P

Ma

b

a

ARR2AA

KGTDGE

1

moRmsra[pAFpssbtpc

rdd

0h

Fluid Phase Equilibria 364 (2014) 6– 14

Contents lists available at ScienceDirect

Fluid Phase Equilibria

j our na l ho me pa ge: www.elsev ier .com/ locate / f lu id

rediction of vapour–liquid coexistence data of Phenylacetylcarbinol

adakashira Harinia, Jhumpa Adhikari a,∗, K. Yamuna Ranib

Department of Chemical Engineering, Indian Institute of Technology Bombay, Mumbai 400076, IndiaChemical Engineering Division, Indian Institute of Chemical Technology, Hyderabad 500607, India

r t i c l e i n f o

rticle history:eceived 1 October 2013eceived in revised form7 November 2013ccepted 30 November 2013vailable online 15 December 2013

a b s t r a c t

Phenylacetylcarbinol (PAC) is an important chiral molecule, the R-isomer of which is used in the manu-facture of several pharmaceutical products and is currently produced by means of biotransformation. Theknowledge of thermodynamic properties of PAC is essential to improve the process involving the sep-aration of PAC from the organic solvent, used in the biotransformation process to extract PAC from theaqueous broth. In spite of its importance, limited experimental vapour pressure data is available on PACin the literature. Hence, in this study, the physical and thermodynamic properties of PAC are predicted

eywords:ibbs ensemble Monte CarloraPPE–UAensity functional theoryroup contribution

using structure property correlations combined with equations of state, and also molecular simulation asthe first step to optimize the process design for the production of PAC. The properties predicted includeliquid and vapour densities at co-existence, enthalpy of vaporization, saturation pressure, critical pointand normal boiling point. The liquid and vapour densities at coexistence and the critical point data fromboth the methods are found to be in agreement.

quation of state

. Introduction

Research and development in areas such as drugs, cos-etics, pesticides, food, etc., has contributed to the evolution

f new molecules whose properties need to be determined.-Phenylacetylcarbinol (PAC), a chiral precursor, is an active phar-aceutical ingredient (API) in manufacturing of various drugs

uch as ephedrine, pseudoephedrine, adrenaline, etc. It is cur-ently produced by means of biotransformation of benzaldehydend pyruvate through whole cell fermentation using baker’s yeast1]. Separation of the API is important in order to maintain theurity of the product and to economize the cost of production.n organic solvent is used to extract PAC from the aqueous broth.urther, distillation is used for separation of PAC from the solventhase, and the design of distillation column requires equation oftate (EoS) information which in turn takes into account criticaltate properties of the individual components. Thus, to achieve aetter separation of the API it is essential to have knowledge of cer-ain physical and thermodynamic properties such as normal boilingoint (Tb), vapour pressure, density (�), critical temperature (Tc),ritical pressure (Pc), heat of vaporization (�Hvap), etc.

Experimental vapour–liquid equilibria (VLE) data of PAC

eported in literature [2] is limited to vapour pressures at threeifferent temperatures, including the Tb. In general, experimentalata on property determination exists primarily for low molecular

∗ Corresponding author. Tel.: +91 22 2576 7245; fax: +91 22 2572 6895.E-mail address: adhikari@che.iitb.ac.in (J. Adhikari).

378-3812/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.fluid.2013.11.044

© 2013 Elsevier B.V. All rights reserved.

weight compounds or for larger molecules at low temperature; as athigher temperatures many compounds undergo thermal decompo-sition. Additionally, performing experiments to determine vapourliquid coexistence properties is expensive and time consumingbecause of the high pressures and temperatures involved. As analternative, the properties that are of interest to a molecule canbe found through quantitative structure property relationships [3]combined with equations of state (EoS) [4]; and also using molec-ular simulation techniques [5].

Quantitative structure property relationships facilitate the pre-diction of physical properties from the structure of a molecule.Joback and Reid [6], Constantinou–Gani [7] and Marrero–Gani (MG)[8] are some of the well-established group contribution meth-ods for prediction of pure component properties. The principle onwhich these methods are based is that the ‘structural aspects of thechemical components are always similar in different molecules’ [6].A wide range of thermodynamic and physical properties (such as Tb,�Hvap, Tc, Pc, critical volume (Vc), viscosity, surface tension, solubil-ity, etc.) can be predicted using these methods. However, it shouldbe noted here that these methods are “inherently approximate”[9] due to the assumption that a group contributes the same valuetowards the calculation of properties irrespective of the moleculeit is present in, and the position it occupies in the molecule. Amongthese methods, MG method has an ability to predict the propertyof a molecule with relatively low average absolute error as it takes

into account the second and third order groups contributions [10].In general, these methods are commonly used in computer aidedproduct design [11] studies to design a new molecule for specificproperty targets.

