Thermophysical Properties of Binary and Ternary Mixtures Containing

Ind. Eng. Chem. Res. 2009, 48, 10065–10076

10065

Thermophysical Properties of Binary and Ternary Mixtures Containing Lactams and Methanol Marıá J. Da´vila, Santiago Aparicio, and Rafael Alcalde* Departamento de Quı´mica, UniVersidad de Burgos, 09001 Burgos, Spain

Thermophysical properties of 2-pyrrolidone (PYR), N-methyl-2-pyrrolidone (NMP), and N-cyclohexyl-2pyrrolidone (CHP) binary and ternary liquid mixtures with methanol are reported at 298.15 K and 0.1 MPa over the full composition range. Excess and mixing properties derived from the experimental ones were correlated using Redlich-Kister (RK) equation, for binary mixtures, and Cibulka (C) equation, for ternary ones. Density Functional Theory (DFT) was also used to analyze structural and energetic features of cyclic lactams in gas phase and methanol solution. Results show the formation of H-bonding and dipolar interactions between cyclic amides and methanol, although these are weakened when a third component is added to the binary mixture, thus decreasing remarkably the values of ternary properties in comparison with binary ones and leading to the weakening of the binary blends’ intermolecular interactions. 1. Introduction Large quantities of solvents are used for numerous processes in the chemical and related industries; thus, the challenge of nonharmful solvents, because of new environmental regulations, has promoted a great development of innovative products to protect the environment.1 Hence, the need for a deep knowledge of thermophysical properties of fluid mixtures has appeared driven both by technological and social demands. Currently, the interest for industrial multicomponent processes is increasing. Thus, thermophysical studies are being developed in parallel to industry advances, contributing to the design, improvement and output of the processes. Moreover, experimental values of thermophysical properties allow establishing new predictive models to determinate the properties necessary for the industry in a fast reliable and economical way. Experimental thermophysical properties are also used to obtain information about the molecular level structure of these systems, as well as about the intermolecular interactions and structural features leading to the behavior and macroscopic properties of fluids.2 Intermolecular interactions are a very complex subject, and thus, experimental results and theoretical models have to be combined to elucidate the fluid structure.3 Methanol, M, is a complex fluid because of its high polarity and strong self-association through hydrogen bonding, thus being a challenging compound for experimental and theoretical studies. Numerous theoretical studies about structure of liquid methanol4 have been made and about methanol hydrogen bonding clusters.5 Methanol is also expected to interact strongly with others fluids by hydrogen-bonding6 forming polymeric chains with different lengths. Thus, strong attractive interactions forming clusters should have a considerable effect on the thermodynamics and structural properties. 2-Pyrrolidone and its derivatives are probably the most important members of the lactams’ family, cyclic amides, because of their wide use in several fields ranging from petrochemical to biological applications. 2-pyrrolidone (PYR), Figure 1, is able to self-associate through hydrogen bonding, forming dimers at low amide concentration or higher oligomers in concentrated solutions.7–13 Some substituted 2-pyrrolidones * To whom correspondence should be addressed. E-mail: [email protected].

are frequently considered as models for interaction studies of complex biomolecules because of the presence in their molecular structure of the peptide moiety. N-Methyl-2-pyrrolidone (NMP), Figure 1, is a dipolar aprotic basic solvent that is frequently used to recover hydrocarbons from petrochemical processes by extractive distillation because of the high solubility ability of NMP for these compounds and the volatility differences among them. Moreover, NMP has large chemical and thermal resistance, low toxicity and high selectivity.14 NMP is also used as an extractive agent for paraffins and aromatics separations. Moreover, solvents frequently used as cleaning agents, such as dichloromethane or toluene, have high volatility, toxicity, and flammability, and they are environment harmful; NMP is a powerful alternative compound to replace them because of its low flammability, low volatility, and nontoxicity to aquatic life. NMP is also used as an ingredient in paint strippers, degreasing and cleaning solvents, as well as a compound in insecticides, herbicides, and fungicides.15 The only disadvantage of NMP is its terathogenic ability. N-Cyclohexyl-2-pyrrolidone (CHP), Figure 1, shows a nonpolar region and a donor-acceptor CO-NH peptide bond, and for this reason, it is frequently use to study hydrophobic interactions16 and to model proteins.17 In methanol blends, the thermodynamic properties exhibit anomalies due to H-bonded associations. Hence, for lactams in methanol solutions, it is possible to obtain valuable information of some properties of peptide compounds in alcohol solutions. Because of the strong hydrogen bonding acceptor ability of the CO oxygen of the lactams, they can establish interactions with the hydrogen bond donor of methanol molecule. Thus, thermophysical properties for solvent blends of lactams with methanol show a complex behavior, and they have been used to obtain more information about the intermolecular interactions,18–34 showing a strongly nonideal behavior. Moreover, PYR/M blends show a remarkable molecular level organization, in which the strong interactions between PYR molecules are maintained through dimers formation. Thus, in this paper, we report the results of a thermophysical study on the properties of PYR, NMP, and CHP methanol solutions. Hence, the binary systems PYR + M, NMP + M, CHP + M, PYR + NMP, PYR+CHP, and NMP + CHP were studied together with the PYR + NMP + M, PYR + CHP +

10.1021/ie900822e CCC: $40.75  2009 American Chemical Society Published on Web 08/25/2009

10066

Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009

Figure 1. Optimized structures with electrostatic potential (ESP) mapped on an electronic density surface isovalue of 0.0004 au calculated at B3LYP/6311++g** theoretical level in IEF-PCM methanol solution. Atom color code: gray ) carbon, white ) hydrogen, red ) oxygen, and blue ) nitrogen. In ESP: red ) negative, blue ) positive. Calculated dipole moment for (black) gas phase and (blue) IEF-PCM methanol solution.

Figure 2. Highest binding energy PYR dimer calculated at B3LYP/6311++G** theoretical level in gas phase and IEF-PCM methanol solution. Atom color code as in Figure 1. Distances in Å, and counterpoise corrected binding energies (∆E) in kJ mol-1. Labels: (black) gas phase, (blue) IEFPCM methanol solution. We report only structures for IEF-PCM methanol solution; gas phase ones are indiscernible.

