Molecular Modeling of Phase Behavior and

K and 1 bar for equimolar mixtures of acetone-chloroform, acetone-methanol, and ... Analysis of the microstructure reveals significant hydrogen bondin...
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J. Phys. Chem. B 2005, 109, 19463-19473

19463

Molecular Modeling of Phase Behavior and Microstructure of Acetone-Chloroform-Methanol Binary Mixtures Ganesh Kamath, Grigor Georgiev, and Jeffrey J. Potoff* Department of Chemical Engineering and Materials Science, Wayne State UniVersity, Detroit, Michigan 48202 ReceiVed: June 28, 2005; In Final Form: August 8, 2005

Force fields based on a Lennard-Jones (LJ) 12-6 plus point charge functional form are developed for acetone and chloroform specifically to reproduce the minimum pressure azeotropy found experimentally in this system. Point charges are determined from a CHELPG population analysis performed on an acetone-chloroform dimer. The required electrostatic surface for this dimer is determined from ab initio calculations performed with MP2 theory and the 6-31g++(3df,3pd) basis set. LJ parameters are then optimized such that the liquidvapor coexistence curve, critical parameters, and vapor pressures are well reproduced by simulation. Histogramreweighting Monte Carlo simulations in the grand canonical ensemble are used to determine the phase diagrams for the binary mixtures acetone-chloroform, acetone-methanol, and chloroform-methanol. The force fields developed in this work reproduce the minimum pressure azeotrope in the acetone-chloroform mixture found in experiment. The predicted azeotropic composition of xCHCl3 ) 0.77 is in fair agreement with the experimental expt ) 0.64. The new force fields were also found to provide improved predictions of the value of xCHCl 3 pressure-composition behavior of acetone-methanol and chloroform-methanol when compared to other force fields commonly used for vapor-liquid equilibria calculations. NPT simulations were conducted at 300 K and 1 bar for equimolar mixtures of acetone-chloroform, acetone-methanol, and methanol-chloroform. Analysis of the microstructure reveals significant hydrogen bonding occurring between acetone and chloroform. Limited interspecies hydrogen bonding was found in the acetone-methanol or chloroform-methanol mixtures.

1. Introduction In separation operations based on distillation, knowledge of the presence of an azeotrope is important since this phenomena limits in the degree of separation that which may be obtained by exploiting vapor-liquid equilibrium (VLE).1-3 While the presence of an azeotrope presents complications in the purification of fluid mixtures, this same phenomena has been exploited in a wide range of technological applications. For example, the binary system HFC-43-10-mee/methanol is part of a new class of cleaning solvents for electronics processing. The presence of an azeotrope in this system allows efficient recovery of the cosolvent mixture through boiling while maintaining the original composition of the liquid phase.4 Azeotropic mixtures of halothane and diethyl ether have been studied extensively as an anesthetic with lower cost and an increased margin of safety over pure halothane.5 The use of molecular simulation for the determination of fluid-phase behavior has become routine and is limited only by the accuracy of the intermolecular potentials used to describe the interactions between molecules. The phase diagrams for azeotropic mixtures of real fluids have been determined by simulation of atomistic force fields for a large number of systems including: ethane/CO2,6-9 ethene/CO2,10 ethene/xenon,10 methanol/n-hexane,8,11 n-heptane/1-pentanol,12 acetone/n-hexane,13 acetonitrile/methanol,14 and dimethyl mercury/n-pentane.15 In many of these studies, excellent agreement with experimental data is achieved, while in some of the more difficult systems, the simulations are qualitatively correct but deviate from experiment by up to 10%. * To whom correspondence should be addressed. E-mail: jpotoff@ chem1.eng.wayne.edu. Fax: 313-577-3810. Tel: 313-577-9357.

Of the systems listed above, only the dimethyl mercury/npentane exhibits minimum pressure (maximum temperature) azeotropy. Such systems make up only 1% of the thousands of binary mixtures known to form azeotropes. The binary mixture acetone/chloroform is another system that displays minimum pressure azeotropy.16-20 It is hypothesized that pure acetone and chloroform, while unable to hydrogen bond as pure fluids, can form a hydrogen-bonded complex when mixed. The systems acetone/methanol and chloroform/methanol are also expected to form hydrogen-bonded complexes between unlike molecules, however, both of these systems have maximum pressure azeotropes.21,22 This suggests that limited hydrogen bonding is occurring between unlike molecules in mixtures of acetone/ methanol and chloroform/methanol. These complex intermolecular interactions provide a stringent test for atomistic force fields. In this work, grand-canonical histogram-reweighting Monte Carlo simulations are used to calculate the pressure-composition diagrams predicted by the optimized potentials for liquid simulations (OPLS)23 and the transferable potentials for phase equilibria (TraPPE).13 Our results show that neither of these intermolecular potentials are able to reproduce the minimum pressure azeotrope found in the acetone/chloroform mixture. To remedy this, new force fields are developed for acetone and chloroform that are parametrized specifically to provide accurate predictions of the vapor-liquid coexistence curve, vapor pressure, and critical properties as well as reproduce the minimum pressure azeotrope found in the acetone-chloroform mixture. These force fields use the same Lennard-Jones plus fixed point charge functional form as OPLS and TraPPE force fields. Unlike the OPLS and TraPPE force fields, which use partial charges derived from a Mulliken analysis, point charges

10.1021/jp0535238 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/21/2005

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TABLE 1: Parameters for Nonbonded Interactions Used in This Work force field

/kb (K)

OPLS-UA TraPPE-UA new

OPLS-UA CDP new

TraPPE-UA

acetone CH3 C Od CH3 C Od CH3 C Od chloroform CH Cl Cl C H Cl C H methanol CH3 OH

σ (Å)

q (e)

80.53 52.85 105.7 98.0 40.0 79.0 98.0 27.0 79.0

3.91 3.75 2.96 3.75 3.82 3.05 3.75 3.82 3.05

0.062 0.30 -0.424 0.0 0.424 -0.424 -0.049 0.662 -0.564

40.26 150.98 138.58 68.94 10.06 138.58 68.94 10.06

3.8 3.47 3.45 3.41 2.81 3.45 3.41 2.81

0.42 -0.14 -0.1686 0.5609 -0.0551 -0.04 -0.235 0.355

98.0 93.0 0.0

3.75 3.02 0.0

0.265 -0.7 0.435

µ (D) 2.91[31] 2.956 2.5024

1.04[31] 1.292

[( ) ( ) ] -

σij rij

6

+

qiqj 4π0rij

CdO CH3-C C-Cl C-H CH3-O O-H

1.229 1.520 1.760 1.070 1.43 0.945

bending

bond angle (deg)

kθ/kb (K)