M. Harini et al. / Fluid Phase Equilibria 364 (2014) 6– 14 7

Nomenclature

API active pharmaceutical ingredientDFT density functional theoryEoS equation of stateGC group contributionGEMC Gibbs ensemble Monte CarloGI group interactionLJ Lennard-JonesMG Marrero–GaniMG–SR Marrero–Gani simultaneous regressionMG-SWR Marrero–Gani step wise regressionPAC phenylacetylcarbinolPR Peng–RobinsonSRK Soave–Redlich–KwongTraPPE–UA transferable potentials for phase

equilibria–united atomvdW van der WaalsVLE vapour–liquid equilibria

pttoFvthRtVvccrs

taaece[[apdtsiahoa0e1teeC

VTPR volume translated Peng–Robinson

In 1873, van der Waals presented the first cubic EoS [9], whichredicts the two phase region and critical phenomena with justwo parameters a and b. Although, this EoS is capable of describinghe effects like evaporation and condensation, the poor predictionsf liquid densities and vapour pressures are the main drawbacks.urther, development in cubic EoS from van der Waals (vdW) toolume translated Peng–Robinson (VTPR), has led to better predic-ions of liquid densities and vapour pressures. Extensive researchas been published in literature [4,12], employing VTPR [13], Pengobinson (PR) [14], Soave–Redlich–Kwong (SRK) [9] and vdW EoSo predict pure component and mixture VLE. The predictions fromTPR are found to be in good agreement with the experimentalalues when compared with other EoS [12]. These EoS require theritical properties as input parameters to compute the VLE of pureompound, which can be predicted from structure property cor-elations; and also can be calculated from the results of molecularimulation.

The molecular simulation approach, on the other hand, is usedo study the thermodynamic properties of molecules with rel-tively good accuracy, provided the parameters of force fieldre accurate. The TraPPE-UA (transferable potentials for phasequilibria–united atom) force field developed by Siepmann and hiso-workers, has been widely used in literature to predict phasequilibrium properties of different compounds such as alkanes15], ethers, ketones, aldehydes, glycols [16], carboxylate esters17], nitrobenzene, nitriles, pyridine[18]; and branched alkenes andlkylbenzenes [19]. The main idea behind this force field is that thearameters are transferable for a given interaction site betweenifferent molecules. For example, the Lennard–Jones (LJ) parame-ers ε/kB and � for a methyl united atom, once determined from aet of experimental data for compounds containing methyl groupsn it, will remain unaffected, whether the methyl group is part ofn alkane, alcohol, ketone, ester, etc. This idea of transferabilityas been applied to various organic compounds in the predictionf boiling points and is found to have deviations about 1–4% forlkanes [15] and alkenes [19]; 0.2–3.6% for ethers and glycols [16];.6–2.7% for ketones and aldehydes [16]; 0.8–1% for carboxylatesters [17]; 0.5–2% for nitrobenzene, nitriles, pyridine [18] and–5% for alkylbenzenes [19]. Moreover, even the group contribu-

ion methods are based on the same principle of transferability,xcept that these methods directly predict thermophysical prop-rties and not the equilibrium properties. Gibbs ensemble Montearlo (GEMC) technique [20] is a molecular simulation tool which

Scheme 1. Structure of PAC. 1–5 CH(aro), 6 C(aro), 7 CH, 8 O(hydroxyl), 9H(hydroxyl), 10 C(carbonyl), 11 O(carbonyl), 12 CH3.

has been widely used in literature [5,15–19] to predict VLE of purecomponents and mixtures.

Considering the commercial importance of the product (PAC),we have studied VLE using two different methods, EoS based onstructure property prediction (MG method) and molecular simula-tions (GEMC with TraPPE-UA force field). The organization of thearticle is as follows. The details on the use of MG property estima-tion method and various EoS have been discussed initially. Specificdetails of the TraPPE-UA force field and determination of unknowntorsional parameters by density functional theory (DFT) for PAC areprovided in the following section, along with the simulation detailson GEMC. In the subsequent section, the vapour–liquid coexistencecurve, vapour pressures and critical points for PAC as predicted byTraPPE-UA force field are presented. These findings are also com-pared with the predictions of various EoS. Finally, the conclusionsof this work are summarized in Section 4.

2. Methodology

This section describes the methodologies employed to deter-mine the vapour liquid coexistence curve of PAC. The structureof the PAC is shown in Scheme 1, along with the representationof various groups present in it. As the thermodynamic propertiesare identical for enantiomers [2], the united-atom representationwhich includes chirality, where non-existent hydrogen would takethe empty position around C7 carbon atom (as shown in Scheme 1)is acceptable for our study.

2.1. Structure property correlations

The determination of thermodynamic and physical propertiesof interest to predict VLE, using MG method [8] has been discussedhere. The property estimation model expression has the followingform,

f (X) =∑

i

NiCi + w∑

j

MjDj + z∑

k

OkEk (1)

where Ci, Dj, Ek are the contributions of the first, second and thirdorder groups of type i, j and k that occur Ni, Mj, Ok times, respec-tively. The left-hand side of Eq. (1), f(X) is a simple function of thetarget property X, such as exponential function of the ratio of prop-erty value to the adjustable parameter. The MG contributions ofvarious groups present in PAC for determination of Tb, Tc, Pc and Vc

are given in Table 1 and will be referred to henceforth as MG-2001.Further, as an extension to MG method, a recent study by Gani’s

group [21] has reported revised and improved model parametersfor pure components using MG method, which take into accountlarge data sets of experimentally measured property values of

various classes of molecules. Two sets of model parameters havebeen reported; one using simultaneous regression (MG–SR) andthe other by step-wise regression (MG–SWR) of the data sets. Inthe present work, we have compared the property estimations of

8 M. Harini et al. / Fluid Phase Equilibria 364 (2014) 6– 14

Table 1MG-2001 contributions for various groups in PAC [8].

