Thermophysical Behavior and Temperature Effect on the N

Densities and dynamic viscosities of the N-methylpyrrolidone/(C1−C10) alkan-1-ols mixed solvents were measured at atmospheric pressure and 293.15, 3...
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Ind. Eng. Chem. Res. 2003, 42, 920-928

Thermophysical Behavior and Temperature Effect on the N-Methylpyrrolidone + (C1-C10) Alkan-1-ols Mixed Solvents Begon ˜ a Garcı´a, Rafael Alcalde, Santiago Aparicio, and Jose´ M. Leal* Universidad de Burgos, Laboratorio de Quı´mica Fı´sica, Facultad de Ciencias, 09001 Burgos, Spain

Jose´ L. Trenzado Universidad de Las Palmas de Gran Canaria, Departamento de Fı´sica, 35017 Las Palmas de Gran Canaria, Spain

Densities and dynamic viscosities of the N-methylpyrrolidone/(C1-C10) alkan-1-ols mixed solvents were measured at atmospheric pressure and 293.15, 303.15, 313.15, and 323.15 K over the whole composition range. The excess and mixing properties deduced from these data were interpreted in terms of intermolecular interactions and structural effects. The Soave-Redlich-Kwong and Peng-Robinson cubic equations of state and the modified extended real associated solution (ERAS) and the Prigogine-Flory-Patterson (PFP) models were used to correlate the excess molar volumes. Several correlation viscosity models were also used in data reduction. Introduction Interactions between unlike molecules appear to be responsible for the properties of mixed solvents, the nature of such interactions being dependent on charge distribution and molecular geometry. Thermophysical properties of liquids provide information of the timeaveraged behavior only; therefore, a deeper insight into the representation of a mixed solvent requires understanding of the dynamical properties of the molecules in the condensed state.1 Extraction and extractive distillation are common processes for the recovery of aromatics. The importance of N-methylpyrrolidone (NMP) in synthesis operations, in petrochemical processes, and in pulse radiolysis generated electron-transfer reactions is well-described in the literature.2 NMP, a highly selective tertiary amide, is a chemically stable, dipolar, nonprotogenic solvent used as an inert medium; NMP constitutes a simple model molecule for the behavior of rigid, nonassociating polar species3 and is assumed to be associated by dipole-dipole interactions (µ30 °C ) 4.09 D),3 the high resulting polarity being attributed to the strong stability facilitated by the planarity of the five-membered ring. On the other hand, alkan-1-ols are polar solvents that are strongly self-associated by hydrogen bonding to different degrees of polymerization depending on the temperature, chain length, and sites of the OH groups.4 Because of its strong H-bond-acceptor ability, the CO oxygen can interact with H-bond-donor alcohols; in addition to dipole-dipole interactions, H-bonding between the oxygen of the amide group and the hydrogen of the OH group is feasible. H-bonds can be formed either by interaction with lone pair of electrons or by electrostatic interaction, giving rise to a linear CdOs HsO moiety.5 This work contributes to the study of amides of industrial interest mixed with alkanols and/or water6,7 and continues a previous contribution on NMP/alkanol mixed solvent by extending the study of densities and dynamic viscosities over the 293.15-323.15 K temperature range;8 from these data, the excess and mixing * Corresponding author. E-mail: [email protected].

