wi - 0.26992wi2
aij ) (1 - kij)xaiiajj b)
∑i ∑j xixjbij bii + bjj 2
bij ) (1 - lij)
(7)
(8)
(9) (10) (11)
Pc (MPa)
w
7.38 4.83 8.1 6.38 4.70 5.78 4.11 2.68
0.225 0.327 0.572 0.635 0.309 0.4624 0.257 0.386
TABLE 5: Mixing Parameters system
kij
lij
refs
CO2/acetonitrile CO2/methanol CO2/ethanol CO2/acetone CO2/acetic acid CO2/toluene CO2/1-octene
0.070 0.057 0.089 0.078 0.020 0.090 0.020
0.000 0.002 0.000 0.072 0.000 0.000 0.004
parameters from ref 19 data from ref 47 parameters from ref 19 parameters from ref 46 data from ref 21 parameters from ref 46 data from our simulation
the following relations by summing the mole fractions xi and yi in each phase to unity 2
∑ i)1
2
xi ) 1 and
yi ) 1 ∑ i)1
(14)
For a fixed temperature and mole fraction xi, VLE calculations can be carried out by using the Newton-Raphson45 (NR) method to solve the nonlinear eqs 13 and 14. The cross interaction parameters kij and lij of binary systems CO2/acetonitrile, CO2/acetone, CO2/ethanol, and CO2/toluene were obtained from refs 19, 46. For the binary systems CO2/ methanol, CO2/acetic acid, and CO2/1-octene, the simplex optimization method was used to determined kij and lij by minimization of the objective function n
F)
∑
m)1
|Pcalc, m - Pexp, m|
(15)
where n is the number of experimental data points. For CO2/ methanol and CO2/acetic acid, VLE data were taken from refs 21 and 47. In the case of the CO2/1-octene system, VLE data from our simulations were used because we could not find vapor-liquid equilibrium data. Table 4 gives the pure component parameters, and Table 5 summarizes the binary cross interaction parameters used in the mixing rules of the Peng-Robnson EOS.
(12) 5. Results
The calculations of VLE are obtained equating the fugacities of each component in the liquid phase and in the vapor phase
φiLxiP ) φiVyiP
Tc (K) 304.2 545.5 513 516.2 508.1 592.75 591.8 567
(6)
where w is Pitzer’s acentric factor. For mixtures, eq 5 is used with a and b being the mixture parameters that are determined by mixing rules. We have chosen the conventional van der Waals mixing and combining rules for a and b parameters
∑i ∑j xixjaij
component carbon dioxide acetonitrile methanol ethanol acetone acetic acid toluene 1-octene
2
where Tci and Pci are the critical temperature and pressure of compound i. The ki term has the form
a)
TABLE 4: Pure Component Parameters (refs 51, 52)
(13)
where φi is the fugacity coefficient of component i, obtained from the Peng-Robinson equation of state. Moreover, we have
Pure Components. The vapor-liquid coexistence curves for all the pure component systems are shown in Figure 1. We reproduce in Figure 1a and b the GEMC simulation results for vapor-liquid coexistence curves of carbon dioxide and acetonitrile presented in our previous work.36 The saturated liquid and vapor densities for CO2 are in good agreement with experiment48 over a large range of temperature. The same
Phase Equilibria in Carbon Dioxide Expanded Solvents
Figure 1. Vapor-liquid coexistence curves for (a) carbon dioxide, (b) acetonitrile, (c) methanol, (d) ethanol, (e) acid acetic, (f) acetone, (g) toluene, and (h) 1-octene. Simulation results are represented in symbols. Experimental data (lines) were taken from refs 48, 53-56.