M, and CHP + NMP + M ternary mixtures in the full composition range at 298.15 K and 0.1 MPa. Moreover, computational studies on selected systems were carried out to get a deeper insight into the short-range intermolecular interactions for the studied compounds. These studies were done according to the Density Functional Theory (DFT) using Gaussian 0335 to infer the lactams and lactams/ methanol complexes energetic and structural features, both in gas phase and methanol solutions. 2. Materials and Methods 2.1. Compounds. The solvents PYR (Fluka, purity >98.0%), NMP (Fluka, purity >99.0%), CHP (Sigma-Aldrich, purity >99.0%), and methanol (Fluka, purity >99.8%) were used without further purification, stored over Fluka 0.3 nm molecular sieves, and degassed with ultrasounds. Their purity was checked by Gas Chromatography and through comparison of thermophysical properties with literature values (Supporting Information, Table S1, refs 36–45 contained therein). A Mettler AT261 microbalance ((1 · 10-5g) was used to prepare the mixture samples, to (1 × 10-4 in the mole fraction. The procedure to

obtain a homogeneous sample distribution for ternary mixtures in the whole composition range was described previously.46 2.2. Instrumentation. Density, F, and speed of sound, u, were measured simultaneously with an Anton Paar DSA 5000 apparatus, by oscillating U-tube method for density ((5 × 10-6 g cm-3), and for speed of sound through the measurement of the traveling time through the sample of an impulse emitted by a piezoelectric transducer to a detector ((0.5 m s-1). Temperature of the cells was controlled by a built-in Peltier device ((1 × 10-2 K) and measured by internal platinum resistance thermometers ((1 × 10-2 K). Calibration was carried out using two reference standards, nonane (Fluka, purity >99.5%) and toluene (Sigma-Aldrich, purity >99.5%), the density values of which were obtained from the literature.44 Dynamic viscosity, η, was measured with an automated Anton Paar AMV200 rolling ball microviscometer by the rolling ball measuring principle. Temperature was controlled using a Julabo F25 external thermostat and measured using a platinum resistance thermometer ((1 × 10-2). The rolling time was measured to ( 1 × 10-2 s, thus dynamic viscosity was obtained with a precision of ( 5 × 10-3 mPa s. Calibration was carried out using dodecane (Aldrich, >99.5%), hexan-1-ol (Fluka, >99.5%), octan-1-ol (Fluka, >99.5%), and decan-1-ol (Fluka, >99.5%) as standards.44 Refractive indices, nD, were measured in relation to the sodium D line by an automated Leica AR600 refractometer ((5 × 10-6). Temperature was controlled by a Julabo F32 external circulator and measured by a platinum resistance thermometer ((1 × 10-2 K). Calibration was performed using double degassed water (Millipore Milli-Q) and a standard oil (nD ) 1.51416) supplied by the manufacturer. Isobaric molar heat capacities, CP, were measured to (1 × 10-2 J mol-1 K-1 by a Setaram micro DSC III calorimeter. It consists of two vessels (reference and measuring) surrounded by a thermostatic liquid (undecane) which ensures a homogeneous temperature, using Peltier elements ((1 × 10-2K) to control the temperature. The measuring principle is based on the Calvet principle which determines the


10067

Figure 3. Highest binding energy (a) PYR + 3M, (b) NMP + 2M, and (c) CHP + 2M complexes calculated at B3LYP/6-311++G** theoretical level in gas phase and IEF-PCM methanol solution. Atom color code as in Figure 1. Distances in Å, and counterpoise corrected binding energies (∆E) in kJ mol-1. Labels: (black) gas phase, (blue) IEF-PCM methanol solution. We report only structures for IEF-PCM methanol solution; gas phase ones are indiscernible.

Figure 4. Density, F, dynamic viscosity, η, and isentropic compressibility, kS, at 298.15 K and 0.1 MPa. Symbols: (O, black) xPYR + (1 - x)M, (O, purple) NMP + (1 - x)M, (4, red) xCHP + (1 - x)M, (∆, orange) xPYR + (1 - x)NMP, (0, green) xPYR + (1 - x)CHP, and (), blue) xNMP + (1 - x)CHP. Experimental points: symbols; fitting equations: lines (Table S5, Supporting Information, and refs 34 and 60).

variation of the heat flow to/from liquid samples, both cells maintained to the same temperature. Measurements were performed according to the isothermal step method,47 with Hexane (Fluka, >99.5%) as the reference material and butan1-ol (Aldrich, >99.5%) as the calibration liquid.43 E Excess molar volume, Vm , mixing viscosity, ∆mixη, and mixing refractive index, ∆mixnD, were evaluated from the experimental data according to well-known thermodynamic expressions.48 Isentropic compressibility, kS, was calculated from Laplace equation. Excess isentropic compressibilities, kSE, and excess molar isobaric heat capacities, CPE, were calculated according to the ideality criteria proposed by Benson et al.49 The excess and mixing properties for the binary systems, XE, were correlated with composition, x, using the Redlich-Kister equation.50 k

XE ) x(1 - x)

∑ A (2x - 1) j

(1)

j)1

Where values of Aj coefficients being obtained by a least-squares procedure with the proper number of coefficients, k, determined by an F-test.51 E Ternary excess and mixing properties (XTER ) were fitted to 52 Cibulka equation

2.3. Density Functional Theory (DFT) Calculations. We have carried out DFT computations on PYR and CHP monomers and complexes formed by these cyclic amides and methanol in gas phase and methanol solution (results for NMP were described in a previous work).34 Computations were carried out using the Becke gradient-corrected exchange functional53 and Lee-Yang-Parr correlation functional with three parameters (B3LYP)54,55 together with 6-311++G** basis sets. Atomic charges were calculated to fit the electrostatic potential56 according to the Merz-Singh-Kollman (MK)57 scheme; the fitting procedure was constrained to reproduce the overall molecular dipole moment. Calculations in methanol solutions were carried out using the self-consistent reaction field approach (SCRF) with the solvent treated as a continuum, using the integral equation formalism of the polarization continuum model approach (IEF-PCM).58 The cavity where the solute is located was built using the united atom model, a value of 1.2 was used to scale the radii and 70 tesserae per sphere were considered. This treatment provides a quantitative estimation of contributions to the total Gibbs energy of solvation. Energy of complexes was calculated as the difference among the complexes and monomers energies with the basis set superposition error (BSSE) corrected according to the counterpoise procedure.59 3. Results and Discussion

XETER

)

E XBIN

+ x1x2x3(B0 + B1x1 + B2x2)

(2)

E where XBIN represents the sum of properties for the three corresponding binary constituents from eq 1 and last term is the so-called ternary contribution to the corresponding property.

