J. Phys. Chem. C 2007, 111, 1451-1458
1451
Vapor-Liquid Equilibria of Diethylamine + Methanol, Diethylamine + Acetone and Diethylamine + Acetonitrile: Predictions of Atomistic Computer Simulations Ganesh Kamath and Jeffrey J. Potoff* Department of Chemical Engineering and Materials Science, Wayne State UniVersity, Detroit, Michigan 48202 ReceiVed: August 15, 2006; In Final Form: October 13, 2006
Histogram-reweighting Monte Carlo simulations in the grand canonical ensemble are used to determine pressure-composition diagrams for diethylamine + methanol, diethylamine + acetone and diethylamine + acetonitrile. Simulations were unable to predict the polyazeotropy found in the diethylamine + methanol mixture at 398 K or the minimum pressure azeotropy found at 348 and 298 K. Simulation predictions of the pressure-composition behavior of diethylamine + acetone and diethylamine + acetonitrile, however, were found to be in close agreement with experiment. Simulations in the isobaric-isothermal ensemble were used to determine the structure of the liquid phase for each of the mixtures described previously and revealed significant association taking place between unlike species.
1. Introduction Nitrogen-containing functional groups are biologically important, being major constituents in amino acids, proteins, and vitamins. Amines are derivatives of ammonia in which one or more hydrogen atoms are replaced by alkyl groups. They form structural moieties for a variety of commercially available drugs such as chlorpheniramine, chlorpromazine, and ephedrine.1 Primary aromatic amines are used as starting materials for the manufacture of azo dyes like methyl orange and sunset yellow.2 Another application of amines is in the petroleum industry, where monoethanolamine is used to strip crude oil of the hydrogen sulfide. This process is often referred to as “sweetening”.3 Hydrogen bonding between amines in condensed phases influences their properties. For example, the normal boiling points of primary, secondary, and tertiary amines are all higher than those of alkanes of similar molecular weight. This phenomenon is observed in other hydrogen bonding fluids such as alcohols, carboxylic acids, and water. Amines display complex phase diagrams when mixed with alcohols, ketones, and nitriles. Experimentally, the diethylamine + methanol system displays a polyazeotrope at 398 K and minimum pressure azeotropy at lower temperatures. Polyazeotropy is a condition where multiple stable azeotropes are present at a particular temperature or pressure. To date, less than 10 binary systems have been identified that display this phenomena. These systems include benzene + hexafluorobenzene,4 acetic acid + isobutyl acetate,5,6 ammonia + 1,1,2,2,2-pentafluoroethane,7 THF + 1,1,1,2,3,4,4,5,5,5-decafluoropentane,8,9 diethylamine + methanol,10,11 and water + nitrogen pentoxide.12 Determination of polyazeotropy experimentally is complicated by the fact that, in many cases, polyazeotropic behavior is only observed for a narrow window of temperatures or pressures. In the case of monoazeotropic behavior, it is possible to classify these systems as having a maximum or minimum pressure azeotrope using only the pure component vapor pressures and infinite dilution activity coefficients.13,14 Accord* Corresponding author. E-mail:
[email protected]. Telephone: 313-577-9357. Fax: 313-577-3810.
