Thermodynamic Analysis of Systems Formed by ... - ACS Publications

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Ind. Eng. Chem. Res. 2010, 49, 12726–12739

Thermodynamic Analysis of Systems Formed by Alkyl Esters with r,ω-Alkyl Dibromides: New Experimental Information and the Use of a Dense Database to Describe Their Behavior Using the UNIFAC Group Contribution Method and the COSMO-RS Methodology Ana Navas, Juan Ortega,* and Toma´s Martıń† Laboratorio de Termodina´mica y Fisicoquı´mica de Fluidos, Parque Cientı´fico-Tecnolo´gico, UniVersidad de Las Palmas de Gran Canaria, Canary Islands, Spain

Jose´ Palomar Seccioń de Ingenierıá Quı´mica (Dpto. de Quı´mica-Fisica Aplicada), UniVersidad Autońoma de Madrid, Cantoblanco, 28049 Madrid, Spain

This is a theoretical study carried out on the experimental data obtained for 90 binary systems comprised of alkyl esters with dibromoalkanes, using data from previous publications and those corresponding to 20 mixtures presented here. The experimental part of this work corresponds to experimental measurements of HEm and VEm at T ) 298.15 K and atmospheric pressure for systems containing propyl alkanoates (methanoate to butanoate) with 1,ω-dibromoalkanes (ω ) 2-6). The systems containing propyl methanoate present HEm > 0, while the remaining ones give values of HEm that follow a sigmoid distribution. The VEm of these mixtures of propyl esters are either positive or negative, depending on the dihalide involved. Positive ones correspond to mixtures with short-chain dibromoalkanes, and contraction effects are observed with the increasing chain length of the dihalide compound. On the whole, experimental information suggests a specific behavior with either positive or negative structural mixing effects depending on the chain length of the compounds. HEm values were estimated theoretically by applying two different types of models. The UNIFAC group contribution model gives good results in the prediction, but only when the Br, Br/carboxylate interaction is considered to vary with the chains of the ester and dibromoalkane; mathematical expressions are presented to describe these variations for the entire set of mixtures. The COSMO-RS quantum-chemical method is also applied to predict HEm values for the systems studied and the results extrapolated to a set of 90 systems (alkyl alkanoates + dibromoalkane), optimizing the model parameters, especially to obtain an adequate description of the Van der Waals interactions. As a result, the optimized COSMO-RS method can be used to interpret the behavior of the HEm for the whole group of alkyl esters + dibromoalkane in terms of the different intermolecular interactions taking place inside the pure compounds and mixtures, especially in relation to the variable effects of the alkyl chains of the components on the mixing enthalpies. 1. Introduction This work is part of a larger study we have been carrying out on systems containing alkyl halides and other components, from which a series of articles have been published,1-6 in an attempt to interpret their behavior in solution and define the nature of the interactions appearing in solutions containing halide derivatives. In previous articles,1-3 the values of excess properE E and Vm , obtained for alkyl (methyl, ethyl, and butyl) ties, Hm alkanoates (methanoate to pentanoate) with six 1,ω-dibromoalkanes (ω ) 2-6) were reported, analyzing the structure of the final mixture. We aim, with this work, to make an additional contribution in two directions: (a) by providing values for properties of a set of systems not published previously (propyl alkanoates) that will verify previous findings for the same group and (b) to establish a more rigorous behavioral model (based on a more extensive database and in-depth knowledge) and to define the complex interactions taking place in the mixing process. * To whom correspondence should be addressed. E-mail: jortega@ dip.ulpgc.es. † Instituto Universitario de Bio-Orgańica Antonio Gonzalez (IUBOAG), Universidad de La Laguna, C/: Astrofı´sico Francisco Sanchez 2, 38026-La Laguna, Tenerife, Spain.

In studies of this kind, it would be logical to expect a direct relationship between values obtained for the excess quantities and the chain lengths of the compounds involved, the ester and the dibromoalkane. In the chemical engineering area, different types of theoretical models, some with macroscopic (UNIFAC) and other with microscopic fundaments (COSMO-RS), are used to try to reproduce the information provided by experimental data of mixing properties. In this way, complementary research has arisen to support the behavioral hypothesis and structural model proposed. The ab initio COSMO-RS7 methodology has E been used in previous works8,9 to estimate the Hm for mixtures containing chlorinated derivatives on the basis of three types of contributions (electrostatic, hydrogen bonds, and Van der Waals), obtaining acceptable results in mixtures of alkyl ethanoates + monochloroalkanes8 and propyl esters + dichloE roalkanes.9 In this work, modeling of Hm with the COSMO-RS method will be carried out with a set of 90 ester + dibromoalkane mixtures, part of which has been subject to experimentation previously,1-3 in an attempt to establish the energetic interactional effects taking place in the mixing process and the nature of these. The strong analytical capacity of this model will help to verify the proposed molecular structure of the final solution and to increase the practicality of the UNIFAC functional group

10.1021/ie101479v  2010 American Chemical Society Published on Web 11/04/2010

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010

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E Figure 1. Plot of experimental values (b) and correlation curves according to eq 1 of Hm vs x1 for binaries x1Cu-1H2u-1COO(CH2)2CH3 + (1 - x1)R,ωBrCH2(CH2)V-2CH2Br measured at T ) 298.15 K. Labels indicate the V values. (a) For u ) 1; (b) for u ) 2; (c) for u ) 3; (d) for u ) 4.