∠CH3sCdO ∠CH3-C-CH3 ∠Cl-C-Cl ∠Cl-C-H ∠CH3-O-H

121.4 117.2 111.2 107.6 108.5

62500 62500 62500 62500 55400

Lorentz-Berthelot combining rules are used to determine cross parameters for Lennard-Jones interactions between sites of different types.25,26

σij ) (σii + σjj)/2

(2)

1.398

ij ) xiijj

(3)

1.70[31] 2.257

2.1. Force Fields. In this work, a number of intermolecular potentials are used. Nonbonded interactions for each force field are given by pairwise additive Lennard-Jones 12-6 (LJ) potentials and Coulombic interactions of partial charges 12

bond length (Å)

1.085

2. Models and Simulation Details

σij rij

vibration

2.9739

for each pseudoatom in the new force field are determined through the application of a CHELPG (charges from electrostatic potentials using a grid based method) analysis to an acetonechloroform dimer optimized at the MP2/6-31+g(d,p) level of theory. Grand-canonical histogram-reweighting simulations are then used to determine the pressure-composition diagrams for the binary mixtures acetone/chloroform, acetone/methanol, and chloroform/methanol. The microstructure of each of these mixtures is determined from Monte Carlo simulations in the isobaric-isothermal ensemble at 300 K and 1 bar. This paper is organized as follows. The specific details for each of the force fields used in this work are given in the next section. Following the description of the various force fields, we explain the strategy used in the development of new force fields for acetone and chloroform. In section 3, the details of the grand-canonical histogram-reweighting and NPT Monte Carlo simulations used in this work are provided. In section 4, the pure component vapor-liquid coexistence curves and vapor pressures are presented for the new force field as well as the OPLS-UA, Chang, Dang, and Peterson (CDP), and TraPPE force fields. This is followed by pressure-composition diagrams and radial distribution functions for acetone/chloroform, acetone/ methanol, and chloroform/methanol mixtures. The conclusions of this work can be found in section 5.

U(rij) ) 4ij

TABLE 2: Geometrical Parameters for Acetone, Chloroform, and Methanol

(1)

where rij, ij, σij, qi, and qj are the separation, LJ well depth, LJ size and partial charges, respectively, for the pair of interaction sites i and j. The primary difference in each of the force fields is in the parameters used to describe the interactions between interaction sites. The nonbonded parameters for each of the force fields used in this work are listed in Table 1, and the specific details of each force field are listed in the following section.

Although alternate combining rules have been suggested,27-29 recent calculations have not shown one combining rule to be consistently better than any of the others.8 For this reason, we retain the Lorentz-Berthelot combining rules. In each of the acetone, chloroform, and methanol models, interaction sites are separated by fixed bond lengths while bond angle bending is controlled by a harmonic potential

Ubend )

kθ (θ - θ0)2 2

(4)

where θ is the measured bond angle, θ0 is the equilibrium bond angle, and kθ is the force constant. All bond lengths, bond angles, and bending constants are listed in Table 2. 2.1.1. Acetone. In each of the force fields, OPLS-UA, TraPPE-UA, and new, a united-atom representation was used. Hydrogens bonded to carbon atoms were grouped together in a single interaction site known as a “pseudoatom”. This is a useful approximation for acetone, since the hydrogens bonded to the methyl group do not participate in hydrogen bonding to any significant extent. The primary benefit of the united-atom scheme over an explicit hydrogen representation is a significant reduction in computational expense with only a minor (potential) loss in accuracy. The selection of appropriate Lennard-Jones and charge parameters is key to the accuracy of a given force field. The OPLS-UA force field was originally parametrized to reproduce liquid densities and heats of vaporization at ambient conditions. Partial charges were determined empirically, guided by ab initio calculations at the HF/6-31g(d) level.30 The TraPPE-UA force field utilizes the OPLS-UA partial charges but makes use of Lennard-Jones parameters optimized to give accurate saturated liquid densities and critical points. The new force field is a natural extension of the OPLS-UA and TraPPE-UA force fields. Partial charges were derived from a CHELPG analysis conducted on an optimized cluster of acetone and chloroform at the MP2/6-31++G(3df,3dp) level of theory. This scheme results in a dipole moment of 2.97 D, which is slightly higher than the experimental gas-phase dipole moment of 2.91 D.31 LennardJones parameters for the dO and CH3 pseudoatoms were taken from the TraPPE-UA force field while the  and σ parameters for the carbonyl carbon were tuned to give an accurate reproduction of saturated liquid and vapor densities as well as vapor pressures. The nonbonded parameters for each of the force fields used in this work are listed in Table 1. 2.1.2. Chloroform. Three force fields for chloroform were used in this work, OPLS-UA, CDP24 (model developed by