ing to Gmehling et al,14 a maximum pressure azeotrope occurs when the following criteria are met
γ∞2 >
P/1 P/2
(1)
where γ∞i and P/i are the infinite dilution activity coefficient and vapor pressure of component i, respectively. A similar expression was derived that stipulates, for a minimum pressure azeotrope, the following condition must be fulfilled
γ∞1 >
P/2 P/1
(2)
Extensions of these criterion have been made for the prediction of polyazeotropy; however, their use requires some knowledge of the binary vapor-liquid equilibria for the system of interest so that derivatives of the excess Gibbs free energy with respect to composition may be calculated.15,16 For systems where no binary VLE data exist, atomistic computer simulations, combined with appropriate molecular models, can be used to predict the pressure-composition and temperature-composition behavior of complex chemical systems, including those that exhibit maximum17-23 or minimum24 pressure azeotropy. To our knowledge, no atomistic simulations have been performed for systems exhibiting polyazeotropy. In this work, we investigate the ability of state-of-the-art force fields to reproduce the azeotropic behavior found in mixtures of diethylamine with polar molecules such as methanol, acetone, or acetonitrile. Simulations are conducted in the grand canonical ensemble, and histogram methods are used for the determination of the phase envelopes.17 Additional calculations are performed in the isobaric-isothermal ensemble to explore the microstructure of these mixtures at equimolar concentrations. Simulations are performed with the transferable potentials for phase equilibria (TraPPE) force field, which was developed specifically for the accurate prediction of vapor-liquid equilibria and contains parameters for diethylamine, acetonitrile,25 methanol,19 and acetone.20
10.1021/jp065276t CCC: $37.00 © 2007 American Chemical Society Published on Web 12/19/2006
1452 J. Phys. Chem. C, Vol. 111, No. 3, 2007
Kamath and Potoff
TABLE 1: Parameters for Nonbonded Interactions Used in This Work force field
σ (Å)
(K)
All bond lengths, bond angles, bending constants, and Fourier constants are listed in Table 2.
q (e)
3. Simulation Details TraPPE-UA
Diethylamine CH3 98.0 CH2 46.0 N 58.0 H 0.0
3.75 3.95 3.52 0.0
0.0 0.18 -0.745 0.385
CH3 C Od CH3 C Od
Acetone 98.0 40.0 79.0 98.0 27.0 79.0
3.75 3.82 3.05 3.75 3.82 3.05
0.0 0.424 -0.424 -0.049 0.662 -0.564
TraPPE-UA
CH3 OH
Methanol 98.0 93.0 0.0
3.75 3.02 0.0
0.265 -0.7 0.435
TraPPE-UA
CH3 C N
Acetonitrile 98.0 60.0 60.0
3.75 3.55 2.95
0.269 0.129 -0.398
TraPPE-UA KP
2. Models and Simulation Details 2.1. Force Fields. In the TraPPE force field, nonbonded interactions between interaction sites in different molecules or interaction sites in the same molecule separated by more than three bonds are described by Lennard-Jones 12-6 potentials and Coulombic interactions of partial charges
U(rij) ) 4ij
[( ) ( ) ] σij rij
12
-
σij rij
6
+
qiqj 4π0rij
(3)
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 united atom (UA) version of TraPPE is used here. While hydrogens bonded to heteroatoms such as oxygen or nitrogen are modeled explicitly, those bonded to carbon atoms are merged to form a single CHx pseudoatom centered on the nucleus of the carbon atom. The Lennard-Jones parameters and partial charges for the molecules of interest to this work are listed in Table 1. To maintain consistency with previous investigations utilizing the TraPPE force field, Lorentz-Berthelot combining rules are used to determine the parameters for Lennard-Jones interactions between pseudoatoms of different type.26,27
σij ) (σii + σjj)/2
(4)
ij ) xiijj
(5)
Pseudoatoms are connected with fixed bond lengths, while bond angle bending is controlled by harmonic potentials
kθ Ubend ) (θ - θ0)2 2
(6)
where θ is the measured bond angle, θ0 is the equilibrium bond angle, and kθ is the force constant. The dihedral angles in diethylamine are governed by the following torsional potential 6
Utorsion ) co +
(ci cos(iθ)) ∑ i)1
(7)
