et

loEG-Cwest

namy wtheionerimto a

eling point of view. Indeed, there have been a number ofsimulations of acetone in water at room tea variety of force elds. The results of thesto a discussion on their validity, in particula

Pereraof difacetonhich i(KBi)

tions. In Eq. (1), Gij represents the KBi between species i and j, cal-culated from the radial distribution function gij(r). Perera andSokolic report a quantitative agreement of the KBi for the KBFF-SPC/E mixture with the experimental values.

Jedlovszky et al. [5] published a work with an eye-catching title:Can existing models qualitatively describe the mixing behavior of ace-tone with water? where the Helmholtz free energy of acetone

kBT @xa

that the different results are just the manifestation of the limita-tions of the calculation techniques. It is our opinion that there issome truth in both arguments, which points out the difculty pre-sented by the problem. On the other hand, simple visual inspectionof the evolution of the system can be used to safely rule out modelsthat display separation, but the apparent mixing does not ensurethermodynamic stability. In conclusion, more studies are neededin order to develop a reliable model to accurately represent ace-tonewater solutions.

The electronic polarization of a single acetone molecule inwater was studied by Georg et al. [10] using an iterative procedure

Corresponding author.E-mail addresses: pereyra@famaf.unc.edu.ar (R.G. Pereyra), asar@famaf.unc.e-

Chemical Physics Letters 507 (2011) 240243

Contents lists availab

y

.edu.ar (M.L. Asar), cari@northwestern.edu (M.A. Carignano).Gij 4p1

0gijr 1

r2dr; 1

showed that with the exception of the combination KBFF-SPC/E, allmodels exhibited phase separation in a certain range of acetonemolar fraction (0.30.7). This demixing was found by studying themicroscopic structure of the system. The non-mixing modelsshowed a considerable clustering of both species, quite evidentfrom the snapshots corresponding to the nal state of the simula-

the original results for the KBFF-SPC/E models was further ana-lyzed by Kang et al. [8]. Even though Jedlovszky et al. used thermo-dynamics integration to calculate D, their method required the useof a tting function that, according to Kang et al. may lead to erro-neous conclusions. Jedlovszky et al. [9] argued about the difcultyin the calculation of the KBi, and the amplication of the errorsresulting from an imperfect determination of the radial distribu-tion functions in the large distance limit. The methods employedby both group of researchers are formally correct and it is possibleing of the model acetone and water.acetonewater mixtures using a setwater (SPC/E [6] and TIP4P [7]) andand KBFF [3]) models. Their study, wtion of the KirkwoodBuff integralsZ0009-2614/$ - see front matter 2011 Elsevier B.V. Adoi:10.1016/j.cplett.2011.04.015mperature [15] usinge simulations gave riser in relation to the mix-and Sokolic [4] studiedferent combinations ofe (FHMK [1], OPLS [2]s based on the calcula-

where Aex is the excess Helmholtz free energy of the mixture withrespect to ideal mixing, xa is the acetone molar fraction, kB is theBoltzmann constant and T is the absolute temperature. A positiveD is necessary to guarantee the stability of the mixture and Je-dlovszky et al. concluded that both systems were thermodynami-cally unstable because D is negative for both cases.

The contradiction between the results of Jedlovszky et al. withD 1 2 ; 2The role of acetone dipole moment in ac

Rodolfo Guillermo Pereyra a, Maria Lila Asar a, Marcea Facultad de Matemtica, Astronoma y Fsica, Universidad Nacional de Crdoba and IFbDepartment of Biomedical Engineering and Chemistry of Life Processes Institute, North

a r t i c l e i n f o

Article history:Received 12 February 2011In nal form 4 April 2011Available online 7 April 2011

a b s t r a c t

We present a molecular dydency of the excess enthalpacetone dipole moment asexcess enthalpy as a functorder to reproduce the expinclude many body terms

1. Introduction

Atomistic simulations of acetonewater solutions have receiveda moderate but continuous attention during the last two decades.Being a textbook example of two miscible liquids, it is very inter-esting the level of difculty that the system presents from a mod-

Chemical Ph

journal homepage: wwwll rights reserved.onewater mixture

A. Carignano b,*

ONICET, Medina Allende s/n, Ciudad Universitaria, X5000HUA Crdoba, Argentinaern University, 2145 Sheridan Road, Evanston, IL 60208, USA

ics simulation study of acetonewater solutions. We focus in the depen-ith the acetone molar fraction. We found that by gradually increasing thesystems gets diluted, the simulations capture the correct behavior for theof acetone molar fraction and temperature. Our results suggest that, inental data for the excess enthalpy, it is necessary to use force elds that

ccount for the polarization of the acetone molecule. 2011 Elsevier B.V. All rights reserved.