Acetone-Chloroform-Methanol Binary Mixtures Chang, Dang, and Peterson), and new. The OPLS-UA force field, like its counterpart for acetone, uses a united-atom representation. The hydrogen and carbon atoms are merged to form a single CH group. Chlorine atoms are modeled explicitly. Parameters were derived with the same methodology described for acetone. The CDP force field uses an explicit hydrogen representation. Partial charges were derived by rescaling the results of fitting to electrostatic potentials obtained from ab initio calculations at the MP2 level with 6-31+G* basis set such that the gas-phase dipole moment was reproduced. Lennard-Jones parameters were fit to reproduce radial distribution functions, liquid densities, and heats of vaporization at 298 K. In the original work, the authors also included polarization effects through a dipole-polarizable formalism. However, in our calculations we found that the addition of dipole polarizability had no effect on the predicted pure component vapor-liquid coexistence curve or vapor pressure. As a result, in this work we have used a nonpolarizable variant of the CDP force field. The new force field is based on the CDP force field. It uses an explicit hydrogen representation and retains the same LennardJones parameters for chlorine and hydrogen atoms. Since the hydrogen atom in chloroform participates in hydrogen bonding, it is important to treat it explicitly. Unlike the CDP force field, partial charges for the new force field were derived from a CHELPG analysis performed on the acetone-chloroform dimer (see acetone, above) and not an isolated molecule. Once the partial charges were determined, the Lennard-Jones parameters for the central carbon were optimized to provide the best reproduction of the vapor-liquid coexistence curve and vapor pressures. 2.1.3. Methanol. The TraPPE-UA force field was used to represent methanol. As in the case of acetone, the CH3 group is treated as a single pseudoatom with identical Lennard-Jones parameters. In the original parametrization, partial charges in this force field were taken from the OPLS-UA force field and the  and σ parameters for oxygen were fit to give an accurate reproduction of the vapor-liquid coexistence curve. The hydrogen bonded to the hydroxyl oxygen is represented explicitly with a point charge without an additional LennardJones term. The TraPPE-UA force field was not modified because preliminary calculations showed that it returned the correct qualitative pressure-composition behavior when mixed with acetone or chloroform. 2.2. Determination of Partial Charges. Many computational methods have been used to determine the net atomic charges of atoms in molecules. A common technique is that of population analysis proposed by Mulliken.32 The OPLS-UA and TraPPE-UA are examples of force fields that utilize point charges derived in part from such an analysis. Mulliken charges are based on orbital occupancies, that is, how much electron density can be associated with each atom’s orbitals. The nuclear charge minus the electron density gives the atomic charge. The Mulliken analysis assumes that the electron density represented by the product of basis functions on different atoms is shared equally by the two atoms. If one atom is more electronegative, has a larger number of basis functions, or these basis functions are more diffuse, the approximation of equal sharing of electron density between neighboring atoms may not be valid. An alternative to the Mulliken analysis are methods that derive partial charges by fitting to reproduce an electrostatic potential energy surface surrounding the molecule. The CHELPG scheme by Breneman et.al.33,34 is one such method and was used to determine partial charges for the new acetone and chloroform force fields presented in this work. As a first step

J. Phys. Chem. B, Vol. 109, No. 41, 2005 19465 of the fitting procedure, the molecular electrostatic potential (MEP) is calculated at a number of grid points spaced 3.0 pm apart and distributed regularly in a cube. The dimensions of the cube are chosen such that the molecule is located at the center with 28.0 pm headspace between the molecule and the end of the box in all three dimensions. All points falling inside the van der Waals radius of the molecule are discarded from the fitting procedure. After evaluating the MEP at all valid grid points, atomic charges are fit to reproduce the MEP. The only additional constraint in the fitting procedure is that the sum of all atomic charges must equal the overall charge of the system. The major difference between this work and others that have used the CHELPG, or similar ESP fitting schemes,36-39 is that ours is the first work to determine partial charges fit to the electrostatic potential surface surrounding a cluster of molecules instead an isolated molecule. In fact, our attempts at using the CHELPG scheme to determine partial charges for isolated acetone and chloroform molecules, while resulting in an excellent pure component phase diagram, produced a pressurecomposition diagram that did not contain an azeotrope (see Supporting Information). We hypothesized that the minimum pressure azeotrope found in the acetone-chloroform mixture was the result of hydrogen bonding between acetonechloroform. An acetone-chloroform dimer was optimized at the MP2/6-31+g(d,p), and point charges for acetone and chloroform were obtained from a CHELPG analysis at the MP2 theory and the 6-31++g(3df,3dp) basis set. These calculations were performed with the Gaussian 03 software package.35 Lennard-Jones parameters for acetone and chloroform were then parametrized according to the scheme outlined above for the individual molecules. 3. Simulation Details 3.1. Grand-Canonical Monte Carlo. Grand-canonical histogram-reweighting Monte Carlo (GCMC) simulations40-42 were used to determine the vapor-liquid coexistence curves and vapor pressures for pure acetone and chloroform as well each of the binary mixtures presented in this work. The insertion of molecules in the GCMC simulations were enhanced through multiple first bead insertions43 and the application of the coupled-decoupled configurational-bias Monte Carlo method.44 Particle identity exchanges were used for mixtures to enhance the acceptance rate for particle insertions and deletions. The fractions of the various moves for each simulation were set to 10% for identity exchanges, 15% for particle displacements, 15% for rotations, 10% configurational-bias regrowths, and 50% for insertions and deletions. Simulations were performed for a system size of L ) 20 Å. Lennard-Jones interactions were truncated at L ) 10 Å, and standard long-range corrections were applied.45,46 An Ewald sum with tinfoil boundary conditions (κ × L ) 5 and Kmax ) 5) was used to calculate the long-range electrostatic interactions.47,48 Simulations were equilibrated for 1 million Monte Carlo steps (MCS) before run statistics were recorded, while production runs were 25 million MCS (pure components) to 50 million MCS (mixtures). Over the course of each simulation, the number of molecules N and energy E were stored in the form of a list, which was updated every 250 MCS. The necessary probability distributions were extracted from this list after the completion of the simulation. Statistical uncertainties for the new force fields were calculated by taking the standard deviation of three separate series of simulations runs, each started from different initial configurations and random number seeds. 3.2. Isobaric-Isothermal Monte Carlo. Monte Carlo simulations in the isobaric-isothermal ensemble were used to

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Figure 1. Vapor-liquid equilibria for acetone. Simulation results are shown as symbols: new (circle), TraPPE (square),13 OPLS-UA (triangle), and experiment (line).51 The inset shows the expanded view of the saturated vapor densities of acetone as predicted by each of the force fields.

investigate the microstructure in equimolar mixtures of acetone/ chloroform, acetone/methanol, and chloroform/methanol. A system size of 500 molecules was used. Simulations were equilibrated for 25 million MCS, after which run statistics were recorded for an additional 25 million MCS. The ratio of moves was 1% volume changes, 14% configurational-bias regrowths, 70% translations, and 15% molecule rotations. Lennard-Jones interactions were truncated at L ) 10 Å and standard longrange corrections were applied.45,46 An Ewald sum with tinfoil boundary conditions (κ × L ) 5 and Kmax ) 5) was used to calculate the long-range electrostatic interactions.47,48 4. Results and Discussion 4.1. Pure Component Vapor-Liquid Equilibrium. 4.1.1. Acetone. The vapor-liquid coexistence curves for acetone as predicted by OPLS-UA, TraPPE, and new force fields are shown in Figure 1. All of the force fields provide reasonable estimates of the saturated liquid densities. Average unsigned deviations of simulation from experiment51 range from less than 1% for the new and TraPPE-UA force fields to 5.5% for OPLS-UA. The new force field yields the best prediction of saturated vapor densities but still show deviations from experiment by as much as 10%. Critical parameters for each of the force fields were estimated by fitting the saturated liquid and vapor densities over the temperature range 300 e T e 480 K to the density scaling law for critical temperature49

Fliq - Fvap ) B(T - Tc)β

(5)

and the law of rectilinear diameters50

Fliq + Fvap ) Fc + A(T - Tc) 2

(6)

where β ) 0.325 is the critical exponent for Ising-type fluids in three dimensions52 and A and B are constants fit to simulation data. The critical properties predicted by each force field are listed in Table 3. The TraPPE and new force fields both predict a critical temperature that is within 1% of experiment. Only the OPLS-UA force field shows any appreciable deviation from experiment for the critical temperature (5%).