quantities deduced enable an interpretation of the mixture behavior. Mass transport and heat transfer are operations directly related to bulk properties such as density and viscosity; however, the wide number of solvents used in chemistry makes it difficult to have accurate data available. Therefore, the development of predictive models over a wide temperature range is important. The correlative abilities of the cubic equations of state proposed by Soave (Soave-RedlichKwong, SRK)9 and Peng and Robinson (PR),10 the modified version of the extended real associated solution (ERAS) model,11 and the Prigogine-Flory-Patterson theory12 were tested. Viscosity data were correlated with eight viscosity models. Experimental Section The solvents, of the highest purity available commercially, were obtained from various sources and used without further purification. The liquids were degassed with ultrasound for several days before use and kept out of the light over Fluka Union Carbide 0.4-nm molecular sieves. The purity was assessed by GC with a Perkin-Elmer 990 gas chromatograph equipped with a Hewlett-Packard 3390A integrator and also by comparison of the densities, viscosities and refractive indices with literature values. To prevent preferential evaporation of the samples, the mixtures were prepared by syringing amounts, weighed to within ∆m ) 10-5 g with a Mettler AT 261 Delta Range balance, into suitably stoppered bottles. The mixtures were fully miscible over the whole composition range. The molar excess volumes were deduced from the densities of the pure liquids and mixtures. The densities, F, were measured with a microcomputer-controlled DMA 58 Anton Paar digital mechanical-oscillator density meter (sample size 0.7 cm3) operating in a static mode; it was equipped with a built-in solid-state thermostat ((0.01 K) and a resident menu-driven program. The proper calibration was achieved at all working temperatures with deionized doubly distilled water and nnonane as reference liquids. The densities were accurate to (3 × 10-5 g cm-3, and the molar excess volumes reproducible to (10-4 cm3 mol-1. Dynamic viscosities,

10.1021/ie0205602 CCC: $25.00 © 2003 American Chemical Society Published on Web 01/07/2003

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Figure 1. Excess and mixing properties for the x1NMP + (1 - x1)alkan-1-ol mixtures at 293.15 K: (a) excess molar volume, VEm; (b) mixing viscosity, ∆mixη; and (c) molar Gibbs free energy of activation of viscous flow, ∆G/E m . Symbols: (b) methanol, (9) ethanol, ([) propan-1-ol, (2) butan-1-ol, (f) pentan-1-ol, (O) hexan-1-ol, (0) heptan-1-ol, (]) octan-1-ol, (4) nonan-1-ol, and (3) decan-1-ol. Solid lines are values from eq 4.

η, were measured with an automated AMV 200 Anton Paar microviscometer calibrated with doubly distilled and deionized water and thermostated ((0.005 K) with an electrically controlled Julabo F-25 bath. A steel ball is introduced into an inclined, sample-filled glass capillary, and the instrument converts the time ((0.01 s) taken for the ball to roll a fixed distance between two magnetic sensors into viscosity measurements ((0.005 mPa s).8 The measurements of F and η were taken using an Anton Paar SPV sample changer; the injection of the sample was automatically achieved with a peristaltic pump, the whole process being controlled by a computer program. Results and Discussion The experimental densities and dynamic viscosities of the x1NMP + (1 - x1)alkan-1-ol mixed solvents measured at different temperatures are listed in Table I of the Supporting Information. Excess thermodynamic properties reflect the nonideal behavior of solvents when different components are mixed and can be attributed to (i) the differences in molecular interactions between like-like and unlike molecules, (ii) the difference in shape and size of the components, and (iii) the reorientation of the molecules in the mixture. From the experimental readings, the excess molar volumes, VEm; mixing viscosities, ∆mixη; and Gibbs free energies of activation of viscous flow, ∆G/E m , were evaluated according to the equations

)

(1)

∆mixη ) η - (x1η1 + x2η2)

(2)

VEm )

(

M1 M2 M - x1 + x2 F F1 F2

∆G/E m ) RT{ln(ηVm) - [x1 ln(η1Vm,1) - x2 ln(η2Vm,2)]} (3) where M represents the molar mass of the mixture, Vm ) (x1M1 + x2M2)/F is the molar volume of the mixture, Vm,i represents the molar volumes of the pure components, and η and ηi are the corresponding dynamic viscosities. Redlich-Kister polynomials,13 eq 4, were

fitted to the excess and mixing properties, YE, by least squares using the Marquardt algorithm p

YE ) x1(1 - x1)

∑ Ak(2x1 - 1)k

(4)

k)0

where p is the polynomial degree. The proper number of Ak fitting coefficients was optimized by an F-test, and the standard deviation σ was defined as

σ)

[

N

]

(YE - YEcal)i2 ∑ i)1 N-f

1/2

(5)

where N represents the number of data points and f is the number of fitting coefficients. Plots of YE vs x1 at 293.15 K are shown in Figure 1 for all ten NMP mixtures. Partial molar quantities are defined as the rate of change with concentration of extensive functions and account for binary and higher-order interactions between components. The NMP partial molar volumes, V h m,1, were evaluated as

h Em,1 V h m,1 ) Vm,1 + V

(6)

where Vm,1 represents the molar volume. Moreover, the E NMP partial excess molar volumes, V h m,1 , were evaluated according to the expression

