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J. Phys. Chem. B 2005, 109, 19463-19473 19463

Molecular Modeling of Phase Behavior and Microstructure of -- 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 - vapor coexistence curve, critical parameters, and vapor pressures are well reproduced by simulation. Histogram- reweighting 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 in the acetone-chloroform mixture found ) in experiment. The predicted azeotropic composition of xCHCl3 0.77 is in fair agreement with the experimental value of xexpt ) 0.64. The new force fields were also found to provide improved predictions of the CHCl3 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 bonding occurring between acetone and chloroform. Limited interspecies hydrogen bonding was found in the acetone-methanol or chloroform-methanol mixtures.

1. Introduction Of the systems listed above, only the dimethyl mercury/n- pentane exhibits minimum pressure (maximum temperature) In separation operations based on distillation, knowledge of azeotropy. Such systems make up only 1% of the thousands of the presence of an azeotrope is important since this phenomena binary mixtures known to form . The binary mixture limits in the degree of separation that which may be obtained 1-3 acetone/chloroform is another system that displays minimum by exploiting vapor-liquid equilibrium (VLE). While the - pressure azeotropy.16 20 It is hypothesized that pure acetone and presence of an azeotrope presents complications in the purifica- chloroform, while unable to hydrogen bond as pure fluids, can tion of fluid mixtures, this same phenomena has been exploited form a hydrogen-bonded complex when mixed. The systems in a wide range of technological applications. For example, the acetone/methanol and chloroform/methanol are also expected binary system HFC-43-10-mee/methanol is part of a new class to form hydrogen-bonded complexes between unlike , of cleaning for electronics processing. The presence however, both of these systems have maximum pressure of an azeotrope in this system allows efficient recovery of the azeotropes.21,22 This suggests that limited hydrogen bonding is cosolvent mixture through boiling while maintaining the original occurring between unlike molecules in mixtures of acetone/ composition of the liquid phase.4 Azeotropic mixtures of methanol and chloroform/methanol. and diethyl have been studied extensively as an anesthetic with lower cost and an increased margin of safety These complex intermolecular interactions provide a stringent over pure halothane.5 test for atomistic force fields. In this work, grand-canonical histogram-reweighting Monte Carlo simulations are used to The use of molecular simulation for the determination of - fluid-phase behavior has become routine and is limited only by calculate the pressure composition diagrams predicted by the optimized potentials for liquid simulations (OPLS)23 and the the accuracy of the intermolecular potentials used to describe 13 the interactions between molecules. The phase diagrams for transferable potentials for phase equilibria (TraPPE). Our azeotropic mixtures of real fluids have been determined by results show that neither of these intermolecular potentials are simulation of atomistic force fields for a large number of systems able to reproduce the minimum pressure azeotrope found in the 6-9 10 10 acetone/chloroform mixture. including: /CO2, ethene/CO2, ethene/xenon, metha- nol/n-hexane,8,11 n-heptane/1-pentanol,12 acetone/n-hexane,13 To remedy this, new force fields are developed for acetone /methanol,14 and dimethyl mercury/n-pentane.15 In and chloroform that are parametrized specifically to provide many of these studies, excellent agreement with experimental accurate predictions of the vapor-liquid coexistence curve, data is achieved, while in some of the more difficult systems, , and critical properties as well as reproduce the the simulations are qualitatively correct but deviate from minimum pressure azeotrope found in the acetone-chloroform experiment by up to 10%. mixture. These force fields use the same Lennard-Jones plus fixed point charge functional form as OPLS and TraPPE force * To whom correspondence should be addressed. E-mail: jpotoff@ fields. Unlike the OPLS and TraPPE force fields, which use chem1.eng.wayne.edu. Fax: 313-577-3810. Tel: 313-577-9357. 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 19464 J. Phys. Chem. B, Vol. 109, No. 41, 2005 Kamath et al.