Figure 2. Clausius-Clapeyron plot for acetone: new (circle), TraPPE (square),13 OPLS-UA (triangle), and experiment (line).51

TABLE 3: Predicted Normal Boiling Points and Critical Properties for Acetone and Chloroform acetone

new TraPPE [13] OPLS-UA expt (51) chloroform new CDP OPLS-UA expt (53)

Tb(K)

Tc (K)

Fc (kg/m3)

Pc (bar)

327.3 ( 0.1 322.0 330.3 329.3 337.35 ( 0.1 337.6 343.8 334.8

508.2 ( 0.2 508.0 526.1 508.1 538.2 ( 0.5 543.1 566.8 537.0

275.5 ( 1 278.0 270.6 273.0 520.9 ( 2 525.1 544.4 516.0

48.5 ( 0.3 55.3 55.9 49.2 55.4 ( 0.5 63.8 73.5 56.5

The Clausius-Clapeyron plots used to determine the critical pressures and normal boiling points are shown in Figure 2. The normal boiling points predicted by each force field are listed in Table 3. The best reproduction of the critical pressure is given by the new force field, which predicts Pc ) 48.52 bar, compared to the experimental value of 49.18 bar.51 The OPLS-UA and TraPPE-UA force fields show deviations from experiment of 13.6% and 12.5%, respectively. As in the case of the critical parameters, all of the force fields predict a normal boiling point that is in close agreement with experiment, with the maximum deviation being 2% (TraPPE-UA). 4.1.2. Chloroform. The vapor-liquid coexistence curves for chloroform as predicted by the OPLS-UA, CDP, and new force fields are shown in Figure 3. As in the case of acetone, all the force fields provide reasonable estimates for the saturated liquid densities. Average unsigned deviations of simulation from experiment53 range from less than 1% for the new and CDP force fields to 2.3% for OPLS-UA. The saturated vapor densities predicted by the new and CDP force fields are in good agreement with the experimental values with average unsigned deviations of 5.0%, while the OPLS-UA under predicts the saturated vapor densities for the entire range of temperatures studied with average deviations from experiment of 25%. The Tc ) 538.2 K and Fc ) 520.9 kg/m3, predicted by the new force field, are within 1% of the experimental values of ) 537.0 K and Fexpt ) 516.0 kg/m3. This is the best Texpt c c prediction of the critical point for chloroform of the three force fields used in this work. Only the OPLS-UA shows appreciable deviation from the experiment for the critical temperature and density (5.5%). The Clausius-Clapeyron plots used to determine the critical pressures and normal boiling points are shown in Figure 4. The OPLS-UA force field under predicts the vapor pressures at all

Acetone-Chloroform-Methanol Binary Mixtures

J. Phys. Chem. B, Vol. 109, No. 41, 2005 19467

Figure 3. Vapor-liquid equilibria for chloroform: new (circle), CDP (square), OPLS-UA (triangle), and experiment (line).53 The inset shows the expanded view of the saturated vapor densities for pure chloroform as predicted by each of the force fields.

Figure 5. Pressure-composition plot for chloroform(1)-acetone(2) at 308.32 K: new (1)/new (2) (circle), CDP(1)/TraPPE(2) (square), and OPLS-UA (1)/OPLS-UA (2) (triangle), and experiment (line).16 The inset shows an expanded view of the minimum pressure azeotrope. Figure 4. Clausius-Clapeyron plot for chloroform: new (circle), CDP (square), OPLS-UA (triangle), and experiment(line).53

temperatures with average deviations from experiment equal to 30%. The CDP and new force fields also under predict vapor pressures by 10% and 15%, respectively, over the temperature range 300 < T < 520 K. The normal boiling points and critical pressures extracted from the Clausius-Clapeyron plots of the vapor pressure data are listed in Table 3. The new force field predicts a normal boiling point for chloroform of Tb ) 337.35 K, which is excellent agreement with the experimental boiling point of Tb ) 334.8 K. The new force field also gave the best prediction of the critical pressure of chloroform Pc ) 55.43 bar, compared to the experimental value of 56.5 bar.53 The OPLSUA over predicts the critical pressure by 30%. 4.2. Acetone-Chloroform. 4.2.1. Phase Behavior. The acetone-chloroform mixture has been widely investigated experimentally and exhibits minimum pressure azeotropy.16-20 The experimental boiling points for acetone and chloroform differ by only 5.5 K. As a general rule for binary mixtures, the closer the boiling points of each of the components are to each other, the greater the probability of azeotropic behavior.54 Furthermore, the vapor pressures of acetone and chloroform are equal at 266.17 K. This intersection of pressure vs temperature curves for each of the pure components is known as a Bancroft point. It has been shown experimentally that approximately 90%

of the binary mixtures that have a Bancroft point exhibit some kind of azeotropic behavior.1 In this section, we apply three different combinations of force fields in the determination of the pressure-composition diagram for this mixture. We refer to calculations utilizing the OPLSUA force fields for both acetone and chloroform as “OPLSUA”. Calculations that use the TraPPE-UA force field for acetone and CDP force field for chloroform are referred to as “TraPPE/CDP”. Finally, simulations that use the force fields developed in this work for acetone and chloroform are simply referred to as “new”. The predictions of simulations, utilizing the OPLS-UA, TraPPE/CDP, and new force fields, for pressure-composition behavior of the acetone-chloroform mixture at 308.32 K are shown in Figure 5. The predicted difference between normal boiling points of the two components was 13.5 and 15.6 K for the OPLS-UA and TraPPE/CDP force fields, respectively. This is well within the 30 K difference normally seen in azeotropic systems.54 On the other hand, neither the OPLS-UA or TraPPE/ CDP force fields show a Bancroft point. As shown in the Pxy plot, both the OPLS-UA and TraPPE/CDP calculations fail to predict any azeotropic behavior for this system. Instead, simulations predict nearly ideal behavior that is well reproduced by Raoult’s Law. We also note that Kranias et al.37 have recently published a force field for acetone based on an anisotropic

