18974
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Transferable Potentials for Phase Equilibria. 7. Primary, Secondary, and Tertiary Amines, Nitroalkanes and Nitrobenzene, Nitriles, Amides, Pyridine, and Pyrimidine Collin D. Wick,†,‡ John M. Stubbs,†,§ Neeraj Rai,† and J. Ilja Siepmann*,† Departments of Chemistry and of Chemical Engineering and Material Science, UniVersity of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, School of Chemical Engineering, Department of Materials Science and Engineering, National Technical UniVersity of Athens, 9 Heroon Polytechniou Street, Zografou Campus, 15780 Athens, Greece, and Department of Chemistry, Grinnell College, 1116 8th AVenue, Grinnell, Iowa 50112-1500 ReceiVed: January 27, 2005; In Final Form: August 3, 2005
The transferable potentials for phase equilibria (TraPPE) force fields are extended to amine, nitro, nitrile, and amide functionalities and to pyridine and pyrimidine. In many cases, the same parameters for a functional group are used for both united-atom and explicit-hydrogen representations of alkyl tails. Following the TraPPE philosophy, the nonbonded interaction parameters were fitted to the vapor-liquid coexistence curves for selected one-component systems. Coupled-decoupled configurational-bias Monte Carlo simulations in the Gibbs ensemble were applied to neat (methyl-, dimethyl-, trimethyl-, ethyl-, diethyl-, or triethyl-)amine, nitromethane, nitroethane, nitrobenzene, acetonitrile, propionitrile, acetamide, propanamide, butanamide, pyridine, and pyrimidine. Excellent agreement with experimental results was found, with the mean unsigned errors being less than 1% for both the critical temperature and the normal boiling temperature. Similarly, the liquid densities at low reduced temperatures are reproduced to within 1%, and the deviation for the critical densities is about 4%. Additional simulations were performed for the binary mixtures of methylamine + n-hexane, diethyl ether + acetonitrile, 1-propanol + acetonitrile, and nitroethane + ethanol. With the exception of the methylamine/n-hexane mixture for which the separation factor is substantially overestimated, agreement with experiment for the other three mixtures is very satisfactory.
1. Introduction Oxygen and nitrogen are by far the most common heteroatoms in organic and pharmaceutical compounds.1 Thus, accurate knowledge of the thermophysical properties of these compounds is vital to describe many chemical and biological processes. Despite this importance, experimental data exist primarily only for low molecular weight compounds or for larger compounds only at low temperatures due to thermal decomposition. Molecular simulation using empirical force fields can circumvent this problem and determine physical properties for larger compounds at elevated temperatures but with an accuracy limited by the force field employed. Starting with a generalized force field for n-alkanes,2,3 this research group has an ongoing goal to create a transferable, computationally efficient force field that gives an accurate description of phase equilibrium, transport, and structural properties over a wide range of physical conditions. This greater transferability is achieved through fitting the force-field parameters to reproduce the entire vapor-liquid coexistence curves (VLCCs) of selected model compounds (instead of just the liquid densities and heats of vaporization at ambient conditions). Called TraPPE (transferable potentials for phase equilibria), this force field has been extended to branched alkanes,4 alkenes, and arenes;5,6 to primary, secondary, and tertiary alkanols;7 and to molecules containing ether, glycol, diol, ketone, or aldehyde * Corresponding author. E-mail:
[email protected]. † University of Minnesota. ‡ National Technical University of Athens. § Grinnell College.
functionalities.8 The TraPPE force field has already found many applications, including retention in chromatographic systems,9,10 octanol-water and hexadecane-water partitioning,11,12 dynamics in biophysical systems,13 design of biomimetic and CO2philic polymers,14,15 miscibility in polymer systems,16 adsorption inpharmaceuticalsolids,17 andtransportpropertiesoflubricants.18-20 For alkanes, the TraPPE force field offers a choice of using either a united-atom (UA) or an explicit-hydrogen (EH) description for CHx groups. The TraPPE explicit-hydrogen (TraPPEEH) force field provides a better description of the shape of alkanes than does the united-atom version. Thus, the TraPPEEH model affords an improved accuracy for the energetics (heat of vaporization) and, correspondingly, saturated vapor pressures, but at a significantly higher computational cost. Presented here is the extension of the TraPPE force field to many common nitrogen-containing functionalities, including amines, nitroalkanes, nitriles, amides, and aromatic heterocycles. In addition to developing a force field that is accurate over a wide range of physical conditions, the TraPPE force field is designed to allow for a high level of transferability. This is achieved by taking special care in the fitting of new parameters so that they can be mixed with existing parameters, allowing for the simulation of a very large number of molecules with a relatively small number of parameters. Of course, other force fields already exist for many nitrogen-containing molecules (e.g, refs 21-32) but none are parametrized to be applicable to more than a small window of physical conditions. The remainder of this article is arranged as follows. Section 2 describes the functional forms, parameters, and the details of the parametrization methodology for each new functional group.