TABLE 1: Parameters for Nonbonded Interactions Used in TABLE 2: Geometrical Parameters for Acetone, This Work Chloroform, and Methanol

force field /kb (K) σ (Å) q (e) µ (D) bond length bond angle kθ/kb vibration (Å) bending (deg) (K) acetone 2.91[31] OPLS-UA CH3 80.53 3.91 0.062 2.956 CdO 1.229 ∠CH3sCdO 121.4 62500 C 52.85 3.75 0.30 CH3-C 1.520 ∠CH3-C-CH3 117.2 62500 Od 105.7 2.96 -0.424 C-Cl 1.760 ∠Cl-C-Cl 111.2 62500 TraPPE-UA CH3 98.0 3.75 0.0 2.5024 C-H 1.070 ∠Cl-C-H 107.6 62500 C 40.0 3.82 0.424 CH3-O 1.43 ∠CH3-O-H 108.5 55400 Od 79.0 3.05 -0.424 O-H 0.945 new CH3 98.0 3.75 -0.049 2.9739 C 27.0 3.82 0.662 Lorentz-Berthelot combining rules are used to determine cross Od 79.0 3.05 -0.564 parameters for Lennard-Jones interactions between sites of chloroform 1.04[31] different types.25,26 OPLS-UA CH 40.26 3.8 0.42 1.292 Cl 150.98 3.47 -0.14 ) + CDP Cl 138.58 3.45 -0.1686 1.085 σij (σii σjj)/2 (2) C 68.94 3.41 0.5609 H 10.06 2.81 -0.0551  ) x  (3) new Cl 138.58 3.45 -0.04 1.398 ij ii jj - C 68.94 3.41 0.235 Although alternate combining rules have been suggested,27-29 H 10.06 2.81 0.355 methanol 1.70[31] recent calculations have not shown one combining rule to be 8 TraPPE-UA CH3 98.0 3.75 0.265 2.257 consistently better than any of the others. For this reason, we O- 93.0 3.02 -0.7 retain the Lorentz-Berthelot combining rules. H 0.0 0.0 0.435 In each of the acetone, chloroform, and methanol models, interaction sites are separated by fixed bond lengths while bond for each pseudoatom in the new force field are determined angle bending is controlled by a harmonic potential through the application of a CHELPG (charges from electrostatic potentials using a grid based method) analysis to an acetone- k + ) θ - 2 chloroform dimer optimized at the MP2/6-31 g(d,p) level of Ubend (θ θ0) (4) theory. Grand-canonical histogram-reweighting simulations are 2 then used to determine the pressure-composition diagrams for where θ is the measured bond angle, θ0 is the equilibrium bond the binary mixtures acetone/chloroform, acetone/methanol, and angle, and kθ is the force constant. All bond lengths, bond angles, chloroform/methanol. The microstructure of each of these and bending constants are listed in Table 2. mixtures is determined from Monte Carlo simulations in the 2.1.1. Acetone. In each of the force fields, OPLS-UA, - isobaric isothermal ensemble at 300 K and 1 bar. TraPPE-UA, and new, a united-atom representation was used. This paper is organized as follows. The specific details for bonded to carbon atoms were grouped together in a each of the force fields used in this work are given in the next single interaction site known as a “pseudoatom”. This is a useful section. Following the description of the various force fields, approximation for acetone, since the hydrogens bonded to the we explain the strategy used in the development of new force do not participate in hydrogen bonding to any fields for acetone and chloroform. In section 3, the details of significant extent. The primary benefit of the united-atom the grand-canonical histogram-reweighting and NPT Monte scheme over an explicit hydrogen representation is a significant Carlo simulations used in this work are provided. In section 4, reduction in computational expense with only a minor (potential) - the pure component vapor liquid coexistence curves and vapor loss in accuracy. pressures are presented for the new force field as well as the The selection of appropriate Lennard-Jones and charge OPLS-UA, Chang, Dang, and Peterson (CDP), and TraPPE parameters is key to the accuracy of a given force field. The - force fields. This is followed by pressure composition diagrams OPLS-UA force field was originally parametrized to reproduce and radial distribution functions for acetone/chloroform, acetone/ liquid and heats of vaporization at ambient conditions. methanol, and chloroform/methanol mixtures. The conclusions Partial charges were determined empirically, guided by ab initio of this work can be found in section 5. calculations at the HF/6-31g(d) level.30 The TraPPE-UA force field utilizes the OPLS-UA partial charges but makes use of 2. Models and Simulation Details Lennard-Jones parameters optimized to give accurate saturated 2.1. Force Fields. In this work, a number of intermolecular liquid densities and critical points. The new force field is a potentials are used. Nonbonded interactions for each force field natural extension of the OPLS-UA and TraPPE-UA force fields. are given by pairwise additive Lennard-Jones 12-6 (LJ) poten- Partial charges were derived from a CHELPG analysis con- tials and Coulombic interactions of partial charges ducted on an optimized cluster of acetone and chloroform at the MP2/6-31++G(3df,3dp) level of theory. This scheme results σ 12 σ 6 q q ) ij - ij + i j in a moment of 2.97 D, which is slightly higher than the U(rij) 4ij [( ) ( ) ] (1) 31 rij rij 4π0rij experimental gas-phase dipole moment of 2.91 D. Lennard- Jones parameters for the dO and CH3 pseudoatoms were taken where rij, ij, σij, qi, and qj are the separation, LJ well depth, LJ from the TraPPE-UA force field while the  and σ parameters size and partial charges, respectively, for the pair of interaction for the carbonyl carbon were tuned to give an accurate sites i and j. The primary difference in each of the force fields reproduction of saturated liquid and vapor densities as well as is in the parameters used to describe the interactions between vapor pressures. The nonbonded parameters for each of the force interaction sites. The nonbonded parameters for each of the force fields used in this work are listed in Table 1. fields used in this work are listed in Table 1, and the specific 2.1.2. Chloroform. Three force fields for chloroform were details of each force field are listed in the following section. used in this work, OPLS-UA, CDP24 (model developed by Acetone-Chloroform-Methanol Binary Mixtures J. Phys. Chem. B, Vol. 109, No. 41, 2005 19465