contribution model, which is frequently used in chemical engineering to predict certain separation processes. Previous works on solutions of 1,ω-dibromoalkanes (ω ) 2-6) and different esters1-3 used two versions of UNIFAC, the simpler Dang and Tassios version,10 applicable only to enthalpies, and the Gmehling et al.11 version, which has a greater capacity to estimate other properties. The latter version is only used here with the original parameters, without attempting to modify them, since this would require additional data for other properties of these mixtures, not available in the literature. The model proposed by Dang and Tassios10 does not produce acceptable results when applied to a single set or pair of parameters for a specific group interaction G/G′. However, in a previous work,3 expressions were proposed with carboxylate/ bromide interaction parameters, aG/G′ ) φ(u,V), variables with the u acid chain of the ester, Cu-1H2u-1CO2R2, and the dibromoalkane V, BrCH2(CH2)V-2CH2Br, producing a good E . This work, therefore, proposes the representation of Hm development of this procedure further, including in these expressions the alkanoic part, R2, of ester (CnH2n+1), in addition

to the acidic part, R1, in R1COOR2. This approach can be verified by applying the COSMO-RS molecular model that uses the structural information of each compound to predict the contribution each one makes to the value estimated for the total energy of the solution. 2. Experimental Section 2.1. Materials. The products used for this work were of the highest commercial quality and were provided by the companies Fluka and Aldrich. Before use, they were degasified with ultrasonification, kept in the dark for several hours, and passed through a Fluka 3A molecular sieve to remove any trace of moisture. The purity of the liquids was verified by gas chromatography in an Agilent HP6890 apparatus, producing values almost identical to those provided by the manufacturer. Nonetheless, to ensure the quality of the products, the densities, F, and refractive indices, nD, were measured at a temperature of 298.15 K and at atmospheric pressure. The measurements were similar to those obtained in a previous work for propyl

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E Figure 2. Plot of experimental values (b) and correlation curves according to eq 1 of Vm vs x1 for binaries x1Cu-1H2u-1COO(CH2)2CH3 + (1 - x1)R,ωBrCH2(CH2)V-2CH2Br obtained at T ) 298.15 K. Labels indicate the V values. (a) For u ) 1; (b) for u ) 2; (c) for u ) 3; (d) for u ) 4.

esters9 and for dibromoalkanes,2 so they are not presented again in this work. E were calcu2.2. Apparatus and Procedure. Values of Vm lated indirectly from density measurements using a DMA-58 Anton Paar vibrating tube densimeter with a precision of (0.02 kg m-3. The apparatus incorporated a Peltier effect, which achieved a temperature control of (0.01 K. The densimeter was calibrated with bidistilled water obtained in our laboratory with a conductance lower than 2 µS and with nonane.12 The synthetic mixtures were prepared according to mass using an electronic balance, AND model ER182A, accurate to (10-5 g. The E was lower than (2 × 10-9 m3 mol-1, while uncertainty in Vm that of the mole fraction was on the order of (5.5 × 10-5. Refractive indices of the pure compounds were measured with an Abbe 320 refractometer from Zuzi, with a reading error of (0.0002 units, maintaining the working temperature constant at 298.15 ( 0.01 K with a Heto Birkerod external circulation water bath. E values were measured directly using a Calvet The Hm MS80D calorimeter from Setaram, Lyon (France), which was

calibrated by applying a Joule effect to a resistance of 1000.2 Ω in one of the two cells, using a known Setaram EJ3 power source, which produced thermograms similar to those of the mixing processes. Different powers were applied to the calibration cell in order to verify the constant of the apparatus over a wide range of energy values. The uncertainty estimated E for the Hm measurements was lower than 1%. The amount of both compounds in each mixture was measured by mass using a Mettler balance, model H10, accurate to (3 × 10-5 g. The uncertainty in the mole fraction was lower than (2 × 10-4. 3. Results Pairs of values [(x1,HEm) and (x1,VEm)] obtained at a temperature of 298.15 K for the mixtures of propyl alkanoate(methanoate to butanoate) (1) + 1,ω-dibromoalkane (2) (ω ) 2-6) are shown in Tables S1 and S2 (Supporting Information), respectively. These data were correlated with a simple polynomial equation, a function of the so-called actiVe fraction, z1, of one


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Figure 3. Representation of equimolar excess properties (b) obtained at T ) 298.15 K for binaries containing propyl esters: Cu-1H2u-1COO(CH2)2CH3 + E E R,ω-BrCH2(CH2)V-2CH2Br. (a) Hm values vs u and (b) Vm vs u. Labels indicate the V values.

of the compounds taken as a reference and represented generically as YEm ) z1(1 - z1)(A0 + A1z1 + A2z21) where z1 )

x1 x1 + k(1 - x1)

(1)

The usefulness of this model was suggested previously.13 In this approach, the parameter k is defined differently in the E E and Vm and is calculated as described in correlation of Hm 1-3 previous works. We call this kV when eq 1 is used for data E E ) and kh for data pairs (x1,Hm ). Values of the treatment (x1,Vm coefficients Ai, kV, and kh, obtained for each system, together E ), are shown in Table S3 with the standard deviations, s(Ym (Supporting Information). This table also shows the values of kr ) r2/r1 and kq ) q2/q1, obtained from the volume, rk, and area, qk, parameters for each compound according to Bondi.14 Parts a-d of Figures 1 and 2 show, respectively, the E E and Vm values and the correlation curves experimental Hm obtained for each mixture with eq 1. HEm values are endothermic for mixtures with propyl methanoate, while for the other esters E values follow a the energetic effects represented by the Hm sigmoid distribution, passing from positive to negative as the E molar fraction of the ester increases. For a given ester, the Hm values increase with the dibromoalkane chain, except for mixtures with propyl butanoate, which have a different arrangement. For VEm values, see parts a-d of Figure 2, expansion effects appear in the mixtures with the shorter-chained dibromoalkanes and contractions as the length of the ester chain increases. The global analysis of the results of these properties is made easier by representing, in parts a and b of Figure 3, the equimolar E E and Vm , as a function of the quantities of both properties, Hm chain length of the compounds used in the study. E (at x ) 0.5) at Part a of Figure 4 shows the values of Hm 298.15 K, calculated with eq 1 for a set of 90 mixtures studied by us as part of the systematic study.1-3 In this group of mixtures, the shorter-chained alkyl alkanoates, such as methyl methanoate, present a clearly endothermic behavior that decreases significantly as the acid chain length of the ester increases (u ) 1f5), reaching systems with small values of