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Figure 6. Radial distribution function for the Oace-HCHCl3 pair interaction for an equimolar mixture of acetone and chloroform at 300 K and 1 bar: new (line), TraPPE/CDP (long dashed line), and OPLSUA/OPLS-UA (dotted line).

united-atom potential that yields a very good reproduction of the pure component phase behavior and vapor pressure. In their work, partial charges were fit using an ESP scheme for an isolated acetone molecule, resulting in a partial charge for oxygen of qO ) -448 e. Because the oxygen partial charge is similar to that of the OPLS-UA and TraPPE-UA force fields, we expect the force field developed by Kranias et al. will exhibit similar qualitative deficiencies. Unlike the OPLS-UA and TraPPE/CDP force fields, the new force fields do have a Bancroft point at 253 K. The existence of such a point, while signaling a high probability that azeotropy exists, does not predict what kind of azeotropic behavior will occur. As shown in Figure 5, the predictions of the new force fields are in qualitative agreement with the experimental data and display minimum pressure azeotropy. The new force fields predict the pressure and composition of the azeotrope as 0.322 bar and xCHCl3 ) 0.77, respectively. These are in good agreement expt with the experimental values of Pexpt azeo ) 0.34 bar and xCHCl3 ) 0.64. Additional Pxy diagrams (see Supporting Information) were determined for the new force fields at 450, 400, and 350 sim ) 0.94 to K. The azeotropic composition shifts from xCHCl 3 0.77 as temperature decreases from 450 to 308.32 K. This behavior is consistent with the experimental shift in the expt composition of the azeotrope from xCHCl ) 0.791 at 453 K to 3 expt xCHCl3 ) 0.64 at 373 K for the acetone-chloroform mixture.17 4.2.2. Microstructure. Isobaric-isothermal simulations at 300 K and 1 bar were performed on equimolar mixture of acetone and chloroform. The site-site radial distribution functions (RDFs) were calculated for each of the force field pairs used in the VLE calculations. In this system, the only possible mechanism for interspecies association is through hydrogen bonding between the oxygen and hydrogen atoms in acetone and chloroform, respectively. The RDFs for the Oace-HCHCl3 pair interactions determined from simulation are shown in Figure 6. The OPLS-UA force field does not show any significant interaction of Oace with HCHCl3. The CDP/TraPPE model shows a small peak at 2.7 Å, which is due to a limited association between chloroform and acetone molecules. The new force field has a more pronounced peak at 2.7 Å because of an increased association between chloroform and acetone. An aggregation analysis was performed on the simulation data. An association was defined as any Oace-HCHCl3 pair with

Figure 7. Snapshot of an equimolar mixture of acetone and chloroform at 300 K and 1 bar for the new force field. Different types of aggregates seen in the configuration: (a) two chloroform molecules bonded to one acetone molecule and (b) a chloroform molecule bonded to an acetone molecule.

an intermolecular distance less than 2.7 Å. A distance of 2.7 Å was chosen because this corresponds to the minimum in the acetone-chloroform dimer interaction energy as predicted by the new force field (-11.55 kJ/mol). This dimer binding energy is in good agreement with the experimental value of -11.3 kJ/ mol.16 As expected from the RDF, no association between acetone and chloroform was found for the OPLS-UA force field. For the CDP/TraPPE pairing, an average of 6% of the total molecules formed hydrogen-bonded aggregates. The new force field showed that 18% of the molecules formed hydrogenbonded aggregates between acetone and chloroform. For the new force field, the average distance for the Oace-HCHCl3 hydrogen bond was 2.4 Å and the ∠CaceOaceHCHCl3 was 120°. The hydrogen bond length of the acetone-chloroform dimer is longer in comparison to that of the water dimer (rH-O ) 1.95 Å),55 resulting in only weak hydrogen-bonding effects on the mixture. In Figure 7, a snapshot from equimolar NPT simulations for the new force fields is shown. The carbonyl oxygen with the two lone pairs of electrons can potentially form two hydrogen bonds. In the simulations of the new force field, a small number of 2:1 (chloroform/acetone) aggregates was found, however, the majority of the aggregates were 1:1, as shown in part c of Figure 7. These data confirm that interspecies association is necessary for the formation of minimum pressure (maximum boiling) azeotropes. 4.3. Acetone-Methanol. 4.3.1. Phase Behavior. In this section, two combinations of force fields are used to determine

Acetone-Chloroform-Methanol Binary Mixtures

Figure 8. Pressure-composition plot for acetone(1)-methanol(2) at 372.8 K: TraPPE(1)/TraPPE(2) (square), new(1)/new(2) (circle), and experiment (line).21 Statistical uncertainties are approximately the size of the symbols. Dashed lines are a guide to the eye.

the pressure-composition behavior for the acetone-methanol mixture. Calculations involving the TraPPE-UA force fields for both acetone and methanol are referred to as “TraPPE”, while calculations involving the new force field for acetone and TraPPE-UA for methanol are referred to as “new/TraPPE”. In Figure 8 the predictions given for both TraPPE and new/ TraPPE for the pressure-composition diagram at 372.8 K are shown in comparison to experiment.21 Experimentally, the Bancroft point for this system is at 385.1 K. The TraPPE and new/TraPPE force fields predict Bancroft points of 415.05 and 393.51 K, respectively. As shown in the Pxy diagram, both sets of force fields predict a maximum pressure azeotrope. The TraPPE force fields predicts an azeotropic composition xTraPPE acetone ) 0.68 and pressure PTraPPE ) 5.45 bar, which is in fair azeo agreement with the experimental composition xexpt acetone ) 0.51 and pressure Pexpt azeo ) 4.05 bar. Part of the deviation from experiment is due to the deviations of the pure component vapor pressures predicted by the TraPPE force field. However, the coexistence curve predicted by TraPPE is significantly wider than that of experiment, signaling that the acetone-methanol interactions defined by the TraPPE force field are weaker than they are in reality. Calculations for the new/TraPPE force fields provide improved estimates of the azeotropic composition xnew acetone ) 0.57 and pressure Pnew azeo ) 4.36 bar. In addition, this combination of force fields results in a narrower phase envelope that is more representative of experimentally seen behavior, especially for mole fractions of acetone greater than 0.5. This shows that the new/TraPPE force field combination provides a better approximation of acetone-methanol cross interactions. 4.3.2. Microstructure. Simulations in the NPT ensemble were conducted at 300 K and 1 bar for an equimolar mixture of acetone and methanol. A combination of TraPPE force fields and new/TraPPE force fields similar to the previously described VLE calculations were used to model the necessary interactions between molecules. This system is more complex than the acetone-chloroform mixture, since methanol can self-associate as well as form hydrogen-bonded complexes with acetone. There are two RDFs of interest with respect to aggregation in this mixture. The first is given by the intraspecies (methanolmethanol) OMeOH-HMeOH interaction, the second is the OaceHMeOH interspecies (acetone-methanol) interaction.