Chang, Dang, and Peterson), and new. The OPLS-UA force of the fitting procedure, the molecular electrostatic potential field, like its counterpart for acetone, uses a united-atom (MEP) is calculated at a number of grid points spaced 3.0 pm representation. The hydrogen and carbon atoms are merged to apart and distributed regularly in a cube. The dimensions of form a single CH group. Chlorine atoms are modeled explicitly. the cube are chosen such that the is located at the Parameters were derived with the same methodology described center with 28.0 pm headspace between the molecule and the for acetone. The CDP force field uses an explicit hydrogen end of the box in all three dimensions. All points falling inside representation. Partial charges were derived by rescaling the the van der Waals radius of the molecule are discarded from results of fitting to electrostatic potentials obtained from ab initio the fitting procedure. After evaluating the MEP at all valid grid calculations at the MP2 level with 6-31+G* basis set such that points, atomic charges are fit to reproduce the MEP. The only the gas-phase dipole moment was reproduced. Lennard-Jones additional constraint in the fitting procedure is that the sum of parameters were fit to reproduce radial distribution functions, all atomic charges must equal the overall charge of the system. liquid densities, and heats of vaporization at 298 K. In the The major difference between this work and others that have original work, the authors also included polarization effects used the CHELPG, or similar ESP fitting schemes,36-39 is that through a dipole-polarizable formalism. However, in our ours is the first work to determine partial charges fit to the calculations we found that the addition of dipole polarizability electrostatic potential surface surrounding a cluster of molecules had no effect on the predicted pure component vapor-liquid instead an isolated molecule. In fact, our attempts at using the coexistence curve or vapor pressure. As a result, in this work CHELPG scheme to determine partial charges for isolated we have used a nonpolarizable variant of the CDP force field. acetone and chloroform molecules, while resulting in an The new force field is based on the CDP force field. It uses an excellent pure component phase diagram, produced a pressure- explicit hydrogen representation and retains the same Lennard- composition diagram that did not contain an azeotrope (see Jones parameters for chlorine and hydrogen atoms. Since the Supporting Information). We hypothesized that the minimum hydrogen atom in chloroform participates in hydrogen bonding, pressure azeotrope found in the acetone-chloroform mixture it is important to treat it explicitly. Unlike the CDP force field, was the result of hydrogen bonding between acetone- partial charges for the new force field were derived from a chloroform. An acetone-chloroform dimer was optimized at CHELPG analysis performed on the acetone-chloroform dimer the MP2/6-31+g(d,p), and point charges for acetone and (see acetone, above) and not an isolated molecule. Once the chloroform were obtained from a CHELPG analysis at the MP2 partial charges were determined, the Lennard-Jones parameters theory and the 6-31++g(3df,3dp) basis set. These calculations for the central carbon were optimized to provide the best were performed with the Gaussian 03 software package.35 reproduction of the vapor-liquid coexistence curve and vapor Lennard-Jones parameters for acetone and chloroform were then pressures. parametrized according to the scheme outlined above for the 2.1.3. Methanol. The TraPPE-UA force field was used to individual molecules. represent methanol. As in the case of acetone, the CH3 group 3. Simulation Details is treated as a single pseudoatom with identical Lennard-Jones 3.1. Grand-Canonical Monte Carlo. Grand-canonical his- parameters. In the original parametrization, partial charges in togram-reweighting Monte Carlo (GCMC) simulations40-42 were this force field were taken from the OPLS-UA force field and used to determine the vapor-liquid coexistence curves and the  and σ parameters for were fit to give an accurate vapor pressures for pure acetone and chloroform as well each reproduction of the vapor-liquid coexistence curve. The of the binary mixtures presented in this work. The insertion of hydrogen bonded to the hydroxyl oxygen is represented molecules in the GCMC simulations were enhanced through explicitly with a point charge without an additional Lennard- multiple first bead insertions43 and the application of the Jones