V h Em,1 ) VEm + (1 - x1)(∂VEm/∂x1)P,T

(7)

with the (∂VEm/∂x1)P,T values were deduced from eq 4. Substitution into eq 7 of the limx1f0(∂VEm/∂x1)P,T and limx1f0VEm ) 0 limiting values enables one to determine ∞ V h m,1 , the partial molar volumes at infinite dilution. Table 1 lists the amide partial excess molar volumes at E,∞ ∞ )V h m,1 - Vm,1. infinite dilution, defined as V h m,1 Likewise, the activation properties listed in Table 2 were evaluated according to

ln(ηVm) ) ln(Nh) -

∆Sqm ∆Hqm + R RT

(8)

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Table 1. NMP Partial Excess Molar Volumes at Infinite Dilution, V h E,∞ m,1, for x1NMP + (1 - x1)Alkan-1-ol Mixtures at Different Temperatures

Scheme 1

3 -1 V h E,∞ m,1 (cm mol )

methanol ethanol propan-1-ol butan-1-ol pentan-1-ol hexan-1-ol heptan-1-ol octan-1-ol nonan-1-ol decan-1-ol

293.15 K

303.15 K

313.15 K

323.15 K

-4.18 -2.60 -1.82 -1.26 -0.94 -0.59 -0.33 0.24 0.37 0.48

-4.35 -2.79 -1.70 -1.38 -0.88 -0.54 -0.38 0.29 0.43 0.75

-4.84 -2.90 -1.62 -1.36 -0.91 -0.56 -0.29 0.27 0.48 0.72

-4.49 -2.69 -1.63 -1.31 -0.68 -0.52 -0.25 0.31 0.54 0.64

Self-aggregation of alcohols primarily depends on chain length,4 although H-bond enthalpies do not differ significantly for the various alcohols (mean value -25 kJ mol-1).14 Pure NMP is associated by dipole-dipole interactions; mixing of alcohols with NMP brings about a breakdown of the alcohol structure, followed by the formation of specific interactions. These effects can, in principle, be explained by the excess and mixing properties, the behavior of which can be ascribed to dispersion forces and specific interactions regarding (a) the size and polar features of the components, (b) the breaking of the alcohol structure followed by interaction between the CO and OH groups, and (c) the chain length effect. The observed exothermic effect suggests that breaking of the alcohol structure is accompanied by specific interactions.15 The data available on vapor-liquid equilibria support the idea that alcohol dissociation prevails; in fact, the dielectric relaxation data reveal relatively stable NMP/alkanol aggregates.3 The excess molar volumes (Figure 1) changed from negative to positive with increasing chain length, whereas mixing viscosities decreased from (roughly) zero for methanol to negative values; the VEm minima/maxima moved from x1 ≈ 0.33 for methanol (1:2 NMP/alcohol aggregates) to x1 ≈ 0.66 for decanol (2:1 NMP/alcohol aggregates). Scheme 1 shows the 1:2 NMP/methanol structure deduced by geometric optimization in Hyperchem and the Fletcher-Reeves algorithm.16 Although the CO H-bond is stronger than the N H-bond, 1:2 aggregates are likely to appear by interaction with two different NMP sites. Such aggregates, however, become unlikely with increasing chain length, and only weak 1:1 or 2:1 associates will appear. Cubic Equations of State (EOS). The macroscopic effects can be caused by several different microscopic properties, and it is not always possible to trace back which microscopic property is the origin for certain behavior. In this context, it is useful to include models such as equations of state. Densities and excess volumes are related to the heaviness of the molecules in a unit volume and have become relevant quantities in the interpretation of interactions in mixed solvents. The interest in cubic EOS has increased in recent years, because they have proven to be valuable for the correlation and prediction of phase equilibria in mixed solvents. To allow EOS to describe nonideal mixed solvents and determine the mixture properties, the choice of a suitable mixing rule plays a key role. Recently, an approach has been proposed that accounts for the effect of density on excess properties of nonideal mixed solvents while giving zero interaction parameters for the ideal-solution limit.17 Although no cubic equation of state can be regarded as ideally suited for predicting

all solvent properties, because of their simplicity, accuracy, and pivotal role in the development of cubic equations of state, the Soave-Redlich-Kwong (SRK)9 and Peng-Robinson (PR)10 EOS were applied successfully to correlate VEm data.18 Under isobaric and isothermal conditions, the excess molar volumes can be evaluated using the equation r