Groups* Occurrence Contribution

First order (Ni) (Tb1i) K (Tc1i) K (Pc1i) bar (Vc1i) cm3/kmolCH(aro) 5 0.8365 2.0337 0.00726 45.39C(aro)–CH 1 0.8665 1.9512 0.011795 73.51OH 1 2.567 5.2188 −0.005401 30.61CH3CO 1 3.1178 7.0058 0.025227 127.99Second order (Mj) (Tb2j) K (Tc2j) K (Pc2j) bar (Vc2j) cm3/kmol

C(aro)–CH–OH 1 0.1005 −1.0107 0.002944 −0.25

aMso(Pi

T

T

(

(

[

acoptTkd

l

TV

incorporation of alpha function. This modification improved the

CH3–CO–CH–OH 1 −0.2987

* No third order groups are involved.

ll the existing model parameters for MG method i.e. MG-2001 [8],G–SR [21], and MG–SWR [21] in the literature. The model expres-

ions for Tb, Tc, Pc, Vc and acentric factor (ω) with the incorporationf adjustable parameters for MG method [8,21] are given belowEqs. (2) to (6)). The values of the model parameters Tb0, Tc0, Pc1,c2, Vc0, ωa, ωb and ωc for MG, MG–SR and MG–SWR are reportedn Table 2.

b = Tb0 ln

⎛⎝∑

i

NiTb1i +∑

j

MjTb2j +∑

k

OkTb3k

⎞⎠ (2)

c = Tc0 ln

⎛⎝∑

i

NiTc1i +∑

j

MjTc2j +∑

k

OkTc3k

⎞⎠ (3)

Pc − Pc1)−0.5 − Pc2 =

⎛⎝∑

i

NiPc1i +∑

j

MjPc2j +∑

k

OkPc3k

⎞⎠ (4)

Vc − Vc0) =

⎛⎝∑

i

NiVc1i +∑

j

MjVc2j +∑

k

OkVc3k

⎞⎠ (5)

exp(

ω

ωa

)]ωb − ωc =

⎛⎝∑

i

Niω1i +∑

j

Mjω2j +∑

k

Okω3k

⎞⎠ (6)

Several correlations for the prediction of vapour pressure arevailable in the literature (such as Miller, Riedel) [22]. Most of theseorrelations require the knowledge of Tb, Tc and Pc of the compoundf interest. Instead, by making use of Tb data alone, the vapourressure of pure component PAC has been estimated via group con-ribution (GC) and group interaction (GI) [23] as described below.his method estimates the slope of the vapour pressure curve withnowledge of a boiling point at a given pressure. The expression

escribing the temperature and vapour pressure is as follows:

og

(Psat

1 atm

)= (4.1012 + dB)

(Trb − 1

Trb − 1/8

)(7)

able 2alues of the adjustable parameters for MG method in literature [8,21].

Property\method MG-2001 MG-SR MG-SWR

Tc0 (K) 231.239 181.674 181.672Pc1 (bar) 5.9837 0.0519 0.0519Pc2 (bar−0.5) 0.1089 0.1155 0.1347Vc0 (cm3/mol) 7.95 14.62 28.00Tb0 (K) 222.543 244.789 244.517ωa (−) NA* 0.9132 0.9808ωb (−) NA 0.0447 0.1055ωc (−) NA 1.0039 1.0012

* NA—not available.

−0.394 −0.002912 5.17

where Trb = T/Tb, with Tb as the boiling point, (which is predictedby MG-2001 [8], MG–SR and MG–SWR parameters [21]); Psat is thesaturation vapour pressure, dB is the slope of the vapour pressurecurve and is calculated from group contributions as follows:

dB =(∑

i

NiCi + GI

)− 0.176055 (8)

where, Ni is the frequency of the group, Ci is the group contributionvalue of particular group i, GI is the total contribution of groupinteraction.

GI = 1n

m∑i=1

m∑j=1

Ci−j

m − 1(9)

where, Ci−j = Cj−i is the group contribution between group i andgroup j, n number of atoms (except hydrogen) and m total numberof interaction groups in the molecule. Table 3 reports the GC and GIcontribution values of various groups available in PAC molecule.

The predicted thermophysical properties by MG-2001 [8], MG-SR [21] and MG-SWR [21] parameters are used further as the inputparameters to study the VLE using various EoS, the details of whichare presented in the next section. Besides, the vapour pressuresas predicted by GC and GI are compared with results of GEMCsimulation in Section 3.

2.2. Equations of state

The simplicity and wide applicability of EoS method, from lightgases to heavy liquids, over broad ranges of temperature andpressure has made this method the most common approach topredict VLE behaviour. Table 4 lists the findings on the progres-sive improvement of cubic EoS along with the parameters. Thetwo constant a and b in vdW EoS correspond to attractive andrepulsive part. The attractive parameter has been further mod-ified by SRK as a temperature dependent parameter with the

prediction of vapour pressures although, resulted in inaccurateprediction of liquid densities. Further, Peng and Robinson sug-gested a slightly different attractive part, which imparted greater

Table 3GC and GI Contributions of PAC for determination of dB [23].