E > 0, or even exothermic values, depending on the dibroHm moalkane chain in the cases of mixtures with methyl butanoate or pentanoate. On the other hand, the variation in the alkyl alkanoate alkanolic chain (n ) 1f4) also produces a lower endothermicity. In other words, low solution energies are E < 150 J mol-1) in mixtures containing obtained (-150 < Hm medium-sized esters (n > 2 and u g 2) with dibromoalkanes, and there is no evidence of a clear effect of the alkyl chains of E values of the mixtures. As the number of the ester on the Hm carbon atoms in the dibromoalkane increases (ν ) 2f6), as is also reflected in the global analysis of the whole group, there is a steady rise in the endothermicity of the mixture (an opposite effect of that produced by the ester chain). This is more pronounced for the smaller esters (methyl methanoate + E < 1200 J mol-1) but tend to dibromoalkane present 800 < Hm converge for the larger esters (butyl butanoate + dibromoalkane E present values of -75 < Hm ≈ 0 J mol-1). Considering these E , represented in data together with the equimolar values of Vm part b of Figure 4 for the entire group of 90 mixtures, a classification can be proposed for the set of systems. These can be separated into four groups, presented in Table 1, which are defined according to the qualitative results of the mixing process. Group I is an extreme case with endothermic [HEm > 100 J mol-1] E > 0] and is composed of mixtures and dilation processes [Vm with short-chained esters. Another extreme case is group IV, E < 0] and composed of systems that present contractions [Vm E low dissolution enthalpies that become exothermic [-100 0 is observed, which an intermediate behavior for which Vm E < 0, has low heats of dissolution [group II], or vice versa Vm with high heats of dissolution [group III]. From this table, the difficulty in interpreting the experimental results on the basis of the different types of intermolecular interactions occurring inside the pure compounds and mixtures becomes evident. In

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Figure 4. Variation of equimolar excess properties at T ) 298.15 K with ester chain length u, for binaries x1Cu-1H2u-1COOCnH2n+1 + (1 - x1)R,ωE E BrCH2(CH2)V-2CH2Br, (0) for n ) 1, (∆) for n ) 2, (9) for n ) 3, (O) for n ) 4 and (a) for Hm and (b) for Vm . Labels indicate the V values. E E Table 1. Classification of Mixtures Formed by (an Alkyl Ester + an r,ω-Dibromoalkane) at T ) 298.15 K, as a Function of the Vm and Hm Valuesa

a E E E E E E E > 0 and Hm > 100 J mol-1. Group II: Vm > 0 and -100 < Hm < 100 J mol-1. Group III: Vm < 0 and Hm > 100 J mol-1. Group IV: [Vm Group I: Vm E < 0] and [-100 < Hm < 100 J mol-1].

spite of this, we attempt to do the analysis of the mixing behavior in the following sections of this paper. 4. Application of the COSMO-RS Model 4.1. Computational Methodology. The molecular geometry of the compounds was optimized by applying a standard calculation procedure similar to that used in previous works.8,9 First of all, the geometries of the components of the mixtures were optimized using the Gaussian 03 software, with a calculation level of B3LYP/6-311++G**.15 The ideal distribution of charge on the molecular surface for each species was estimated from the COSMO continuous solvation model, at theory level BVP86/TZVP/DGA1. The corresponding COSMO files were used as an entry in the COSMOtherm statistical thermodynamics E values of the mixtures studied at software16 to calculate the Hm

the working temperature. In accordance with the quantumchemistry method chosen, the density functional and the base functions, the BP_TZVP_C21_0106 parametrization was used, which is necessary to calculate the physicochemical data and contains parameters intrinsic to COSMOtherm17 and specific parameters of the elements. 4.2. Analysis of the Results Obtained in Application of the COSMO-RS Model. This method is applied to get structural information of the alkyl alkanoate + dibromoalkane system from estimates of HEm, and especially from the different contributions associated with the hydrocarbon chains of the ester and dibromoalkane. The COSMO-RS quantum-chemical model has E recently been shown to be effective at predicting the Hm of analogous natural mixtures, such as ester + monochloroalkane8 and ester + dichloroalkane,9 obtaining quantified information


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Figure 5. The (a,b) σ profile and (c,d) σ potential for Cu-1H2u-1COOCnH2n+1 and R,ω-BrCH2(CH2)V-2CH2Br. Labels indicate the u, n, and V values. The top of the figure shows the distribution of charge density for several molecules.

for the different intermolecular interactions (Van der Waals, electrostatic and hydrogen bonds) between the components of the mixture. 4.2.a. Description of the Pure Compounds with COSMORS. The COSMO-RS method can be used to predict the thermodynamic properties of pure fluids and mixtures using only information from the electronic structures of the individual molecules.7 It uses the distribution of polarized charge on the electronic density surface of the molecules, which is represented

by the σ-profile histogram (see Figure 5). The different molecular interactions in the fluid (electrostatic, Van der Waals, or hydrogen bond) are formulated as a function of the polarity surface areas of the individual species. Therefore, the σ profiles predicted by COSMO-RS constitute an intuitive, simple, and graphical guide to interpret the physicochemical behavior of the compounds. Part a of Figure 5 shows the σ profile of three alkyl alkanoates representative of the group of esters studied here: methyl methanoate (u ) 1, n ) 1), methyl butanoate (u

12732


E Figure 6. Representation of equimolar Hm , experimental vs calculated by COSMO-RS for binaries x1Cu-1H2u-1COOCnH2n+1 + (1 - x1)R,ωBrCH2(CH2)V-2CH2Br, (0) for n ) 1, (∆) for n ) 2, ()) for n ) 3, (O) for n ) 4, (a) by COSMO-RS with original parameters and (b) by COSMO-RS with optimized parameters.

E Figure 7. Variation of global Hm values, experimental (9) and calculated by COSMO-RS (0), with the acidic part of alkanoate u, for binaries Cu-1H2u-1COOCH3 + 1,6-BrCH2(CH2)4CH2Br. Plot of the partial contribuE E E tion of the method: (2) Hm (VdW), (b)Hm (Misfit), and (+)Hm (HB).

