Fluid Phase Equilibria 240 (2006) 46–55

Application of TraPPE-UA force field for determination ofvapor–liquid equilibria of carboxylate esters

Ganesh Kamath, Jason Robinson, Jeffrey J. Potoff∗Department of Chemical Engineering and Materials Science, Wayne State University, Detroit, MI 48202, USA

Received 31 August 2005; received in revised form 11 November 2005; accepted 16 November 2005Available online 6 January 2006

Abstract

The transferability of Lennard–Jones parameters in the united-atom force field known as “transferable potentials for phase equilibria” (TraPPE-UA) is assessed through vapor–liquid equilibria calculations performed on carboxylate esters. In the TraPPE-UA force field, non-bonded interactionsare governed by a Lennard–Jones plus fixed point charge functional form. Partial charges are borrowed from the optimized potentials for liquidsimulations (OPLS) force field [Briggs, Nguyen, Jorgensen, J. Phys. Chem. 95 (1991) 3315]. No reparameterization of pseudo-atoms occurs inthis work. Instead, the molecules of interest are built from pseudo-atoms parameterized in previous installments of the TraPPE-UA force field.C re used tod yl propionatea e + methanola acetate) to4 for methyla erpredicoa hat thea©

K

1

tgiilopuii

signsters.l pro-tate,with

rmineers.

e toand

thel orten-. Towhich,

0d

onfigurational-bias Monte Carlo simulations in the grand canonical ensemble, combined with histogram-reweighing techniques, aetermine the vapor–liquid coexistence curves, vapor pressures and critical points of the esters methyl acetate, ethyl acetate, methnd vinyl acetate. Pressure-composition diagrams are calculated for methyl acetate + ethyl acetate at 313.15 K and methyl acetatt 323.15 K. Average deviations in the saturated liquid densities and critical temperatures from experiment vary from 1.8% (methyl.2% (vinyl acetate), while the critical densities for all four esters are predicted to within 0.8%. The pressure-composition diagramscetate + ethyl acetate and methyl acetate + methanol agree qualitatively with experiment, but quantitative differences exist due to the ovtionf the pure component vapor pressures. For the methyl acetate + methanol system the predicted azeotropic composition ofxAcOMe = 0.66 is in goodgreement with the experimental value ofx

exptAcOMe = 0.65. Analysis of the microstructure of the methyl acetate + methanol mixture shows t

ddition of methyl acetate has little effect on the self-association of methanol molecules through hydrogen bonding.2005 Elsevier B.V. All rights reserved.

eywords: Simulation; Ester; TraPPE-UA; Force field; Vapor–liquid

. Introduction

Esters are functional derivatives of carboxylic acids wherehe hydroxyl (–OH) group is replaced by an alkoxy (–OR)roup[1]. Esters are produced commonly by hydrolysis and are

mportant in biochemical synthesis of fats from carbohydratesn plants and animals. Industrial applications of esters includeubricants, plasticizers, agricultural chemicals, in manufacturef inks for printing, plastic production, synthetic flavoring,reservatives, adhesives and form alternates to gasoline, beingsed in the making of biodiesel fuels[2,3]. Vinyl acetate is used

n manufacturing a wide variety of polymers that have end usesn paints and plastics[4].

∗ Corresponding author. Tel.: +1 313 577 9357; fax: +1 313 577 3810.E-mail address: jpotoff@chem1.eng.wayne.edu (J.J. Potoff).

Vapor–liquid equilibrium data are necessary for the deof separation processes required in the purification of eSuch data exist for methyl acetate, ethyl acetate and methypionate, but not for vinyl acetate. In the case of vinyl aceprediction of saturated liquid densities can be performeda correlation developed by Daubert and Danner[5]. A num-ber of experimental studies have been undertaken to detethe vapor–liquid equilibria of binary mixtures containing estExamples include esters + alkanes[6], alkenes[7], alcohols[8],carboxylic acids[9], nitriles [10] and CO2 [11].