VEm

xi(V h m,i - Vm,i) ∑ i)1

)

(9)

where r represents the number of components in the mixture and Vm,i is the molar volume. The partial molar volume for the ith component, V h m,i, is defined as

( ) ( )

V h m,i ) -

∂P ∂ni

T,V,n

∂P ∂Vm

-1

(10)

T,n

with the two partial derivatives of eq 10 being evaluated using the cubic EOS 11

P)

nRT n2a V - nb (V + δ1nb)(V + δ2nb)

(11)

where n is the number of moles in the mixture, with δ1 ) 1 and δ2 ) 0 for SRK and with δ1 ) 1 + x2 and δ2 ) 1 - x2 for PR. It would be desirable to find expressions for a and b such that eq 9 yields a mixture volume that matches the VEm values at any concentration, pressure, and temperature. To determine the a (attractive) and b (repulsive) factors, two simple mixing rules were introduced r

a)

xixj(1 - kij)(aiaj)0.5 ∑ ∑ i)1 j)1 r

b)

r

(12)

r

xixj(1 - mij)(bibj)0.5 ∑ ∑ i)1 j)1

(13)

The ai and bi factors for the pure components are evaluated as

R2Tci2 R a i ) K2 Pci i

(14)

RTci bi ) K 1 Pci

(15)

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Figure 2. Plots of experimental and correlated excess molar volume, VEm, for x1NMP + (1 - x1)alkan-1-ol mixtures at 293.15 K: (a) SRK with R1 mixing rule, (b) SRK with R2 mixing rule, (c) PR with R1 mixing rule, and (d) PR with R2 mixing rule. Solid lines are correlated values; symbols are as in Figure 1. q Table 2. Equimolar Activation Enthalpies, ∆Hm,0.5 (kJ mol-1), and Equimolar Activation Entropies, q -1 -1 ∆Sm,0.5 (J mol K ), for x1NMP + (1 - x1)Alkan-1-ol Mixtures

q ∆Hm,0.5 q ∆Sm,0.5

methanol

ethanol

propan-1-ol

butan-1-ol

pentan-1-ol

hexan-1-ol

heptan-1-ol

octan-1-ol

nonan-1-ol

decan-1-ol

10.75 -179.59

11.44 -179.39

12.50 -178.29

13.16 -177.93

14.32 -175.71

13.18 -181.72

15.08 -177.53

15.46 -178.46

17.92 -171.58

18.32 -172.07

with

Ri ) [(1 + mi)(1 - Tri0.5)]2

(16)

mi ) K3 + K4ωi - K5ωi2

(17)

and

where Pci and Tci stand for the critical pressure and temperature, respectively, for the ith component; ωi is the acentric factor; and the values for K are K1 ) 0.086 64, K2 ) 0.427 48, K3 ) 0.480, K4 ) 1.574, and K5 ) 0.176 for SRK9 and K1 ) 0.0778, K2 ) 0.457 24, K3 ) 0.374 64, K4 ) 1.542 26, and K5 ) 0.269 92 for PR.10 For the first mixing rule (R1), in eq 13, the values of mij ) 0 and kij in eq 12 were deduced by fitting the VEm data; in the second mixing rule (R2), the two parameters were also fitted. The fitting parameters were determined by least squares, using the Newton-Raphson method.18 Table II of the Supporting Information (refs 19-36 contained therein) lists the properties of pure components evaluated by application of cubic EOS; the correlation parameters for all systems and temperatures are listed in Table III of the Supporting Information, along with the standard deviations. Despite the pronounced nonideality of the systems investigated and the empirical nature of the SRK and PR equations, the cubic EOS used here correlate reasonably well the volumetric properties; they reproduce fairly well the experimental curves (Figure 2), and the parameters deduced for binary mixtures can be used further to predict properties for ternary systems. The two equations yield fair results with low deviations and lead to similar results if the same mixing rule is used; only the s-shaped curve for heptanol was poorly correlated by the one-parameter mixing rule. Modified Extended Real Associated Solution (ERAS) Model. Originally proposed by Heintz,27 the formulation of the ERAS model was reviewed and extended to binary mixtures of components with similar degrees of association, giving rise to the modified ERAS model applied to the VEm data in this work. The physi-