3.1. Computations on Pure Lactams and Lactams/Methanol Complexes. Figure 1 shows the results for cyclic lactams at B3LYP/6-311++G** theoretical level in gas phase and M solution (parameters are reported in Tables S2 and S3, Supporting Information). Electrostatic potential surface (EPS) shows

10068


E Figure 5. Excess molar volume, Vm , mixing viscosity, ∆mixη, excess isentropic compressibility, kSE, mixing refractive index, ∆mixnD, excess isobaric molar heat capacity, CPE, and excess molar Gibbs energy of activation, ∆G*mE, at 298.15 K and 0.1 MPa. Colors as in Figure 4. Experimental points: symbols; fitting equations: lines (Table S5, Supporting Information, and refs 34 and 60).

E E jm j P,m Figure 6. Partial molar excess volume, V , and partial molar excess isobaric heat capacity, C , of the i-compound in the binary mixtures reported in Figure 4 at 298.15 K and 0.1 MPa. Colors as in Figure 4.

a positive region on the hydrogen attached to the amide nitrogen in PYR; thus PYR has the largest dipole moment among the studied lactams, increasing from gas phase to methanol solution. EPS, for NMP and CHP, show the amide nitrogen immersed

in an hydrophobic region, hindering H-bonding development through this site. The calculated dihedral angles (11-10-13-15 and 11-1013-16 in Tables S2 and S3, Supporting Information) show one


10069

E E E Figure 7. Excess molar volume, Vm,TER , ternary contribution of excess molar volume, Vm,TER - Vm,BIN , mixing viscosity, ∆mixηTER, and ternary contribution of mixing viscosity, ∆mixηTER - ∆mixηTER, mixing refractive index, ∆mixnD,TER, and ternary contribution of mixing refractive index, ∆mixnD,TER - ∆mixnD,BIN, for the x1PYR + x2CHP + (1 - xi1 - x2)M ternary system at 298.15 K and 0.1 MPa.

E E E Figure 8. Excess isentropic compressibility, kS,TER , ternary contribution of excess isentropic compressibility, kS,TER - kS,BIN , excess isobaric molar heat E E E capacity, CP,TER , and ternary contribution of excess isentropic compressibility, CP,TER - CP,BIN , for the x1PYR + x2CHP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

of the hydrogens of methyl and cyclohexyl groups eclipsing the carbonyl oxygen both for NMP and CHP, stabilizing both configurations by mean of interactions among the hydrogen atom and the strongly negative carbonyl oxygen. In Table 1, we report the main molecular parameters for the three studied molecules. The charge in the carbonyl oxygen is larger in absolute value in methanol solution, thus justifying the increase in the dipole moment on going to solution. On the other hand, lactam monomers show length increase for the carbonyl bond and decrease in the amide bond from gas phase to methanol solution, matching up with the dipole moment increase in 40% (PYR), 42% (NMP) and 47% (CHP) respectively, because of the selfconsistent reaction field interaction with these groups. Therefore, in methanol solution, the oxygen bonds are weakened whereas nitrogen ones are reinforced. The changes of energy upon going

to M solutions, ∆E () Esol - Egas), and the total Gibbs energy of solvation, ∆Gsol, as a sum of electrostatic, ∆Gelec, and nonelectrostatic ∆Gnonelec terms, are reported in Table 2. PYR shows the larger ∆Gsol, and thus, we may conclude that it is more efficiently solvated by surrounding M than NMP or CHP molecules. NMP and CHP show the largest nonelectrostatic contributions due to the large requirement of work to build the PCM cavity. Besides, PYR differ from the other two lactams in the capability of building open or hexagonal cyclic dimers, Figure 2, being the last one more probable, both in gas phase and methanol solution, which is in agreement with literature results.13 Complexes PYR + 3M, NMP + 2M,34 and CHP + 2M have been studied in gas phase and in methanol solution, Figure 3, to analyze short-range lactam/methanol hydrogen bonding.

10070


E E j m,i j P,i Figure 9. Partial excess molar volume of i-compound, V , and partial excess isobaric molar heat capacity, C , in the x1PYR + x2CHP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

E E E Figure 10. Excess molar volume, Vm,TER , ternary contribution of excess molar volume, Vm,TER - Vm,BIN , mixing viscosity, ∆mixηTER, and ternary contribution of mixing viscosity, ∆mixηTER - ∆mixηTER, mixing refractive index, ∆mixnD,TER, and ternary contribution of mixing refractive index, ∆mixnD,TER - ∆mixnD,BIN, for the x1CHP + x2NMP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