Molecular simulations are becoming a viable alternativexperiments for the prediction of vapor–liquid equilibriaphysical properties of complex chemical systems. Key topredictive capability of any simulation is the potential mode“force field” used in the calculations. The transferable potials for phase equilibria (TraPPE) is one such force fielddate, an extensive parameter library has been created,includes alkanes[12,13], alkenes[14], alcohols[16], ethers

378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved.oi:10.1016/j.fluid.2005.11.034

G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55 47

glycols, aldehydes, ketones[17], carboxylic acids[18] amines,nitriles and amides[19]. The key idea in this force field is that oftransferability, i.e. parameters for a particular functional groupremain unchanged, regardless of the atomic makeup of the restof the molecule. For example, Lennard–Jones parameters for amethyl pseudo-atom, once parameterized through the simula-tion of alkanes, remain unchained, whether the methyl group ispart of an alcohol, ketone, carboxylic acid, etc.

In previous installments of the TraPPE force field, free param-eters were always available for optimization with respect tothe reproduction of experimental vapor–liquid equilibria. In thiswork, we use simulations of esters to assess the transferabilityof the TraPPE pseudo-atom Lennard–Jones parameters whenfree parameters arenot available. Grand canonical histogram-reweighing Monte Carlo simulations utilizing the TraPPE forcefield are used to determine the vapor–liquid equilibria, vaporpressures and critical properties of methyl acetate, ethyl acetate,methyl propionate and vinyl acetate. Additional calculations areperformed for the binary mixtures methyl acetate + ethyl acetateand methyl acetate + methanol. To maintain consistency withprevious TraPPE force field parameterizations, partial chargeswere taken from the OPLS-UA force field for methyl acetate[20], while Lennard–Jones parameters for each pseudo-atomwere taken from the following sources: CH2(sp3), CH3 (n-alkanes[12]), CH, CH2(sp2) (alkenes[14]), O (CO2 [15]),

O (ethers[17]), C(sp2) (carboxylic acids[18]). Necessaryb g ant f theO rc d byfi rtreeF

ls ofT tionI ram-r rka es,v ethya y thT ed bp eta

at 313.15 K and methyl acetate + methanol at 323.15 K. An anal-ysis of the microstructure of the methyl acetate + methanol mix-ture is also presented. The conclusions of this work can be foundin Section5.

2. Force field

The calculations performed in this work are based on theTransferable Potentials for Phase Equilibria (TraPPE) series offorce fields. TraPPE is a united-atom force field, which meansthat hydrogens bonded to carbon atoms are grouped together toform a single interaction site, or “pseudo-atom”. Non-bondedinteractions are given by pairwise additive Lennard–Jones (LJ)potentials combined with partial charges

U(rij) = 4εij

[(σij

rij

)12

−(

σij

rij

)6]

+ qiqj

4πε0rij(1)

whererij, εij, σij, qi, andqj are the separation, LJ well depth, LJsize and partial charges, respectively, for the pair of interactionsitesi andj.

Unlike previous TraPPE-UA papers, no parameter fitting wasdone in this work. Instead, parameters were taken from exist-ing TraPPE-UA parameterizations and combined to form themolecules of interest. Lennard–Jones parameters for the methylpseudo-atom were taken from the TraPPE-UA alkane param-e fromc x-i eters r theC enepT stersw tate[ inec n siteso

σ

ε

TT

ate

L

onded interactions, such as bond lengths, angles, bendinorsional potentials were taken from previous installments oPLS-UA [20] and TraPPE[17] force fields. Missing Fourieonstants for specific torsional potentials were determinetting a cosine series to ab initio data collected at the Haock level of theory with the 6-31g+(d,p) basis set.

This paper is organized as follows. The specific detairaPPE force field implementation are given in the next sec

n Section3, the details regarding the grand canonical histogeweighing andNPT Monte Carlo simulations used in this wore provided. In Section4, the vapor–liquid coexistence curvapor pressures and critical points for methyl acetate,cetate, methyl propionate and vinyl acetate as predicted braPPE force field are presented. These results are followressure composition diagrams for methyl acetate + ethyl ac

able 1raPPE-UA parameters for non-bonded interactions

Site Molecule

CH3 (O) [12] Methyl acetate/methyl propionateO [16] All

C (O) [18] AllO [15] All

CH3 (C) Methyl acetate/ethyl acetate/vinyl acetCH3 (CH2) Ethyl acetate/methyl propionateCH2 (O) [12] Ethyl acetateCH2 (C) [12] Methyl propionateCH2 (CH) [14] Vinyl acetateCH (CH2) [14] Vinyl acetateCH3 Methanol