3.1. Grand Canonical Monte Carlo. Grand canonical histogram-reweighting Monte Carlo simulations17 were used to determine the vapor-liquid coexistence curves and vapor pressures for pure diethylamine as well each of the binary mixtures presented in this work. The insertion of molecules in the GCMC simulations were enhanced through the application of the coupled-decoupled configurational-bias Monte Carlo method.28 Particle identity exchanges were used in mixture calculations to enhance the sampling of composition space. 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. All simulations were performed for a system size of L ) 25 Å, which resulted in liquid phases containing approximately 100 molecules. Lennard-Jones interactions were truncated at L ) 10 Å, and standard long-range corrections were applied.29,30 An Ewald sum with tinfoil boundary conditions (κ × L ) 5 and Kmax ) 5) was used to calculate the long-range electrostatic interactions.31,32 Simulations were equilibrated for one million Monte Carlo steps (MCS) before run statistics were recorded. 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. 3.2. Isobaric-Isothermal Monte Carlo. Monte Carlo simulations in the isobaric-isothermal ensemble were used to investigate the microstructure of equimolar mixtures of diethylamine + methanol, diethylamine + acetone, and diethylamine + acetonitrile. 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% configurationalbias regrowths, 70% translations, and 15% molecule rotations. A greater fraction of translational moves was performed compared to rotations due to the lower efficiency of the translational move with respect to sampling of configurational space. Rotational degrees of freedom for these small molecules are also effectively sampled through the configurational-bias regrowth move. Test calculations were used to verify that the results of the NPT simulations were not affected by the distribution of Monte Carlo move types. Lennard-Jones interactions were truncated at L ) 10 Å, and standard long-range corrections were applied.29,30 An Ewald sum with tinfoil boundary conditions (κ × L ) 5 and Kmax ) 5) was used to calculate the long-range electrostatic interactions.31,32 4. Results and Discussion 4.1. Diethylamine. To reduce computational requirements, a united-atom force field was used for mixture calculations involving diethylamine. However, the Lennard-Jones parameters for the N-H moiety were originally determined in the context of an explicit atom force field.25 To assess the effect of the united-atom approximation on the predictive capability of the force field, the coexistence densities and vapor pressures for the UA version of the TraPPE force field were determined and are presented in Figure 1. Calculations performed with the united-atom version of the force field produced saturated liquid
Vapor-Liquid Equilibria of Diethylamine
J. Phys. Chem. C, Vol. 111, No. 3, 2007 1453
TABLE 2: Geometrical Parameters for Diethylamine, Acetone, Acetonitrile, and Methanol vibration
bond length [Å]
bending
bond angle [deg]
CdO CH3-C CH3-O O-H CH2-N N-H
1.229 1.520 1.43 0.945 1.448 1.01
∠CH3-CdO ∠CH3-C-CH3 ∠CH3-O-H
121.4 117.2 108.5
62 500 62 500 55 400
kθ/kb [K]
C-N
1.157
∠CH3-CH2-N ∠CH2-N-H ∠CH2-N-CH2 ∠C-C-N
109.5 112.9 109.5 180
28 300 31 250 25 178 0.0
Dihedral
c0
c1
c2
c3
c4
c5
c6
CH3-CH2-N-H CH2-N-CH2-CH3
190.0 1466
47.8 -2188
105 1381
-105 -890
0 329
0 -137
0 52.6
and vapor densities that were in close agreement with the original explicit atom results of Wick et al.25 at temperatures below 400 K. As the critical point is approached, however, minor deviations between the TraPPE-UA and TraPPE-EH force fields are observed. Critical parameters were determined by fitting the saturated liquid and vapor densities over the temperature range 300 e T e 460 K to the density scaling law for critical temperature33
where β ) 0.325 is the critical exponent for Ising-type fluids in three dimensions35 and A and B are constants fit to simulation data. TraPPE-UA predicts Tc ) 501 K and Fc ) 248 kg/m3, compared to 502 K and 245 kg/m3 predicted by the TraPPEEH force field. A comparison between the vapor pressures predicted by the TraPPE-UA and TraPPE-EH force fields is presented in Figure 2. TraPPE-UA predicts vapor pressures approximately 12% higher than those of TraPPE-EH. Previous calculations of the TraPPE-UA alkane force field, from where the CH3 parameters were taken for diethylamine, have shown an overprediction of the vapor pressure of 10-20%. The deviations of our UA implementation of the TraPPE force field for diethylamine are largely due to this “built-in” error.36 For simplicity, we have not modified any of the parameters for N or H atoms in