term. The TraPPE-UA force field was not modified coupled-decoupled configurational-bias Monte Carlo method.44 because preliminary calculations showed that it returned the Particle identity exchanges were used for mixtures to enhance correct qualitative pressure-composition behavior when mixed the acceptance rate for particle insertions and deletions. The with acetone or chloroform. fractions of the various moves for each simulation were set to 2.2. Determination of Partial Charges. Many computational 10% for identity exchanges, 15% for particle displacements, methods have been used to determine the net atomic charges 15% for rotations, 10% configurational-bias regrowths, and 50% of atoms in molecules. A common technique is that of for insertions and deletions. Simulations were performed for a 32 population analysis proposed by Mulliken. The OPLS-UA and system size of L ) 20 Å. Lennard-Jones interactions were TraPPE-UA are examples of force fields that utilize point truncated at L ) 10 Å, and standard long-range corrections were charges derived in part from such an analysis. Mulliken charges applied.45,46 An Ewald sum with tinfoil boundary conditions (κ are based on orbital occupancies, that is, how much electron × L ) 5 and Kmax ) 5) was used to calculate the long-range can be associated with each atom’s orbitals. The nuclear electrostatic interactions.47,48 Simulations were equilibrated for charge minus the electron density gives the atomic charge. The 1 million Monte Carlo steps (MCS) before run statistics were Mulliken analysis assumes that the electron density represented recorded, while production runs were 25 million MCS (pure by the product of basis functions on different atoms is shared components) to 50 million MCS (mixtures). Over the course equally by the two atoms. If one atom is more electronegative, of each simulation, the number of molecules N and energy E has a larger number of basis functions, or these basis functions were stored in the form of a list, which was updated every 250 are more diffuse, the approximation of equal sharing of electron MCS. The necessary probability distributions were extracted density between neighboring atoms may not be valid. from this list after the completion of the simulation. Statistical An alternative to the Mulliken analysis are methods that uncertainties for the new force fields were calculated by taking derive partial charges by fitting to reproduce an electrostatic the standard deviation of three separate series of simulations potential energy surface surrounding the molecule. The CHELPG runs, each started from different initial configurations and scheme by Breneman et.al.33,34 is one such method and was random number seeds. used to determine partial charges for the new acetone and 3.2. Isobaric-Isothermal Monte Carlo. Monte Carlo simu- chloroform force fields presented in this work. As a first step lations in the isobaric-isothermal ensemble were used to 19466 J. Phys. Chem. B, Vol. 109, No. 41, 2005 Kamath et al.

Figure 1. Vapor-liquid equilibria for acetone. Simulation results are shown as symbols: new (circle), TraPPE (square),13 OPLS-UA Figure 2. Clausius-Clapeyron plot for acetone: new (circle), TraPPE (triangle), and experiment (line).51 The inset shows the expanded view (square),13 OPLS-UA (triangle), and experiment (line).51 of the saturated vapor densities of acetone as predicted by each of the force fields. TABLE 3: Predicted Normal Boiling Points and Critical Properties for Acetone and Chloroform 3 investigate the microstructure in equimolar mixtures of acetone/ Tb(K) Tc (K) Fc (kg/m )Pc (bar) chloroform, acetone/methanol, and chloroform/methanol. A acetone new 327.3 ( 0.1 508.2 ( 0.2 275.5 ( 1 48.5 ( 0.3 system size of 500 molecules was used. Simulations were TraPPE [13] 322.0 508.0 278.0 55.3 equilibrated for 25 million MCS, after which run statistics were OPLS-UA 330.3 526.1 270.6 55.9 recorded for an additional 25 million MCS. The ratio of moves expt (51) 329.3 508.1 273.0 49.2 chloroform new 337.35 ( 0.1 538.2 ( 0.5 520.9 ( 2 55.4 ( 0.5 was 1% volume changes, 14% configurational-bias regrowths, CDP 337.6 543.1 525.1 63.8 70% translations, and 15% molecule rotations. Lennard-Jones OPLS-UA 343.8 566.8 544.4 73.5 interactions were truncated at L ) 10 Å and standard long- expt (53) 334.8 537.0 516.0 56.5 range corrections were applied.45,46 An Ewald sum with tinfoil boundary conditions (κ × L ) 5 and Kmax ) 5) was used to The Clausius-Clapeyron plots used to determine the critical calculate the long-range electrostatic interactions.47,48 pressures and normal boiling points are shown in Figure 2. The normal boiling points predicted by each force field are listed in 4. Results and Discussion Table 3. The best reproduction of the critical pressure is given ) 4.1. Pure Component Vapor-Liquid Equilibrium. 