water mixtures for two model combinations (KBFF-TIP4P andKBFF-SPC/E) was calculated using the thermodynamic integrationmethod. The authors studied the thermodynamic stability of thesemixtures using the D parameter dened as

xa1 xa @2Aex

le at ScienceDirect

sics Letters

l sevier .com/locate /cplet t

modied charge distribution, hereafter referred to as CHARM-M27aq. We want to emphasize that we are not proposing a new

The calculation of the average enthalpy of the system was per-

xing a = 1. The magnitude of a increases as water is added to

Table 1Acetone molar fraction (xa) and number of acetone (Na) and water(Nw) molecules for all simulated systems.

xa Na Nw

0.00 0 16000.01 16 15840.05 80 15200.10 160 14400.20 320 12800.30 480 11200.40 640 9600.50 800 8000.60 960 6400.70 1120 4800.80 1280 3200.90 1440 1600.95 1520 800.99 1584 161.00 1600 0

0.0 0.2 0.4 0.6 0.8 1.0x

a

-0.8

-0.4

0.0

0.4

0.8

1.2

1.6

hex

[kJ/m

ol]

Figure 1. Excess enthalpy for the acetonewater solution as a function of theacetone molar fraction. The dashed blue line corresponds to experimental data [14],the black circles are simulation results with CHARMM27 model, and the reddiamonds correspond to the modied CHARMM27aq model. The two green

hysics Letters 507 (2011) 240243 241model for acetone to be used in general simulations. This is ratheran ad hoc model intended to illustrate the effect of dipole momentand to be used within the scope of this Letter. To represent thewater molecules, we use the TIP5P-E model [17], which performwell in an ample range of temperature including the supercooledregime and standard ambient conditions. The original CHARMM27model is an all atom model already used by Martin and Biddy [18]to study vapor pressure and heat of vaporization of pure acetone. Adetailed description of this model can be found elsewhere [16,18]and here we only recall its charge distribution: 0.55e on the centralcarbon neutralized by an opposite charge on the oxygen atom, themethyl groups carry 0.27e on the carbons and 0.09e on eachhydrogen. The resulting equilibrium (it is a exible model) dipolemoment is 3.68 D.

Molecular dynamics simulations of acetonewater mixtureswere performed with the Gromacs simulation package, v.4.5.1[19]. All simulations were performed in the NPT ensembles, witha total of N = 1600 molecules in a cubic box with periodic bound-ary conditions. The numbers of acetone and water molecules wereselected to represent 15 different concentrations, varying the ace-tone molar fraction from 0 to 1, as detailed in Table 1. The dynamicequations were integrated with the leap-frog algorithm with atime step of 0.001 ps and the temperature was controlled using aNoseHoover thermostat with a time constant of 0.1 ps. The isotro-pic pressure coupling was done using the Parrinello-Rahman algo-rithm with a time constant of 0.1 ps. A spherical cutoff at 0.9 nmwas imposed for all LennardJones and short-range electrostaticinteractions, and the long-range electrostatic interactions were ac-involving a sequential application of Monte Carlo and QuantumMechanics methodologies. When the calculations converged toan electrostatic equilibrium, the acetone dipole moment (la)reached the value of 4.8 D, which represents an increase of 60%with respect to the gas phase value (2.9 D). This result can be ex-plained in terms of the high dielectric constant of the medium(w = 78) surrounding the acetone [11] and is consistent with thedipole moment of 3.3 D corresponding to neat liquid acetone(a = 20). At this point, it is important to note that the dipole mo-ments of the OPLS and KBFF models are 2.35 D and 3.31 D, respec-tively. Moreover, both groups of researchers (Perera-Sokolic andJedlovszky et al.) have agreed that the OPLS acetone does notmix with water and the controversy involves the KBFF acetone.