diethylamine. Better agreement of the TraPPE-UA force field with experiment could likely be achieved through a slight increase in the Lennard-Jones well depth N for the nitrogen atom. Linear interpolation between calculated coexistence points was used to determine the normal boiling point Tb ) 328 K, which is in close agreement with the TraPPE-EH prediction of Tb ) 329 K. Linear extrapolation of the vapor pressure curve to the critical temperature was used to determine the critical pressure of Pc ) 41 bar (TraPPE-UA), which is in close agreement with the experimental value of 44.0 bar.37 Isobaric-isothermal simulations were performed at 300 K and 1 bar for pure diethylamine. These conditions correspond to a density of 704 kg/m3. The nitrogen-hydrogen radial distribution function (RDF) was extracted from these simulations and is shown in Figure 3. For completeness, the RDF for the TraPPE-EH force field was also calculated. As shown in the Figure, the use of explicit hydrogens has little effect on the structure of the condensed phase. The small peak at 2.7 Å in the RDF shows evidence of weak association between diethylamine molecules. This is in contrast to calculations for primary alcohols,19 where the RDF show significant association taking place. This is expected, but yet unverified, experimental behavior because the methanol oxygen has twice as many lone pair electrons as the nitrogen in diethylamine. In addition, hydrogen bonding to the methanol oxygen is less sterically hindered than to the nitrogen atom in diethylamine. The molecular mechanics force fields used in this work do not model lone pair electrons explicitly and instead treat electrostatic interactions, including hydrogen bonding, as effective interactions governed by atom centered partial charges. Comparing the partial charges of the atoms that take part in association, qN ) -0.745, qH ) 0.385
Figure 1. Vapor-liquid coexistence curves for diethylamine. Symbols denote simulation results: TraPPE-EH (squares)25 and TraPPE-UA (circles).
Figure 2. Clausius-Clapeyron plot for diethylamine. Symbols denote simulation results: TraPPE-EH (squares), TraPPE-UA (circles). The solid line represented experimental data.11
Fliq - Fvap ) B(T - Tc)β
(8)
and the law of rectilinear diameters34
Fliq + Fvap ) Fc + A(T - Tc) 2
(9)
1454 J. Phys. Chem. C, Vol. 111, No. 3, 2007
Kamath and Potoff
Figure 3. Radial distribution function for the N-H pair interaction in diethylamine at 300 K and 1 bar. The radial distribution function contains interactions of hydrogens bonded to nitrogen only. TraPPEUA (line) and TraPPE-EH (squares).
(diethylamine), and qO ) -0.70, qH ) 0.435 (ethanol) shows that the Coulombic interactions of diethylamine and ethanol should be of similar strength. However, diethylamine has two ethyl groups that block access of the positively charged hydrogen site to nitrogen, which results in reduced hydrogen bonding. The results illustrate that steric hindrance likely plays a more important role in self-association than the number of lone pair electrons available to act as hydrogen bond acceptors. Nuclear magnetic resonance (NMR) experiments of diethylamine in cyclohexane suggest the presence of cyclic tetramers in equilibrium with monomers .38 However, a cluster analysis, using a liberal definition of an H-bond (any H-N distance of 2.4 Å or less with no energetic or geometrical constraints), performed on configurations saved from the Monte Carlo simulation, revealed that 88% of the molecules were in the form of monomers, 11% were dimers, with the remaining 1% of the molecules existing as linear trimers. At no point in the simulations were any cyclic structures observed. To assess the impact of a nonpolar solvent on the aggregation of diethylamine molecules, additional NPT