These complexes show intermolecular distances remarkably low, assuring the formation of H-bondings, decreasing on going to methanol solution. The binding energies are remarkably large especially for PYR/3 M complexes, although they decrease on going to M solutions. Hence, intermolecular interactions among lactams and methanol molecules are very effective. The solvation at low amide concentration, as the IEF-PCM model describes considering complexes surrounded by a medium that mimics M, is also efficient. 3.2. Thermophysical Properties of the Binary Constituents. The properties of PYR + M, CHP + M, and PYR + NMP, and derived excess and mixing ones are reported in Figures 4-6 and Tables S4 and S5 (Supporting Information); results for NMP/M,34 NMP/CHP, and PYR/CHP binary constituents were reported earlier.60 Experimental results for density, dynamic viscosity and isentropic compressibility, Figure 4, show the lactam/lactam mixtures tend to ideal/linear behavior whereas lactams/M mixtures show stronger deviations respect ideality/ linearity. This effect is more remarkable for PYR/M because of PYR self-associations in its pure state. The three studied

lactams in methanol have an efficient packing by H-bonding network heteroassociation mainly through PYR + 3M, NMP + 2M,34 and CHP + 2M aggregates, which are favored as previously showed through DFT computations.34 Excess molar volumes, Figure 5, for lactam/M mixtures are negative in the whole composition range, therefore systems have a strong packing effect by heteroassociations between both molecules through H-bonding. The structural changes upon mixing are remarkable for NMP and CHP, considering that despite of the dipolar ordering in their pure compounds, H-bonding is only developed in the presence of M molecules. The PYR structuring through dimers in the pure state evolves through interaction with M molecules upon mixing as the very negative excess molar volume, with minimum in M rich regions, show. Mixing viscosities for lactam/methanol systems are negative in the whole composition range, except for NMP/M blends that show values close to zero, which is in agreement with the development of H-bonding heteroassociations. Maxima and minima for the studied excess and mixing properties point to the formation of CHP + 2 M and PYR + 3 M heteroasso-


10071

E E E Figure 11. Excess isentropic compressibility, kS,TER , ternary contribution of excess isentropic compressibility, kS,TER - kS,BIN , excess isobaric molar heat E E E capacity, CP,TER , and ternary contribution of excess isentropic compressibility, CP,TER - CP,BIN , for the x1CHP + x2NMP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

E E j m,i j P,i Figure 12. Partial excess molar volume of i-compound, V , and partial excess isobaric molar heat capacity, C , in the x1CHP + x2NMP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

ciations, which are favored as previously showed by DFT computations. Partial molar properties are reported in Figure 6, and the infinite values of these properties are shown in Table 3, showing an efficient solvation of the three lactams in M, with strong heteroassociations mainly in M rich regions. At infinite dilution of M in lactam, negative partial excess molar volumes of M show that this molecule fits properly within lactams structure, as well as they fit in the M H-bonding network at low amide concentrations. PYR/NMP and PYR/ CHP systems show small negatives excess volume values in the whole composition range which mean in practice an effective packing because of the resemblance of both molecules, whereas NMP/CHP mixture shows positive excess volume because of expansive effects rising from the presence of cyclohexyl ring. Mixing viscosity of lactam/lactam mixtures is negative in the whole composition range except for PYR/CHP; this is due to the strong dipolar interactions

between both cyclic amides, turning out a very effective packing. In PYR/NMP mixing process, resemblance sizes and geometric shapes contribute to an efficient packing as well, however PYR-PYR interactions are weakened because of NMP and vice versa, thus negative values of mixing viscosity in PYR/NMP and NMP/CHP rule out H-bonding heteroassociations, with this behavior being confirmed by the excess and mixing properties. 3.3. Properties of PYR/CHP/M Ternary Mixtures. Excess and mixing properties for the ternary system are plotted in Figures 7-9 with the experimental data and fitting results reported in Tables S6-S7 (Supporting Information). Figure 7a shows negative excess volume in the whole composition range, increasing with M concentration. Moreover, Figure 7b shows a positive ternary contribution with a maximum reported in Table S8 (Supporting Information). This behavior is due to the disruptive effects of the simultaneous presence

10072


E E E Figure 13. Excess molar volume, Vm,TER , ternary contribution of excess molar volume, Vm,TER - Vm,BIN , mixing viscosity, ∆mixηTER, and ternary contribution of mixing viscosity, ∆mixηTER - ∆mixηTER, mixing refractive index, ∆mixnD,TER, and ternary contribution of mixing refractive index, ∆mixnD,TER - ∆mixnD,BIN, for the x1PYR + x2NMP + (1 - x1 - x2) M ternary system at 298.15 K and 0.1 MPa.

E E E Figure 14. Excess isentropic compressibility, kS,TER , ternary contribution of excess isentropic compressibility, kS,TER - kS,BIN , excess isobaric molar heat E E E capacity, CP,TER , and ternary contribution of excess isentropic compressibility, CP,TER - CP,BIN , for the x1PYR + x2NMP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

of PYR, CHP and M molecules, which hinders the development of heteroassociations, and thus being the property mainly controlled by geometric factors. Mixing viscosity, Figure 7c, is negative except at high cyclic amide concentration, rising when M concentration decrease in the mixture. Ternary contribution, Figure 7d, is negative, and the minimum position shows geometric factors and heteroassociation of 1 PYR:1 CHP:2 M type. Mixing refractive index is positive in the whole composition range, Figure 7e, being negative the respective ternary contribution, Figure 7f. This is in agreement with the behavior of excess molar volume and mixing viscosity, a less compressible mixture with the maxima located at almost equal quantities of the three molecules, because of the disruptive effect rising from the presence of the two lactams simultaneously. Excess isentropic compress-

ibility, Figure 8a, shows negative values, decreasing with the M concentration. Its ternary contribution, Figure 8b, shows negative values in the full composition range except at high PYR concentration, with the maximum located in 2PYR/1CHP/2M composition ratio, thus showing how geometric factors control the system behavior. Excess isobaric heat capacity, Figure 8c, shows a complex behavior with maximum and minimum, the intermolecular associations are weakened upon mixing and, due to the hydrophobic character of the cyclohexyl group of CHP, heteroassociation formation is hindered. Excess partial molar volumes for both lactams, Figure 9a and b, are negative except for CHP in rich zones of PYR, pointing to the development of interactions through hydrogen bonding, being these interactions stronger for high alkanol


10073

E E j m,i j P,i Figure 15. Partial excess molar volume of i-compound, V , and partial excess isobaric molar heat capacity, C , in the x1PYR + x2NMP + (1 - x1 - x2)M ternary system at 298.15 K and 0.1 MPa.