) 4, n ) 1), and butyl butanoate (u ) 4, n ) 4). The three esters present peaks at ∼0.013 and ∼0.009 e/Å2 corresponding to the oxygens of the carbonyl groups (the charge is shown in red at the top of Figure 5) and the ester (the surface charge is shown in a yellow-orange color), respectively. These groups present a concentration of electronic charge in the region of high polarity (σHB > 0.0085 e/Å2) and are considered hydrogen bond “acceptors”. For the case of methyl methanoate, the peak has shifted to 0.012 e/Å2, indicating a slightly less basic oxygen in the carbonyl group (this is why the charge has an orange color). The distribution of charge density around zero (-0.0085 < σ < 0.0085 e/Å2) corresponds to nonpolar groups of the alkanoate, and the positive values are assigned to the carbon atoms (green

in the surface charge) and negative to the hydrogen atoms (pale blue). Part a of Figure 5 shows how the charge density in the nonpolar region of the σ profile increases with the length of the hydrocarbon chains of the alkyl alkanoate. For methyl methanoate, in addition to the peaks mentioned previously, there is a clearly acidic peak at -0.01 e/Å2, which corresponds with the hydrogen of the aldehyde group. Part b of Figure 5 shows the σ profile of the two 1,ω-dibromoalkanes with ω ) 2 and ω ) 6, which present a peak at ∼0.007-0.008 e/Å2 corresponding to Br atoms (yellow in the surface charge), with a reduced basicity for the 1,2-dibromoethane. The peaks associated with the alkyl groups appear in the nonpolar region (represented in green and pale blue), and the intensity increases with the chain of the halogenated compound. Another peak appears for the 1,2-dibromoethane, at -0.004 e/Å2, and for the dibromohexane, at -0.009 e/Å2, and corresponds to the H atoms bound to the halogenated carbons. These groups present a greater acidity than the other C-H groups (intense blue in the molecular surface charge), especially as the dibromoalkane chain decreases in length. The COSMO-RS methodology also gives the σ potential of a compound, which describes the affinity of the solvent studied to interact with compounds with a charge density [pX(σ)] with polarity σ. As shown in part c of Figure 5, the alkyl alkanoates will establish strongly repellent interactions with basic groups, although this repulsion decreases in esters with slightly acidic groups, such as methyl methanoate. On the contrary, the esters present strongly attractive interactions with acidic groups, which are greater as the chain length increases. The σ potential for the dibromoalkanes formed a parabola centered around σ ) 0, see part d of Figure 5, showing strong repellent interactions for acidic and basic groups, although the latter seemed to diminish with the alkyl chain of the dibromoalkane as its C-H group became more acidic. All information provided by COSMO-RS shows that the molecules of both components, ester and dibromoalkane, have only a limited ability to interact within the pure fluid (asymmetric σ profiles), except for the more amphoteric esters, such as methyl methanoate, and in general, the interaction capacity of the mixture is also reduced since its components do not present complementary σ profiles, with the presence of polar

Ind. Eng. Chem. Res., Vol. 49, No. 24, 2010 Table 2. Contribution to Equimolar Excess Enthalpies for E E COSMO-RS [Hm (Misfit, MF), Hm (Van der Waals, VdW), E Hm (Hydrogen Bond, HB)] for Ester (Component 1) and r,ω-Dibromoalkane (Component 2) in the Mixture and in Pure Compounds, eq 6 at T ) 298.15 K component 1 mixture

component 2

1,2-dibromoethane -1067 1,3-dibromopropane -1062 1,4-dibromobutane -938 1,5-dibromopentane -864 1,6-dibromohexane -808

-7606 -7338 -6913 -6514 -6147

25 66 79 81 83

-45 0 360 634 904

10738 9982 9312 8771 8312

-50 -12 -1 0 0

methyl ethanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-1567 -1515 -1377 -1338 -1340

-9262 -8891 -8365 -7886 -7450

-55 -13 -1 0 0

-315 -208 190 452 696

11904 11084 10366 9790 9296

-56 -14 -1 0 0

methyl propanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-1317 -1218 -1111 -1112 -1158

-10408 -9955 -9371 -8848 -8375

-52 -13 -1 0 0

-464 -335 27 242 445

12670 11812 11077 10490 9983

-53 -13 -1 0 0

methyl butanoate + 1,2-dibromoethane -1130 1,3-dibromopropane -986 1,4-dibromobutane -895 1,5-dibromopentane -927 1,6-dibromohexane -1002

-11465 -10968 -10350 -9802 -9306

-51 -47 -1 0 0

-564 -413 -77 106 374

13401 12525 11788 11197 10685

-52 -13 -1 0 0

methyl pentanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-930 -750 -674 -722 -818

-12322 -11797 -11157 -10597 -11086

-49 -12 -1 0 0

-638 -473 -161 3 155

-20421 -25712 -30943 -36033 -41006

-49 -12 -1 0 0

ethyl methanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-1177 -1116 -1016 -995 -1005

-9193 -8813 -8289 -7815 -7384

5 44 56 58 59

-290 -196 155 391 620

11842 11019 10304 9731 9241

-48 -12 -1 0 0

ethyl ethanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

Table 2. Continued component 1 mixture 1,5-dibromopentane 1,6-dibromohexane

-1471 -1368 -1355 -1244 -1290

-10506 -10059 -10265 -8947 -8472

-54 -13 -1 0 0

-475 -331 38 270 477

12778 11918 9924 10590 10082

-55 -13 -1 0 0

-604 -172 -113 72 234

13426 12544 11799 11205 10691

-52 -13 -1 0 0

-682 -502 -193 -42 103

14041 13149 12411 11821 11307

-51 -12 -1 0 0

-742 -549 -257 -130 -9

14588 13698 12969 12386 11876

-49 -12 -1 0 0

-436 -314 16

12711 11852 11120

-46 -11 -1

ethyl propanoate + 1,2-dibromoethane -1148 1,3-dibromopropane -987 1,4-dibromobutane -902 1,5-dibromopentane -924 1,6-dibromohexane -1007

-11432 -10924 -10302 -9749 -9249

-51 -12 -1 0 0

ethyl butanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-959 -762 -678 -724 -823