simulations were performed for mixtures containing 25, 50, and 75 mol % diethylamine in n-hexane. The addition of n-hexane resulted in a slight increase in the number of dimers present in solution (15%), but as in the case of neat diethylamine, no cyclic tetramers were observed. These simulation results are consistent with previous modeling by the extended real associated solution model (ERAS), where the association constant for methanol is approximately 1000 times larger than that for diethylamine.39 4.2. Diethylamine-Methanol. At 398 K, the diethylamine + methanol mixture forms one of the few systems that exhibits polyazeotropy, a condition where more than one azeotrope is observed at a particular temperature or pressure.10,11 The complexity of the phase diagram is increased, though, due to the fact that experiments at 348 and 298 K revealed only a single minimum pressure azeotrope. The predictions of simulations for the pressure-composition behavior of the diethylamine + methanol mixture at 398 and 348 K are shown in Figure 4. At 398 K, the predictions of the TraPPE-UA force field are not in agreement with the experimental data. Instead of a polyazeotrope, simulation predicts a single maximum pressure azeotrope with Psim azeo ) 10.5 bar and xamine ) 0.61. The predicted composition for maximum pressure azeotrope is in good agreement with the experimental value of xexpt amine ) 0.62. The predictions of simulation for the azeotropic pressure are less robust and overpredict the experimental value of 7.15 bar by 47%. Simulations were unable to reproduce the
Figure 4. Pressure-composition plot for diethylamine(1) + methanol(2). Top plot is for 398 K and bottom plot 348 K. Simulation (circles) and experiment (line).10
minimum pressure azeotrope. Simulations performed at 348 K reveal a maximum pressure azeotrope at a composition of 77 mol % diethylamine instead of the minimum pressure azeotrope found experimentally. Overall, the width of the phase envelopes predicted by simulation is significantly wider than experiment, signaling that unlike molecule interactions between diethylamine and methanol are underpredicted by the TraPPE force field. Minimum pressure azeotropy requires that interactions between unlike molecules be stronger than that of like molecules. Calculation of the pairwise interaction energies for methanolmethanol, diethylamine-diethylamine, and diethylaminemethanol dimers, as described by the TraPPE-UA force field, reveals that the methanol-methanol interaction is the strongest of the three types of possible intermolecular interactions. Reparameterization of the force fields to reproduce the minimum pressure azeotropy of the diethylamine + methanol system may be possible using the methodology described in recent calculations of minimum pressure azeotropy for the acetone + chloroform mixture.24 However, the polyazeotropy displayed at 398 K, and the disappearance of it at 348 K, implies that the strength of the unlike molecule interactions is not constant, but is instead a function of both composition and temperature. The addition of polarizability to the force field, with a possible coupling between Lennard-Jones and Coulombic terms,40 provides a means to account for the change in intermolecular interactions due to the local solvation environment around each molecule. It is expected that such a force field will yield improved predictions of the phase behavior for this system, and we intend to test this hypothesis in a future project. In the diethylamine + methanol mixture, there are four possible binary interactions that can be considered hydrogen
Vapor-Liquid Equilibria of Diethylamine
J. Phys. Chem. C, Vol. 111, No. 3, 2007 1455
Figure 6. Pressure-composition plot for diethylamine(1) + acetone(2) at 323 K. TraPPE(1)/TraPPE(2) (squares), TraPPE(1)/KP(2) (circles), and experiment (line).46
Figure 5. Radial distribution functions for the hydrogen bonding interactions in an equimolar mixture of diethylamine and methanol at: 398 K (line), 348 K (dashed line) and 298 K (dotted line). Top plot: (a) O(alcohol)‚‚‚H(alcohol), (b) N(amine)‚‚‚ H(amine). Bottom plot (c) O(alcohol)‚‚‚H(amine), (d) N(amine)‚‚‚H(alcohol).