Table 1. Main Monomers’ Parameters Calculated at B3LYP/ 6-311++G** Theoretical Level in Gas Phase and Methanol Solution (IEF-PCM)a

PYR NMPb CHP

q(MK)

C(O)-O/Å

C(O)-N/Å

N-C(O)-O/deg

-0.605 -0.754 -0.592 -0.725 -0.623 -0.757

1.2152 1.2339 1.2181 1.2337 1.2181 1.2353

1.3700 1.3497 1.3712 1.3549 1.3712 1.3558

125.99 125.86 125.77 125.71 125.77 125.92

a q(MK) ) Merz-Singh-Kollman charges for carbonyl oxygen. Bold numbers: methanol solution. b Data from ref 34.

Table 2. Changes of Energy (∆E ) Esol - Egas), Gibbs Energies of Solvation (∆Gsol), and Electrostatic (∆Gelec) and Nonelectrostatic (∆Gnonelec) Contributions to the ∆Gsol Calculated at B3LYP/ 6-311++G** Theoretical Level in Methanol Solutions (IEF-PCM) for PYR, NMP, and CHPa

PYR NMPb CHP a

∆E

∆Gelec

∆Gnonelec

∆Gsol

-45.27 -31.51 -33.60

-47.57 -34.14 -35.10

7.20 13.81 13.93

-40.33 -20.33 -21.13

All energies in kJ mol-1. b Data from ref 34.

E,∞ jm Table 3. Infinite Dilution Partial Excess Molar Volume, V , and j E,∞ Infinite Dilution Partial Excess Isobaric Molar Heat Capacity, C P , for xPYR + (1 - x)M, xCHP + (1 - x)M, and xPYR + (1 - x) at a 298.15 K and 0.1 MPa E,∞ jm j PE,∞/J mol-1 K-1 V /cm3 mol-1 C

(1) PYR + (2) M (1) CHP + (2) M (1) PYR + (2) NMP

(1)

(2)

(1)

(2)

-5.6046 -5.0941 -1.1556

-2.2830 -2.8588 -1.1242

12.84 3.65 2.99

3.44 -1.19 2.75

a The numbers in brackets show the compound for which the property is reported for each mixture.

concentration. Moreover, M partial excess molar volume, Figure 9c, shows H-bonding formation and effective packing of this molecule within lactams’ rich fluids. Excess partial heat capacity, Figure 9d and e, have a difficult interpretation. For CHP at high PYR concentration, it shows negative values, therefore dipolar interaction are weakened upon PYR concentration rising. Strongly negative values in the partial excess property for M, Figure 9f, in the rich CHP zone, show also interaction weakening. For PYR, an increasing of the

property with the CHP mole fraction is obtained, thus PYR shows remarkable affinity for CHP molecules. Values for M shows that it has more affinity for PYR than for CHP molecules. 3.4. Properties of CHP/NMP/M Ternary Mixtures. Excess and mixing properties for this ternary system are plotted in Figures 10-12 and experimental data are reported in Tables S9-S10 (Supporting Information). Excess molar volume is negative in the full composition range, except for low methanol concentrations, Figure 10a, and the ternary contribution, Figure 10b, of the property positive in the full composition range. Therefore, H-bonding formation is hindered in the mixture when both amides are present, due to the differences in their sizes and shapes. Mixing viscosity, Figure 10c, is negative in the full composition range and its ternary contribution, Figure 10d, is positive except in rich lactam zones, with a maximum (Table S11, Supporting Information) located in 1CHP/1NMP/2M composition ratio. This shows that the simultaneous presence of both amides hinders the H-bonding development with methanol molecules. Mixing refractive index, Figure 10e, shows positive values, and ternary contribution, Figure 10f, is mainly negative in the whole composition range, with minimum values suggesting preferential interaction for a 1CHP/1NMP/2M composition ratio. Thus, both lactams lead to a disruptive effect on methanol H-bonding network. Excess isentropic compressibility, Figure 11a, and its ternary contribution, Figure 11b, show mainly negative values, pointing to the weakening of the H-bonding formed in lactams/M. Excess isobaric heat capacity, Figure 11c, and its ternary contribution, Figure 11d, show small values, with positive and negative regions. Thus, the results show that heteroassociation formation or disruptive effects prevails depending on the mixture composition. Steric effects are also remarkable considering the necessary lactams’ adaptation to the dominated methanol liquid structure to develop interactions by H-bonding. Partial molar properties are reported in Figure 12. Excess partial molar volumes, Figure 12a - c, are negative except for the cyclic lactams at high lactam concentration, thus heteroassociation seems to be intense except among cyclic amides, increasing dipolar interaction in M poor blends. Excess partial heat capacities are reported in Figure 12d and e, being negative for the three molecules, except at high M

10074


concentration, showing the highest value for CHP in NMP/M mixtures, increasing with the M concentration. Hence, a greater affinity of CHP for M molecules may be inferred. Values for NMP in CHP/M mixture increase with M concentration because of high CHP concentrations that hinder interaction among NMP and M molecules. Values for M show that the ability to develop heteroassociation with NMP is larger than with CHP because of the cyclohexyl bulky group leading to greater steric effects. 3.5. Properties of PYR/NMP/M Ternary Mixtures. Excess and mixing properties are plotted in Figures 13-15 and experimental data are reported in Tables S12-S13 (Supporting Information). Excess molar volume is negative, Figure 13a, being the ternary contribution, Figure 13b, of the property positive in the whole composition range, inferring a slight expansion of the binary systems when the second lactam is added. Thus, this ternary mixture has weak heteroassociations, being its structure controlled by geometric factors. Mixing viscosity, Figure 13c, is negative in the full composition range. Its ternary contribution, Figure 13d, is small and positive with a minimum at 2PYR/1NMP/1M (Table S14, Supporting Information), pointing to heteroassociation weakening compared with the binary mixtures. Mixing refractive index, Figure 13e, shows mainly positive values, with its ternary contribution, Figure 13f, being negative, with a minimum that suggest a preferential interaction for 1PYR/1NMP/2M composition ratio. Thus, geometric effects prevail over heteroassociations by H-bondings. Excess isentropic compressibility, Figure 14a, is always negative, with maximum values in the rich M region, and its ternary contribution, Figure 14b, mainly showing negative values, changing to positive with a maximum in the M poor region. This behavior shows how the presence of M controls the H-bonding formation, being the more favored interaction of 1PYR/1NMP/2M type. Excess molar isobaric heat capacity, Figure 14c, is positive in the full composition range, whereas the ternary contribution, Figure 14d, is negative except in the poor CHP regions. Therefore, a disruptive effect when CHP molecules are added to the mixture may be inferred leading to a hindering of H-bonding formations. Partial molar properties are reported in Figure 15. Excess partial molar volumes, Figure 15a-c, are negative for the three compounds, although more negative values are obtained in the M rich regions close to infinite dilution. For M in CHP/ NMP large values of the property in both lactam rich regions are obtained. Thus, from these tendencies, the existence of strong interaction between lactam and M may be inferred, but it discards the development of ternary interactions. Excess partial heat capacities for both lactams, in Figure 15d and e, are negative for the three compounds, except at high PYR concentration. Values for both lactams increase with M concentration, showing the greater affinity of PYR for M molecules. Values for M decrease when both lactams are simultaneously present in the mixture, although M is able to develop heteroassociation with both lactams, increasing the affinity in the infinite dilution region. 4. Concluding Remarks Lactam/M binary systems show strong deviations of ideality. CHP/M system shows the strongest structuring by H-bondings compared with the other two systems, being the smallest values of the properties for PYR/M, because of the residual PYR-PYR homoassociations remaining in the binary mixture. Lactam/lactam mixtures show an almost ideal