1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-764 -529 -451 -512 -631

-12319 -11790 -11148 -10581 -10066

-50 -12 -1 0 0

ethyl pentanoate + -17361 -16809 -16158 -15584 -15062

-49 -12 -1 0 0

propyl methanoate + 1,2-dibromoethane -1039 -2841,0 1,3-dibromopropane -929 -2351,0 1,4-dibromobutane -853 -1742,0

-1 39 50

component 2

E E E E E E Hm,1(MF) Hm,1(vdW) Hm,1(HB) Hm,2(MF) Hm,2(vdW) Hm,2(HB)

-870 -1199,0 -919 -616,0

52 53

215 410

10536 10033

0 0

-582 -416 -66 130 305

13490 12611 11869 11278 10766

-54 -13 -1 0 0

-680 442 -191 -41 103

14045 13154 12415 11825 11311

-51 -12 -1 0 0

-760 -565 -278 -152 -35

14583 13689 12960 12378 11868

-50 -12 -1 0 0

-539 -390 -88 83 252

13428 12553 11819 11233 10725

-45 -11 -1 0 0

-663 -483 -156 8 162

14102 13217 12482 11893 11381

-52 -13 -1 0 0

-741 1023 -255 -128 -6

14587 13698 12969 12386 11875

-50 -12 -1 0 0

-809 -602 -331 -228 -132

15054 14167 13451 12878 12374

-49 -12 -1 0 0

propyl ethanoate +

E E E E E E Hm,1(MF) Hm,1(vdW) Hm,1(HB) Hm,2(MF) Hm,2(vdW) Hm,2(HB)

methyl methanoate +

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608 757 855 835 761

10476 10967 11585 12134 12634

-29 12 23 24 24

propyl propanoate + 1,2-dibromoethane -958 1,3-dibromopropane -761 1,4-dibromobutane -675 1,5-dibromopentane -729 1,6-dibromohexane -1021

-12325 -11789 -11147 -10574 -10065

-50 -12 -1 0 0

propyl butanoate + 1,2-dibromoethane 1,3-dibromopropane 1,4-dibromobutane 1,5-dibromopentane 1,6-dibromohexane

-762 -522 -444 -501 -623


-2039 -1895 -1835 -1876 -1955


302 493 579 537 440


-767 -532 -453 -505 -633

-13104 -12553 -11903 -11328 -10806

-48 -12 -1 0 0

butyl methanoate + -11506 -11016 -10407 -9864 -9371

-6 32 43 45 46

butyl ethanoate + 12844 13364 13999 14563 15076

-27 12 23 24 24

butyl propanoate + -13062 -12510 -11859 -11285 -10762

-49 -12 -1 0 0

butyl butanoate + 1,2-dibromoethane -1182 1,3-dibromopropane -306 1,4-dibromobutane -229 1,5-dibromopentane -93 1,6-dibromohexane -438

-13745 -13184 -12531 -11955 -11429

-47 -13 -1 0 0

groups of different chemical natures. The similarity of the σ profiles of the esters and the dibromoalkanes in Figure 5, with the majority of the electronic density concentrated in the area of low polarity (-0.0085 < σ < 0.0085 e/Å2), is a sign of low heats of solution in the ester-dibromoalkane mixtures, except for the cases mentioned for short-chained alkanoates. 4.2.b. Estimation of HEm with COSMO-RS. Part a of Figure 6 shows the values found for HEm at 298.15 K and an intermediate composition, for the set of 90 mixtures of Cu-1H2u-1CO2CnH2n+1 (n ) 1-4, u ) 1-5) + R,ω-BrCH2(CH2)V-2CH2Br (ω ) ν ) 2-6), versus the predictions of the standard COSMO-RS method. It can be observed that the theoretical results deviate significantly from the measured values, with exothermic estimaE in contrast to real results. Moreover, this method tions of Hm does not qualitatively describe the effect of the alkyl chains of the compounds in the mixtures, since the deviations from experimental values vary depending on the series studied. It seems clear that it is necessary to carry out a fine-tuning of the general parameters of the method, especially those involved in the Van der Waals interactions, to be able to adequately describe the thermodynamic properties of systems that include haloge-

12734


E Figure 8. Variation of global Hm values, experimental (9) and calculated by COSMO-RS (0), with the alkanolic part of alkanoate n, for binaries HCOOCnH2n+1 + 1,6-BrCH2(CH2)4CH2Br. Plot of the partial contribution E E E of the method: (2) Hm (VdW), (b) Hm (Misfit), and (+) Hm (HB).

Figure 10. Representation of equimolar HEm values obtained for the binaries: Cu-1H2u-1COOCnH2n+1 + R,ω-BrCH2(CH2)V-2CH2Br, for u ) 1, n ) 1, V E values; ) 3-6 and u ) 4, n ) 4, V ) 3-6. (9) From experimental Hm E E contributions of COSMOS-RS: (gray) Hm (VdW), and (striped) Hm (Misfit).

obtained after optimizing the parameters are shown in Figure 6b, in which the model gives a reasonable description of the E behavior of the Hm values for the whole set of 90 mixtures obtaining a linear-regression between the experimental and calculated values, with statistical coefficients of r2 ) 0.98 and E ) ) 100 J mol-1. In other words, COSMO-RS represents s(Hm E values of the increased ester chain length in the effect on Hm relation to the dibromoalkane chain, taking into account the fact that the final values are net enthalpies, corresponding to the algebraic sum of several contributions associated with different types of interactions, including electrostatic (Misfit), Van der Waals (VdW), and hydrogen bond (H-Bond) ones, so HEm ) HEm(Misfit) + HEm(H-Bond) + HEm(VdW)

(2)

Also, each summand of eq 2 is the result of the contribution of each component to the interaction, such that HEm(Misfit) ) x1[HE1 (Misfit)] + x2[HE2 (Misfit)]

(3)

HEm(VdW) ) x1[HE1 (VdW)] + x2[HE2 (VdW)]

(4)