agreement was found by Harris et al.39 For acetonitrile, the vapor-liquid coexistence data of our simulations is only in qualitative agreement with experiment. Accurate densities were obtained in the vapor phase for temperatures below 150 °C, while the liquid phase densities are approximately 15% low over the entire temperature range. These deviations for acetonitrile simulations may be explained by the fact that the potential parameters used were not optimized for vapor-liquid equilibrium. At high CO2 solubility (at relatively high pressures), the mixture is dominated by carbon dioxide molecules. At low pressures where acetonitrile is the dominant species, the choice of the acetonitrile molecular model may influence the mixture vapor-liquid equilibrium properties. However, in the current work, we are interested in volume expansion (eq 1), which is always close to unity at low CO2 solubility.46 Thus, our results for the binary CO2/acetonitrile mixture should not be significantly affected by the current three-site model for acetonitrile. After we started this work, optimized potential for acetonitrile parametrized for vapor-liquid equilibrium calculations was published.49 The vapor-liquid coexistence curves of methanol and ethanol are shown in Figure 1c and d. The simulations accurately reproduced experimental data of saturated liquid densities for methanol and ethanol. Saturated vapor densities are also in good agreement with experiment. The saturated liquid and vapor densities predicted by our Monte Carlo calculations of acetic acid and acetone are also in close agreement with experiment presented in Figure 1e and f. The results of the pure component simulations for toluene and 1-octene is displayed in Figure 1g and h. The agreement with experimental results is also good for these two solvents. Thus, by using the GEMC method, we were able to reproduce accurately vapor-liquid coexistence curves of pure component systems including carbon dioxide, methanol, ethanol, acetic acid, acetone, toluene, and 1-octene. Our simulations take advantage of intermolecular potentials developed for phase equilibria existing in the literature.41,42,44 Mixtures. Our previous simulation of acetonitrile expansion with carbon dioxide36 was extended to a variety of new solvents binaries with CO2. The results are compared with our experimental data and also to Peng-Robinson equation of state calculations. CO2 Expanded Acetonitrile and Acetone. Figure 2 shows simulations and Peng-Robinson equation of state results together with experiment data of the liquid-phase volume expansion by CO2 for acetonitrile at 25 °C and acetone at 30 °C. For both solvents, our simulations are in good agreement
J. Phys. Chem. B, Vol. 110, No. 26, 2006 13199
Figure 2. Volume expansion in carbon dioxide-acetonitrile at 25 °C (a) and in carbon dioxide-acetone at 30 °C (b).
Figure 3. Liquid-phase carbon dioxide mole fractions for CO2/CH3CN and CO2/CH3COCH3 mixtures.
with experimental results. For both mixtures, the volume of the liquid phase varies exponentially with pressure (i.e., CO2 addition), starting with a gradual increase at low pressures and leading to a progressively larger increase at higher pressure. The Peng-Robinson equation of state calculations give a good estimate of the volume expansion in the CO2/acetone system. However, the PR-EOS results tend to underestimate the volume expansion. The evolution with pressure of carbon dioxide mole fraction in the liquid phase is shown in Figure 3 for CO2/CH3CN and CO2/CH3COCH3 mixtures. As can be seen from the plots, solubilities up to 65% in the CO2 mole fraction were achieved in both solvents at pressure below 5 MPa. Figure 3 shows an approximately linear relationship between total pressure and CO2 composition in the range of pressures studied. This trend is usually observed in binary mixtures composed of CO2 and an organic solvent at pressures below 5 MPa.50 The effect of pressure on the densities of the two mixtures is shown in Figure 4. For acetone and acetonitrile mixtures with carbon dioxide, the liquid-phase densities increase with pressure and show maxima at high pressures. CO2 Expanded Methanol, Ethanol, and Acetic Acid. The liquid-phase volume expansion results of our simulations for CO2/CH3OH at 30 °C, CO2/CH3CH2OH at 25 °C, and CO2/ CH3COOH at 25 °C are shown in Figures 5 and 6. For the binary mixtures of carbon dioxide with methanol and ethanol, the results are in close agreement with experiment data. For the binary mixture of carbon dioxide with acetic acid, the experimental results are reproduced at low pressure, while at high pressure, the calculated volume expansion values are lower than those found in experiment. As in the case of CO2 expanded acetonitrile and acetone, the volume expansion curves for the three mixtures also show exponential increase with pressure. The PR-EOS is able to predict the experimental volume expansions of the binary systems CO2/CH3OH and CO2/
13200 J. Phys. Chem. B, Vol. 110, No. 26, 2006
Figure 4. Simulated liquid densities for CO2/CH3CN and CO2/ CH3COCH3 mixtures.
Figure 5. Volume expansions in carbon dioxide-methanol at 30 °C (a) and carbon dioxide-ethanol at 25 °C (b).
Figure 6. Volume expansions in carbon dioxide-acetic acid at 25 °C.
CH3CH2OH reasonably well. For CO2/CH3COOH binary system, molecular simulation gives volume expansion results in better agreement with experimental data than the PR-EOS predictions. The calculated CO2 mole fractions in the liquid phase are presented in Figure 7 for CO2/CH3OH, CO2/ CH3CH2OH, and CO2/CH3COOH mixtures. Carbon dioxide solubility in acetic acid extends to 60% in mole fractions at pressure below 5 MPa. In this pressure range, the molar solubilities of CO2 in ethanol and methanol are only arround 45 and 35%, respectively. As in CO2/acetonitrile and CO2/ acetone mixtures, linear behavior in CO2 composition is also seen in Figure 7 for the three mixtures at pressures below 5 MPa. The liquid-phase densities results for CO2/acetic acid, CO2/ ethanol, and CO2/methanol are displayed in Figure 8. The liquid densities in CO2/ethanol and CO2/methanol are similar and increased with increasing mole fractions of CO2. In CO2/acetic acid, a different trend is seen. When the CO2 mole fraction is increased, the liquid-phase densities of CO2/acetic acid mixture
Houndonougbo et al.