4.1.1. by the new force field, which predicts Pc 48.52 bar, compared 51 Acetone. The vapor-liquid coexistence curves for acetone as to the experimental value of 49.18 bar. The OPLS-UA and predicted by OPLS-UA, TraPPE, and new force fields are shown TraPPE-UA force fields show deviations from experiment of in Figure 1. All of the force fields provide reasonable estimates 13.6% and 12.5%, respectively. As in the case of the critical of the saturated liquid densities. Average unsigned deviations parameters, all of the force fields predict a normal of simulation from experiment51 range from less than 1% for that is in close agreement with experiment, with the maximum the new and TraPPE-UA force fields to 5.5% for OPLS-UA. deviation being 2% (TraPPE-UA). - The new force field yields the best prediction of saturated vapor 4.1.2. Chloroform. The vapor liquid coexistence curves for densities but still show deviations from experiment by as much chloroform as predicted by the OPLS-UA, CDP, and new force as 10%. Critical parameters for each of the force fields were fields are shown in Figure 3. As in the case of acetone, all the estimated by fitting the saturated liquid and vapor densities over force fields provide reasonable estimates for the saturated liquid the temperature range 300 e T e 480 K to the density scaling densities. Average unsigned deviations of simulation from 53 law for critical temperature49 experiment 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 F -F ) B(T - T )â (5) liq vap c agreement with the experimental values with average unsigned deviations of 5.0%, while the OPLS-UA under predicts the and the law of rectilinear diameters50 saturated vapor densities for the entire range of temperatures studied with average deviations from experiment of 25%. F +F liq vap The T ) 538.2 K and F ) 520.9 kg/m3, predicted by the )F + A(T - T ) (6) c c 2 c c new force field, are within 1% of the experimental values of expt ) Fexpt ) 3 Tc 537.0 K and c 516.0 kg/m . This is the best where â ) 0.325 is the critical exponent for Ising-type fluids prediction of the critical point for chloroform of the three force in three dimensions52 and A and B are constants fit to simulation fields used in this work. Only the OPLS-UA shows appreciable data. The critical properties predicted by each force field are deviation from the experiment for the critical temperature and listed in Table 3. The TraPPE and new force fields both predict density (5.5%). a critical temperature that is within 1% of experiment. Only The Clausius-Clapeyron plots used to determine the critical the OPLS-UA force field shows any appreciable deviation from pressures and normal boiling points are shown in Figure 4. The experiment for the critical temperature (5%). 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 of the binary mixtures that have a Bancroft point exhibit some kind of azeotropic behavior.1 temperatures with average deviations from experiment equal In this section, we apply three different combinations of force to 30%. The CDP and new force fields also under predict vapor fields in the determination of the pressure-composition diagram pressures by 10% and 15%, respectively, over the temperature for this mixture. We refer to calculations utilizing the OPLS- range 300 < T < 520 K. The normal boiling points and critical UA force fields for both acetone and chloroform as “OPLS- pressures extracted from the Clausius-Clapeyron plots of the UA”. Calculations that use the TraPPE-UA force field for vapor pressure data are listed in Table 3. The new force field acetone and CDP force field for chloroform are referred to as predicts a normal boiling point for chloroform of Tb ) 337.35 “TraPPE/CDP”. Finally, simulations that use the force fields K, which is excellent agreement with the experimental boiling developed in this work for acetone and chloroform are simply point of Tb ) 334.8 K. The new force field also gave the best referred to as “new”. prediction of the critical pressure of chloroform Pc ) 55.43 bar, The predictions of simulations, utilizing the OPLS-UA, compared to the experimental value of 56.5 bar.53 The OPLS- TraPPE/CDP, and new force fields, for pressure-composition UA over predicts the critical pressure by 30%. behavior of the acetone-chloroform mixture at 308.32 K are 4.2. Acetone-Chloroform. 4.2.1. Phase Behavior. The shown in Figure 5. The predicted difference between normal acetone-chloroform mixture has been widely investigated boiling points of the two components was 13.5 and 15.6 K for experimentally and exhibits minimum pressure azeotropy.16-20 the OPLS-UA and TraPPE/CDP force fields, respectively. This The experimental boiling points for acetone and chloroform is well within the 30 K difference normally seen in azeotropic differ by only 5.5 K. As a general rule for binary mixtures, the systems.54 On the other hand, neither the OPLS-UA or TraPPE/ closer the boiling points of each of the components are to each CDP force fields show a Bancroft point. As shown in the Pxy other, the greater the probability of azeotropic behavior.54 plot, both the OPLS-UA and TraPPE/CDP calculations fail to Furthermore, the vapor pressures of acetone and chloroform are predict any azeotropic behavior for this system. Instead, equal at 266.17 K. This intersection of pressure vs temperature simulations predict nearly ideal behavior that is well reproduced curves for each of the pure components is known as a Bancroft by Raoult’s Law. We also note that Kranias et al.37 have recently point. It has been shown experimentally that approximately 90% published a force field for acetone based on an anisotropic 19468 J. Phys. Chem. B, Vol. 109, No. 41, 2005 Kamath et al.