behavior, but having a certain structural rearrangement and dipolar interactions upon mixing. Ternary systems show strong deviations from ideality because of the existence of strong heteroassociations competing with homoassociations through H-bonding. Nevertheless, the simultaneous presence of two lactams and M molecule hinders the development of heteroasocciations, in comparison with binary systems, because of the less compact packing obtained. This effect is stronger when the ternary mixture contains CHP, because of the bulky and hydrophobic character of the cyclohexyl group. Thus, ternary systems do not tend to the simultaneous formation of complexes between the three constituent molecules. In spite of the large binary lactam-M interactions remaining in the ternary mixture, they are weakened when the concentration of the second lactam rises. Acknowledgment The financial support by Junta de Castilla y Leoń, Project BU020A07, and Ministerio de Educacioń y Ciencia, Project CTQ2005-06611/PPQ, Spain, is gratefully acknowledged. Supporting Information Available: Thermophysical properties of pure solvents, calculated molecular parameters of PYR, calculated molecular parameters of CHP, binary mixtures properties, fitting coefficients for binary mixtures excess and mixing properties, x1PYR + x2CHP+ (1 - x1 x2)M ternary mixture properties, fitting coefficients for x1PYR + x2CHP+ (1 - x1 - x2)M ternary mixture excess and mixing properties, maxima and minima for the ternary contributions to excess and mixing properties for x1PYR + x2CHP+ (1 x1 - x2)M, x1CHP + x2NMP+ (1 - x1 - x2)M ternary mixture properties, fitting coefficients for x1CHP + x2NMP+ (1 - x1 - x2)M ternary mixture excess and mixing properties, maxima and minima for the ternary contributions to excess and mixing properties for x1CHP + x2NMP + (1 - x1 x2)M, x1PYR + x2NMP+ (1 - x1 - x2)M ternary mixture properties, fitting coefficients for x1PYR + x2NMP + (1 x1 - x2)M ternary mixture excess and mixing properties), and maxima and minima for the ternary contributions to excess and mixing properties for x1PYR + x2NMP + (1x1 x2)M.This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Poliakoff, M.; Fitzpatrick, J. M.; Farren, T. R.; Anastas, P. T. Green Chemistry: Science and Politics of Change. Science 2002, 297, 807–810. (2) Marcus, Y. Solvent Mixtures. Properties and SelectiVe SolVation; Marcel Dekker: New York, 2002. (3) Murrell, J. N.; Jenkins, A. D. Properties of Liquids and Solutions; John Wiley & Sons Ltd.: Chichester, 1994. (4) Jorgenson, W. L. Quantum and Statistical Mechanical Studies of Liquids 0.11. Transferable Intermolecular Potential Functions - Application to Liquid Methanol Including Internal-Rotation. J. Am. Chem. Soc. 1981, 103, 341–345. (5) Staib, A. Theoretical Study of Hydrogen Bond Dynamics of Methanol in Solution. J. Chem. Phys. 1998, 108, 4554–4562. (6) Simonson, J. M.; Bradley, D. J.; Busey, R. H. Excess Molar Enthalpies and the Thermodynamics of (Methanol + Water) to 573 K and 40 MPa. J. Chem. Thermodyn. 1987, 19, 479–492. (7) Jadzyn, J.; Malecki, J.; Jadzyn, C. Dielectric Polarization of 2-Pyrrolidinone-Benzene Solutions. J. Phys. Chem. 1978, 82, 2122– 2130. (8) Walmsey, J. A. Self-Association of 2-Pyrrolidinone. 2. Spectral and Dielectric Polarization Studies of Benzene Solutions. J. Phys. Chem. 1978, 82, 2031–2035.