10.1021/jp0504827 CCC: $30.25 © 2005 American Chemical Society Published on Web 09/15/2005
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TABLE 1: Nonbonded TraPPE Parameters for Nitrogen-Containing Molecules functional group alkyl tail
arene amine
nitro
nitrile
amide
N(aro)
TABLE 2: TraPPE Bond Lengths for Nitrogen-Containing Molecules
model
pseudoatom
σ (Å)
/kB (K)
q (e)
functional group
UA UA EH EH EH UA EH EH EH EH EH EH UA EH UA/EH UA/EH UA UA EH EH UA/EH EH EH EH EH UA UA UA
CH3 CH2 C(methyl) C(methylene) H(alkyl) CH(aro, not R) CR(amine) N(1° amine) N(2° amine) N(3° amine) H(1° amine) H(2° amine) CR(aro, nitro) CR(nitro) N(nitro) O(nitro) CHRx (nitrile) C(sp, nitrile) CR(nitrile) C(sp, nitrile) N(nitrile) N(1° amide) H(1° amide) C(carbonyl) O(carbonyl) N-(CH)-CH N-(CH)-N CH-(N)-CH
3.75 3.95 3.3 3.65 3.31 3.74 σ(Calkyl) 3.34 3.52 3.78 0 0 4.50 σ(Calkyl) 3.31 2.90 σ(CHx) 3.55 σ(Calkyl) 3.48 2.95 3.34 0 3.72 3.05 3.74 3.90 3.45
98 46 4 5 15.3 48 (Calkyl) 111 58 12 0 0 15 (Calkyl) 40 80 (CHx) 60 (Calkyl) 67.5 60 111 0 34 79 48 47 28
0 0 0 0 0 0 +0.18 -0.892 -0.745 -0.54 +0.356 +0.385 +0.14 +0.14 +0.82 -0.48 +0.269 +0.129 +0.269 +0.129 -0.398 -0.8 +0.4 +0.424 -0.424 +0.33 +0.66 -0.66
alkyl tail
Section 3 briefly summarizes the simulation details for the onecomponent and binary phase diagrams. Section 4 presents the calculated phase diagrams for the compounds used in the parametrization and for additional compounds and mixtures used to demonstrate the transferability of the new force-field parameters. 2. Force-Field Development The TraPPE-UA force field utilizes pseudoatoms located at carbon centers for alkyl groups, and the TraPPE-EH model treats all hydrogens explicitly, with interaction sites located at the centers of carbon-hydrogen bonds in addition to sites located at carbon atoms. A simple pairwise-additive potential consisting of Lennard-Jones (LJ) 12-6 and Coulombic terms is used to model the nonbonded interactions:
[( ) ( ) ]
uNB(rij) ) 4ij
σij rij
12
-
σij rij
6
+
qiqj 4π0rij
(1)
where rij, ij, σij, qi, and qj are the site-site separation, LJ well depth, LJ diameter, and partial charges on beads i and j, respectively. The TraPPE parameters for the LJ diameter, LJ well depth, and partial charge for all interaction sites used in this work are listed in Table 1. For unlike interactions, the standard Lorentz-Berthelot combining rules were used.33,34 For the LJ interactions, a site-site-based spherical potential truncation at either 12 or 14 Å is used together with analytical tail corrections for the energy and pressure.35,36 Electrostatic interactions were computed using the Ewald summation technique, with κL ) 5.6 and tin-foil boundary conditions.36 As previously implemented for the TraPPE-UA and TraPPEEH force fields, the nonbonded interactions are calculated for all intermolecular interactions and for intramolecular interactions among united atoms, heavy atoms (C, O, and N), and polar hydrogens separated by four or more bonds. The TraPPE-EH
arene amine nitro nitrile amide
N(aro)
model
type
length (Å)
ref
UA EH EH UA EH EH UA/EH UA/EH UA EH UA/EH EH EH EH EH UA
CHx-CHy C-C C-H CHx=CHy C-N N-H C-N N=O CHx-C(sp) C-C(sp) CtN C-C(carbonyl) CdO C-N N-H CH(aro)-N(aro)
1.54 1.535 0.55 1.40 1.448 1.01 1.49 1.225 1.54 1.535 1.157 1.52 1.229 1.448 1.01 1.40
2 3 3 6 26 26 27 27 2 3 24 23 8 26 26 6
bond-center hydrogens of a given CHx group contribute only to the nonbonded interactions when the carbon atom of this group participates too. For six-membered aromatic rings, the TraPPE-UA force field utilizes three additional partial charges to explicitly represent the out-of-plane quadrupole moment.6 These charge sites are located symmetrically on the 6-fold axis with a positive charge of +2.42 e placed in the benzene plane and two compensating negative partial charges at a distance of 0.785 Å representing the π-electron clouds on both sides.37 It should be noted that these unprotected partial charges require special care for mixtures containing aromatic molecules and hydrogen-bond donor molecules,17 but such cases are not investigated here. With the exception of rigid aromatic rings, all alkyl groups and functional groups are treated as semiflexible groups with fixed bond lengths but bending and torsional degrees of freedom. The parameters for the bonded interactions for all molecules investigated in this work are listed in Tables 2-4. As has been the case for most molecules that can be described by the TraPPE force field, the bonded parameters were not directly parametrized but were taken from various literature sources (see Tables 2-4). For semiflexible units, beads separated by two bonds interact via a harmonic bending potential:
ubend(θ) )
kθ (θ - θ0)2 2
(2)
where θ, θ0, and kθ are the current bond angle, the equilibrium bond angle, and the force constant, respectively. The parameters for the equilibrium bond angles and force constants are listed in Table 3. For dihedral interactions, one of a set of cosine series was used:
utors,A(φ) ) c1[1 + cos(φ)] + c2[1 - cos(2φ)] + c3[1 + cos(3φ)] (3) utors,B(φ) ) c1[1 - cos(3φ)]
(4)
6
utors,C(φ) ) c0 +
[ci cos(iθ)] ∑ i)1
(5)
