Density, viscosity and refractive index of binary liquid mixtures at 293.15, 298.15, 303.15, 308.15 and 313.15 K

Experimental Thermal and Fluid Science 37 (2012) 1–11

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Density, viscosity and refractive index of binary liquid mixtures at 293.15, 298.15, 303.15, 308.15 and 313.15 K R.K. Shukla ⇑,1, Atul Kumar 2, Naveen Awasthi 1, Urvashi Srivastava 3, V.S. Gangwar 1 Department of Chemistry, VSSD College, Kanpur 208 002, India

a r t i c l e

i n f o

Article history: Received 29 January 2011 Received in revised form 23 July 2011 Accepted 25 August 2011 Available online 6 September 2011 Keywords: Viscosity Refractive index Associational behavior Ramaswamy and Anbananthan (RS) Prigogine–Flory–Patterson (PFP) Density McAllister

a b s t r a c t Densities, viscosities and refractive indices were measured for the binary liquid mixtures formed by formamide, N-methylacetamide, di-methylformamide and di-methylacetamide with acetonitrile at (T = 293.15, 298.15, 303.15, 308.15 and 313.15) K and atmospheric pressure over the whole concentration range. Lorentz–Lorentz (L–L) relation, Prigogine–Flory–Patterson model (PFP), model devised by Glinski and Ramaswamy and Anbananthan (RS) models were used to study the associational behavior of weakly interacting liquids from viscosity and refractive index data. These non-associated and associated models were compared and also tested for different systems. The measured properties were fitted to Redlich–Kister polynomial relation to estimate the binary coefficients and standard errors. Furthermore, McAllister multi body interaction model was used to correlate the binary properties. Conclusively, viscosities and refractive indices of binary liquid mixture can be better understood from these models and interactions and association constant can be well predicted. The associated processes yield fair agreement between theory and experiment as compared to non-associated processes. Ó 2011 Elsevier Inc. All rights reserved.

1. Introduction Density, viscosity and refractive index are important basic data used in process simulation, equipment design, solution theory and molecular dynamics [1,2]. A better understanding of viscosity is of considerable physico-chemical interest and is essential in designing calculations involving heat transfer, mass transfer and fluid flow. Knowledge of viscosity is widely used in processing and product formulations [3] in many industrial applications. The solvents chosen in the present work have technical and industrial importance. Roy et al. [4] measured densities and viscosities of binary liquid mixtures of formamide with 2-methoxy ethanol, acetophenon, acetonitrile, 1,2-dimethoxy ethane and dimethyl surfoxide at 298.15, 308.15 and 318.15 K over the entire composition range at 0.1 m Pa and obtained the values of excess molar volume, VE, viscosity deviation, Dg and deviation in isentropic compressibility Dk. In this work, we present the experimental data on density, refractive index and viscosity of binary liquid mixtures of formamide, N-methyl acetamide (NMA), di-methylformamide (DMF) and di-methylacetamide (DMA) with acetonitrile at (T = 293.15, ⇑ Corresponding author. Tel.: +91 0512 2560070, mobile: +91 9838516217; fax: +91 2563842. E-mail address: [email protected] (R.K. Shukla). 1 Address: Department of Chemistry, VSSD College, Nawabgang, Kanpur 208 002, India. 2 Present address: Department of Chemistry, PSIT, Kanpur, India. 3 Present address: Department of Chemistry, PSAT, Kanpur, India. 0894-1777/$ - see front matter Ó 2011 Elsevier Inc. All rights reserved. doi:10.1016/j.expthermflusci.2011.08.005

298.15, 303.15, 308.15 and 313.15) K and atmospheric pressure over the whole concentration range. These data were analyzed in terms of Lorentz–Lorentz (L–L) relation [5], Prigogine–Flory–Patterson model (PFP) [6–10], model devised by Glinski [11] and the model of Ramaswamy and Anbananthan (RS) [12]. RS and model devised by Glinski (associated) are based on the association constant as an adjustable parameter where as PFP model (non-associated) is based on the additivity of liquids. For that purpose, we selected the liquids containing poor interacting properties having immense sense of technological significance in chemical industries. From these results, deviation in viscosity, Dg and deviation in refractive index, Dn were calculated and fitted to the Redlich– Kister type polynomial equation [13] to derive the binary coefficients and the standard errors. An attempt has also been made to correlate the experimental properties with the McAllister equation [14] which is based on Eyring’s theory of absolute reaction rates and for liquids, the free energy of activation for viscosity are additive on a number fraction and that interactions of like and unlike molecules. The mixing behavior of such liquid mixtures containing acetonitrile is interesting due to presence of cyano group coupled with amide linkage resulting interactions in the liquid mixtures. The association phenomenon has been related usually to the different quantity from additivity and the model [12] is simple averaged geometrical derivations in terms of equilibrium. The associational behavior of liquids and their correlation with molecular interactions has also been made using different liquid models. This is our first attempt to correlate all the models (associated and

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R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11

non-associated) in predicting the associational behavior of binary liquid mixtures.

experiment was repeated four times at each temperature for all composition and results were averaged. The viscosity g of the liquid was then calculated from the following relationship

2. Experimental section

m ¼ g=q ¼ kðt  Þ

2.1. Materials High purity and AR grade samples of formamide, N-methylacetamide, di-methyl formamide and di-methyl acetamide and acetonitrile used in this experiment were obtained from Merck Co., Inc., Germany and purified by distillation in which the middle fraction was collected. The liquids were stored in dark bottles over 0.4 nm molecular sieves to reduce water content and were partially degassed with a vacuum pump. The purity of each compound was checked by gas chromatography and the results indicated that the mole fraction purity was higher than 0.99. All the materials were used without further purification. The purity of chemicals used was confirmed by comparing the densities and viscosities with those reported in the literature as shown in Table 1.