Groups (GC) Occurrences (Ni) Contribution (Ci × 103)

OH 1 758.4218C=O 1 255.848CH3 1 13.3063CH 1 45.7437CH(aro) 5 32.7177C(aro) 1 69.8796Ortho (correction) 1 −45.0531

Group (GI) Contribution (Ci−j × 103)OH–ketone −1181.5990

M. Harini et al. / Fluid Phase Equilibria 364 (2014) 6– 14 9

Table 4Cubic EoS with parameters [4].

EoS Expression Constants

vdW (1873) P = RTv−b

− av2 a = R2T2

c64Pc

b = RTc8Pc

SRK (1972) P = RTv−b

− a(T)v(v+b) a (T) = a˛ (T)

˛ (T) = [1 + (0.48 + 1.5746ωi − 0.17ω2i)(1 − T0.5

r,i)]

2

PR (1976) P = RTv−b

− a(T)v(v+b)+b(v−b) ˛ (T) = [1 + (0.37464 + 1.54226ωi − 0.2699ω2

i)(1 − T0.5

r,i)]

2

VTPR (1982) P = RTv+c−b

− a(T)(v+c)(v+c+b)+b(v+c−b) a (T) = 0.4572

R2T2c

Pc˛ (T) b = 0.0778 RTc

Pc

idwdfit

mpbiaia˛tattaa˛rev

˛

utruA(Ffuca

TG

angle, and the equilibrium bending angle, respectively. The bondlength and bond angle parameters (k� , �eq) are reported in Table 7.

mprovement in prediction of vapour pressures and better pre-iction of liquid densities. Later, VTPR EoS has been developed,hich takes into account the volume translation correction, c intro-uced by Peneloux et al. [24] and, also incorporates an alphaunction developed by Twu et al. [25]. This incorporation resultedn greater improvement of accuracy in prediction of liquid densi-ies.

The vapour liquid coexistence curve for PAC has been deter-ined using various EoS; the input parameters to which are

rovided by the predictions of structure property relationships,ased on group contributions. The vdW EoS requires Tc and Pc as

nputs to compute VLE; where as SRK and PR require Tc, Pc and ω;nd VTPR needs an additional input of Vc, so as to calculate Zc. Thesenputs are computed using parameters given by MG-2001, MG-SRnd MG-SWR as described in the previous section. In VTPR, the Twu

function (Table 4) has been chosen for an accurate description ofhe vapour pressures of the pure components. The parameters N, Mnd L are generally obtained by fitting the function to experimen-al pure component vapour pressures and, sometimes, additionallyo liquid heat capacities. Since, there is limited experimental datavailable for PAC, generalized Twu � parameters (N, M, L) obtaineds personal communication to the author [26] are used to compute(T) using Eq. (10). Further details on this generalization is given ineference [25] by Twu et al. Table 5 reports the value of the param-ters N, M and L which are used to compute ˛0(T) and ˛1(T) and thealue of ω is obtained from MG method [21] (MG-SR, MG-SWR).

(T) = ˛0 (T) − ω [˛1 (T) − ˛0 (T)] (10)

The EoS approach has been employed to determine VLE, whichses fugacity coefficients to account for the real behaviour in bothhe liquid and the vapour phase. Upon solving the cubic EoS, threeoots are obtained, of which the smallest root corresponds to liq-id volume and the largest root corresponds to vapour volume.n iterative procedure is performed until the computed fugacity

expression derived from EoS) [9] for both the roots are identical.urther, the liquid and vapour coexistence densities are computedrom corresponding volumes. The resulting vapour pressures, liq-id and vapour coexistence densities obtained from various EoS are

ompared with the results predicted by the molecular simulationpproach in Section 3.

able 5eneralized Twu parameters [26].

Case Generalized parameters ˛o ˛1

Tr > 1 N −0.20000 −8.00000M 4.963070 1.248089L 0.401219 0.024955

Tr ≤ 1 N 2.321304 2.808870M 0.918870 0.785345L 0.104877 0.511334

c = −0.252 RTcPc

(1.5448Zc − 0.4024)

˛(T) = TN(M−1)r exp[L(1 − TNM

r )]

2.3. Force field and simulation details

2.3.1. Force fieldThe force field employed to describe the interactions in PAC is

the TraPPE-UA force field. This force field has been used success-fully to determine VLE accurately for different organic compounds,including aromatic compounds [19]. In this force field, a unitedatom is defined, where all the hydrogen atoms connected to acarbon are grouped together to form a single interaction site. How-ever, the hydrogen bonded to a heteroatom such as in the hydroxylgroup has been treated as explicit. The structure of PAC with unitedatoms representation is shown in Scheme 1. The aromatic ring isassumed to be rigid as it has been reported in the literature [19], thatflexibility of bending and dihedral angles in aromatic rings haveshown a negligible effect on the accuracy of the VLE. The side chainis considered as semi-flexible; with fixed bond lengths, but withbending and torsional degrees of freedom. The TraPPE-UA forcefield accounts for both bonded and non-bonded interactions.