- 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 OPLS- UA/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 Figure 7. Snapshot of an equimolar mixture of acetone and chloroform force fields do have a Bancroft point at 253 K. The existence at 300 K and 1 bar for the new force field. Different types of aggregates of such a point, while signaling a high probability that azeotropy seen in the configuration: (a) two chloroform molecules bonded to exists, does not predict what kind of azeotropic behavior will one acetone molecule and (b) a chloroform molecule bonded to an occur. As shown in Figure 5, the predictions of the new force acetone molecule. fields are in qualitative agreement with the experimental data and display minimum pressure azeotropy. The new force fields an intermolecular distance less than 2.7 Å. A distance of 2.7 Å predict the pressure and composition of the azeotrope as 0.322 was chosen because this corresponds to the minimum in the ) - bar and xCHCl3 0.77, respectively. These are in good agreement acetone chloroform dimer interaction energy as predicted by with the experimental values of Pexpt ) 0.34 bar and xexpt ) the new force field (-11.55 kJ/mol). This dimer binding energy azeo CHCl3 0.64. Additional Pxy diagrams (see Supporting Information) is in good agreement with the experimental value of -11.3 kJ/ were determined for the new force fields at 450, 400, and 350 mol.16 As expected from the RDF, no association between K. The azeotropic composition shifts from xsim ) 0.94 to acetone and chloroform was found for the OPLS-UA force field. CHCl3 0.77 as temperature decreases from 450 to 308.32 K. This For the CDP/TraPPE pairing, an average of 6% of the total behavior is consistent with the experimental shift in the molecules formed hydrogen-bonded aggregates. The new force composition of the azeotrope from xexpt ) 0.791 at 453 K to field showed that 18% of the molecules formed hydrogen- CHCl3 expt ) - 17 bonded aggregates between acetone and chloroform. For the xCHCl 0.64 at 373 K for the acetone chloroform mixture. 3 new force field, the average distance for the O -H 4.2.2. Microstructure. Isobaric-isothermal simulations at ace CHCl3 hydrogen bond was 2.4 Å and the ∠C O H was 120°. 300 K and 1 bar were performed on equimolar mixture of ace ace CHCl3 - acetone and chloroform. The site-site radial distribution func- The hydrogen bond length of the acetone chloroform dimer is ) tions (RDFs) were calculated for each of the force field pairs longer in comparison to that of the dimer (rH-O 1.95 55 used in the VLE calculations. In this system, the only possible Å), resulting in only weak hydrogen-bonding effects on the mechanism for interspecies association is through hydrogen mixture. bonding between the oxygen and hydrogen atoms in acetone In Figure 7, a snapshot from equimolar NPT simulations for - the new force fields is shown. The carbonyl oxygen with the and chloroform, respectively. The RDFs for the Oace HCHCl3 pair interactions determined from simulation are shown in Figure two lone pairs of electrons can potentially form two hydrogen 6. The OPLS-UA force field does not show any significant bonds. In the simulations of the new force field, a small number of 2:1 (chloroform/acetone) aggregates was found, however, the interaction of Oace with HCHCl3. The CDP/TraPPE model shows a small peak at 2.7 Å, which is due to a limited association majority of the aggregates were 1:1, as shown in part c of Figure between chloroform and acetone molecules. The new force field 7. These data confirm that interspecies association is necessary has a more pronounced peak at 2.7 Å because of an increased for the formation of minimum pressure (maximum boiling) association between chloroform and acetone. azeotropes. An aggregation analysis was performed on the simulation 4.3. Acetone-Methanol. 4.3.1. Phase Behavior. In this - data. An association was defined as any Oace HCHCl3 pair with section, two combinations of force fields are used to determine Acetone-Chloroform-Methanol Binary Mixtures J. Phys. Chem. B, Vol. 109, No. 41, 2005 19469