where φ is the current dihedral angle, and ci are constants either taken directly from existing force fields or parametrized to match the dihedral distributions of other force fields (for torsional type C). The latter is necessary because, although some other force fields include scaled nonbonded interactions between atoms
18976 J. Phys. Chem. B, Vol. 109, No. 40, 2005
Wick et al. they are often not available and are much less reliable than the low-temperature liquid densities. 2.A. Primary, Secondary, and Tertiary Amines. The primary, secondary, and tertiary TraPPE-EH amine models were parametrized to reproduce the VLCCs of methyl-, dimethyl-, and trimethylamine, respectively. The fitting procedure included specific LJ parameters and charges for the different types of amine nitrogens and a common partial charge for all types of R-carbons. The partial charges on the polar hydrogens are determined by the requirement that a given CRx NHy group (with x + y ) 3) is neutral. Finally, all alkyl carbon LJ parameters and alkyl hydrogens were taken from the TraPPE-EH alkane force field.3 Thus, in this case, it is advantageous to start the fitting procedure with trimethylamine because this molecule requires only three new parameters (LJ well depth, diameter, and partial charge for the nitrogen atom). This parametrization also determines the partial charge for the R-carbon (as specified by the neutrality constraint). Transferring this partial charge of the R-carbon allows separate fits for methylamine and dimethylamine, each requiring only three new parameters. 2.B. Nitroalkanes and Nitrobenzene. The parameters for the nitro group were fit to the VLCC of nitromethane. In this case, only the LJ parameters for the methyl carbon and hydrogen were directly transferred from the TraPPE-EH alkane model.3 Using the LJ parameters and partial charges of previous nitro force fields27,31 as initial guides, we fit the LJ parameters and partial charges for the oxygen and nitrogen atoms of the nitro group in a concerted manner (with the partial charge for the R-carbon fixed by the neutrality constraint for the CRNO2 unit). Thereafter, the nitro group oxygen and nitrogen parameters were transferred for nitrobenzene, thus leaving only the LJ parameters for the aromatic R-carbon as adjustable parameters. It should be noted that the united-atom representation is used for nitrobenzene, thus the aromatic carbon linker taken from toluene6 was used as a starting point for this fit. 2.C. Nitriles. The TraPPE-UA and TraPPE-EH nitrile models were parametrized to acetonitrile with the charges for the nitrile nitrogen, sp carbon (synperiplanar), and R-alkyl carbon taken from another force field proposed by Edwards et al.,7 and the LJ parameters for the nitrogen and sp carbon adjusted to reproduce the VLCC. The R-alkyl carbon LJ parameters are the same as for either the TraPPE-EH alkane carbon or the TraPPE-UA alkyl pseudoatom, depending on the model being used. 2.D. Amides. The TraPPE-EH amide force field was parametrized for acetamide. The initial parameters for the -NH2 group were taken from the primary amine model, the carbonyl group
TABLE 3: TraPPE Bending Parameters for Nitrogen-Containing Molecules model
type
θ0 (deg)
kθ/2kB (K/rad2)
ref
UA EH EH EH UA EH EH EH EH EH UA EH EH UA/EH UA/EH UA EH EH UA/EH EH EH EH EH EH EH EH UA UA
C-C-C C-C-C C-C-H H-C-H C=C=C C-C-N H-C-N C-N-H C-N-C H-N-H C=C-N C-C-N H-C-N C-N=O O=N=O C-C-C(sp) C-C-C(sp) H-C-C(sp) C-C(sp)tN C-C-C(dO) H-C-C(dO) C-C(dO)-N C-CdO O-C-N H-N-H C(dO)-N-H C=C=N N=C=N
114.0 112.7 110.7 107.8 120 109.5 109.5 112.9 109.5 106.4 120 111.1 105.0 111.5 125.0 114.0 112.7 110.7 180 112.7 110.7 115.7 121.4 122.9 106.4 109.5 120 120
31 250 29 382 18 883 16 617 fixed 28 300 17 624 31 250 25 178 21 955 fixed 31 724 17 624 40 284 40 284 31 250 29 382 18 883 fixed 29 382 18 883 35 225 31 250 40 257 21 955 17 624 fixed fixed
2 3 3 3 6 26 26 26 26 26 6 27 27 27 27 2 3 3 7, 24 3 3 see text 8 23 this work this work 6 6
functional group alkyl tail
arene amine
arene/nitro nitro
nitrile
amide
N(aro)
separated by three bonds, the TraPPE force field usually does not. The values used for the dihedral potentials are listed in Table 4. The general methodology for the development of the TraPPE force field is to parametrize specific new functional groups while minimizing the modification of other interaction sites that are directly connected to the new functional group. For example, although the LJ parameters of R-carbons are transferred as much as possible from alkanes, in almost all cases a partial charge needs to be added to the R-carbon to yield a good representation of the change in the charge distribution caused by a neighboring atom with different electronegativity. This principle is followed to provide greater transferability, which allows for the straightforward simulation of molecules containing multiple functional groups without having to fit any additional parameters. During the parameter fitting procedure, an attempt is made to simultaneously fit (if available) the liquid density at low reduced temperatures, the normal boiling temperature, and the critical temperature. The critical densities were not used here because
TABLE 4: TraPPE Torsional Parameters for Nitrogen-Containing Molecules functional group
model
type
eq