The non-bonded interactions are given by pair wise additive LJand Coulombic potentials for partial charges as given by Eq. (11).

u(rij) = 4εij

[(�ij

rij

)12

−(

�ij

rij

)6]

+ qiqj

4�εorij(11)

where rij, εij, �ij, qi and qj are the site-site separation distance, the LJwell depth, the LJ diameter, and the partial charges on united atomsi and j, respectively. Lorentz–Berthelot mixing rules are used todetermine parameters for LJ cross-interactions between differentunited atoms. These interactions are computed for intermolecularinteractions and intramolecular interactions of united atoms sep-arated by four or more bonds. The parameters for the non-bondedinteractions for PAC are listed in Table 6.

Rigid bond lengths are used for bonded interactions, while bondangle is controlled by a harmonic potential specified by

ubend = k�

2

(� − �eq

)2(12)

where k� , �, and �eq are the bending force constant, the bending

The following sets of cosine series expressions are employed fortorsional interactions of united atoms separated by three bonds and

Table 6TraPPE-UA parameters for non-bonded interactions for PAC.

Group ε/kB (K) � (Å) q (e) Reference

CH3 98.0 3.75 0.000 [16]CH 10.0 4.33 0.265 [16]O(hydroxyl) 93.0 3.02 −0.700 [16]C(carbonyl) 40.0 3.82 0.424 [16]O(carbonyl) 79.0 3.05 −0.424 [16]H(hydroxyl) 0.0 0.00 0.435 [16]C(aro) 21.0 3.88 0.000 [19]CH(aro) 50.5 3.695 0.000 [19]

10 M. Harini et al. / Fluid Phase Equilibria 364 (2014) 6– 14

Table 7TraPPE-UA force field parameters for bonded interactions of PAC.

Vibration Bond length R0 (Å) Reference

CH(aro)–CH(aro) 1.40 [19]CH(aro)–C(aro)C(aro)–CH 1.54 [19]CH–O(hydroxyl) 1.43 [27]O(hydroxyl)–H(hydroxyl) 0.945 [27]CH–C(carbonyl) 1.52 [16]C(carbonyl)–CH3

C(carbonyl)–O(carbonyl) 1.229 [16]Bending K�/2kB (K/rad2) �0 (deg) Reference

CH(aro)–CH(aro)–CH(aro) 1 × 10−05 120.0 [19]CH(aro)–CH(aro)–C(aro)CH(aro)–C(aro)–CH(aro)C(aro)–CH–O(hydroxyl) 25200.0 109.47 [27]C(carbonyl)–CH–O(hydroxyl)C(aro)–CH–C(carbonyl) 31250.0 112.0 [27]CH–O(hydroxyl)–H(hydroxyl) 27700.0 108.5 [27]CH–C(carbonyl)–O(carbonyl) 31250.0 121.4 [16]O(carbonyl)–C(carbonyl)–CH3

CH–C(carbonyl)–CH3 31250.0 117.2 [16]Torsion Constants (K) Equation type Reference

CH(aro)–CH(aro)–CH(aro)–CH(aro) – (13) [19]CH(aro)–C(aro)–CH(aro)–CH(aro)CH(aro)–CH(aro)–C(aro)–CH(aro)CH(aro)–CH(aro)–CH(aro)–C(aro)C(aro)–CH–O(hydroxyl)–H(hydroxyl) C0: 215.96 C1: 197.33 (14) [27]

3: −173.92 C1: −736.90 (14) [16]

3: −293.23

afinncOEf

u

t

u

u

u

tobpPbsole

Table 8Missing groups’ torsional parameters for PAC.

Torsion Constants (K) Equation

C(aro)–CH–C(carbonyl)–CH3 C0: 801.6 C1: 701.8 (16)C2: −190.9 C3: −134.1C4: 274.7 C5: 117.3

CH(aro)–C(aro)–CH–C(carbonyl) C0: 1034.0 C1: −2258.0 (15)O(hydroxyl)–CH–C(carbonyl)–O(carbonyl)

C0: 653.2 C1: 569.9 (16)C2: 156.0 C3: 2328.0C4: 0.37 C5: 2.71

O(hydroxyl)–CH–C(carbonyl)–CH3 C0: 734.3 C1: 647.0 (16)C2: −74.6 C3: −471.2

H(hydroxyl)–O(hydroxyl)–CH–C(carbonyl) C2: 31.46 CC(aro)–CH–C(carbonyl)–O(carbonyl) C0: 2035.58

C2: 57.84 C

re given by Eqs. (13)–(16). Eq. (13) is employed for rigid torsionsor all values of x; where, x varies from 1 to ntorloop. For example,n the aromatic ring of the PAC molecule, ntorloop stands for theumber of torsion loops, and is a variable which determines theumber of stable, equilibrium values for the torsion angle. In theurrent case, ntorloop is taken to be 1. Eqs. (14) and (15) are thePLS cosine series and TraPPE simple cosine series, respectively.q. (16) corresponds to Compass cosine series generally employedor asymmetric torsions.

torsion () ={

∞ if∣∣ − C(x)

∣∣> C0

0 otherwise(13)

where is the torsion angle, C(x) is the equilibrium value oforsion angle and tolerance (C0) is taken to be 3.1459 K.

torsion () = C0 + C1 [1 + cos()] + C2 [1 − cos(2)]

+ C3 [1 + cos(3)] (14)

torsion () = Co (1 − cos (2 [ − �])) + C1 (15)

torsion () = Co (1 − cos ( − C3)) + C1 (1 − cos (2 ( − C4)))