cally based ERAS model combines a chainlike association theory with the free volume contribution based on Flory’s equation of state.37 Application of this theory to strongly polar solvents is not feasible; however, combined with the associated solution model, it gives rise to a reliable general EOS. The model allows the VEm values to be split into the two components involving free volume effects that arise from the chemical (H-bonding) and physical (van der Waals interactions) contributions

VEm ) VEphys + VEchem

(18)

The modified ERAS model yields correlation parameters with physical meanings and extends its capability to mixtures susceptible to cross-association.11 The ERAS model has the advantage of requiring only a reduced number of data pairs of pure components; the values at 298.15 K were taken from the literature23-31 and used further at the other working temperatures studied (Table II of the Supporting Information). The properties needed for pure NMP were deduced from the excess molar volumes and excess molar enthalpies reported for NMP/cyclohexane;32,38 the NMP parameters reported were recalculated using the modified ERAS model (Table II of the Supporting Information). The ERAS model involves three different parameters: Flory’s parameter XAB, the complexation constant KAB, and the complexation molar volume ∆v/AB. As outlined earlier,11 the VEm data were correlated by a simulated annealing algorithm that enables a global optimization and yields correlation parameters without the restrictions of other methods. This algorithm was applied to phase equilibria39 and found to be highly efficient; it was processed in MATLAB with the only restrictions being ∆v/AB < 0 and KAB > 0, with no restrictions on XAB. Table 3 lists the parameters deduced for each mixture, along with the standard deviations. Except for the smaller alkanols, Figure 3a displays the correlative ability of the model regarding the shape and the two edges of the VEm curves. The two contributions to VEm, eq 18, had opposite signs (Figure 4a). Likewise,

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Figure 3. Plots of experimental and correlated excess molar volume, VEm, for x1NMP + (1 - x1)alkan-1-ol mixtures at 293.15 K: (a) modified ERAS and (b) PFP. Solid lines are correlated values, and symbols are as in Figure 1.

Figure 4. Plots of excess molar volume, VEm, for x1NMP + (1 - x1)methanol mixtures at 293.15 K: (a) modified ERAS model showing physical and chemical contributions; (b) PFP model showing interaction, free volume and pressure contributions; (b) experimental data in both plots.

the vaporization enthalpies for pure compounds were determined at 293.15 K using the parameters of the modified ERAS model (Table 4) along with the literature values; the good agreement achieved between experimental and calculated data is reflected by the efficient minimization.11 Prigogine-Flory-Patterson (PFP) Model. Flory’s model37 has often been used to correlate second-order properties such as VEm, HEm, and CEp and was applied successfully to correlate VEm data of NMP/alkan-1-ol binary mixtures.41 To interpret the molecular shape, size, and momentum effects in binary mixtures, application of the PFP model over a broad temperature

range is advisable. The excess molar volumes can be split into three contributions E E E VEm ) Vfree volume + Vinteractional + Vp/ effect

(19)

The interaction contribution is proportional to the only correlation parameter, χ12; the free volume contribution arises from the difference between the expansion degrees of the two components; and the pressure contribution depends on the difference in internal pressure and reduced volume of the components.42 The parameters for pure components required in the calculations are listed in Table II of the Supporting Information. Although PFP is a one-parameter model in nature, the

∆Hvm (experimental) (kJ mol-1)

compound

293.15 K

298.15 K

NMP methanol ethanol propan-1-ol butan-1-ol pentan-1-ol hexan-1-ol heptan-1-ol octan-1-ol nonan-1-ol decan-1-ol