bonding. These are intraspecies interactions of N(amine)‚‚‚ H(amine) and O(alcohol)‚‚‚H(alcohol), and the interspecies interactions of N(amine)‚‚‚H(alcohol) and O(alcohol)‚‚‚H(amine). Simulations in the isobaric-isothermal (NPT) ensemble were performed for equimolar mixtures at 398, 348, and 298 K to investigate the structure of the liquid phase. Pressures for the NPT simulations were fixed at values slightly higher than the saturation pressure at each temperature to ensure the simulations were thermodynamically stable. Radial distribution functions were calculated from the simulations and are shown in Figure 5. The RDFs show that association is taking place in the liquid phase via each of the proposed combinations of hydrogen bonding interactions. For the alcohol self-interaction O(alcohol)‚‚‚H(alcohol), a peak is found at 1.8 Å at all temperatures, increasing in height with decreasing temperature. This peak at 1.8 Å is consistent with previous studies involving methanol or methanol mixtures.19,24,41-43 It has been shown that methanol selfassembles into long chain structures in the pure state, as well as when in a binary mixture with a nonpolar or polar second component. Examination of molecular configurations from the NPT simulations of the diethylamine + methanol mixture show similar chain formation between methanol molecules in this mixture. An aggregation analysis performed on the configurations collected at 300 K revealed 55% of the aggregates contained only methanol, while the remaining 45% contained
both methanol and diethylamine. A small number of aggregrates containing only diethylamine were also observed. The average number of methanol-methanol hydrogen bonds per hydroxyl group were calculated. Methanol molecules were considered hydrogen bonded to each other if the O(alcohol)‚‚ ‚O(alcohol) distance was less than 3.5 Å. The number of hydrogen bonds per methanol was 1.77, which is lower than the 2.07 hydrogen bonds per hydroxyl group reported for pure methanol.19 This is expected because some of the methanol molecules participate in interspecies association with diethylamine, as shown by the RDF in Figure 5. A similar decrease in the number of hydrogen bonds per hydroxyl group for methanol-methanol interactions has been reported for binary mixtures of methanol with other polar components.24,43 Of the two types of interspecies hydrogen bonding interactions shown in the system, the O(alcohol)‚‚‚H(amine) interaction is the most common, as evidenced by the larger peak displayed in the RDF at approximately 2.0 Å compared to that of the N(amine)‚‚‚H(alcohol) interaction. This is due in part to the amine nitrogen being less accessible to hydrogen bonding interactions than the alcohol oxygen because it is surrounded by two ethyl moieties and a hydrogen atom. In addition, the overall strength of the diethylamine-alcohol interaction in the N(amine)‚‚‚H(alcohol) H-bonding mode is weakened by unfavorable Coulombic interactions between hydrogen atoms. Experimentally collected infrared spectra suggest that N(amine)‚‚‚H(alcohol) interactions are stronger than H(amine)‚‚‚O(alcohol).44,45 Calculation of the moleculemolecule interaction energy given by the TraPPE force field yields -18.6, -19.3, and -25.7 kJ/mol at the equilibrium spacing and orientation for the diethylamine-diethylamine, diethylamine-methanol, and methanol-methanol interactions, respectively. Because the diethylamine-methanol interaction predicted by the TraPPE force field is weaker than the methanol-methanol interaction, maximum pressure azeotropy is predicted at 348 and 298 K instead of the correct minimum pressure azeotrope. 4.3. Diethylamine-Acetone. Diethylamine and acetone have nearly equal vapor pressures from their normal boiling points to critical temperatures. Experiments to determine the pressure composition behavior of the diethylamine + acetone mixture have shown that this system exhibits maximum pressure azeotropy.10,46 In Figure 6, the predictions of the TraPPE force field for the pressure-composition diagram at 323.15 K are presented. Additional calculations utilizing a revised version of the TraPPE force field for acetone, denoted KP, were performed
1456 J. Phys. Chem. C, Vol. 111, No. 3, 2007
Figure 7. Radial distribution functions for an equimolar mixture of diethylamine and acetone at 300 K and 1 bar. Results of simulations using the Kamath-Potoff force field for acetone for the H(amine)‚‚‚ O(acetone) interaction are represented with a solid line, while results from calculations using the TraPPE-UA acetone force field are represented by squares. Amine self-interactions between nitrogen and the hydrogen bonded to nitrogen (Hamine‚‚‚Namine) are shown as open circles.