+ C2 (1 − cos (3 ( − C5))) (16)

The equations and the values of the parameters used to describehe various dihedrals in PAC are given in Table 7. However, somef the dihedrals (shown in Table 8) present in PAC have noteen reported in literature previously. These additional torsionalotentials are necessary to model the conformational behaviour ofAC accurately. Parameters for missing torsional potentials haveeen determined using the DFT approach. This approach has been

uccessfully used to determine missing torsions in various otherrganic compounds including organic cyclic molecules [28], acry-ates [29], cyclic alkanes and ethers [30], etc. Scans of the potentialnergy surface have been performed at 5◦ interval from −180◦

C4: -175.6 C5: 178.1CH(aro)–C(aro)–CH–O(hydroxyl) C0: 966.3 C1: −100.3 (15)

to 180◦ at the B3PW91 level of theory [31] using 6 – 31++G(d,p)basis set using the Gaussian 03 software [32]. The coefficientsin Eqs. (15) and (16) are determined by fitting the equations tothe DFT derived potential energy surfaces with the curve fittingtoolbox (cftool) in Matlab®. Fig. 1 shows the torsional energyfrom potential energy scans as a function of dihedral angle forC(aro)–CH–C(carbonyl)–CH3. As observed from Fig. 1, the compasscosine series equation (Eq. (16)) is in excellent agreement withDFT derived results. The slight discrepancy in the fit observed atthe second maxima is similar to that reported in literature for DFTcalculated torsional energies of ethers and esters [33].

2.3.2. Molecular simulationThe MCCCS Towhee package [34,35] version 7.2 has been used to

perform all molecular simulations reported in this study. To deter-mine the VLE data for PAC, constant (total) volume Gibbs ensembleMonte Carlo [20] (GEMC-NVT) simulations have been performed ina temperature range of 375 K to 600 K at intervals of 25 K. There aretwo simulation boxes (one representing the liquid phase and the

other a vapour phase) with no interface. Initial configurations ofmolecules are arranged in simple cubic lattices with 260 moleculesin liquid box and 40 in the vapour box. Periodic boundary condi-tions have been applied in all three directions of the cubic box.

M. Harini et al. / Fluid Phase E

Fig. 1. Torsional energy as a function of dihedral angle of PAC forCsE

Auta

aGubcp1

omocTi

3

m3taaf

3

p(i

TP

(aro)–CH–C(carbonyl)–CH3. Potential energy scans at B3PW91/6 – 31++G(d,p) arehown as open circles. The solid line is the fit to the cosine series represented byq. (16) to the DFT data.

cut-off distance of 14 A with analytical tail correction has beensed. Coulombic interactions are computed using Ewald summa-ion method and the parameters corresponding to these are chosens recommended by Towhee manual [34].

Criteria for VLE include equality of temperatures, pressuresnd molar Gibbs free energies of the two coexisting phases.EMC-NVT method satisfies the criteria for VLE by performing vol-me exchange moves, inter box particle exchange moves, intraox particle swap moves, aggregation bias volume moves [36],onfigurational biased Monte Carlo moves, center of mass dis-lacement moves and rotational moves in the frequency ratio0:10:5:5:20:25:25.

Each GEMC-NVT simulation has been allowed to equilibratever 200,000 Monte Carlo cycles and averages have been deter-ined over the subsequent 100,000 production cycles. Block size

f 1000 Monte Carlo cycles have been used to calculate the statisti-al uncertainties (standard deviation) during the production runs.he analyses of the GEMC-NVT simulation predictions are reportedn Section 3.2.

. Results and discussion

An extensive literature survey has shown that limited experi-ental vapour pressure data is available for PAC [2] at temperatures

39 K and 409 K, as well as the Tb of 479 K. We have attemptedo generate VLE data for PAC, required in process design, by EoSpproach using MG-2001, MG-SR and MG-SWR parameters and,lso, molecular simulations. The discussion based on the resultsrom both the methods is given below.

.1. Structure property correlation

To verify the accuracy of the MG method in this case, we firstredicted the Tb of PAC to enable comparison with experimentTable 9) using MG-2001, MG-SR and MG-SWR parameters. Its found that the Tb is ∼45 K higher than the value reported in

able 9roperty data as predicted by MG method and GEMC-NVT simulation.

Property GEMC-NVT MG MG

Tb (K) 511 (2) 524 (6) 526Tc (K) 763 (4) 724 (6) 723Pc (bar) 35 (1) 37.9 (9) 37 (Vc (cm3/mol) 450 (1) 456 (8) 454ω 0.310 (8) NA* 0.89

* NA—not available.