Ind. Eng. Chem. Res., Vol. 48, No. 22, 2009 (9) Dachwitz, E.; Stockhausen, M. Dielectric-Relaxation of 2-Pyrrolidinone and Some N-Substituted, Related-Compounds in the LiquidState. Ber. Bunsenges. Phys. Chem. Phys. 1985, 89, 959–961. (10) Beine, A. H.; Dachwitz, E.; Wodniok, L.; Stochhausen, M. On the Assessment of Dielectric-Relaxation Parameters of Liquids. Z. Naturforsch. 1986, 41, 1060–1070. (11) Yekeler, H. Solvent Effects on Dimeric Self-Association of 2-Pyrrolidinone: An Ab Initio Study. J. Comput.-Aided Mol. Des. 2001, 15, 287–295. (12) Prokopenko, N. A.; Bethea, I. A.; Clemens, C. J.; Klimek, A.; Wargo, K.; Spivey, C.; Waziri, K.; Grushow, A. The Effect of Structure on Hydrogen Bonding: Hydrogen Bonded Lactam Dimers in CCl4. Phys. Chem. Chem. Phys. 2002, 4, 490–495. (13) Shchavlev, A.E.; Pankratov, A. N.; Borodulin, V. B.; Chaplygina, O. A. DFT Study of the Monomers and Dimers of 2-Pyrrolidone: Equilibrium Structures, Vibrational, Orbital, Topological, and NBO Analysis of Hydrogen-Bonded Interactions. J. Phys. Chem. A 2005, 109, 10982–10996. (14) Mueller, E.; Hoehfeld, G. World Petroleum Congresses (8th); Applied Science: London, 1971; p 211. (15) Wypych, G. New Trends Based on Patent Literature. Handbook of SolVents; ChemTec Publishing: Toronto, 2001. (16) Mooijman, F. R.; Engberts, J. B. F. N. Kinetic Medium Effects in N-Cyclohexyl-2-Pyrrolidone Water MixturessEvidence for a Low Critical Hydrophobic Interaction Concentration. J. Org. Chem. 1989, 54, 3993–3995. (17) Lawson, E. Q.; Sadler, A. J.; Harmatz, D.; Brandau, D. T.; Micanov, R.; MacElroy, R. D.; Middaugh, C. R. A Simple ExperimentalModel for Hydrophobic Interactions in Proteins. J. Biol. Chem. 1984, 259, 2910–2912. (18) Granshan, V. A.; Kirillova, O. G. Physicochemical Analysis of N-Methyl-R-Pyrrolidinone-Methanol System. Zh. Prikl. Khim. 1970, 43, 1875–1881. (19) Joly, R. D.; Mermet-Dupin, M. Hebd. Seanc. Acad. Science. Ser. C 1975, C280, 1363. (20) Awwad, A. M.; Al-Mashhadani, A. M.; Tawfeek, E. A. Excess Volumes of (N-Methylpyrrolidone + Isoalkanol) at 298.15 K. J. Chem Thermodyn. 1986, 18, 131–133. (21) Dachwitz, E.; Stockhausen, M. A. Dielectric-Relaxation Study of Self and Heteroassociation in Binary-Liquid Mixtures of 3 Pyrrolidinones with Alcoholes and Water. Ber. Bunsenges. Phys. Chem. 1987, 91, 1347–1351. (22) Garcıá, B.; Herrera, C.; Leal, J. M. Shear Viscosities of BinaryLiquid Mixturess2-Pyrrolidone with 1-Alkanols. J. Chem. Eng. Data 1991, 36, 269–274. (23) Garcıá, B.; Herrera, C.; Leal, J. M. Thermodynamics of 2-Pyrrolidinone + Normal-Alkanol Binary-MixturessActivation Properties. Thermochim. Acta 1991, 180, 159–167. (24) Mehta, S. K.; Chauhan, R. K.; Dewan, R. K. Excess Volumes and Isentropic Compressibility’s of Pyrrolidin-2-one-Alkanol (C-1-C-5) Binary Mixtures. J. Chem. Soc., Faraday Tran. 1996, 92, 1167–1173. (25) Mehta, S. K.; Chauhan, R. K.; Triphati, A.D. Excess Molar Enthalpies of Mixtures of Pyrrolidin-2-one with Methanol, or Ethanol, or Propan-1-ol, or Butan-1-ol, or Pentan-1-ol at the Temperature 303.15 K. J. Chem Thermodyn. 1997, 29, 353–358. (26) Lo´pez, E. R.; Garcıá, J.; Fernańdez, J. Excess Properties of Some Methanol plus Amide Systems Proposed as Working Fluids for Absorption Machines. J. Chem. Eng. Data 1999, 44, 309–313. (27) Garcıá, B.; Alcalde, R.; Aparicio, S.; Leal, J. M. Volumetric Properties, Viscosities and Refractive Indices of Binary Mixed Solvents Containing Methyl Benzoate. Phys. Chem. Chem. Phys. 2002, 4, 5833– 5840. (28) Zielkiewicz, J. Excess Gibbs Energies and Excess Molar Volumes for Binary Mixtures: (2-Pyrrolidone plus Water), (2-Pyrrolidone plus Methanol), and (2-Pyrrolidone plus Ethanol) at the Temperature 313.15 K. J. Chem. Thermodyn. 2002, 34, 1693–1701. (29) Garcıá, B.; Alcalde, R.; Aparicio, S.; Leal, J. M.; Trenzado, J. L. Thermophysical Behavior and Temperature Effect on the N-Methylpyrrolidone plus (C-1-C-10) Alkan-1-ols Mixed Solvents. Ind. Eng. Chem. Res. 2003, 42, 920–928. (30) Zielkiewicz, J. Preferential Solvation in {Amide Plus Alcohol} Binary Mixtures. Part 2. The N-Methylpyrrolidinone plus Methanol Mixture at T ) 313.15 K: Thermodynamic Results and Molecular Dynamics Calculations. Phys. Chem. Chem. Phys. 2003, 5, 3193–3201. (31) Horstmann, S.; Fischer, K.; Gmehling, J. Isothermal VaporLiquid Equilibrium and Excess Enthalpy Data for the Binary Systems Water plus Sulfolane and Methanol plus N-Methyl-2-Pyrrolidone. J. Chem. Eng. Data 2004, 49, 1499–1503.