O MethanolH Methanol

etters in parentheses indicate the atom a particular site is bonded to.

d

.

leyte

ter set[12], the carbonyl carbon parameters were takenarboxylic acids[18], the carbonyl oxygen from carbon diode model[15] and the ether oxygen from the ether paramet[17]. For vinyl acetate, the Lennard–Jones parameters foH2(sp2) and CH(sp2) pseudo-atoms were taken from the alkarameterization[14]. These parameters are listed inTable 1.he partial charges for the pseudo-atoms in carboxylate eere taken from the OPLS-UA force field for methyl ace

20]. Lorentz–Berthelot combining rules are used to determross-parameters for Lennard–Jones interactions betweef different type[21,22]

ij = σii + σjj

2(2)

ij = √εiiεjj (3)

ε/kb (K) σ (A) qi (e)

98.0 3.75 0.2555.0 2.80 −0.4041.0 3.90 0.5579.0 3.05 −0.45

98.0 3.75 0.0598.0 3.75 0.0

46.0 3.95 0.2546.0 3.95 0.0585.0 3.675 0.047.0 3.73 0.2598.0 3.75 0.26593.0 3.02 −0.70.0 0.0 0.435

48 G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55

Table 2TraPPE-UA force-field parameters for bonded interactions

Vibration Molecule Bond length (A)

C O All 1.2C O All 1.344C CH3 All 1 .520O CH3 All 1 .41CH2 CH3 Methyl propionate/ethyl acetate 1.54CH2 CH Vinyl acetate 1.33O CH3 Methanol 1.43O H Methanol 0.945Bend (Eq.(4)) Bond angle,θ0 (◦) kθ/kb (K)

∠C O CH3 115 62500∠O C O 125 62500∠O C CH3 110 70600∠O C CH3 125 62500∠ CH3 O H 108.5 55400

Pseudo-atoms are connected by bonds of fixed length, while aharmonic potential is used to control bond angle bending

Ubend= kθ

2(θ − θ0)2 (4)

whereθ is the measured bond angle,θ0 is the equilibrium bondangle andkθ is the force constant. All bond lengths, bond anglesand bending constants are listed inTable 2.

A cosine series is employed for all torsional interactions ofpseudo-atoms separated by three bonds

Utorsion = c0 + c1[1 + cos(φ)] + c2[1 − cos(2φ)]

+ c3[1 + cos(3φ)] (5)

whereφ is the dihedral angle andci are Fourier constants. Theci constants used in this work are listed inTable 3. Fourierconstants for the OC CHx CHx and C O CHx CHy tor-sional potentials are the same as those used for ethers andketones[17]. A torsional potential has been defined for theC C O R interaction in methyl acetate for the OPLS-UA forcefield [20]. However, additional torsional potentials were neces-sary to model accurately the conformational behavior of othercarboxylate esters. Parameters for missing torsional potentialswere developed based on ab initio torsional profiles of methyland vinyl acetate. Scans of the potential energy surface wereperformed at the HF/6-31g+(d,p) level with the Gaussian 03sO theC e.W pti-m ientsw -t inM

unc-ta cu-l nots theC da pec-

Table 3TraPPE-UA force-field parameters for torsional interactions

Torsion (Eq.(5)) c0/kb (K) c1/kb (K) c2/kb (K) c3/kb (K)

CHx O C O 4716.0 2194.0 2059.0 −153.4CHx O C CHy 0.0 2158.0 2098.0 197.3CH2 CH O C 0.0 1698.0 1564.0 86.5CH O C CHx −14.48 993.1 520.7 −138.5CHy CHx C O [17] 2035.58 −736.9 57.84 −293.23CHy CHx O C [17] 0.0 725.35 163.75 558.2

Fig. 1. Torsional energy as function of dihedral angle in methyl acetate. Poten-tial energy scans at the HF/6-31+g(d,p) level are shown as symbols, while thesolid lines are the fit of the cosine series to the ab initio data. Top and bottomplots correspond to the CH3 O C CH3 and CH3 O C O dihedral angles,respectively.

troscopy[24]. This is an improvement over the previous estimateof 9.26 kcal/mol derived from MM2 calculations[20]. As shownin the figure, the cosine series provides an excellent reproductionof the ab initio derived potential energy surface.