nitrile alkyl alkyl nitro nitro nitro nitro amine amine amine/amide amine amine amide amide amide
UA/EH EH EH UA/EH EH EH EH EH EH EH EH EH EH EH EH
C-C-C-C H-C-C-H C-C-C-H C-C-N-O H-C-N-O C-C-N-O H-C-C-N H-C-N-H H-C-N-C C-C-N-H C-N-C-C H-C-C-N (H/C)-C-C-N (H/C)-C-CdO H-N-CdO
3 4 4 5 5 5 5 5 5 5 5 5 5 5 5
c0 (K) 0 69.2 75.4 69.2 165 199 174 190 1466 438 438 438 1585
c1 (K)
c2 (K)
c3 (K)
335 717 854 -41.4 -40.8 -41.4 -219 -109 -37.0 47.8 -2188 481 481 481 -163
-68.2
791
-14.5 80.4 -14.5 63.7 12.5 4.69 105 1381 150 150 150 -629
-19.1 -41.0 -19.1 4.98 -102 -142 -105 -890 -115 -115 -115 0
c4 (K)
8.03 16.0 8.03 8.19 0.21 0.10 0 329 -0.57 -0.57 -0.57 0
c5 (K)
-2.91 -5.44 -2.91 -2.63 -0.03 -.01 0 -137 0.08 0.08 0.08 0
c6 (K)
ref
0.95 1.68 0.95 0.78 0 0 0 52.6 -0.01 -0.01 -0.01 0
24 3 10 27 27 27 27 26 26 26 26 26 26 26 23
Transferable Potentials for Phase Equilibria parameters were taken from the TraPPE-UA ketone model,8 and the alkyl group parameters were taken from the TraPPE-EH alkane model.3 Parameters not available from this previous work, including the bending parameters centered on the carbonyl carbon, were taken from several sources including the OPLSUA amide model23 (kθ and θ0 for OdC-N and kθ for C-CN) and from geometric considerations (θ0 for C-C-N) such that the equilibrium bond angles around the sp2 carbon totaled 360°. Parameters for the torsional interaction OdC-N-H were taken from the OPLS-UA model,23 and others were taken from the TraPPE-EH amine force field. Initial testing indicated the strength of the intermolecular interactions was too great; so the partial charges on the -NH2 group were reduced, and the LJ parameters on the carbonyl carbon were optimized to reproduce the experimental vapor pressures. Interestingly, with this partial charge set, there is good agreement with the experimental gas-phase dipole moment for acetamide, 3.76 ( 0.08 D,38 and the average dipole moment for the TraPPE-EH acetamide in the vapor phase at 500 K, 3.69 ( 0.04 D. In contrast, the average liquid-phase dipole moment is 4.61 ( 0.02 D at 500 K despite the nonpolarizable nature of the model. This is due to different predominant conformations observed in the liquid and vapor phases. 2.E. Pyridine and Pyrimidine. Pyridine was utilized as a model compound to fit parameters for a nitrogen atom in a sixmembered aromatic heterocycle. In this case, the LJ parameters for the neighboring CH(aro) united atoms and out-of-plane partial charges were taken directly from the TraPPE-UA benzene model.6 Use of the out of plane charges is justified because the values of -5.6 ( 2.8 × 10-26 and -6.2 ( 1.5 × 10-26 esu cm2 for the quadrupole moments of benzene and pyridine, respectively, are rather similar.39 The partial charge for the nitrogen (and hence the partial charges of the neighboring carbons as set by the neutrality constraint for the CH-N-CH segment) was calculated from the gas-phase dipole moment.38 Thus, only the LJ parameters for N(aro) remained as adjustable parameters for the VLCC of pyridine. Once these parameters were determined, the LJ parameters and partial charges for N(aro) and for a CH(aro) bonded to a single N(aro) were transferred for the pyrimidine model. Thus, the only remaining adjustable parameters for pyrimidine were the LJ parameters for the CH(aro) united atom that is surrounded by two N(aro) because its partial charge is fixed by the requirement that the molecule be neutral. 3. Simulation Details 3.A. Vapor-Liquid Coexistence Curves. A combination of the Gibbs Ensemble Monte Carlo (GEMC)40-42 and coupleddecoupled configurational-bias Monte Carlo (CBMC)4,43-45 methods was used to simulate the one-component vapor-liquid equilibria of amines, nitroalkanes, nitriles, amides, nitrobenzene, and pyridine. The canonical version of the Gibbs ensemble40 utilizes two simulation boxes without a direct interface, but in thermodynamic contact. CBMC swap moves are used to reach phase equilibrium (i.e., equal chemical potential) between the two phases, and volume exchange moves between the boxes are used to equilibrate their pressure. To thermally equilibrate each box, translational and rotational moves for all molecules and CBMC conformational moves for semiflexible molecules were performed. For each compound, the system size (i.e., total number of molecules, N; see Table 5) and system volume (sum of the two simulation boxes) were chosen to ensure that, when about 30% of the molecules populate the vapor phase, the linear dimension of the liquid box always remains greater than twice
J. Phys. Chem. B, Vol. 109, No. 40, 2005 18977 TABLE 5: System Sizes Used for Simulations compound(s)
total number of moleculesa
methylamine dimethylamine trimethylamine ethylamine diethylamine triethylamine nitromethane nitroethane nitrobenzene acetonitrile propionitrile acetamide propanamide butanamide pyridine pyrimidine nitromethane/ethanol methylamine/n-hexane acetonitrile/diethyl ether acetonitrile/1-propanol
400 & 800 400 300 300 250 250 300 & 600 250 250 300 & 600 & 1200 & 2400 300 300 300 300 300 & 600 250 500 300 300 300
a For binary systems, the distribution of the molecules over the two different compounds was adjusted to reflect the dependence of the overall composition on the state point.