HEm(H-Bond) ) x1[HE1 (H-Bond)] + x2[HE2 (H-Bond)] E Figure 9. Variation of global Hm values, experimental (9) and calculated by COSMO-RS (0), with the dibromoalkane chain length V, for binaries HCOO(CH2)2CH3 + R,ω-BrCH2(CH2)V-2CH2Br. Plot of the partial contriE E E butions of the method: (2) Hm (VDW), (b) Hm (Misfit), and (+) Hm (HB).

nated compounds. Therefore, in a previous work,8 optimized values were already proposed for COSMO-RS to estimate the E Hm values of ester + chloroalkanes. Here, we proceed in the same way; using the extensive experimental database provided here and in previous works,1-3 the original parametrization of the COSMO-RS model can be revised in an attempt to improve E values. predictions of the Hm The optimization procedure results in the following changes: (i) standard COSMO-RS parameters, τ(Br,Br) ) -48.6 kJ/mol/ nm2, τ(Br,H) ) -20.6 kJ/mol/nm2, R ) 5950 kJ/mol/Å2, and Chb) 83690 kJ/mol/Å; (ii) optimized COSMO-RS parameters, τ(Br,Br) ) -68.0 kJ/mol/nm2, τ(Br,H) ) -65.9 kJ/mol/nm2, R′ ) 5355 kJ/mol/Å2, and Chb ) 16 738 kJ/mol/Å2. The results

(5) With component 1 corresponding to the ester and component 2 to the dibromoalkane. The contributions of each summand in eqs 3-5 to the final values of HEm are obtained by the expressions E HEi (Interaction) ) Hi,E mixture(Interaction) - Hi,pure (Interaction) (6)

Owing to the favorable results obtained with the COSMORS model optimized for the mixtures studied, a detailed analysis E was then carried out of the influence on Hm of the alkyl chain length of its components relative to the contribution of the different intermolecular interactions to the energy of the mixture. 4.2.c. The Effect of the Chain Length of Alkyl Alkanoate (Cu-1H2u-1COOCnH2n+1) (u and n). Figure 7 shows the effect of the increased length of the acid chain, u, of the E for methyl alkanoate systems, ester on the net values of Hm


12735

E Figure 11. Variation of equimolar Hm (b), at T ) 298.15 K, with ester chain length u, for binaries Cu-1H2u-1COO(CH2)2CH3 + R,ω-BrCH2(CH2)V-2CH2Br and theoretical estimations (O) by (a) UNIFAC10 and (b) modified UNIFAC.11 Labels indicate the V values.

Table 3. Equations Obtained to Calculate the Values of Interaction E of Binaries (Cu-1H2u-1CO2CnH2n-1 Parameters for Estimating the Hm + r,ω-BrCH2(CH2)W-2CH2Br) by the UNIFAC Model compound methyl methanoate ethyl methanoate propyl methanoate butyl methanoate methyl ethanoate ethyl ethanoate propyl ethanoate butyl ethanoate methyl propanoate methyl butanoate methyl pentanoate ethyl propanoate ethyl butanoate ethyl pentanoate propyl propanoate propyl butanoate butyl propanoate butyl butanoate

aG/G′ -19.43/V -15.99/V -10.95/V -12.26/V -11.22/V -17.80/V -10.86/V -10.25/V

+ + + + + + +

0.74V + 17.30 0.567V - 2.98 0.694V - 14.38 0.633V - 19.45 0.257V - 2.03 0.362V - 5.09 0.764V - 16.81 1.15V - 22.01

-8.95/V + 1.238v + 71.17/u - 39.89 -9.112/V + 1.167V + 55.46/u - 39.80 -8.23/V + 1.275V + 25.13/u - 35.52 -8.92/V + 1.44V - 22.90/u - 37.58

aG′/G 25.99 33.00 37.00 45.00 31.69 30.01 45.50 54.95 40.50 50.08 59.97 42.12 58.01 75.42 60.00 76.00 68.05 81.95

Cu-1H2u-1COOCH3 + 1,6-dibromohexane, when varying u ) 1f5. It can be observed that the endothermicity of the mixture is significantly reduced with the number of carbons in the acid part, and there is an acceptable agreement between experimental measurements and predictions of the optimized COSMO-RS method. The same figure shows the contributions in the method of the different intermolecular interactions (Misfit, Van der E values of this group, where n ) Waals, and H-bond) to the Hm 1 and ω ) 6. It can be observed that the Van der Waals E (VdW), make the largest contribution, which interactions, Hm determines the endothermic nature of the mixture. This is also shown in Table 2, where the endothermic nature of the mixture is due to Van der Waals interactions between molecules of the dibromoalkane, which are more effective than those occurring in the ester-dibromoalkane mixture. However, the reduction E (VdW) with the increase in acid chain length of the ester in Hm (u ) 1f5) is associated with an increase in Van der Waals interactions between the H of the ester and the Br of dibromoalkane. Figure 7 also illustrates the important role of electrostatic type (Misfit) interactions in the set of systems. In this case,

E (Misfit) contribution is exothermic for all of the the Hm mixtures (u ) 2f5), except for the methanoate (u ) 1), since the repellent interactions between the molecules in the final mixture are weaker than in the initial pure fluids. In the case of methyl methanoate, u ) 1, this effect is reduced owing to the slightly acidic nature of the H of the aldehyde group, which makes the ester-ester interactions governed by the aldehyde group more favorable, see Figure 5. This explains E (Misfit) for the methyl methanoate + why the value of Hm 1,6-dibromohexane system is slightly higher than zero. It can also be observed how the increases in alkyl chain length of E (Misfit) in the the alkanoate have no noticeable effect on Hm interval u ) 2f5. This is coherent with the fact that this series of esters presents almost identical σ-potential values, in other words, an analogous capacity to establish electrostatic interactions with the medium. E (H-Bond), the findings of Regarding the contribution of Hm the optimized COSMO-RS method seem to indicate a negligible E values of the mixtures contribution (almost zero) to the Hm studied, see Figure 7, which can be interpreted as a negligible effect of the formation/rupture of hydrogen bonds in this group. The next step was to study the influence of the alkanolic chain E values in the length n of the ester R1COOCnH2n+1 on the Hm dibromoalkane mixtures. Figure 8 shows the evolution of the E values for the alkyl experimental and theoretical equimolar Hm methanoate HCOOCnH2n+1 + 1,6-dibromohexane mixtures, from n ) 1f4, and shows a good agreement among them. The same figure also shows the variation in interactional contribuE E E (Misfit), Hm (H-Bond), and Hm (VdW) as tions of the model: Hm a function of n. A comparison of Figures 7 and 8 shows a similar E evolution of the Hm values. From this, we can deduce that the addition of a -CH2- group to the ester has a similar effect on the mixing process, regardless of its position in the ester (acidic or alkanolic part). This was also illustrated when the UNIFAC model was applied in previous works.19-21 4.2.d. The Effect of the Chain Length (W ) ω) of the Dibromoalkane (r,ω-BrCH2(CH2)W-2CH2Br). The influence of the chain length of the dibromoalkane was analyzed by the procedure indicated previously. In Figure 9, the equimolar E values of the five systems of propyl methanoate + 1,ωHm