3. Simulation details

3.1. Grand canonical Monte Carlo

Grand canonical histogram-reweighing Monte Carlo simula-tions [25–28] were used to determine the vapor–liquid coex-istence curves and vapor pressures for pure methyl acetate,ethyl acetate, methyl propionate and vinyl acetate as wellas the binary mixtures methyl acetate + ethyl acetate andmethyl acetate + methanol. The insertion of molecules in theGCMC simulations were enhanced through multiple first beadinsertions[29] and the application of the coupled-decoupledconfigurational-bias Monte Carlo method[30]. Particle identityexchanges were used for mixtures to enhance the acceptancerate for particle insertions and deletions. The fractions of thevarious moves for each simulation were set to 10% for identityexchanges (mixtures), 15% for particle displacements, 15% forrotations, 10% configurational bias regrowths and 60% for inser-tions and deletions (50% for mixtures). Simulations were per-

oftware[23]. Scans were performed at 10◦ intervals for theC O C and C O C C dihedrals in methyl acetate and

H2 CH O C and CH O C CH3 dihedrals in vinyl acetatith the exception of the dihedral angle of interest, full oizations were performed at each point. Fourier coefficere determined by fitting Eq.(5) to the ab initio derived poten

ial energy surfaces with the curve fitting toolbox (cftool)atlab.In Fig. 1, the relative potential energy surfaces as a f

ion of dihedral angle are presented for the CH3 O C CH3nd CH3 O C O dihedrals in methyl acetate. Similar cal

ations performed for the dihedrals in vinyl acetate arehown. Ab initio calculations predict a rotational barrier forH3 O C CH3 dihedral of 13.9 kcal/mol, which is in googreement with the value of 15 kcal/mol obtained from IR s

G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55 49

Fig. 2. Vapor–liquid coexistence curves for methyl acetate: TraPPE (circle), OPLS-UA (plus), ethyl acetate (square), methyl propionate (diamond)and vinyl acetate(triangle). Solid lines and stars denote experimental coexistence densities[35], or the predictions of correlations[5], and critical points. Statistical uncertainties inthe predicted saturated liquid and vapor densities are 0.2% and 1% of the reported values, respectively.

formed for a system size ofL = 25A for methyl acetate andL =30A for all other esters. Lennard–Jones interactions were trun-cated at 10A, and standard long-range corrections were applied[31,32]. An Ewald sum with tinfoil boundary conditions wasused to calculate the long range electrostatic interactions[33,34].Simulations were equilibrated for 1 million Monte Carlo steps(MCS) before run statistics were recorded, while productionruns were 25 million MCS (pure components) to 50 million MCS(mixtures). Over the course of each simulation, the number ofmoleculesN and energyE (or N1, N2 andE for binary mix-tures) were stored in the form of a list, which was updatedevery 250 MCS. The necessary probability distributions wereextracted from this list after the completion of the simulation.Statistical uncertainties in the predicted vapor–liquid equilibriaand critical points were calculated by performing three indepen-dent sets of simulations with different random number seeds andinitial configurations. The standard deviation of the results fromthe three simulation sets was used as the statistical uncertaintyestimate.

3.2. Isobaric-isothermal Monte Carlo

Monte Carlo simulations in the isobaric-isothermal ensem-ble were used to investigate the microstructure of an equimo-lar mixture of methyl acetate + methanol. A system size of5 fo2 r ana mec tiona wert erea sw tion

[33,34]. A system size of 250 molecules was used to determinethe radial distribution functions for neat methyl acetate.