45.25 37.27 40.87 45.84 49.63 55.31 61.84 67.39 70.92 75.69 79.94

52.80b 37.43c 42.309b 47.45c 42.35c 56.94b 61.61c 66.81c 70.98c 76.86c 81.50c

0.0564 0.0345 0.0540 0.1044 0.1791 0.1456 0.1390 0.0449 0.0727 0.0629 -11.744 -8.762 -7.767 -7.854 -7.786 -7.449 -5.411 -5.525 -5.355 -5.169

∆Hvm (modified ERAS model) (kJ mol-1)

35.100 29.488 39.469 32.243 29.997 34.385 8.485 7.603 14.587 17.251

a Experimental values at 298.15 K are shown for comparative purposes. b Reference 26. c Reference 40.

159.589 199.797 381.256 227.097 126.094 88.936 22.727 11.339 8.025 6.662 33.669 32.895 37.256 34.145 27.588 33.869 9.916 10.943 13.985 16.888 0.0580 0.0386 0.0298 0.0898 0.1623 0.1503 0.0885 0.0563 0.0696 0.0526 -11.706 -8.763 -7.830 -7.854 -7.606 -7.308 -5.496 -5.349 -5.203 -5.098 190.225 200.407 397.402 245.638 127.069 90.158 15.321 6.048 8.536 7.026 30.241 32.398 36.968 34.314 26.386 33.021 8.329 7.285 13.526 16.398 methanol ethanol propan-1-ol butan-1-ol pentan-1-ol hexan-1-ol heptan-1-ol octan-1-ol nonan-1-ol decan-1-ol

33.595 32.680 35.805 33.835 25.183 32.383 11.097 9.065 13.060 15.919

188.664 200.425 390.386 256.941 125.585 93.119 23.791 6.511 8.927 7.589

-11.555 -8.759 -7.823 -7.854 -7.503 -7.208 -5.528 -5.577 -5.159 -5.033

0.0588 0.0390 0.0284 0.0802 0.1600 0.1503 0.1437 0.0781 0.0795 0.0508

σ KAB XAB (J cm-3) σ KAB XAB (J cm-3)

Table 4. Enthalpies of Vaporization, ∆Hvm, for the Pure Components at 293.15 K Calculated with the Parameters of the Modified ERAS Modela (Table II of the Supporting Information)

-11.743 -8.762 -7.861 -7.853 -7.705 -7.395 -5.445 -5.440 -5.324 -5.122

0.0544 0.0352 0.0426 0.0798 0.1717 0.1488 0.1679 0.1035 0.0658 0.0542

191.356 186.106 362.423 149.820 121.407 87.036 16.255 5.502 7.563 6.023

σ ∆v/AB (cm3 mol-1) KAB XAB (J cm-3) σ

323.15 K

XAB (J cm-3)

KAB

∆v/AB (cm3 mol-1)

313.15 K 303.15 K

∆v/AB (cm3 mol-1) ∆v/AB (cm3 mol-1)

293.15 K

3 -1 Table 3. Parameters and Standard Deviations, σ, Corresponding to the Modified ERAS Model Applied to the Correlation of VE m (cm mol ) for x1NMP + (1 - x1)Alkan-1-ol Mixtures at Different Temperatures

Ind. Eng. Chem. Res., Vol. 42, No. 4, 2003 925

Figure 5. Plots of PFP model parameter, χ12, as a function of number of carbon atoms, n, in the alkan-1-ol for the x1NMP + (1 - x1)alkan-1-ol mixtures at (a) 293.15, (b) 303.15, (c) 313.15, and (d) 323.15 K. Symbols are as in Figure 1.

standard deviations provided exhibit fair behavior (Figure 3b). The fitting was performed using a simulated annealing algorithm for global optimization. The interaction parameter, χ12 (Table IV of the Supporting Information), changed from negative for smaller alkanols to positive for larger ones. The χ12 values, processed at all working temperatures, reveal that the shorter the chain length and the lower the temperature, the stronger the interactions (Figure 5). The s-shaped curve corresponds reasonably for heptanol, if one considers that unlike interaction forces are stronger for the smaller alcohols and weaker for higher alcohols. It can then be concluded that the PFP model reflects the main features of VEm for these strongly heteroassociated mixtures. Figure 4b shows plots of the three VEm components for methanol, the interaction contribution prevailing.