12736


E Figure 12. Variation of equimolar Hm (b), at T ) 298.15 K, with ester chain length u, for binaries: Cu-1H2u-1COOCnH2n+1 + R,ω-BrCH2(CH2)V-2CH2Br and theoretical estimations (O) by UNIFAC with parameters obtained by eqs 13-16 (a) for n ) 1, (b) for n ) 2, (c) for n ) 3, (d) for n ) 4. Labels indicate the V values

BrCH2(CH2)V-2CH2Br (V ) ω ) 2f6) are compared. This E shows an opposite effect of that observed before for the Hm values, with an increase in the endothermicity of the mixture as the value of V increases. The figure also shows the different intermolecular interactions involved in the mixing process. It is noteworthy that the contribution of the Van der Waals E (VdW), is numerical and quantitatively interactions, Hm similar, both for the dibromoalkanes series (V ) 2f6) and for the alkyl alkanoate series (u ) 1f5, n ) 1f4) with 1,6-dibromohexane, showing that the addition of a methyl group in both components has a similar effect on the excess quantities. Another only slightly significant effect corresponds E (H-Bond), in to the contribution of the hydrogen bonds, Hm the series of dibromoalkanes with propyl methanoate. However, the main difference in the findings compared with the studies carried out to date was associated with the HEm(Misfit) term, as shown in Figure 9 for the set propyl methanoate + 1,ω-BrCH2(CH2)V-2CH2Br (V ) ω ) 2f6). In this case, the contribution of the electrostatic type (dipole-dipole, polar-

izability, etc.) of intermolecular interactions is clearly E (Misfit) increases with exothermic, although the value of Hm the chain length, V, of the dibromoalkane, making an endotherE . Analysis of the mic contribution to the net value of Hm E Hm(Misfit) values shows that the exothermicity of this contribution is associated with a decrease in the repellent interactions between the molecules of the pure components compared with those in the final mixture or solution. It was already mentioned previously that the esters have a strongly basic group (CdO), see Figure 5, that favors the interactions in the mixture with short-chained dibromoalkanes presented by the more acidic E (Misfit) contribution C-H groups. Table 2 shows that the Hm of the dibromoalkane to eq 3 changes from strongly negative to positive values as the chain length of the dibromoalkane increases (V ) 2f6). E values of two sets of In summary, Figure 10 shows the Hm mixtures with clearly different behaviors. On the one hand, the mixtures of the smaller esters, methyl methanoate (n ) 1, u ) 1) with dibromoalkanes, present a strongly endothermic mixing


12737

E Figure 13. Representation of the surfaces corresponding to the distribution of interaction parameters obtained in the estimation of Hm by the UNIFAC method10 for binaries: Cu-1H2u-1COOCnH2n-1 + R,ω-BrCH2(CH2)V-2CH2Br and using eqs 13-16 from Table 2 as function of u and V.

process, with experimental values of HEm of around 1000 J mol-1. On the other hand, mixtures with the larger esters, such as butyl E = butanoate (n ) 4, u ) 4) with dibromoalkanes, generate Hm 0. Figure 10 shows that both groups of mixtures with very different behaviors actually present similar HEm(Misfit) contributions. Therefore, the differences must only be associated with the Van der Waals interactions, which are not as strong in the mixtures with short-chained esters. The figure does not show E (H-Bond) contributions, which were insignificant for all the Hm the series shown. 5. Application of the UNIFAC Model In previous studies,1-6 on analogous groups of mixtures, the UNIFAC group contribution model10,11 was used to estimate E the Hm values and showed that the parameters originally proposed for the bromide/carboxylate interaction do not adequately reproduce the experimental values. Estimates for the propyl alkanoate + dibromoalkane mixtures with both versions of the model10,11 produced the results shown in Figure 11. In order to increase the utility of the method in the version proposed by Dang and Tassios10 that was applied to systems containing dihalides, two important aspects were taken into consideration. On the one hand, to distinguish the carboxylate/Br interaction, G/G′ is useful for monobromides and also for carboxylate/

dibromide, as a consequence of a differentiated configurational behavior, which gives rise to different net dipolar moments in both types of molecules (e.g., 2.04 × 10-30 C m for the monobromoethane and 1.04 × 10-30 C m for the 1,2-dibromoethane, see ref 22), which is transcendent in the net intermolecular interactions. On the other hand, and as demonstrated in previous studies,3,20 better results are achieved with the method when it is considered that the parameters of the carboxylate/ Br,Br interaction are dependent on the chain length of the components of the mixture. This is also suggested by COSMORS, which uses independent structural information for each compound to estimate the contribution of each one to the total interaction energy. Hence, a general mathematical expression can be written for the interaction parameters aG/G′ ) φ(u,V), in which u corresponds to the acid part of the propyl alkanoate Cu-1H2u-1CO2C3H7 and V corresponds to the chain of the dibromoalkane BrCH2(CH2)V-2CH2Br. Hence, the desired relationship is of the type n

aG/G′ ) φ(u, V) )