4. Results and discussion

4.1. Pure component vapor–liquid equilibria

The vapor–liquid coexistence curves for methyl acetate, ethylacetate, methyl propionate and vinyl acetate as predicted by theTraPPE-UA force field are shown inFig. 2. For comparison,we include vapor–liquid equilibrium data for methyl acetate aspredicted by the OPLS-UA force field[20]. Average unsigneddeviations of TraPPE-UA from experiment[35] for saturatedliquid densities were calculated as: 2.67% for methyl acetate,3.5% for ethyl acetate, 1.46% for methyl propionate and 4.2%for vinyl acetate. In the case of vinyl acetate, we were unableto locate experimental vapor liquid equilibrium data and insteadhave compared the predictions of simulation with a correlationfor saturated liquid densities by Daubert and Danner[5]. Over-all, the predictions of the TraPPE-UA force field are excellent,especially considering that no tuning of parameters occurred inthis work. While the pseudo-atoms used here were all param-eterized in similar bonding environments, the partial chargedistribution across pseudo-atoms in esters is significantly dif-ferent than the partial charge distributions in the molecules forw is is as ard–Jr cefi ver-p .5%f ithu itical

00 molecules was used. Simulations were equilibrated5 million MCS, after which run statistics were recorded fodditional 25 million MCS. The ratio of moves was 1% voluhanges, 14% configurational bias regrowths, 70% transland 15% molecule rotations. Lennard–Jones interactions

runcated atL = 10A and standard long-range corrections wpplied[31,32]. An Ewald sum with tinfoil boundary conditionas used to calculate the long range electrostatic interac

r

se

s

hich the pseudo-atoms were originally parameterized. Thtrong demonstration of the general transferability of Lennones parameters in the TraPPE-UA force field. InTable 4weeportTc, Tb, ρc andPc as predicted by the TraPPE-UA foreld. The critical temperatures for all of the molecules are oredicted, ranging from 1.8% for methyl propionate to 5

or vinyl acetate. Critical densities are all well predicted, wnsigned deviations from experiment <1% in all cases. Cr

50 G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55

Table 4Predicted normal boiling points and critical properties of esters

Tc (K) ρc (kg/m3) Pc (bar) Tb (K)

Methyl acetate TraPPE-UA 521.2 ± 0.7 321.7 ± 1.0 53.9 ± 0.4 326.7 ± 0.2OPLS-UA 555.5 ± 0.7 315.1 ± 1.0 60.6 ± 0.4 351.0 ± 0.2Experiment[35] 506.8 325.2 46.9 329.9

Ethyl acetate TraPPE-UA 547.5 ± 0.8 305.4 ± 1.1 49.5 ± 0.5 348.5 ± 0.5Experiment[35] 523.2 307.7 38.5 350.2

Methyl propionate TraPPE-UA 540.0 ± 0.4 312.2 ± 1.0 45.7 ± 0.5 342.2 ± 0.4Experiment[35] 530.5 312.4 40.0 352.0

Vinyl acetate TraPPE-UA 553.9 ± 0.3 316.4 ± 0.8 51.8 ± 0.3 351.7 ± 0.1Correlation[5] 524.0 318.8 42.5 345.6

temperatures and densities for each of the esters were deter-mined by fitting the saturated liquid and vapor densities over thetemperature range 300≤ T ≤ 460 K to the density scaling lawfor critical temperature[36]

ρliq − ρvap = B(T − Tc)β (6)

and the law of rectilinear diameters[37]

ρliq + ρvap

2= ρc + A(T − Tc) (7)

whereβ = 0.325 is the critical exponent for Ising-type fluids inthree dimensions[38] andA andB are the constants fit to simula-tion data. While the mixed-field finite-size scaling methodologyprovides a potentially more accurate algorithm for the determi-nation of critical points[39], the added computational expenseof such analysis was not viewed necessary given the approxi-mate nature of the potential models studied in this work. Thiscomputational expense results from the need to collect high pre-cision histogram data near the critical point for multiple systems

sizes on the order of a few thousand molecules and isO(102)times greater than that required to generate an entire phasediagram.

The Clausius–Clapeyron plots used to determine the criti-cal pressures and normal boiling points are shown inFig. 3.The TraPPE-UA force field predicts vapor pressures for methylacetate and ethyl acetate that are in close agreement with exper-iment, with deviations of approximately 10%. The TraPPE-UArepresentation of vinyl acetate was found to underpredict thevapor pressure at higher temperatures, which is the result ofa nearly 30 K overprediction of the critical temperature. As inthe case of saturated liquid densities, no experimental resultswere available for comparison for vinyl acetate so the resultsof simulation were compared to quasi-experimental data in theform of correlations[5]. Normal boiling points were deter-mined by interpolation of the Clausius–Clapeyron plots usingEq. (8) and are listed inTable 4. The maximum deviation inTbwas found for methyl propionate, which was 2.8% lower thanexperiment. Critical pressures were calculated from the

F PLS in( inyl a portedv

ig. 3. Clausius–Clapeyron plots for methyl acetate: TraPPE (circle), Otriangle). Solid lines denote experiment[35] or correlations in the case of values.