The thermodynamic properties of solutions are often analyzedin terms of excess functions. Among them, the excess enthalpy isan experimentally accessible quantity. There are several calorimet-ric studies about the acetonewater mixture [1215], where theexcess enthalpy has been measured in a wide range of concentra-tions and several temperatures. Moreover, Perera and Sokolic [4]suggested that in order to build force elds it is more advisableto consider excess quantities rather than tting the energy anddensity to their experimental values. In this work, we analyzethe excess enthalpy for an acetone/water mixture as a functionof concentration and the acetone dipole moment. We found thata concentration dependent acetone dipole moment is key in orderto reproduce the experimental excess enthalpy. An increasing di-pole moment for decreasing acetone concentration favors the mix-ing of the solution.

2. Computational details

For this work we use the CHARMM27 acetone model [16] with a

R.G. Pereyra et al. / Chemical Pcounted for using the PME algorithm. In all cases, the total simula-tion time was 10 ns, and the rst 2 ns was discarded from theanalysis to allow for the equilibration.the system as it is discussed below.

3. Simulations results

Figure 1 summarizes the results for the excess enthalpy hex

(=Hex/N) as a function of the acetone molar fraction xa, calculatedat a temperature of 300 K and a pressure of 1 atm. The dashed blueline represents the experimental values reported by Benedetti et al.[14] and the black circles are the results of simulations using theCHARMM27 acetone in combination with TIP5P-E water. The sim-ulations produced a positive hex over the whole range of concentra-formed using the usual thermodynamic equation:

hHi hUi phVi 3

where the angular brackets indicate time average, U is the internalenergy of solution, p the reference pressure of the simulations and Vthe volume.

In order to modify the dipole moment of the originalCHARMM27 acetone, we scaled all the charges in the model by afactor a. For the pure acetone system, we maintain the model bydiamonds indicate the values explicitly adjusted. (For interpretation of thereferences to colour in this gure legend, the reader is referred to the web versionof this article.)

tions, but the experimental data switch from positive values forconcentrated acetone solutions (high xa) to negative values fordilute solutions (low xa). The shape of the excess enthalpy curveobserved in the experiments can be interpreted in terms of the rel-ative interaction strength between components of the system. Forthe dilute limit, the acetoneacetone interaction being weakerthan the acetonewater interaction results in a negative excess en-thalpy. For the acetone rich limit, the waterwater interactionbeing stronger than the acetonewater interaction results in a po-sitive excess enthalpy. One possible source for the discrepancies isthe incorrect treatment of the molecules vibrations. However theeffect of the vibrations is very small, as calculated by Jancs [20].Considering the work of Georg et al. [10], we propose a continuousincrement of the acetone dipole moment. From a physical point ofview, this polarization of the acetone molecules is a response to thehigh dielectric constant of the water. Here we force the polariza-tion by scaling the charges of the model acetone by a factor a

unmodied model. For high molar concentrations the two modelsare very similar each other and produce essentially the same diffu-sion coefcient.

280 300 320 340 360T [K]

-0.8

-0.4

0.0

0.4

0.8

hex [k

J/mol]

Figure 3. Excess enthalpy as a function of temperature for three different acetonemolar fraction: xa = 0.2 (black symbols), 0.4 (red symbols) and 0.6 (green symbols).The lled circles are the simulation results calculated with CHARMM27aq, and opensquares are the experimental data of Lwen and Schulz [15]. (For interpretation of

0.0 0.2 0.4 0.6 0.8 1.0x

a

800

850

900

950

1000

[k

g/m3 ]

Figure 4. Density of the acetonewater solution as a function of acetone molarfraction. The blue open squares correspond to experiments [21], black circles are

242 R.G. Pereyra et al. / Chemical Physics Letters 507 (2011) 240243(>1). The criterium used to select the scaling factor a and its depen-dency with acetone molar fraction xa is to reproduce, as best aspossible, the experimentally determined excess enthalpy forxa = 0.5 and xa = 0.2. Using these two xed values, and forcinga = 1 for xa = 1 we obtain a quadratic equation foraxa 0:0883 0:2385xa 1:1502x2a . With this concentrationdependent model, the excess enthalpy ts extremely well theexperimental data as is also displayed in Figure 1. No signs of seg-regation were observed during the simulations at any concentra-tion, whether by visually inspecting the trajectory or analyzingthe time stability of the potential energy and total density.

In Figure 2 we show the acetone dipole moment as a function ofacetone molar fraction, calculated with CHARMM27aq. From thepure acetone to the innitely dilute limit, there is an increase ofthe dipole moment from 3.68 D to 4.19 D. This last value is notas high as the one predicted by Georg et al. [10], but our resultsin line with their ndings. Our results suggest that in order toreproduce the excess enthalpy, it is necessary to have a modelfor which the dipole moment increases as the dilution increases.In other words, polarization effects on the acetone molecule arevery important, and its neglect leads to the wrong dependency ofexcess enthalpy with the acetone molar fraction.