quilibria 364 (2014) 6– 14 11

literature. Thus, the MG method is overestimating the Tb. The MGmethod has also been used to determine the Tc, Pc, Vc and ω asreported in Table 9. Fig. 2(a) shows the ln P vs 1/T plot determinedfrom GI method; with Tb predicted from MG method (Eq. (2)) asthe input parameter in Eq. (7), to predict the vapour pressure.The predictions of vapour pressure using GI with Tb as input fromMG-2001, MG-SR and MG-SWR coincide, as the Tb predicted fromthese parameters show less deviation among each other (Table 9).Also, the GI predictions match well with the experimental dataas temperature increases (as shown in Fig. 2(a)). Further, bymaking use of critical property data and ω value (when required)as estimated using MG-2001, MG-SW and MG-SWR parameters;the vapour liquid coexistence curves have been determined usingvarious EoS such as, SRK, PR and VTPR. The coexistence vapourphase densities as predicted by PR and VTPR EoS are in excellentagreement and SRK EoS consistently overestimates both PR andVTPR predictions (Figs. 3 and 4). For the liquid phase, SRK consis-tently underestimates the coexistence densities as compared toPR and VTPR (Figs. 3 and 4). The agreement between PR and VTPRpredictions improve as temperature increases with the use of MG-SR parameters (Fig. 3). The predictions of VTPR using MG-2001,MG-SW and MG-SWR parameters coincide with each other.

3.2. Molecular simulations

The wide variations in the coexistence liquid densities as pre-dicted by different EoS (with the same Tc, Pc, Vc and ω values as inputparameters), as shown in Figs. 3 and 4 provides the motivation toinvestigate the VLE using molecular simulation tools to allow us tocarry out a fundamental study, the accuracy of which is limited bythe force field selected. TraPPE-UA has been successfully employedpreviously to determine VLE of various organic compounds [16–19]and hence, we have chosen TraPPE-UA as the force field to describeall the interactions to model PAC.

Single box NPT Monte Carlo simulation has been performed atroom temperature (300 K) and atmospheric pressure (101.325 kPa),to compute the density of PAC. The density obtained from simula-tion (1.07 g/cm3) is found to be in good agreement with theoreticalvalue reported in literature [37] (1.119 g/cm3). Hence, it can bepresumed that the TraPPE-UA force field is adequately accurate topredict the VLE of PAC. The properties predicted by performing con-stant volume GEMC include saturation pressure, Tb, �Hvap, liquidand vapour coexistence densities and critical properties.

Fig. 2 illustrates a comparison of simulation generated vapourpressures with the predictions of GI method, various EoS for a tem-perature range of 300 K to 600 K and the available experimentaldata. It can be observed that at low temperatures the predictionsby molecular simulations and GI match well, thereafter above 525 Kthe deviation between the two predictions increase (Fig. 2(a)).Whereas, the predictions of PR and VTPR EoS match well with GEMCpredictions at high temperatures and deviate significantly at lowtemperatures (Fig. 2(b)). The SRK EoS constantly overestimates the

vapour pressures. Although, it is to be noted that the slope of lnP versus 1/T curve as predicted by SRK EoS and GEMC predictionsmatch well. The deviation in the predictions of SRK and PR EoSfrom molecular simulations could be due to the wide variation in

-SR MG-SWR Experimental [2]

(6) 527 (6) 479 (1) (8) 723 (8) NA*

1) 41 (1) NA (8) 454 (8) NA(5) 0.95 (5) NA

12 M. Harini et al. / Fluid Phase Equilibria 364 (2014) 6– 14

Fig. 2. Comparison between vapour pressures from (a) GI method and (b) EoS approach with GEMC simulations obtained in this work and experimental data [2].

input

tmacttbpSif

b

Fig. 3. Comparison of predicted densities of PAC from various EoS (using

he ω value as predicted from MG-SR, MG-SWR parameters andolecular simulation (Table 9). Furthermore, this deviation can be

scribed to the drawback of SRK EoS as stated earlier in this arti-le. In addition, the deviation can also be attributed partially tohe use of structure property predictions, due to the shortcomingshat occur because of the inherently approximate nature of the GCased calculations. The predicted vapour pressures using MG-SWRarameters match with the estimated vapour pressures using MG-R parameters and hence, are not shown in Fig. 2(b). With increase

n temperature, the GEMC and GI predicted vapour pressures areound to be in good agreement with experimental data.

In the molecular simulation predictions, the accuracy is limitedy that of the TraPPE-UA force field. However, as noted previously,

Fig. 4. Comparison of predicted densities of PAC from various EoS (using inputs

s from MG-SR parameters, MG-2001 parameters) and GEMC simulation.

as only limited experimental data is available, these methodsallow us to estimate the VLE of PAC as the first step towardsthe development of solvent extraction methods. The Tb deter-mined from molecular simulation is around 510 K, which liesbetween the prediction of the MG method and that reportedfrom experiment (Table 9). This mismatch in GEMC predictedTb value from experiment can be due to the limitations ofthe TraPPE-UA force field. As also mentioned in the introduc-tion, TraPPE-UA force field predictions of the Tb are known to

deviate from experiment by 3% for benzene to almost 5% too lowfor naphthalene. In case of PAC, the Tb predicted by this force field isoverestimated by 6% which is unlike the generally underestimatedTb reported by Wick et al. [19] for alkylbenzenes. However, as the

from MG-SWR parameters, MG-2001 parameters) and GEMC simulation.