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 Figure 9. Radial distribution function for the oxygen-hydrogen pair 21 experiment (line). Statistical uncertainties are approximately the size interaction in an equimolar acetone(1)-methanol(2) mixture at 300 K of the symbols. Dashed lines are a guide to the eye. and 1 bar: top plot, OMeOH-HMeOH pair interaction; bottom plot, Oace- - - HMeOH pair interaction; TraPPE(1)/TraPPE(2) (dashed line), new(1)/ the pressure composition behavior for the acetone methanol TraPPE (2) (line). mixture. Calculations involving the TraPPE-UA force fields for both acetone and methanol are referred to as “TraPPE”, while The oxygen-hydrogen intermolecular RDFs were calculated calculations involving the new force field for acetone and for each of the force field pairs and are shown in Figure 9. The TraPPE-UA for methanol are referred to as “new/TraPPE”. top plot shows the predictions for TraPPE and new/TraPPE force In Figure 8 the predictions given for both TraPPE and new/ fields for the intraspecies O -H interaction. A peak at TraPPE for the pressure-composition diagram at 372.8 K are MeOH MeOH 21 1.8 Å for both combinations of force fields agrees with the shown in comparison to experiment. Experimentally, the previous simulations performed on methanol and methanol Bancroft point for this system is at 385.1 K. The TraPPE and mixtures11,57 and signifies significant methanol-methanol hy- new/TraPPE force fields predict Bancroft points of 415.05 and drogen bonding. The reduction in RDF peak height for the new/ 393.51 K, respectively. As shown in the Pxy diagram, both sets TraPPE combination compared to TraPPE is a result of the of force fields predict a maximum pressure azeotrope. The TraPPE increased attraction between acetone and methanol. The bottom TraPPE force fields predicts an azeotropic composition xacetone plot shows the RDF for the interspecies O -H pair ) TraPPE ) ace MeOH 0.68 and pressure Pazeo 5.45 bar, which is in fair interaction. The new/TraPPE calculations result in a peak height expt ) agreement with the experimental composition xacetone 0.51 three times that of the TraPPE force field. This is further expt ) - and pressure Pazeo 4.05 bar. Part of the deviation from evidence of the increased acetone methanol interaction in the experiment is due to the deviations of the pure component vapor new/TraPPE combination. pressures predicted by the TraPPE force field. However, the Following the procedure defined in the work of Chen et al.,11 coexistence curve predicted by TraPPE is significantly wider the average number of methanol-methanol hydrogen bonds per than that of experiment, signaling that the acetone-methanol hydroxyl group were calculated. Methanol molecules were interactions defined by the TraPPE force field are weaker than considered hydrogen bonded to each other if the OMeOH-OMeOH they are in reality. distance was less than 3.5 Å. For TraPPE, the number of Calculations for the new/TraPPE force fields provide im- hydrogen bonds per methanol was 1.67, while new/TraPPE gave new ) proved estimates of the azeotropic composition xacetone 0.57 1.26. These results are lower than the 2.07 hydrogen bonds per new ) 11 and pressure Pazeo 4.36 bar. In addition, this combination of hydroxyl group reported for pure methanol. Acetone, being force fields results in a narrower phase envelope that is more strongly polar, provides screening between methanol molecules, representative of experimentally seen behavior, especially for which reduces intraspecies hydrogen bonding. In addition, in mole fractions of acetone greater than 0.5. This shows that the the new/TraPPE system significant acetone-methanol hydrogen new/TraPPE force field combination provides a better ap- bonding is able to occur, which detracts from the number of proximation of acetone-methanol cross interactions. methanol molecules that are able to form hydrogen bonds with 4.3.2. Microstructure. Simulations in the NPT ensemble each other. were conducted at 300 K and 1 bar for an equimolar mixture A hydrogen bond analysis (cutoff of 2.4 Å for O-H of acetone and methanol. A combination of TraPPE force fields separation) was also performed. Calculations utilizing the and new/TraPPE force fields similar to the previously described TraPPE force field found acetone-methanol aggregates ac- VLE calculations were used to model the necessary interactions counting for 25.2% of the total number of aggregates but only between molecules. This system is more complex than the 9.6% of the methanol molecules. For the new/TraPPE force acetone-chloroform mixture, since methanol can self-associate fields, a similar analysis shows acetone-methanol aggregates as well as form hydrogen-bonded complexes with acetone. There constitute 48% of the total aggregates and 28% of the methanol are two RDFs of interest with respect to aggregation in this molecules. For the new/TraPPE force fields, approximately 9% mixture. The first is given by the intraspecies (methanol- of the acetone-methanol aggregates were larger than the dimers methanol) OMeOH-HMeOH interaction, the second is the Oace- and involved either short chains (2-3 ) hydrogen HMeOH interspecies (acetone-methanol) interaction. bonded to acetone or two unchained methanols h-bonding in a 19470 J. Phys. Chem. B, Vol. 109, No. 41, 2005 Kamath et al.

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.