the LJ potential cutoff. A minimum of 10 000 MC cycles (with N moves per cycle) of equilibration preceded any production run, and a minimum of 40 000 MC cycles of production were performed for each state point. The fraction of CBMC particle swap moves throughout the production periods is set to a value that yields one accepted swap move about every 5-10 MC cycles. The computer time required per cycle depends on the system size (i.e., the number of interaction sites), the complexity of the molecules (i.e., a larger number of expensive CBMC moves are required for more complex molecules), and the temperature (i.e., lower temperatures require a larger fraction of attempted particle swap moves). For example, 1000 MC cycles for TraPPE-EH propionitrile at T ) 348 K and acetamide at T ) 500 K require about 1700 and 2100 s of CPU time on a Pentium Xeon processor at 1.8 GHz, and 1000 MC cycles for pyridine at T ) 468 K and pyrimidine at T ) 440 K require about 1400 and 2400 s of CPU time on a Pentium IV processor at 3.2 GHz. The normal boiling points (Tb) were calculated via the Clausius-Clapeyron equation, and the critical temperatures (Tc) and densities (Fc) were calculated using the saturated density scaling law and the law of rectilinear diameters with a scaling exponent of β* ) 0.325.42,46,47 To explore the effect of system size on the vapor-liquid coexistence properties, we carried out additional simulations for methylamine, nitroethane, acetonitrile, and pyridine using larger systems. As can be seen from the data presented in Figure S1 (Supporting Information), doubling the system size does not lead to significant changes in the simulation results. 3.B. Binary Phase Diagrams. For binary systems, the simulations were carried out mostly in the constant-pressure (NpT) version of the Gibbs ensemble,41 where volume moves are performed separately for each phase to equilibrate with an external pressure bath. All other MC moves are the same as those for regular GEMC. For the binary mixture of methylamine/ n-hexane, the canonical version was used; i.e., the total system volume and not the external pressure is used as the thermodynamic constraint. Four binary systems were investigated: TraPPE-EH methylamine with TraPPE-EH n-hexane at T ) 293.15 K, TraPPEEH nitroethane with TraPPE-UA ethanol at p ) 101.325 kPa, TraPPE-UA acetonitrile with TraPPE-UA 1-propanol at p )
18978 J. Phys. Chem. B, Vol. 109, No. 40, 2005 55 kPa, and TraPPE-UA acetonitrile with TraPPE-UA diethyl ether at T ) 293.65 K. These binary mixtures were selected to probe the transferability to a mixture with a nonpolar compound (e.g., n-hexane), a mixture with a polar compound that does not involve hydrogen bonding (e.g., diethyl ether), and mixtures with polar compounds that also involve hydrogen bonding (e.g., primary alcohols). Because these mixture calculations are substantially more expensive and experimental data are not available in all cases for mixtures involving the three different types of probe molecules, only four representative cases were studied here. The force-field parameters are not tabulated here for the TraPPE-UA alkanol and ether models but can be found elsewhere.7,8 The Lorentz-Berthelot combining rules33,34 are also applied to all mixture calculations, although Potoff et al.48 have shown that use of different combining rules (e.g., the Kong combining rules49) may lead to better agreement for binary mixtures. It should be noted that all compounds used in this study contain interaction sites of multiple types and that, in our opinion, it would not be warranted to apply different combining rules to the unlike interactions involving two molecules of the same type or two molecules of different types. Thus, consistency dictates that the same combining rules employed throughout the development of a force field need also be applied to mixture simulations. For binary systems, some trial and error is required to find suitable values for the overall number and ratio of the two molecule types (and the overall volume) because the composition changes dramatically as a function of the state point (either temperature or pressure). Nevertheless, these numbers were made sufficiently large to maintain liquid boxes with a linear dimension larger than twice the potential cutoff and vapor boxes containing about a third of the total number of molecules. Each simulation was equilibrated a minimum of 20 000 MC cycles until both densities and compositions fluctuated around mean values. Following equilibration, a minimum of 100 000 MC cycles of production were performed. To improve the sampling for the methylamine/n-hexane mixture, particle swatch moves50 were utilized. The swatch move exchanges two molecules that share a similar architecture but vary in length. This was done because, at the thermodynamic conditions used (specifically with a temperature of 293.15 K), swap moves of n-hexane into the dense liquid phase had a prohibitively low acceptance rate. The use of the swatch move required the addition of a single n-propane molecule that swaps readily between the liquid and vapor phases, and swatch moves between n-propane and n-hexane were performed to transfer n-hexane between the liquid and vapor phases, requiring only the exchange of methyl and butyl groups. The smallest number of n-hexane molecules present in a simulation run was 60; thus the effect of the single n-propane impurity is presumed to have a negligible effect on the phase diagram. 4. Results and Discussion 4.A. Vapor-Liquid Coexistence Curves. The VLCCs for methylamine, dimethylamine, and triethylamine are shown in Figure 1, and the corresponding critical constants and normal boiling point are listed in Table 6. As mentioned above, these three compounds were used here to fit the TraPPE-EH parameters for primary, secondary, and tertiary amines. As should be expected from this training set, agreement with the available experimental data51 is excellent over the entire VLCC for all three compounds, with the critical and boiling temperatures reproduced to within about 1%. It should be noted that the liquid
Wick et al.