∑au

i-1

i

i)0

n

+

∑bV

i-1

i

(7)

i)0

Application of the UNIFAC model to the database of alkyl alkanoates + dibromoalkanes (90 binary systems) was carried

12738


out by first calculating a pair of values for the G/G′ interaction mentioned previously, which are optimum for each individual mixture. To implement the method, previously published data must be used,19-21 corresponding to primary or basic ester/ alkane systems. Marquardt’s algorithm was applied,23 using a least-squares procedure to optimize the following objective function: N

OF ) [

∑ (H

E,exp m,i

E,cal 2 - Hm,i ) /N]1/2

(8)

E for the group of produce highly acceptable estimates of Hm alkyl ester + dibromoalkane systems, or that the addition of a methyl group to the ester, either in the acidic or the alkanoic E values, which is logical part, has a similar effect on the Hm for a model that is initially blind to the position of a functional group. It would be interesting in a future study to extend the approach followed here further, to draw comparisons with mono- and dihalide systems.

i)1

where N is the number of experimental points. When represented graphically, the values followed a regular distribution with the ester chain (u) and that with the dibromoalkane (V). The whole procedure produced individual expressions similar to eq 7 for systems with methanoates, ethanoates, and a third group for mixtures with propanoates, butanoates, and pentanoates. The final step of the results obtained in the nonlinear regressions involved proposing a constant parameter for the ester/Br,Br interaction, and to express the opposite, the Br,Br/ester interaction, an expression that was a function of chain length was more appropriate. Hence, the interaction parameters, depending on the nature of the ester, are expressed in Table 3 for the 90 mixtures studied. Parts a-d of Figure 12 show the experimental values of HEm together with those obtained using the parameters obtained from the expressions given in Table 3. Predicted values of this property can be observed to be very acceptable and very different from those obtained with the original parameters.10 Nevertheless, there are slight differences in the values estimated for the mixtures with butanoates, for which it is not easy to illustrate a tendency with a model that does not include esters with longer acid chains. Parts a-d of Figure 13 show the distribution of the interaction parameter for mixtures of propyl esters as a function of the chain lengths on both components. 6. Conclusions E E and Vm values of binary mixtures of propyl esters Hm (methanoate to butanoate) and R,ω-dibromoalkanes (R ) 1, ω ) 2-6) have been measured at a temperature of 298.15 K and at atmospheric pressure. The experimental data have been compiled in a database constructed as part of a systematic study on a total of 90 binary mixtures, establishing a classification based on the sign of these properties. The classification reflects a degree of complexity in the interpretation of the behavior of the group of mixtures, owing to the evolution of contrasting effects that vary in relation to the chain length of the compounds and their chemical nature. Two different types of thermodynamic models are used to study the behavior of these mixtures. The COSMO-RS method presents the quantification of different contributions due to electrostatic (Misfit), Van der Waals (VdW), and hydrogen bond (H-Bond) interactions (Table 2). The latter were the least significant in all cases studied. The COSMORS methodology only analyzes the influence of the chain length of the mixtures’ components, giving explanations about the different contributions shown. On the whole, acceptable values for the mixing energies are obtained by this method. The results of the COSMOS-RS have also confirmed some ideas proposed previously,3,20 such as considering the interaction parameters as being dependent on the chain length (Table 3) of the compounds for the UNIFAC model, which

Acknowledgment The authors thank to Ministerio Ciencia e Innovacioń for financial support (CTQ2009-12482, CTQ2008-05641) and are very grateful to Centro de Computacioń Cientı´fica de la Universidad Autońoma de Madrid for use their computational facilities. Supporting Information Available: Tables containing the experimental values of excess enthalpies, excess volumes and correlation coefficients. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Ortega, J.; Ortega Navas, A.; Plaćido, J. J. Chem. Thermodyn 2007, 39, 128–141. (2) Ortega, J.; Navas, A.; Plaćido, J.; Toledo, F. J. J. Chem. Thermodyn. 2006, 38, 585–598. (3) Navas, A.; Ortega, J.; de la Nuez, I. J. Chem. Thermodyn. 2009, 41, 1222–1231. (4) Ortega, J.; Marrero, E. J. Chem. Thermodyn. 2007, 39, 742–757. (5) Ortega, J.; Marrero, E.; Toledo, F. J.; Espiau, F. J. Chem. Thermodyn. 2005, 37, 1332–1346. (6) Ortega, J.; Marrero, E.; Toledo, F. J. J. Chem. Thermodyn. 2006, 38, 1139–1149. (7) Klamt, A. COSMO-RS: From Quantum Chemistry to Fluid Phase Thermodynamics and Drug Desing, first ed., Elsevier: Amsterdam, 2005. (8) Ortega, J.; Marrero, E.; Palomar, J. Ind. Eng. Chem. Res. 2008, 47, 3253–3264. (9) Marrero, E.; Ortega, J.; Palomar, J. J. Chem. Thermodyn. 2009, 41, 367–382. (10) Dang, J.; Tassios, D. P. Ind. Eng. Chem. Process Des. DeV. 1986, 25, 22–31. (11) Gmehling, J.; Li, M.; Schiller, M. Ind. Eng. Chem. Res. 1993, 32, 178–193. (12) Ortega, J.; Espiau, F.; Toledo, F. J. J. Chem. Thermodyn. 2004, 36, 193–209. (13) Ortega, J.; Espiau, F.; Wisniak, J. Ind. Eng. Chem. Res. 2010, 49, 406–421. (14) Bondi, A. Physical Properties of Molecular Crystals, Liquids and Glasses; Wiley: New York, 1968. (15) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian03, reVision B.05; Gaussian, Inc.: Wallingford, CT, 2004. (Gaussian). (16) Eckert, F. ; Klamt, A. COSMOtherm, Version C2.1, Release 01.06, COSMOlogicGmbH & Co. KG, Leverkusen, Germany, 2006.

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ReceiVed for reView July 11, 2010 ReVised manuscript receiVed October 7, 2010 Accepted October 12, 2010 IE101479V

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