aggregation since they are separated by large numbers of 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 Figure 10. Snapshot of an equimolar mixture of acetone and methanol utilizing the CDP force field for chloroform and the TraPPE at 300 K and 1 bar for the new/TraPPE force field: (a) acetone- force field for methanol are referred to as CDP/TraPPE. methanol configuration, (b) methanol-acetone aggregates, and (c) Calculations utilizing the force field for chloroform developed methanol-methanol aggregate. in this work and the TraPPE force field for methanol are referred to as new/TraPPE. As in the acetone-chloroform and acetone- - similar fashion as the acetone-chloroform . Examples of methanol systems, the chloroform methanol mixture has a these aggregates are shown in Figure 10, which is a snapshot Bancroft point, which is located at 354.1 K. The CDP/TraPPE force fields predict TBancroft ) 364.4 K, while the new/TraPPE taken from the equilibrated NPT simulations of the new/TraPPE ) force fields. In parts b and c, the snapshot is decomposed into combination returns TBancroft 354.1 K. - acetone-methanol and methanol-methanol aggregates, respec- The pressure composition diagrams predicted by these two tively. As shown in the Figure 10, methanol forms chains sets of force fields are shown in Figure 12 and compared to varying from dimers to octamers, with only a small number of experiment. Both force fields predict a maximum pressure ) cyclic structures. azeotrope, with azeotropic compositions of xchloroform 0.61 and In Figure 11 the distribution of methanol-methanol ag- 0.625 for the CDP/TraPPE and new/TraPPE force fields, gregates is presented. Within the error of the calculation, the respectively. These values are in good agreement with the expt ) TraPPE and new/TraPPE force fields provide identical estimates experimental value of xchloroform 0.65. Greater deviations are of the cluster size distribution. The data show that the limited found in the prediction of the azeotropic pressure. CDP/TraPPE amount of interspecies association that occurs in this system predicts an azeotropic pressure of 1.08 bar, compared to the has only a small effect on the aggregation behavior of methanol experimental value of 0.89 bar. The new/TraPPE force fields ) with other methanol molecules. The most probable cluster size predict Pazeo 0.92 bar. The new/TraPPE force fields predict consists of four methanols, and nearly 35% of all methanol greater attraction between chloroform and methanol than CDP/ molecules can be found participating in a linear tetramers, with TraPPE, which results in a lower estimate of azeotropic pressure, only a small fraction of cyclic structures. The formation of a narrower liquid-vapor region, and an overall improved methanol tetramers in the acetone-methanol mixture is con- estimate of the pressure-composition behavior. sistent with previous simulations of dilute methanol in super- 4.4.2. Microstructure. Isobaric-isothermal simulations at critical carbon dioxide57 and methanol in n-hexane.11 Unlike 300 K and 1 bar were performed on an equimolar mixture of the dilute solution case, where methanols are most likely to exist chloroform and methanol to determine the microstructure of this as monomers or dimers,11,57 the majority of methanol molecules system. In this mixture, there are two possible modes of in our equimolar mixture participate in aggregates of 2-8 association. The first is the expected methanol self-association, molecules. This is expected, since the closer proximity of given by the OMeOH-HMeOH pair interaction. The second is the methanol molecules to each other in an equimolar mixture interspecies association defined by the interaction of the provides more opportunity for intraspecies association. Methanol chloroform hydrogen with the methanol hydroxyl group: OMeOH- molecules in dilute solution have limited opportunities for HCHCl3. The radial distribution functions for these pair interac- Acetone-Chloroform-Methanol Binary Mixtures J. Phys. Chem. B, Vol. 109, No. 41, 2005 19471

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 ap- proximately 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 chloroform- methanol 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 Figure 15. Fraction of methanol aggregates as functions of aggregate shown in the bottom plot in Figure 13. sizes at 300 K and 1 bar in an equimolar mixture of chloroform and The average number of hydrogen bonds per hydroxyl group, methanol: CDP(1)/TraPPE(2) (square) and new(1)/TraPPE (2) (square). using a 3.5 Å cutoff between O -O atoms, was Dashed lines are a guide to the eye. The inset shows the fraction of MeOH MeOH methanol molecules found in aggregates of particular sizes. 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 to the results for the acetone-methanol system because of reduced slightly due to the enhanced CHCl3-MeOH interaction, reduced interspecies hydrogen bonding. which reduces the number of hydroxyl groups available for An aggregation analysis was performed where a methanol- methanol-methanol hydrogen bonding. The average number chloroform aggregate was defined as any two molecules with - of hydrogen bonds per hydroxyl group is increased compared OMeOH HCHCl3 separations of less that 2.4 Å. For the CDP/ 19472 J. Phys. Chem. B, Vol. 109, No. 41, 2005 Kamath et al.

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