Figure 7. Liquid-phase carbon dioxide mole fractions for CO2/CH3OH, CO2/CH3CH2OH, and CO2/CH3COOH mixtures.
Figure 8. Simulated liquid densities for the mixtures CO2/CH3OH, CO2/CH3CH2OH, and CO2/CH3COOH.
remain constant within the error bars for mole fractions less than 0.35, while decreasing densities are observed for mole fractions above 0.35. This may be explained by the fact that the liquid density of CO2/organic solvent mixtures is primarily determined by the liquid density of the solvent at low CO2 mole fractions and by pure CO2 density at high CO2 content. However, the volume expansion of the liquid phase by CO2 is dominant at high pressure, resulting in a distinctive maximum in the saturated liquid density of the binary mixture.19 Thus, in most cases, at low pressure when the solubility of CO2 is low, the saturated liquid density of CO2 expanded organic solvent binary mixture increased with increasing pressure or CO2 mole fraction due to the solvent compression. A different trend is seen in the CO2/acetic acid mixture because the saturated liquid density of neat acetic acid is relatively high and the effect of compressibility is negligible at low CO2 mole fractions. On the other hand, when the solubilization of CO2 becomes important, the expansion of the liquid phase dominates and the liquid density of the mixture decreases with increasing solubility of CO2. CO2 Expanded Toluene and 1-Octene. The last two mixtures that were simulated are CO2/toluene at 30 °C and CO2/1-octene at 60 °C. The calculated and experimental results of the volume expansions in these two mixtures are presented in Figure 9. The observed volume expansion trends are reproduced for both mixtures by our simulations. However, the calculated values are higher for pressure greater than 4 MPa in the CO2/1-octene system. The correlation results with the Peng-Robinson equation of state are in good agreement with experimental results in the case of CO2/toluene mixture. The PR-EOS calculations of CO2/1-octene volume expansion are in close agreement with our simulation results. This is not surprising because VLE data from our simulation were used to determine the mixing
Phase Equilibria in Carbon Dioxide Expanded Solvents
Figure 9. Volume expansions in carbon dioxide-toluene at 30 °C (a) and carbon dioxide-1-octene at 60 °C (b).
J. Phys. Chem. B, Vol. 110, No. 26, 2006 13201 ments were performed for CO2 expanded acetonitrile, acetone, methanol, ethanol, acetic acid, toluene, and 1-octene by using a high-pressure Jerguson view cell. Using the Gibbs ensemble Monte Carlo method, molecular simulations were performed for the same binary systems to calculate liquid-phase volume expansion, densities, and CO2 mole fractions for pressures up to 5 MPa. Simulations and experiments are in good agreement, illustrating the predictive power of modern molecular simulations. Conventional approaches for predicting phase equilibria properties use empirical equations of state. They are usually excellent correlation tools, but often lack in predictive power for complex systems. We have used the Peng-Robinson equation of state to model the volume expansion properties for the seven binary systems. In several cases, molecular simulations results were in better agreement with experimental data than the results of the Peng-Robinson equation of state modeling. An additional advantage of molecular simulations is that it can give molecular-level details not available from EOS. Thus, this work has shown that simulations constitute a powerful predictive tool for accurately modeling phase equilibrium behavior in CO2 expanded organic solvents, a novel class of liquids which are being applied to limit the use of environmentally hazardous organic solvents. Acknowledgment. This work is supported by the National Science Foundation grant EEC-0310689 providing for the University of Kansas Center for Environmentally Beneficial Catalysis.
Figure 10. Liquid-phase carbon dioxide mole fractions for CO2/ CH3C6H5 and CO2/C8H16 mixtures.
Figure 11. Simulated liquid densities for the mixtures CO2/CH3C6H5 and CO2/C8H16.
parameters for CO2/1-octene because of the lack of experimental data. The effect of pressure on CO2 mole fractions in the liquid phase is plotted in Figure 10. For both mixture systems, approximately 65% mole fraction for CO2 composition is reached for the pressure range below 5 MPa. In this pressure range, the total pressure in the liquid phase increases linearly with CO2 mole fractions, as seen for the other mixtures discussed above. The corresponding densities of the liquid phase for each mixture are shown in Figure 11. For both mixtures, the densities increase with CO2 solubility as generally seen above. 6. Conclusion By considering the potential application of CO2 expanded organic solvent media in engineering processes, we have shown in the present work that the use of published force field parameters and standard combining rules allowed reliable prediction of phase equilibrium properties for carbon dioxide expanded organic liquids. For this, volume expansion experi-
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