Figure 1. Vapor-liquid coexistence curves for methylamines. The experimental data for methylamine,63,71 dimethylamine,64,72 and trimethylamine65,66,72 are shown as plusses, crosses (and horizontal dotted lines because the critical density is not available), and stars, respectively. Simulation data for the TraPPE-EH force field are depicted as open circles, squares, and triangles, respectively. Simulation data for methylamine using the OPLS-AA force field26 are shown as filled circles.
densities at low reduced temperature and the critical temperatures are also well reproduced; the agreement with the experimental data for the critical densities is less satisfactory. The main reason might be a failure of the TraPPE force field to yield an accurate acentric factor for the VLCCs (also, this is hard to judge because saturated vapor pressures at higher temperatures are often not available). Furthermore, experimental measurements of the critical density are more difficult than the determination of the critical temperature, and the former might be less reliable. For comparison, the VLCC of methylamine for the OPLSAA force field26 is also shown. As is evident, the OPLS-AA model for methylamine yields a liquid density that agrees with experiment only close to its boiling point (the condition used for its parametrization) but shows significantly larger deviations at elevated temperatures and a critical temperature that is underestimated by more than 10%. The VLCCs for ethylamine, diethylamine, and triethylamine are compared to the experimental data in Figure 2 and Table 6. The excellent agreement obtained for these homologues of the methylamines shows that the amine parameters can be transferred to other amines beyond the training set. In particular, it should be pointed out that the TraPPE-EH force field correctly reproduces the fact that the critical temperatures of the three methylamines are very close with dimethylamine possessing the highest critical temperatures and the fact that the critical temperatures of the ethylamines are well separated with triethylamine possessing the highest critical temperature. This again demonstrates that a molecular-mechanics force field, together with detailed simulations of the packing in the liquid phase, can provide accuracies that go well beyond the usual group additivity concepts.52 The VLCCs for two nitroalkanes and nitrobenzene are depicted in Figure 3, and selected data are listed in Table 6. Agreement with the experimental data51,53 for TraPPE-EH nitromethane (used in the parametrization) and nitroethane (used to test for transferability) is very good (e.g., the differences in their boiling points and near-ambient saturated liquid densities of about 3% and 10% are well reproduced) with the exception of the critical temperature of nitroethane that is underestimated by 2%, thereby leading the TraPPE-EH force field to predict a lower critical temperature for nitroethane than for nitromethane, in apparent disagreement with the experimental data. As also observed for methylamine, the OPLS-AA force field for nitromethane27 agrees relatively well with the experimental
Transferable Potentials for Phase Equilibria
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TABLE 6: Comparison of Critical Properties, Normal Boiling Points, and Heats of Vaporizationa compound methylamine dimethylamine trimethylamine ethylamine diethylamine triethylamine nitromethane nitroethane nitrobenzene acetonitrile
propionitrile acetamide propanamide butanamide pyridine
pyrimidine
force field
Tc (K)
Fc (g/cm3)
Tbb (K)
∆Hvap (kJ/mol)
TraPPE-EH OPLS-AA26 exp38,63 TraPPE-EH exp38,64 TraPPE-EH exp38,51 TraPPE-EH exp38,67,68 TraPPE-EH exp38,67,68 TraPPE-EH exp38,65,69 TraPPE-EH OPLS-AA27 exp38,65,69 TraPPE-EH exp38,70 TraPPE-UA exp TraPPE-UA N ) 600 N ) 1200 N ) 2400 TraPPE-EH N ) 600 OPLS-UA24 Edwards22 exp51,70 TraPPE-UA TraPPE-EH exp51,70 TraPPE-EH exp TraPPE-EH exp TraPPE-EH exp TraPPE-UA N ) 600 OPLS-AA25 exp57 TraPPE-UA exp
4292 3805 431 4432 438 4333 433 4524 456 5022 4983 5391 536 5892 5494 588 5822 593 7472 n/a 5491 5471 5471 5481 5471 5451 5641 6092 545 5561 5551 561 7473 n/a 7382 n/a 7484 n/a 6183 6172 6082 620 6104 n/a
0.2525 0.2588 0.224 0.2536 n/a 0.2454 0.234 0.2575 0.244 0.2452 0.243 0.2542 0.257 0.3618 0.3729 0.352 0.3423 0.318 0.3722 n/a 0.2491 0.2521 0.2511 0.2501 0.2491 0.2511 0.2501 0.2592 0.237 0.2532 0.2521 0.240 0.2973 n/a 0.2862 n/a 0.2773 n/a 0.3283 0.3262 0.3276 0.327 0.3364 n/a
2661 2503 267 2781 281 2722 275 2903 291 3301 329 3533 362 3742 3541 374 3881 387 4811 484 3541 3551 3541 3551 3561 3551 3541 3831 355 3631 3671 370 4941 494 4961 495 5081 504 3912 3901 3901 389 3961 397
27.32 24.810 25.6 27.81 26.4 22.71 22.9 28.61 n/a 30.71 29.1 26.68 31.0 36.02 32.010 34.0 36.82 38.0 47.32 n/a 31.01 30.91 30.91 30.91 31.71 31.71 29.91 35.51 29.8 32.11 33.71 31.8 52.94 52.94 55.28 37.8 37.8 35.2
Figure 2. Vapor-liquid coexistence curves for ethylamines. The experimental data for ethylamine,67,72 diethylamine,68,73 and triethylamine51,68,72 are shown as plusses, stars, and crosses, respectively. Simulation data for the TraPPE-EH force field are depicted as open circles, squares, and triangles, respectively.