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Figure 9. Radial distribution function for the oxygen-hydrogen pair interaction in an equimolar acetone(1)-methanol(2) mixture at 300 K and 1 bar: top plot, OMeOH-HMeOH pair interaction; bottom plot, OaceHMeOH pair interaction; TraPPE(1)/TraPPE(2) (dashed line), new(1)/ TraPPE (2) (line).

The oxygen-hydrogen intermolecular RDFs were calculated for each of the force field pairs and are shown in Figure 9. The top plot shows the predictions for TraPPE and new/TraPPE force fields for the intraspecies OMeOH-HMeOH interaction. A peak at 1.8 Å for both combinations of force fields agrees with the previous simulations performed on methanol and methanol mixtures11,57 and signifies significant methanol-methanol hydrogen bonding. The reduction in RDF peak height for the new/ TraPPE combination compared to TraPPE is a result of the increased attraction between acetone and methanol. The bottom plot shows the RDF for the interspecies Oace-HMeOH pair interaction. The new/TraPPE calculations result in a peak height three times that of the TraPPE force field. This is further evidence of the increased acetone-methanol interaction in the new/TraPPE combination. Following the procedure defined in the work of Chen et al.,11 the average number of methanol-methanol hydrogen bonds per hydroxyl group were calculated. Methanol molecules were considered hydrogen bonded to each other if the OMeOH-OMeOH distance was less than 3.5 Å. For TraPPE, the number of hydrogen bonds per methanol was 1.67, while new/TraPPE gave 1.26. These results are lower than the 2.07 hydrogen bonds per hydroxyl group reported for pure methanol.11 Acetone, being strongly polar, provides screening between methanol molecules, which reduces intraspecies hydrogen bonding. In addition, in the new/TraPPE system significant acetone-methanol hydrogen bonding is able to occur, which detracts from the number of methanol molecules that are able to form hydrogen bonds with each other. A hydrogen bond analysis (cutoff of 2.4 Å for O-H separation) was also performed. Calculations utilizing the TraPPE force field found acetone-methanol aggregates accounting for 25.2% of the total number of aggregates but only 9.6% of the methanol molecules. For the new/TraPPE force fields, a similar analysis shows acetone-methanol aggregates constitute 48% of the total aggregates and 28% of the methanol molecules. For the new/TraPPE force fields, approximately 9% of the acetone-methanol aggregates were larger than the dimers and involved either short chains (2-3 methanols) hydrogen bonded to acetone or two unchained methanols h-bonding in a

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Figure 11. Fraction of methanol aggregates as a function of aggregate size at 300 K and 1 bar in an equimolar acetone(1)-methanol(2) mixture: TraPPE(1)/TraPPE(2) (square) and new(1)/TraPPE (2) (circle). Dashed lines are a guide to the eye. The inset shows the fraction of methanol molecules found in aggregates of particular sizes.

Figure 10. Snapshot of an equimolar mixture of acetone and methanol at 300 K and 1 bar for the new/TraPPE force field: (a) acetonemethanol configuration, (b) methanol-acetone aggregates, and (c) methanol-methanol aggregate.

similar fashion as the acetone-chloroform trimer. Examples of these aggregates are shown in Figure 10, which is a snapshot taken from the equilibrated NPT simulations of the new/TraPPE force fields. In parts b and c, the snapshot is decomposed into acetone-methanol and methanol-methanol aggregates, respectively. As shown in the Figure 10, methanol forms chains varying from dimers to octamers, with only a small number of cyclic structures. In Figure 11 the distribution of methanol-methanol aggregates is presented. Within the error of the calculation, the TraPPE and new/TraPPE force fields provide identical estimates of the cluster size distribution. The data show that the limited amount of interspecies association that occurs in this system has only a small effect on the aggregation behavior of methanol with other methanol molecules. The most probable cluster size consists of four methanols, and nearly 35% of all methanol molecules can be found participating in a linear tetramers, with only a small fraction of cyclic structures. The formation of methanol tetramers in the acetone-methanol mixture is consistent with previous simulations of dilute methanol in supercritical carbon dioxide57 and methanol in n-hexane.11 Unlike the dilute solution case, where methanols are most likely to exist as monomers or dimers,11,57 the majority of methanol molecules in our equimolar mixture participate in aggregates of 2-8 molecules. This is expected, since the closer proximity of methanol molecules to each other in an equimolar mixture provides more opportunity for intraspecies association. Methanol molecules in dilute solution have limited opportunities for

aggregation since they are separated by large numbers of solvent molecules. The transition from limited aggregation of methanol in dilute solutions to the formation of extensive chain structures at higher concentrations has been demonstrated in previous calculations for methanol/n-hexane mixtures.11 4.4. Chloroform-Methanol. 4.4.1. Phase Behavior. In this section, two combinations of force fields are used to predict the pressure-composition behavior of this mixture. Calculations utilizing the CDP force field for chloroform and the TraPPE force field for methanol are referred to as CDP/TraPPE. Calculations utilizing the force field for chloroform developed in this work and the TraPPE force field for methanol are referred to as new/TraPPE. As in the acetone-chloroform and acetonemethanol systems, the chloroform-methanol mixture has a Bancroft point, which is located at 354.1 K. The CDP/TraPPE force fields predict TBancroft ) 364.4 K, while the new/TraPPE combination returns TBancroft ) 354.1 K. The pressure-composition diagrams predicted by these two sets of force fields are shown in Figure 12 and compared to experiment. Both force fields predict a maximum pressure azeotrope, with azeotropic compositions of xchloroform ) 0.61 and 0.625 for the CDP/TraPPE and new/TraPPE force fields, respectively. These values are in good agreement with the expt experimental value of xchloroform ) 0.65. Greater deviations are found in the prediction of the azeotropic pressure. CDP/TraPPE predicts an azeotropic pressure of 1.08 bar, compared to the experimental value of 0.89 bar. The new/TraPPE force fields predict Pazeo ) 0.92 bar. The new/TraPPE force fields predict greater attraction between chloroform and methanol than CDP/ TraPPE, which results in a lower estimate of azeotropic pressure, a narrower liquid-vapor region, and an overall improved estimate of the pressure-composition behavior. 4.4.2. Microstructure. Isobaric-isothermal simulations at 300 K and 1 bar were performed on an equimolar mixture of chloroform and methanol to determine the microstructure of this system. In this mixture, there are two possible modes of association. The first is the expected methanol self-association, given by the OMeOH-HMeOH pair interaction. The second is the interspecies association defined by the interaction of the chloroform hydrogen with the methanol hydroxyl group: OMeOHHCHCl3. The radial distribution functions for these pair interac-