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Figure 6. Plots of (a) Nissan-Grunberg, d; (b) Heric, γ12; and (c) McAllister, ν12, viscosity models parameters as a function of number of carbon atoms, n, in the alkan-1-ol for the x1NMP + (1 - x1)alkan-1-ol mixtures at (A) 293.15, (B) 303.15, (C) 313.15, and (D) 323.15 K.

Viscosity Models. Viscosity is an important transport property for pure liquids and mixed solvents. The information it provides in chemical engineering for the evaluation of mass transport has increased considerably the interest in developing correlation and prediction models for viscosity data.43 Viscous forces appear when adjacent layers of a fluid move with different speeds. The force needed to make a fluid layer move in relation to a neighbor layer is called shear, and a Newtonian fluid is one with a constant ratio of the shear stress to the shear rate. Viscosity reflects the internal friction of a fluid and provides a measure of the extent of interactions in mixed solvents. In this work, the correlation abilities of seven models was tested: the one-parameter models by Nissan and Grunberg44 and Hind et al.;45 the two-parameter models by Heric,46 Lobe,47 McAllister48 (with three-body interactions), and Cao et al.36 (UNIMOD); and the three-parameter model by Auslander.49 The equations of these models are

Nissan-Grunberg (1949) ln(η) ) x1 ln(η1) + x2 ln(η2) + x1x2d

(20)

Hind et al. (1960) η ) x12η1 + x22η2 + 2x1x2η12

(21)

Heric (1966) ln(η) ) x1 ln(η1) + x2 ln(η2) + x1 ln(M1) + x2 ln(M2) ln(x1M1 + x2M2) + x1x2[γ12 + γ21(x1 - x2)] (22) Lobe (1973)

[

ν ) f1ν1 exp f2R12 ln

( )] ν2 ν1

[

+ f2ν2 exp f1R21 ln

( )] ν2 ν1

(23)

McAllister (three-body interactions, 1960) ln(νM) ) x13 ln(ν1M1) + x23 ln(ν2M2) + 3x12x2 ln(ν12) + M2 2 M2 + 3x12x2 ln + + 3x22x1 ln(ν21) - ln x1 + x2 M1 3 3M1 M2 1 2M2 + x23 ln (24) 3x22x1 ln + 3 3M1 M1

(

(

)

)

(

( )

)

Cao et al. (1992) r

ln(ν) )

∑ i)1

r

∑ i)1

φi ln(νi) + 2

φi ln

() xi

-

φi

n iqi r φ1 θij ln(τij) (25) ri j)1 i)1 r

∑ where

(

τij ) exp -

∑

)

z Uji - Uii 2 RT

Auslander (1965) η)

η1x1(x1 + B12x2) + η2[A21x2(B21x1 + x2)] x1(x1 + B12x2) + (A21x2)(B21x1 + x2)

(26)

where νi represents the kinematic viscosity (ν ) η/F) of the ith component; Mi and M are the molecular weights of the ith component and of the mixture, respectively; and fi represents the volume fraction of component i. In the Cao model, eq 25, φi is the average fractional area, θij is the local composition, ni is a model constant, and qi and ri are the van der Waals properties of the pure components. The other symbols are the least-squares fitting parameters of viscosity data obtained using the Marquardt algorithm. Table V of the Supporting Information contains the results for all models at all temperatures, along with the standard deviations. As a rule, the models by Teja (one-parameter), McAllister (two-parameter), and Auslander (three-parameter) yielded smaller deviations and provided good correlations. By contrast, the Nissan-Grunberg, Hind et al., and Cao et al. models gave worse results. The low correlation ability of the Cao et al. group contribution model for these mixtures should be noted, as was already reported for different amide/alkanol or amide/water solvents.7,8 The parameters of some of the models are plotted in Figure 6. Concluding Remarks The structure of NMP/alcohol mixtures is governed by the disruption of alcohol H-bonds, partially balanced by formation of NMP heteroaggregates; these aggregates are stronger for shorter alcohols and decrease in