and are also presented. The Kamath-Potoff (KP) acetone force field features a revised partial charge distribution, specifically fit to reproduce the electrostatic potential energy surface around an acetone-chloroform dimer and altered Lennard-Jones parameters for the carbonyl carbon, which were optimized to minimize the deviation of simulation predictions from experimental vapor-liquid equilibrium data.24 Simulations with the TraPPE force field were unable to predict the maximum pressure azeotrope and instead show nearly ideal mixture (Raoult’s law) behavior. Predictions of TraPPE + KP(acetone) yield a pressure-composition diagram that is in close agreement with experiment, including the prediction of a maximum pressure azeotrope. The azeotropic composition of xsim amine ) 0.51 is identical to that reported by experiment, and the predicted azeotropic pressure is within 1.1% of the experimental value of Pexpt azeo ) 0.96 bar. Comparison of the Lennard-Jones and partial charges between the TraPPE and KP acetone force fields illustrates how small changes in force field parameters can impart significant effects on the predicted mixture vapor-liquid equilibria. Furthermore, the improved performance of the KP acetone force field demonstrates the effectiveness of using mixture calculations in the development of force field parameters.47,48 While the parameters for the KP force field were developed specifically to reproduce the minimum pressure azeotropy present in the acetone + chloroform system, these parameters also yield improved predictions in the diethylamine + acetone mixture as well as acetone + methyl acetate49 The structure of the liquid phase was investigated with NPT Monte Carlo simulations performed at 300 K and 1 bar. Radial distribution functions were determined from these simulations for the two possible hydrogen bonding interactions: N(amine)‚‚‚H(amine) and H(amine)‚‚‚O(acetone). These RDF are shown for the TraPPE and KP force fields in Figure 7. The RDF for the H(amine)‚‚‚O(acetone) interaction is very similar to the H(amine)‚‚‚O(methanol) RDF shown in Figure 5. Evidence of cross-species association is given by the peak at approximately 2 Å. As shown in the diethylamine + methanol system, the presence of a second polar component (acetone) has little effect on the liquid structure of diethylamine. An analysis of the number of diethylamine clusters and diethylamine-acetone complexes revealed that the majority (98%) of associated clusters were of the 1:1 interspecies type.
Kamath and Potoff
Figure 8. Pressure-composition plot for diethylamine(1) + acetonitrile(2) at 323 K. Simulation (circles) and experiment (line).10,46 Dashed lines between simulation data are provided as a guide to the eye.
This is due primarily to the geometry of the acetone molecule, where the lone pair electrons, or in the case of the force fields used here, an atom centered partial charge, on the carbonyl oxygen are not shielded by other atoms. As a result, there are many possible diethylamine-acetone conformations that will result in the formation of a hydrogen bond. On the surface, observing more diethylamine-acetone than diethylaminediethylamine clusters might suggest unlike molecule interactions are more favorable than those between like molecules and hence lead to minimum pressure azeotropy. However, this system has been shown experimentally and through simulation to display maximum pressure azeotropy. Calculation of the total interaction energies (molecule-molecule) between pairs of molecules yielded a diethylamine self-interaction that was approximately 10% stronger than the diethylamine-acetone cross-interaction. These results show that, while specific favorable pair interactions between atoms in molecules may lead to the formation of associated clusters of molecules, the presence of such complexes cannot be used to infer preferential molecule-molecule interactions. 