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Figure 12. Pressure-composition plot for chloroform(1)-methanol(2) at 323.15 K: CDP (1)/TraPPE(2) (square), new(1)/TraPPE (2) (circle), and experiment (line).22 Statistical uncertainties are approximately the size of the symbols. Dashed lines are a guide to the eye.

Figure 14. Snapshot of an equimolar mixture of chloroform and methanol at 300 K and 1 bar for the new/TraPPE force field: (a) configuration of chloroform-methanol, (b) typical chloroformmethanol aggregate, and (c) typical methanol-methanol aggregate.

Figure 13. Radial distribution function for the oxygen-hydrogen pair interaction in an equimolar chloroform(1)-methanol(2) mixture at 300 K and 1 bar: top plot, OMeOH-HMeOH pair interaction and bottom plot, OMeOH-HCHCl3 pair interaction; CDP (1)/TraPPE(2) (dashed line) and new(1)/TraPPE(2) (solid line).

tions are presented in Figure 13. The large peak at 1.8 Å for the OMeOH-HMeOH interaction shows that the presence of chloroform in the mixture causes little change in the aggregation behavior of methanol molecules with each other. The slightly increased chloroform-methanol interactions defined by the new/ TraPPE force fields do not have any significant effect on the microstructure of methanol. In comparison, a very weak interspecies association is predicted by both force fields, as shown in the bottom plot in Figure 13. The average number of hydrogen bonds per hydroxyl group, using a 3.5 Å cutoff between OMeOH-OMeOH atoms, was determined to be 1.97 for CDP/TraPPE and 1.80 for new/ TraPPE. The CDP/TraPPE results are close the value of 2.07 reported for pure methanol.11 The new/TraPPE results are reduced slightly due to the enhanced CHCl3-MeOH interaction, which reduces the number of hydroxyl groups available for methanol-methanol hydrogen bonding. The average number of hydrogen bonds per hydroxyl group is increased compared

Figure 15. Fraction of methanol aggregates as functions of aggregate sizes at 300 K and 1 bar in an equimolar mixture of chloroform and methanol: CDP(1)/TraPPE(2) (square) and new(1)/TraPPE (2) (square). Dashed lines are a guide to the eye. The inset shows the fraction of methanol molecules found in aggregates of particular sizes.

to the results for the acetone-methanol system because of reduced interspecies hydrogen bonding. An aggregation analysis was performed where a methanolchloroform aggregate was defined as any two molecules with OMeOH-HCHCl3 separations of less that 2.4 Å. For the CDP/

19472 J. Phys. Chem. B, Vol. 109, No. 41, 2005 TraPPE force fields, 11% of the total aggregates involved chloroform-methanol aggregation. For the new/TraPPE force fields, this is increased to 18%. In Figure 15, the distribution of aggregates containing only methanol is presented. As in the case of the acetone-methanol system, the increased interspecies interaction does not cause any significant change in the selfaggregation behavior of methanol molecules. Both sets of force fields predict aggregates of 2-8 molecules, with the majority of methanol molecules forming tetramers. 5. Conclusions New force fields for acetone and chloroform have been presented that yield accurate predictions of the saturated liquid and vapor densities, vapor pressures, and critical points. These force fields reproduce the interspecies hydrogen bonding found in the acetone-chloroform system and provide improved estimates of the pressure-composition behavior of the binary mixtures acetone-chloroform, acetone-methanol, and methanolchloroform. Overall, these results show that fitting partial charges to reproduce the electrostatic potential energy surface surrounding a hydrogen-bonded dimer, instead of isolated molecules, is an effective technique for the development of nonpolarizable force fields for polar molecules. Simulations in the isobaric-isothermal ensemble were used to investigate the microscopic properties of the binary mixtures acetone-chloroform, acetone-methanol, and chloroformmethanol at 300 K and 1 bar. While the acetone-chloroform and acetone-methanol mixtures both exhibit hydrogen bonding between unlike molecules, only the acetone-chloroform system exhibits minimum pressure azeotropy. This is because there is no intraspecies association in the acetone-chloroform mixture, while methanol is extensively hydrogen bonded in the methanolacetone mixture. These results suggest that, for minimum pressure azeotropy to occur in mixtures of polar molecules, the number of molecules participating in interspecies association must be greater than the number of molecules participating in intraspecies association. Acknowledgment. The authors would like to thank H. B. Schlegel for useful discussions. The authors acknowledge the CPU time provided by Grid Computing at Wayne State University. Financial support from NSF CTS-0138393 is gratefully acknowledged. Supporting Information Available: Graphs showing pressure-composition plots for chloroform(1)-acetone(2) mixtures at varying temperatures and tables of selected coexistence points for the plots. Graphs showing the radial distribution function for the OMeOH-OMeOH pair interaction in acetone-methanol and methanol-chloroform mixtures. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Malesinski, W. Azeotropy and other Theoretical Problems of Vapour-Liquid Equilibrium; Interscience Publishers: New York, 1965. (2) Seider, W. D.; Seader, J. D.; Lewin, D. R. Process Design Principles: Synthesis, Analysis and EValuation; Wiley: New York, 1998. (3) Widag, S.; Seider, W. D. AIChE J. 1996, 42, 96. (4) http://www.dupont.com/vertrel/prod/index.html. (5) Busato, G. A.; Bashein, G. Update Anaesth. 2004, 18, 1. (6) Fincham, D.; Quirke, N.; Tildesley, D. J. J. Chem. Phys. 1986, 84, 4535. (7) Liu, A.; Beck, T. L. J. Phys. Chem. B 1998, 102, 7627. (8) Potoff, J. J.; Errington, J. R.; Panagiotopoulos, A. Z. Mol. Phys. 1999, 97, 1073.