Figure 3. Vapor-liquid coexistence curves for nitros. The experimental data for nitromethane,53,65,69 nitroethane,70,74 and nitrobenzene74 are shown as plusses (and a solid line), crosses, and stars, respectively. Simulation data for the TraPPE-EH force field are depicted as open circles, squares, and triangles, respectively. Simulation data for nitromethane using the OPLS-AA force field27 are shown as filled circles.
41.2
a The subscripts give the statistical errors of the last digit(s). Heats of vaporization are given for a temperature close to the boiling point. b All experimental normal boiling points are averages of the values listed in ref 51.
liquid density at low temperatures but underpredicts the normal boiling and critical temperatures by 5 and 7%, respectively. Another force field for nitromethane fitted to reproduce its crystal structure was shown previously to underpredict the liquid densities throughout the entire experimental range.31,54 The TraPPE-UA model for nitrobenzene yields a good fit to the liquid density and normal boiling point, but experimental data for its critical constants are unfortunately not available. Figure 4 depicts the VLCCs for acetonitrile and propionitrile for the TraPPE-UA and TraPPE-EH force fields, the OPLSUA force field (acetonitrile only),24 available experimental data,51 and the Rackett equation (propionitrile).55 For clarity, only one set of symbols was used for both the TraPPE-UA and TraPPE-EH nitrile force fields because they overlapped significantly on the scale of the VLCCs (however, the numerical data are listed separately in the Supporting Information, Table S4). The OPLS-UA force field24 yields liquid densities that are slightly too low at low temperatures and too high at high temperatures, thereby overestimating the critical temperature by
Figure 4. Vapor-liquid coexistence curves for nitriles. The experimental data for acetonitrile75 and propionitrile55 are shown as stars/ solid lines and crosses/dotted lines, respectively. Simulation data for both TraPPE (UA and EH) force fields are depicted as open circles and squares, respectively. Simulation data for acetonitrile using the OPLS-UA force field24 are shown as filled circles.
3% but showing good agreement with experiment for the normal boiling point. An earlier force field for acetonitrile developed by Edwards et al.22 gives consistently liquid densities that are too high (not shown), leading to a critical temperature and boiling point that are much higher than those for experiment (listed in Table 6). Both the TraPPE-UA and TraPPE-EH force fields give excellent agreement with the experimental VLE
18980 J. Phys. Chem. B, Vol. 109, No. 40, 2005
Figure 5. Clausius-Clapeyron plots of the saturated vapor pressure vs inverse temperature as predicted for acetamide (circles), propanamide (squares), and butanamide (triangles) along with correlation plots to experimental data56 (solid line) and the normal boiling points51 (stars).
Figure 6. Vapor-liquid coexistence curves for pyridine and pyrimidine. The experimental data57 for pyridine and pyrimidine are shown as crosses and stars, respectively. Simulation data for the TraPPE-UA force field are depicted as open circles and squares, respectively. Simulation data for pyridine using the OPLS-AA force field25 are shown as filled circles.
properties for acetonitrile, including the boiling point. This is significant for the TraPPE-UA force field because it underpredicts the boiling point for alkanes3,4 but appears to work better for more polar molecules.7,8 The agreement with experiment for propionitrile is good for both TraPPE force fields for liquid densities and critical temperatures, but unlike acetonitrile, the agreement for the boiling point is significantly better for the TraPPE-EH force field, which is usually the case when the TraPPE-EH and TraPPE-UA force fields are compared.3 Again, no additional parameters were fit for the modeling of propionitrile. The TraPPE-EH models for acetamide, propanamide, and butanamide give excellent descriptions of the experimental vapor pressures56 up to their boiling points fit to the Antoine equation (see Figure 5). Table 6 lists the calculated critical properties and boiling points for these three amides, but because their critical temperatures are over 700 K, experimental data are not available for comparison. The VLCCs for pyridine and pyrimidine computed for the TraPPE-UA force field are compared with experiment57 and simulation data (pyridine only) for the OPLS-AA force field25 in Figure 6, and the critical properties and normal boiling points are listed in Table 6. The TraPPE-UA force-field results for the saturated liquid densities are in excellent agreement with the experimental values. The OPLS-AA force field, on the other hand, is only accurate at lower temperatures, but the deviations are significant at higher temperatures. As a result, the OPLSAA force field underpredicts the critical temperature by 12 K and the TraPPE-UA force field agrees well with the experimental value of 620 K. Both the OPLS-AA (pyridine only) and
Wick et al.