-UA (plus), ethyl acetate (square), methyl propionate (diamond) and vyl acetatecetate[5]. Statistical uncertainties in the vapor pressures are <1% of the re

G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55 51

Fig. 4. Radial distribution functions for oxygen–methyl pair interactions inmethyl acetate at 300 K and 1.2 bar. Simulation results for the TraPPE-UA andOPLS-UA[20] force fields are shown as circles and lines, respectively. Top plot:OE–MeE pair interaction. Bottom plot: O–MeE pair interaction.

Clausius–Clapeyron plots with the following expression:

ln Pc = C + D

Tc(8)

wherePc is the critical pressure,C and D are the constantsderived from fitting Eq.(8) to the vapor pressure-temperaturedata andTc is the critical temperature. The TraPPE-UA forcefield overpredicts the critical pressure for all of the esters studiedhere, with deviations from +14.2% for methyl propionate to+28.6% for ethyl acetate.

4.2. Liquid structure of methyl acetate

Two radial distribution functions (RDF) were calculated forneat methyl acetate from isobaric-isothermal simulations at1.2 bar and 300 K and are presented inFig. 4. These conditionscorrespond to a density of 894.3 kg/m3, which is the same asthe saturated liquid density. In this discussion, O is the carbonyloxygen, OE is the ester oxygen and MeE is the alkoxy methylgroup. The top plot shows the intermolecular RDF for the MeEpseudo-atom with OE, while the bottom plot is MeE with O.Both of the predicted RDF are in close agreement with thosepredicted by the OPLS-UA force field[20], illustrating the factthat liquid phase structure is only weakly affected by the choiceof parameters for dispersive interactions. Neither RDF revealsany significant association in the liquid phase. This is what onew simi

4

urec mixtT nly

Fig. 5. Pressure composition diagram for methyl acetate (1) + ethyl acetate (2)at 313.15 K. Simulation results are shown as circles while a solid line is used todenote experimental data[40].

minor deviations from Raoult’s Law. The primary source ofdiscrepancies between simulation and experiment arise fromthe overprediction of each of the pure component vapor pres-sures. This results in a shift of the entire coexistence curve topressures approximately 12% higher than experiment. The coex-istence curve predicted by simulation is only slightly wider thanexperiment, suggesting that revised intermolecular force fieldsthat reproduce accurately the pure component vapor pressuresshould be able to yield predictions that are in quantitative agree-ment with experiment. Additional calculations were performedfor the system methyl acetate + methanol. Experimentally, themethyl acetate + methanol mixture has been shown to exhibitmaximum pressure azeotropy[40]. The normal boiling pointsfor methyl acetate and methanol differ by only 8.04 K. As ageneral rule for binary mixtures, the closer the normal boilingpoints of each of the components are to each other, the greaterthe probability of azeotropic behavior[41]. Furthermore, thevapor pressures of methyl acetate and methanol are equal at283.0 K. This intersection of pressure versus temperature curvesfor each of the components is known as a Bancroft point. Ithas been shown experimentally that approximately 90% of thebinary mixtures that have a Bancroft point exhibit some kind ofazeotropic behavior[42]. Fig. 6shows the vapor pressure versusinverse temperature plot for simulation results as well as exper-imental values for methanol and methyl acetate. Simulations ofthe TraPPE-UA force field predict a Bancroft point at 293 K inc

ldf owni eO l[ res-sw aluex

1 alueP UA

ould expect, since carboxylate esters have boiling pointslar to those of alkanes of the same molecular weight.