Kamath et al. (9) Stoll, J.; Vrabec, J.; Hasse, H. AIChE J. 2003, 49, 2187. (10) Weitz, S. L.; Potoff, J. J. Fluid Phase Equilib. 2005, 234, 144. (11) Chen, B.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2001, 105, 3093. (12) Khare, R.; Sum, A. K.; Nath, S. K.; Pablo, de J. J. J. Phys. Chem. B 2004, 108, 10071. (13) Stubbs, J. M.; Potoff, J. J.; Siepmann, J. I. J. Phys. Chem. B 2004, 108, 17596. (14) Sum, A. K.; Sandler, S. I.; Bukowski, R.; Szalewicz, K. J. Chem. Phys. 2002, 116, 7637. (15) Lagache, M. H.; Ridard, J.; Ungerer, P.; Boutin, A. J. Phys. Chem. B 2004, 108, 8419. (16) Apelblat, A.; Tamir, A.; Wagner, M. Fluid Phase Equilib. 1980, 4, 229. (17) Campbell, A.; Musbally, G. M. Can. J. Chem. 1970, 48, 3173. (18) Durov, V. A.; Shilov, I. Y. J. Chem. Soc., Faraday Trans. 1996, 92 (19), 1559. (19) Hopkins, J. A.; Bhethanabotla, V. R.; Campbell, S. W. J. Chem. Eng. Data 1994, 39, 488. (20) Kojima, K.; Tochigi, K.; Kurihara, K.; Nakamichi, M. J. Chem. Eng. Data 1991, 36, 343. (21) Wilsak, R. A.; Campbell, S. W.; Thodos, G. Fluid Phase Equilib. 1986, 28, 13. (22) Goral, M.; Kolasinska, G.; Oracz, P.; Warycha, S. Fluid Phase Equilib. 1985, 23, 89. (23) Jorgensen, W. L.; Madura, J. D.; Swenson, C. J. J. Am. Chem. Soc. 1984, 106, 6638. (24) Chang, T. M.; Dang, L. X. J. Phys. Chem. B 1997, 101, 3413. (25) Lorentz, H. A. Ann. Phys. 1881, 12, 127. (26) Berthelot, D. C. R. Hebd. Seances Acad. Sci. 1898, 126, 1703. (27) Fender, B. E. F.; Halsey, G. D., Jr. J. Chem. Phys. 162, 63 1881. (28) Smith, F. T. Phys. ReV. A 1972, 5, 1708. (29) Kong, C. L. J. Chem. Phys. 1973, 59, 2464. (30) Jorgensen, J. L.; Tirado-Rives J. J. Am. Chem. Soc. 1988, 110, 1657. (31) Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids, Fundamentals; Clarendon Press: Oxford, U.K., 1984; Vol 1. (32) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (33) Breneman, C. M.; Wilberg, K. B. J. Comput. Chem. 1990, 11, 361. (34) Cox, S. R.; Williams, D. E. J. Comput. Chem. 1981, 2, 304. (35) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, Englewood Cliffs, NJ, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision A.1; Gaussian, Inc.: Pittsburgh, PA, 2003. (36) Delhommelle, J.; Tschirwitz, C.; Ungerer, P.; Granucci, G.; Millie, P.; Pattou, D.; Fuchs, A. D. J. Phys. Chem. B 2000, 104, 4745. (37) Kranias, S.; Pattou, D.; Levy, B.; Boutin, A. Phys. Chem. Chem. Phys. 2003, 5, 4175. (38) Bayly, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269. (39) Cornell, W. D.; Cieplak, P.; Bayly, C. I.; Kollman, P. A. J. Am. Chem. Soc. 1993, 115, 9620. (40) Ferrenberg, A. M.; Swendsen, R. H. Phys. ReV. Lett. 1988, 61, 2635. (41) Ferrenberg, A. M.; Swendsen, R. H. Phys. ReV. Lett. 1989, 63, 1195. (42) Potoff, J. J.; Panagiotopoulos, A. Z. J. Chem. Phys. 1998, 109, 10914. (43) Esselink, K.; Loyens, L. D. J. C.; Smit, B. Phys. ReV. E 1995, 51, 1560. (44) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1999, 103, 4508. (45) McDonald, I. R. Mol. Phys. 1972, 23, 41. (46) Wood, W. W. J. Chem. Phys. 1968, 48, 415. (47) Ewald, P. P. Ann. Phys. 1921, 64, 253. (48) Allen, M. P.; Tildesley, D. J. Computer Simulation of Liquids, 1st ed.; Oxford University Press: New York, 1987. (49) Rowildson, J. S.; Widom, B. Molecular Theory of Capillarity; Clarendon Press: Oxford, U.K., 1982.

Acetone-Chloroform-Methanol Binary Mixtures (50) Rowlinson, J. S.; Swinton, F. L. Liquids and Liquid Mixtures, 3rd ed.; Butterworth: London, 1982. (51) Smith B. D.; Srivastava R. Thermodynamic data for pure compounds, Part A Hydrocarbons and Ketones; Elsevier: New York, 1986. (52) Privman, V. G. L. Encyclopedia of Applied Physics, Trigg ed.; Wiley-VCH: Berlin, Germany, 1998; Vol. 23, p 41. (53) Smith B. D.; Srivastava R. Thermodynamic data for pure compounds, Part B Halogenated Hydrocarbons and Alcohols; Elsevier: New York, 1986.

J. Phys. Chem. B, Vol. 109, No. 41, 2005 19473 (54) King C. J. Separation Processes, 2nd ed.; McGraw-Hill: New York, 1980. (55) Kastanov, S.; Augustasson, A.; Luo, Y.; Guo, J.-H.; Sathe, C.; Rubensson, J.-E.; Siegbahn, H.; Nordgren, J.; Agren, H. Phys. ReV. B 2004, 69, 24201. (56) Jorgensen, W. L. J. Phys. Chem. 1986, 90, 1276. (57) Stubbs, J. M.; Siepmann, J. I. J. Chem. Phys. 2004, 121, 1525. (58) Stubbs, J. M.; Siepmann, J. I. J. Phys. Chem. B 2002, 106, 3968.