Figure 7. Pressure-composition diagrams. The experimental data58 and the TraPPE-EH simulation data for methylamine (i) and n-hexane at T ) 293.15 K are shown as dotted lines and squares, respectively. These simulations were carried out in the canonical ensemble; i.e., statistical uncertainties (standard error of the mean from block averages) are shown for both pressure and composition. The experimental data58 and the TraPPE-UA simulation data for diethyl ether (i) and acetonitrile at T ) 293.65 K are shown as solid lines and circles, respectively.
TraPPE-UA (pyridine and pyrimidine) force fields predict the normal boiling points within 2% of the experimental values. 4.B. Binary Phase Diagrams. The pressure-composition phase diagrams for the binary mixtures consisting of methylamine and n-hexane and of dimethyl ether and acetonitrile are depicted in Figure 7. The TraPPE-EH force field was used for the former mixture because the EH representation is significantly more accurate for the nonpolar alkanes, whereas the TraPPEUA version was used for the latter mixture containing two polar species. Compared to the experimental data for methylamine/ n-hexane,58 the TraPPE-EH model underpredicts the amount of methylamine in the hexane-rich phase but yields satisfatory agreement for the amine-rich phase. The underprediction of the solubility of the polar amine in the nonpolar hexane-rich phase is likely due to the use of a fixed-charge force field that does not account for the polarization of the hexane solvent by the amine solute. Similar observations were made previously for binary mixtures of alkanols and alkanes.59 Although it is possible for weakly polar fluids, such as carbon dioxide, to balance the strength of the LJ and Coulombic interactions to yield very satisfactory agreement for mixtures with alkanes,60 this does not work for dipolar and hydrogen-bonding fluids and a polarizable force field would be required to overcome this limitation.61 Agreement with the experimental data58 for the binary diethyl ether and acetonitrile mixture is significantly better. Albeit caused by the fact that the saturated vapor pressure of neat diethyl ether is somewhat overestimated by the TraPPEUA model,8 the separation factor is overestimated at higher diethyl ether concentrations. Figure 8 depicts the temperature-composition phase diagrams for the binary mixtures of nitroethane and ethanol and of 1-propanol and acetonitrile. With the exception of nitroethane, for which the TraPPE-EH model is used, the compounds are represented by the TraPPE-UA force field. The normal boiling points are well reproduced for all four compounds, as can be seen from the endpoints of the binary diagrams. The calculated phase diagram for nitroethane and ethanol shows excellent agreement with experiment,62 with only a slight underestimation of the amount of nitroethane in the nitro-rich phase but an even better agreement for the ethanol-rich phase. Similarly, the experimental phase diagram58 for the mixture of 1-propanol with acetonitrile is very well reproduced. Overall, the four binary phase diagrams demonstrate that the TraPPE force field allows for a rather accurate treatment of the
Transferable Potentials for Phase Equilibria
J. Phys. Chem. B, Vol. 109, No. 40, 2005 18981 References and Notes
Figure 8. Temperature-composition diagrams. The experimental data62 and the simulation data for TraPPE-EH nitroethane (i) and TraPPE-UA ethanol at p ) 101.325 kPa are shown as solid lines and circles, respectively. The experimental data58 and the TraPPE-UA simulation data for 1-propanol (i) and acetonitrile at p ) 55 kPa are shown as dotted lines and squares, respectively.
cross interactions among different polar functional groups without the need for specific binary interaction parameters. 5. Conclusions The TraPPE force field was extended to amine, nitro, nitrile, and amide functional groups and to pyridine and pyrimidine, i.e., the most common nitrogen-containing functionalities. Thereby, the type of molecules that can be modeled with the TraPPE force field is vastly increased. Because of the parametrization strategy (emphasizing transferability), the VLCCs and other thermophysical properties of a very large number of molecules can be predicted with the parametrization of only a few functional groups. This is evident from the equally accurate results obtained for many molecules that were not directly used in the parametrization of the nitrogen-containing functional groups. The TraPPE-EH force field shows consistently very satisfactory agreement with experiment for all pure phase properties, and the TraPPE-UA force field yields good agreement with experiment for the liquid densities and critical temperatures but boiling points that are slightly too low for molecules with longer alkyl tails. Comparison of binary phase diagrams with experimental data indicates that the TraPPE force field yields an accurate representation of the cross interactions of different functional groups, except for the solubility of polar molecules, such as the amines, in alkanes where the shortcomings of a computationally efficient fixed-charged force field are more evident. Acknowledgment. Financial support from the National Science Foundation (CTS-0138393), an NSF-MPS Distinguished International Postdoctoral Fellowship (C.D.W.), a DOE Computational Science Graduate Fellowship (C.D.W.), a Frieda Martha Kunze Fellowship (J.M.S.), and a University of Minnesota Doctoral Dissertation Fellowship (J.M.S.) are gratefully acknowledged. Part of the computer resources were provided by the Minnesota Supercomputing Institute. Supporting Information Available: Tables S1-S6 list the numerical simulation data for the saturated liquid and vapor densities and the saturated vapor pressures that are graphically depicted in Figures 1-6. Tables S7 and S8 list the numerical simulation data for the binary phase diagrams shown in Figures 7 and 8. Figure S1 shows a comparison of simulation data obtained using different system sizes.
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