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strength with increasing temperature. The SoaveRedlich-Kwong and Peng-Robinson cubic EOS combined with a simple two-parameter mixing rule gave good VEm correlations. The ERAS and PFP models yielded low deviations, in particular the one-parameter PFP model. The simulated annealing algorithm used in the ERAS and PFP models provided good global optimization; the main drawback is the difficulty in attaining convergence, but this algorithm provides global not local minima. The viscosity models studied yielded low deviations, with the models by Nissan and Grunberg and Hind et al. being best. The Cao et al. model gave large deviations and it is not recommended for these systems. The three-body interaction models by Teja and McAllister are most convenient for these mixtures. Acknowledgment The financial support by the Spanish Junta de Castilla y Leo´n, Project BU05/99, and Ministerio de Ciencia y Tecnologı´a, project PPQ2002-02150, is gratefully acknowledged. Supporting Information Available: Measured densities and dynamic viscosities (Table I), pure solvent parameters (Table II), cubic equation of state parameters (Table III), PFP parameters (Table IV), and viscosity model parameters (Table V) are reported as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Marcus, Y. The Properties of Solvents; Wiley: Chichester, U.K., 1999. (2) Archer, W. A. Industrial Solvents Handbook; Marcel Dekker: New York, 1996; Chapter 7. (3) Dachwitz, E.; Stockhausen, M. A Dielectric relaxation study of self- and heteroassociation in binary liquid mixtures of three pyrrolidinones with alcohols and water. Ber. Bunsen-Ges. Phys. Chem. 1987, 91, 1347. (4) Dewan, R. K.; Metha, S. K.; Parashar, R.; Harkiran Kaur, S. Topological investigation on associations of alkanol. J. Chem. Soc., Faraday Trans. 1992, 88, 227. (5) Laurence, C.; Berthelot, C.; Helbert, M. Stereochimie de la liaison hydrogene sur le groupe carbonyle. Spectrochim. Acta A 1985, 41, 883. (6) Hoyuelos, F. J.; Garcı´a, B.; Alcalde, R.; Ibeas, S.; Leal, J. M. Shear viscosities of binary mixtures of pyrrolidin-2-one with C6-C10 n-alkan-1-ols. J. Chem. Soc., Faraday Trans. 1996, 92, 219. (7) Garcı´a, B.; Alcalde, R.; Leal, J. M.; Matos, J. S. Solutesolvent interactions in Amide-Water Mixed Solvents. J. Phys. Chem. B 1997, 101, 7991. (8) Garcı´a, B.; Alcalde, R.; Aparicio, S.; Leal, J. M. The N-methylpyrrolidone-(C1-C10) alkan-1-ols solvent systems. Phys. Chem. Chem. Phys. 2002, 4, 1170. (9) Soave, G. Equilibrium constants from a modified RedlichKwong equation of state. Chem. Eng. Sci. 1972, 27, 1197. (10) Peng, D. Y.; Robinson, B. A new two-constant equation of state. Ind. Eng. Chem. Fundam. 1976, 15, 59. (11) Pin˜eiro, A.; Amigo, A.; Bravo, R.; Brocos, P. Re-examination and symmetrization of the adjustable parameters of the ERAS model. Review on its formulation and application. Fluid Phase Equilib. 2000, 173, 211. (12) Van, H. T.; Patterson, D. Volume of mixing and the p* effect: Hexane isomers with normal and branched hexadecane. J. Solution Chem. 1982, 11, 793. (13) Redlich, O.; Kister, A. T. Algebraic representation of thermodynamic properties and the classification of solutions. Ind. Eng. Chem. 1948, 40, 345. (14) Huyskens, P. Molecular structure of liquid alcohols. J. Mol. Struct. 1983, 100, 403. (15) Hammert, I.; Feinbue, A.; Herkner, K.; Bittrich, H. J. Exzess enthalpien von Mischungen aus dipolar aprotischen komponenten und alkanolen. Zur Phys. Chem. 1990, 271, 1133.

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Received for review July 26, 2002 Revised manuscript received November 25, 2002 Accepted December 4, 2002 IE0205602