In Figure 3 we show the excess enthalpy as a function of tem-perature for three different acetone molar concentrations, calcu-lated with the CHARMM27aq model. In order to compare withexisting experimental results, these simulations were performedat a pressure of 4 atm, although the differences with the resultscorresponding to 1 atm are not very signicant. Experimentaland simulations results show a monotonic increase in the excess

0.0 0.2 0.4 0.6 0.8 1.0x

a

3.6

3.8

4.0

4.2

a [D

]Figure 2. Average dipole moment of the acetone molecules as a function of theacetone molar fraction.enthalpy with increasing temperature. The agreement betweenthe simulations and experiments is very good for the whole tem-perature range and the three studied concentrations.

In Figure 4 we show the density of the solution as a function ofits composition, for systems at 300 K and a pressure of 1 atm. Eventhough the original and modied models produce qualitativelysimilar results, the modied model gives a much better predictionof the density, especially for the xa < 0.8. The increase of the ace-tones dipole favors a tighter acetonewater interaction with theresults of a larger density than the original model. Finally, weinvestigate the effect of the increase of the dipole moment onthe diffusion coefcient of acetone. The results are shown in Figure5. The experimental values display a minimum at xa = 0.18. Thesimulations capture the presence of a minimum, however thedependency of D with xa is weaker than in the experiments. It isimportant to note that for dilute solutions the CHARMM27aqmod-el gives values of D closer to the experimental ones than the

the references to colour in this gure legend, the reader is referred to the webversion of this article.)the simulation results using the CHARMM27 model and the red diamond is theresults of the present work. (For interpretation of the references to colour in thisgure legend, the reader is referred to the web version of this article.)

4. Discussion

The development of force elds for atomistic simulations usu-

molar fraction from 3.68 D for pure acetone to 4.19 D for the in-nite dilution limit, which represent an increment of 14%. This is areasonable charge redistribution if we consider that the dielectricconstant of the systems increases from 20 to 78. It is importantto mention that we have attempted to reproduce the experimentaldependency of hex with xa without changing the model parameterswith the systems composition. However, it was not possible for usto nd appropriate model parameters to obtain at least the quali-tative behavior displayed by the experimental curve.

Acknowledgments

Marcelo Carignano acknowledges the support from NSF (GrantCHE-0957653).

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0.0 0.2 0.4 0.6 0.8 1.0x

a

1

2

3

4

5D

[10-9

m

2 s-

1 ]

Figure 5. Diffusion coefcient of acetone as a function of acetone molar fraction.The blue open squares correspond to experiments [22], black circles are thesimulation results using the CHARMM27 model and the red diamond is the resultsof the present model.

R.G. Pereyra et al. / Chemical Physics Letters 507 (2011) 240243 243ally involves quantum mechanical calculations, and comparisonof simulation results with experimental measurements in orderto rene the model parameters. Currently there are several forceelds libraries that can be used, with a different degree of success,for basically any molecule of interest. In the great majority of cases,force elds are constructed out of pair additive terms, with nomany body corrections or local effects to account for the particularenvironment surrounding a given molecule. The case of acetone inwater is one of those situations in which many body effects appearto be necessary in order to properly describe the system. Our workshows that a gradual increment of the acetone dipole moment, asthe system gets diluted, leads to the correct dependency of the ex-cess enthalpy. The increment is almost linear with the acetone[8] M. Kang, A. Perera, P.E. Smith, J. Chem. Phys. 131, 157101.[9] P. Jedlovszky, A. Idrissi, G. Jancs, J. Chem. Phys. 131 (2009) 157102.[10] H.C. Georg, K. Coutinho, S. Canuto, Chem. Phys. Lett. 429 (2006) 119.[11] G. Oster, J. Am. Chem. Soc. 68 (1946) 2036.[12] B.A. Coomber, C.J. Wormald, J. Chem. Therm. 8 (1976) 793.[13] M.A. Villaman, H.C. van Ness, J. Chem. Eng. Data 29 (1984) 429.[14] A.V. Benedetti, M. Cilense, D.R. Vollet, R.C. Montone, Thermochim. Acta 66

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The role of acetone dipole moment in acetonewater mixtureIntroductionComputational detailsSimulations resultsDiscussionAcknowledgmentsReferences