4.4. Diethylamine-Acetonitrile. The diethylamine + acetonitrile mixture is another that is capable of interspecies hydrogen bonding. Like diethylamine + acetone, this system displays maximum pressure azeotropy.10,46 Unlike the other systems investigated here, the vapor pressures of diethylamine and acetonitrile differ significantly at all temperatures, and no Bancroft point is observed. This system is one of approximately 400 that show an azeotrope despite the absence of Bancroft point.50 The predictions of simulation for pressure-composition behavior of the diethylamine + acetonitrile mixture at 323 K are shown in Figure 8. The simulation results are in close agreement with experiment. At pressures above 0.5 bar, there is a slight overprediction of the mole fraction of acetonitrile in the liquid phase. This implies the TraPPE force field is underpredicting slightly interactions between diethylamine and acetonitrile. The predicted azeotropic composition of 10 mol % acetonitrile is an exact match to experiment. The azeotropic pressure is slightly overpredicted (+1.6%), which is due in part to the overprediction of the vapor pressure of pure diethylamine. Isobaric-isothermal simulations at 300 K and 1 bar were performed on equimolar mixture of diethylamine and acetonitrile, and the site-site radial distribution functions (RDF) were calculated. Nitrogen in acetonitrile can hydrogen bond with hydrogen in diethylamine to form 1:1 complexes or 1:2 complexes. The RDF for the N(nitrile)‚‚‚H(amine) and N(amine)‚‚‚H(amine) pair interactions determined from simula-
Vapor-Liquid Equilibria of Diethylamine
J. Phys. Chem. C, Vol. 111, No. 3, 2007 1457 reproduction of the polyazeotropy in the diethylamine + methanol mixture will likely require the inclusion of multibody effects such as polarizability. Investigation of the liquid-phase structure revealed significant association occurring between unlike components. Despite this association, the overall moleculemolecule interactions were always found to be more favorable for like molecule interactions than those between unlike molecules, leading to the maximum pressure azeotropy observed in all cases. Acknowledgment. We acknowledge the CPU time provided by Grid Computing at Wayne State University and financial support from the National Science Foundation (CTS-0522005, CTS-0228400).
Figure 9. Radial distribution functions for nitrogen-hydrogen pair interactions in an equimolar diethylamine + acetonitrile mixture at 300 K and 1 bar. N(nitrile)‚‚‚ H(amine) (line) and N(amine)‚‚‚H(amine) (dashed line).
tion are shown in Figure 9. The RDF for the interspecies association is similar to those determined for the diethylamine + methanol and diethylamine + acetone mixtures. The peak at 2 Å for the N(nitrile)‚‚‚H(amine) interactions signifies the formation of interspecies hydrogen-bonded aggregates. The number of hydrogen-bonded aggregates were determined by defining a “hydrogen bond” as any H-N distance less than 2.1 Å. Approximately 85% of the molecules were found to exist as monomers, while 14% of the molecules participated as dimers and another 1% as timers. No aggregates larger than three molecules were observed in the NPT simulations. Of the aggregates, 98% were formed from unlike molecules, while only 2% of the aggregates were due to diethylamine self-association. NMR experiments performed on mixtures of diethylamine and acetonitrile have shown evidence of the interspecies association reported here and indicate that diethylamineacetonitrile hydrogen bonds are stronger than those between diethylamine molecules.38 While the interactions between pairs of atoms may be stronger, the overall molecule-molecule interactions must be more favorable between like molecules than unlike molecules to produce the maximum pressure azeotrope displayed by this mixture. Energy calculations on the TraPPE force field show that molecule-molecule interactions between diethylamine molecules are approximately 20% larger than those between complete molecules of diethylamine and acetonitrile. 5. Conclusions The TraPPE force field was used to determine the pressurecomposition diagrams for the binary mixtures diethylamine + methanol, diethylamine + acetone, and diethylamine + acetonitrile. For the diethylamine + methanol system, simulations were unable to predict the polyazeotrope at 398 K and instead predicted a single maximum pressure azeotrope. At lower temperatures, such as 348 and 298 K, simulations continued to predict maximum pressure azeotropy in contrast to the experimentally observed minimum pressure azeotropy. For the diethylamine + acetone system, simulations of the TraPPE force field failed to produce the experimentally determined maximum pressure azeotrope, while simulations performed with a revised version of the TraPPE acetone force field produced results for the pressure-composition diagram that were in close agreement with experimental values. Simulations of the TraPPE force field for acetonitrile and diethylamine produced pressure-composition behavior in close agreement with experimental data. While the diethylamine + acetone and diethylamine + acetonitrile mixtures are well represented by fixed charge force fields,
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