.3. Binary mixture phase behavior

In Fig. 5, the predictions of TraPPE-UA for the pressomposition diagram of the methyl acetate + ethyl acetateure at 313.15 K are shown in comparison to experiment[40].his mixture of two very similar components displays o

-

-

omparison to the experimental value of 283 K.In Fig. 7, the predictions of the TraPPE-UA force fie

or the pressure composition diagram at 323.15 K are shn comparison to experiment[40] and the predictions of thPLS-UA force fields for methyl acetate[20] and methano

43]. The TraPPE-UA force field predicts a maximum pure azeotrope with an azeotropic compositionxTraPPE

AcOMe = 0.66,hich is in excellent agreement with the experimental v

exptAcOMe = 0.65. The predicted azeotropic pressurePTraPPE

azeo =.14 bar is about 30% higher than the experimental vexptazeo= 0.884 bar. Calculations performed with the OPLS-

52 G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55

Fig. 6. Clausius–Clapeyron plot for methyl acetate (circles) and methanol(squares). Lines denote experimental data[35,45].

force fields for methyl acetate and methanol failed to showazeotropic behavior, highlighting the importance of dispersiveinteractions in the accurate prediction of fluid phase equilibria.The phase envelope predicted by the TraPPE-UA force field issignificantly wider than experiment, especially for systems richin methyl acetate. Clearly, the unlike molecule interactions asdefined by the TraPPE-UA series of force fields is too weakfor this mixture. Unlike previous calculations for systems suchas alkane + CO2 (non-polar + quadrupolar)[15], alkane + H2S(non-polar + dipolar)[44], both molecules in this mixture havesignificant dipole moments. Therefore, it is not immediatelyclear as to whether the source of the discrepancies betweensimulation and experiment is an underprediction of dispersiveinteractions between unlike molecules or a hypothetical failureof the models to reproduce interspecies hydrogen bonding.

F ixturea rian-g

Fig. 8. Radial distribution functions for the oxygen–hydrogen pair interactionin an equimolar mixture of methyl acetate + methanol mixture at 300 K and1.2 bar. Top plot: OMeOH–HMeOH. Bottom plot: OAcOMe–HMeOH (solid line),OEAcOMe–HMeOH (dashed line).

4.3.1. MicrostructureSimulations in theNPT ensemble were conducted at 300 K

and 1.2 bar for an equimolar mixture of methyl acetate andmethanol. Methanol is well-known to self-associate via hydro-gen bonding[46]. In addition, the carbonyl (O) and etheroxygens (OE) of methyl acetate may act as hydrogen bondacceptors, and hence in this mixture cross-associations betweenmethanol and methyl acetate molecules are possible. Thereare three radial distribution functions of interest with respectto aggregation in this mixture. The first is given by theintraspecies (methanol–methanol) OMeOH–HMeOH interaction,the second is the OAcOMe–HMeOH interspecies (methyl acetate–methanol) interaction and third is the OEAcOMe–HMeOH inter-species (methyl acetate–methanol) interaction.

The oxygen–hydrogen intermolecular radial distributionfunctions extracted from theNPT simulations are shown inFig. 8. The top plot shows the predictions for the intraspeciesOMeOH–HMeOH interaction. A peak at 1.8A agrees with theprevious simulations performed on methanol and methanol mix-tures [16,47–49], and signifies extensive methanol–methanolhydrogen bonding. The bottom plot shows the RDF for theinterspecies OAcOMe–HMeOH and OEAcOMe–HMeOH pair inter-actions. In comparison to the OMeOH–HMeOH RDF, the OAcOMe–HMeOH RDF also presents a peak at 1.8A, but it is much lower inmagnitude. This shows that some interspecies hydrogen bondingis occurring, but not to the extent of the intraspecies hydrogenbHs y as ture.

t al.[ ondsp erec

ig. 7. Pressure composition plot for methyl acetate (1) + methanol (2) mt 323.15 K. Symbols are as follows: TraPPE-UA (circles), OPLS-UA (tles), experimental data (line)[40].

onding between methanol molecules. The RDF for OEAcOMe–MeOH pair interaction displays only a tiny bump at 1.8A, whichhows that OEAcOMe–HMeOH hydrogen bonding does not plaignificant role in the phase behavior or structure of this mix

Following the procedure defined in the work of Chen e16],the average number of methanol–methanol hydrogen ber hydroxyl group were calculated. Methanol molecules wonsidered hydrogen bonded to each other if the OMeOH–OMeOH

G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55 53

Fig. 9. Snapshot of an equimolar mixture of methyl acetate + methanol at 300 K and 1.2 bar for the TraPPE-UA force field: (a) methyl acetate/methanol configuration,(b) methyl acetate–acetone aggregates, (c) methanol–methanol aggregates.

distance was less than 3.5A. The average number of hydro-gen bonds per methanol was 2.0, which is close to the valueof 2.07 reported for pure methanol at similar conditions[16].This is unlike the mixture acetone + methanol, where acetonemolecules were able to substitute for methanol, reducing theaverage number of hydrogen bonds per methanol molecule to1.67 [49]. These results suggest that methyl acetate has littleaffect on the hydrogen bonding between methanol molecules.