10075

(32) Gonza´lez, J. A.; Cobos, J. C.; de la Fuente, I. G. Thermodynamics of Binary Mixtures Containing N-Alkylamides. J. Mol. Liq. 2004, 115, 93–103. (33) Aparicio, S.; Garcıá, B.; Alcalde, R.; Da´vila, M. J.; Leal, J. M. PVTx Measurements of the N-Methylpyrrolidone/Methanol Mixed Solvent: Cubic and SAFT EOS Analyses. J. Phys. Chem. B 2006, 110, 6933–6942. (34) Aparicio, S.; Alcalde, R.; Davila, M. J.; Garcia, B.; Leal, J. M. Measurements and Predictive Models for the N-Methyl-2-Pyrrolidone/ Water/Methanol System. J. Phys. Chem. B 2008, 112, 11361–11373. (35) 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.; 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. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (36) Garcıá, B.; Hoyuelos, F. J.; Alcalde, R.; Leal, J. M. Molar Excess Volumes of Binary Liquid Mixtures: 2-Pyrrolidinone with C-6-C-10 N-Alkanols. Can. J. Chem. 1996, 74, 121–127. (37) PirilaHonkanen, P. V.; Ruostesuo, P. A. Thermodynamic and Spectroscopic Properties of 2-Pyrrolidinones 0.1. Excess Molar Volumes of 2-Pyrrolidinone + Dichloromethane, + Dimethylsulfoxide, + Acetone, + 2-Propanol, and + Water. J. Chem. Eng. Data 1987, 32, 303– 306. (38) Hradetzky, G.; Hammerl, I.; Bittrich, H. J.; Wehner, K.; Kisan, W. SelectiVe SolVents, 31st ed.; Elsevier: Amsterdam, 1989. (39) Riddick, J. A.; Bunger, W. B.; Sakano, T. K. Organic SolVents Physical Properties and Methods of Purification; John Wiley and Sons: New York, 1986. (40) Yang, C.; Xu, W.; Ma, P. Thermodynamic Properties of Binary Mixtures of p-Xylene with Cyclohexane, Heptane, Octane, and N-Methyl2-pyrrolidone at Several Temperatures. J. Chem. Eng. Data 2004, 49, 1794–1801. (41) Henni, A.; Hromek, J. J.; Tonitwechwuthikul, P.; Chakma, A. Volumetric Properties and Viscosities for Aqueous N-Methyl-2-Pyrrolidone Solutions from 25 °C to 70 °C. J. Chem. Eng. Data 2004, 49, 231– 234. (42) Vasilev, V. A.; Novikov, A. N. Thermochemical and Volume Properties of the N-Methylpyrrolidone-Water System at 288-323 K. IzV. Vyssh. Uchebn. ZaVed. Khim. Khim. Tekhnol 1989, 32, 5–56. (43) Zabransky, M.; Ruzicka, V.; Mayer, V.; Domalski, E. S. Heat Capacity of Liquids: Volume 1sCritical Review and Recommended Values. J. Phys. Chem. Ref. Data Monograph 6; American Chemical Society: Washington, DC, 1996. (44) Lemmon, E. W.; McLinden, M. O.; Friend, D. G. Thermophysical Properties of Fluid Systems. In NIST Chemistry WebBook; NIST Standard Reference Database Number 69; Linstrom, P. J. Mallard, W. G., Eds.; National Institute of Standards and Technology: Gaithersburg, MD, 2005; http://webbook.nist.gov. (45) Naziev, Y. M.; Shahverdiyev, A. N.; Hasanov, V. H. The (p, p, T) of (Methanol plus Benzene) and (Methanol plus Ethylbenzene). J. Chem. Thermodyn. 2005, 37, 1268–1275. (46) Alcalde, R.; Aparicio, S.; Garcia, B.; Davila, M. J.; Leal, J. M. Solute-Solvent Interactions in Lactams-Water Ternary Solvents. New. J. Chem. 2005, 29, 817–825. (47) Cerdeirinã, C. A.; Migues, J. A.; Carballo, E.; Tovar, C. A.; de la Puente, E.; Romanı´, L. Highly Precise Determination of the Heat Capacity of Liquids by DSC: Calibration and Measurement. Thermochim. Acta 2000, 347, 37–44. (48) Garcıá, B.; Aparicio, S.; Alcalde, R.; Leal, J. M. Preferential Solvation in Ternary Solutions Containing Methylbenzoate. A KirkwoodBuff Fluctuation Theory Study. J. Phys. Chem. B, 2003, 107, 13478–13486. (49) Benson, G. C.; Kiyohara, O. Evaluation of Excess Isentropic Compressibilities and Isochoric Heat-Capacities. J. Chem. Thermodyn. 1979, 11, 1061–1064.

10076


(50) Redlich, O.; Kister, A. T. Algebraic Representation of Thermodynamic Properties and the Classification of Solutions. Ind. Eng. Chem. 1948, 40, 345–348. (51) Bevington, P. Data Reduction and Error Analysis for the Physical Sciences; McGraw-Hill: New York, 1969. (52) Cibulka, I. Estimation of Excess Volume and Density of Ternary Liquid-Mixtures of Non-Electrolytes from Binary Data. Collect. Czech. Comm. 1982, 47, 1414–1419. (53) Becke, A. D. Density-Functional Exchange-Energy Approximation with Correct Asymptotic-Behavior. Phys. ReV. A 1988, 38, 3098–3100. (54) Lee, C.; Yang, W.; Parr, R. G. Development of the Colle-Salvetti Correlation-Energy Formula into a Functional of the Electron Density. Phys. ReV. B 1988, 37, 785–789. (55) Becke, A. D. Density-Functional Thermochemistry 0.3. The Role of Exact Exchange. J. Chem. Phys. 1993, 98, 5648–5662. (56) Singh, U. C.; Kollman, P. A. An Approach to Computing Electrostatic Charges for Molecules. J. Comput. Chem. 1984, 5, 129– 145.

(57) Besler, B. H.; Merz, K. M.; Kollman, P. A. Atomic Charges Derived from Semiempirical Methods. J. Comput. Chem. 1990, 11, 431– 439. (58) Cances, E.; Mennucci, B. New Applications of Integral Equations Methods for Solvation Continuum Models: Ionic Solutions and Liquid Crystals. J. Math. Chem. 1998, 23, 309–326. (59) Boys, S. F.; Bernardi, F. Calculation of Small Molecular Interactions by Differences of Separate Total EnergiessSome Procedures with Reduced Errors. Mol. Phys. 1970, 19, 553–566. (60) Davila, M. J.; Alcalde, R.; Aparicio, S. Pyrrolidone Derivatives in Water Solution: An Experimental and Theoretical Perspective. Ind. Eng. Chem. Res. 2009, 48, 1036–1050.

ReceiVed for reView May 19, 2009 ReVised manuscript receiVed July 16, 2009 Accepted July 20, 2009 IE900822E

Thermophysical Properties of Binary and Ternary Mixtures Containing

Recommend Documents