M. Harini et al. / Fluid Phase E

Fpt

dbromufM

fsvrrdwEtplmhsGncta6

pla(wvni

meb(wo

ig. 5. Estimated heat of vaporization of PAC obtained from GEMC simulation com-ared with the predictions of Riedel equation estimation at Tb . The line is a guide tohe eye.

eviation in Tb is less than 10% we conclude that the VLE predictedy GEMC-NVT simulations (in conjunction with TraPPE-UA) iseasonably accurate. Fig. 5 presents the estimated value of �Hvap

f PAC for the specified temperature range. A comparison has beenade with �Hvap as predicted by Riedel equation at boiling point

sing MG-2001, MG-SR and MG-SWR parameters. As observedrom Fig. 5, the value of �Hvap has been underestimated when

G-SR and MG-2001 parameters are employed.As experimental data on coexistence densities is not available

or PAC, the pure component saturated vapour and liquid den-ities computed from molecular simulations are compared witharious EoS. Figs. 3 and 4 report the VLE of PAC for a temperatureange of 300 K to 800 K by using MG-SR and MG-SWR parameters,espectively. On comparison, from Figs. 3 and 4, VTPR predictedensities are in good agreement with molecular simulation results,hen compared to SRK and PR EoS. It can be seen that the SRK

oS predictions underestimate the liquid densities as comparedo that from GEMC significantly while overestimating the vapourressures (Fig. 2). On the other hand, PR predictions overestimate

iquid densities when compared to GEMC predictions while esti-ating comparable vapour pressures (Fig. 2). However, we note

ere that the force field based GEMC predictions may not be theame as may possibly be determined from experiments. As theEMC method cannot be used when the temperatures approachear the critical temperature [5], the molecular simulation dataould not be computed at temperatures beyond 600 K. We observehat the densities of both the liquid and vapour phases are similarnd the boxes representing the two phases switch identities above00 K.

Furthermore, to determine the critical properties, the pure com-onent GEMC generated VLE data is fitted to the density scaling

aws using an Ising-type exponent. The scaling law for density near critical point is given by,

�liq − �vap

2

)= a0

(1 − T

Tc

)ˇ

(17)

here �liq is the coexistence liquid density, �vap is the coexistenceapour density, Tc is the critical temperature, is the critical expo-ent and a0 is a fitting constant. For a 3-D Ising fluid, the value of ˇ

s 0.325.The critical point for a pure component system can be deter-

ined by fitting the coexistence densities to the density scaling lawquation along with the law of rectilinear diameters and is giveny, ) ( )

�liq + �vap

2= �c + b1 1 − T

Tc(18)

here, �c is the critical density and b1 is a constant. The valuef a0 and b1 are found to be 0.6389 g/cm3 K� and 0.3497 g/cm3,

quilibria 364 (2014) 6– 14 13

respectively. The Tc and �c from GEMC simulation are found to be763.0 K and 0.333 g/cm3, respectively. The Pc has been estimatedby fitting the vapour pressure data to Antoine equation and ω iscalculated from vapour pressure data corresponding to reducedtemperature, Tr (=T/Tc) of 0.7. The ω value determined by molecularsimulation (Table 9) deviate significantly (∼67%) from the predic-tions of MG-SR and MG-SWR parameters. The literature reportedω values for aromatic compounds such as ethylbenzene, toluene,phenol and o-xylene are 0.303, 0.262, 0.310 and 0.444, respectively[22]. These ω values lie in the range of GEMC predicted ω value forPAC. Thus, we believe that the molecular simulation predictionsare relatively accurate as compared to MG predictions. The GEMCpredicted Tc value (reported in Table 9) overestimate MG methodpredictions by less than 5.24%; while Pc, Vc and Tb values have beenunderestimated by a maximum of 17.14%, 1.33% and 3.13%, respec-tively. It may be noted here that the deviations are measured asthe percentage of the absolute value of the difference in the GEMCpredictions and the corresponding MG method estimates relativeto the GEMC predicted values and only the maximum deviationsare reported here.

4. Conclusion

The modelling of VLE is an important source of uncertainties inchemical industry for the design of various separation processessuch as distillation, stripping and solvent extraction. The thermo-physical properties of PAC, determined using structure propertycorrelations and molecular simulation techniques, in the absenceof extensive experimental data have been reported in this study. Instructure property correlations, MG method reported parameters(viz, MG-2001, MG-SR, MG-SWR) have been utilized to determinethe critical properties and the boiling point of PAC. Further, VLE hasbeen determined by the use of various EoS by making use of thepredicted critical property data. Alternatively, GEMC-NVT simula-tions have been carried out to determine VLE and the critical point,where unknown torsions of the PAC molecule (modelled usingTraPPE-UA force field) have been determined from DFT approach.There is an excellent agreement in the coexistence vapour densitiesfrom molecular simulation, PR and VTPR EoS. The estimated coex-istence liquid densities from molecular simulation match well withthe predictions of VTPR EoS using MG-2001, MG-SR and MG-SWRparameters. However, the coexistence liquid densities as predictedby the MG parameters in the VTPR EoS show larger deviation fromGEMC results at low temperatures. The vapour pressures as pre-dicted by GI method and GEMC simulations are comparable to theexperimental data with increase in temperature. The normal boil-ing point temperature determined from molecular simulation isfound to lie in between the predictions of the MG method and theexperimentally reported data.

Acknowledgements

The author M. Harini is grateful to Council of Scientific andIndustrial Research (CSIR), New Delhi for financial support. We,also, thank Computer Centre at Indian Institute of Technology, Bom-bay for providing the computational resources.

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