To further quantify the nature of hydrogen bonding, an analy-sis was performed to determine the number of aggregates wherethe O H (AcOMe–methanol) and OH (methanol–methanol)distance was less than 2.4A. Under these conditions we con-sider the molecules in question to be hydrogen-bonded. Asimilar analysis was not performed for OEAcOMe–HMeOH inter-actions because previous calculations for the radial distributionfunctions (Fig. 8) did not show this interaction to be a signifi-cant source of intermolecular hydrogen bonding. A distance of2.4A was selected because this corresponds to a minimum inthe OAcOMe–HMeOH radial distribution function. The analysisrevealed that methyl acetate–methanol aggregates account for7.3% of the total number of aggregates, which corresponds to2% of methanol molecules. Only 1.4% of the methyl acetate–methanol aggregates were larger than dimers, and involvedeither short chains of methanol molecules hydrogen bondedto methyl acetate or one methanol molecule associated with

methyl acetate. Examples of these aggregates are shown inFig.9, which is a snapshot taken from the equilibratedNPT sim-ulations. In parts (b) and (c), the snapshot is decomposed intomethyl acetate–methanol and methanol–methanol aggregates,respectively. As shown inFig. 9, methanol forms chains pri-marily, varying in length from 2 to 12 molecules. Only a smallnumber of cyclic structures were detected.

5. Conclusions

The TraPPE-UA force field has been used to predict thevapor–liquid coexistence curves, vapor pressures and criticalpoints for methyl acetate, ethyl acetate, methyl propionateand vinyl acetate. No parameterization of any interaction sitesoccurred. Instead, Lennard–Jones parameters were taken fromprevious parameterizations of the TraPPE-UA force field foralkanes[12], alcohols[16], ethers[17] and carboxylic acids[18],while partial charges were “borrowed” from the OPLS-UA forcefield[20]. Overall, a good reproduction of experimental data wasachieved. The saturated liquid densities predicted for methylacetate, ethyl acetate, methyl propionate and vinyl acetate arewithin 4.2% of experiment. The predicted vapor pressures werewithin 20% of the experimental values, with the exception ofmethyl propionate. Critical temperatures are slightly overpre-dicted (2–5%, depending on molecule), while critical densities

54 G. Kamath et al. / Fluid Phase Equilibria 240 (2006) 46–55

are within 0.8% of experiment. For comparison, we note that incases where the TraPPE-UA force field has been fit to a specificmolecule of a homologous series, the mean unsigned devia-tions from experiment for the saturated liquid densities, criticaltemperature and critical density are generally under 1%, whilevapor pressures are typically overpredicted by approximately20%.

Pressure composition diagrams were determined for thebinary mixtures methyl acetate + ethyl acetate and methylacetate + methanol. The TraPPE-UA force field gave a goodqualitative reproduction of experimental data, including repro-duction of the azeotrope present in the methyl acetate + methanolsystem. Significant quantitative deviations were found betweensimulation and experiment, due in part to the inaccuracy in theprediction of the pure component vapor pressures. An analysisof the liquid phase structure of an equimolar mixture of methylacetate and methanol at 300 K and 1.2 bar reveals limited inter-species hydrogen bonding and little disruption of the hydrogenbonded chain structures of methanol molecules found in the neatliquid.

List of symbolsA fitting parameter for law of rectilinear diametersB fitting parameter for critical temperature scaling lawc0, c1, c2, c3 Fourier constantsC, D fitting parameter for critical pressurek

k

N

PP

q

r

TT

T

U

U

U

Gβ

ε ten

ε

θ

θ

ρ

ρ

ρ

σ ntiaφ

A

TS-0 uter

resources used in this work were provided by the Grid Com-puting Resource at Wayne State University.

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