ð1Þ

where g is the dynamic viscosity, q is the density, t is the flow time, m is the kinematic viscosity, and k and  are the viscometer constant and the Hagen Bach correction factor respectively. The calibration of the viscometer was carried out with doubly distilled water and doubly distilled benzene. Care was taken to reduce evaporation during the measurements. The estimated uncertainty in viscosity measurements was within ±0.001 m Pa s and reproducible to ±9.8  103 m Pa s. Refractive indices were measured using a thermostatically controlled Abbe refractometer model, Atago-3T. For every sample, the measurements were repeated three times and mean value were taken in each calculation. The uncertainty in the refractive index measurements was accurate to ±0.0001. 3. Modeling

2.2. Apparatus and procedure

3.1. Ramaswami and Anbananthan model

Before each series of experiments, we calibrated the instrument at atmospheric pressure with doubly distilled water. The uncertainty in the density measurement was within ±6.7 kg m3 of the published values. The densities of the pure components and their mixtures were measured with the bi-capillary pyknometer. The liquid mixtures were prepared by mass in an air tight stopped bottle using an electronic balance model SHIMADZUAX-200 accurate to within ±0.1 mg. The average uncertainty in the composition of the mixtures was estimated to be less than ±0.0001. All molar quantities were based on the IUPAC relative atomic mass table. The viscosities of pure liquids and the mixtures were measured at atmosphere pressure and at different temperatures using Canon Ubbelohde suspended-level viscometer. The viscometer was immersed in a well stirred water bath (Raga Industries) with temperature control to ±0.01 K. The flow time was recorded with a digital stopwatch capable of measuring time to within ±0.01 s. Each

Ramswamy and Anbananthan [12] proposed the model based on the assumption of linearity of acoustic impedance with the mole fraction of components. Further it is assumed, that any physical property such as viscosity, refractive index, and surface tension, which are based on linearity can be predicted [15–19]. Further Glinski [11] assumed that when solute is added to solvent the molecules interact according to the equilibrium as:

A þ B ¼ AB

ð2Þ

and the association constant Kas can be defined as;

K as ¼

½AB ½A½B

ð3Þ

where A is amount of solvent and B is amount of solute in the liquid mixture.

Table 1 Comparison of density, viscosity and refractive index with literature data for pure components at 293.15, 298.15, 303.15, 308.15 and 313.15 K.

a

Compound

T

a  103 K

bT  1012 Pa

V/cm3 mole1

qexp/g cm3

qa/g cm3

gexp/m Pa s

glita/m Pa s

nExp

nlita

Acetonitrile

293.15 298.15 303.15 308.15 313.15

1.2762 1.2943 1.3151 1.3300 1.3420

108.8470 113.5441 119.1053 123.1860 126.5467

51.5379 52.5540 53.0841 53.5551 53.9776

0.7865 0.7811 0.7733 0.7665 0.7605

0.7822 0.77649 0.77125 – –

0.3699 0.3426 0.3201 0.3408 0.3348

– 0.3410 0.3240 – –

1.3409 1.3402 1.3392 1.3283 1.3260

1.34411 1.34163 – – –

Formamide

293.15 298.15 303.15 308.15 313.15

0.9431 0.9515 0.9570 0.9594 0.9656

43.9231 45.1146 45.8963 46.2463 47.1502

39.7879 39.8937 40.0355 40.1784 40.5145

1.1320 1.1290 1.1250 1.1210 1.1117

1.1339 1.12915 – – –

3.7542 3.3220 2.9663 2.6531 2.4039

3.7640 3.302 – – –

1.4409 1.4370 1.4359 1.4280 1.4250

1.44754 1.44682 – – –

NMA

293.15 298.15 303.15 308.15 313.15

1.1095 1.1224 1.1349 1.1440 1.1364

71.5118 74.0374 76.5384 78.3887 76.8504

76.4404 76.8502 76.9311 77.2074 77.7246

0.9563 0.9512 0.9502 0.9468 0.9405

– – 0.9520 0.94604 –

3.3712 3.3643 3.3512 3.2310 3.1020

– – 3.35 3.23 3.012

1.4279 1.4270 1.4261 1.4250 1.4230

– – – 1.4253 –

N,N-DMF

293.15 298.15 303.15 308.15 313.15

1.0844 1.0899 1.0970 1.1108 1.1187

66.7696 67.7959 69.1223 71.7621 73.3117

76.5260 76.9287 77.5984 78.1126 78.3807

0.9551 0.9501 0.9419 0.9357 0.9325

0.94873 0.94387 0.9412 – 0.9310

0.9224 0.8006 0.7399 0.7214 0.7204

0.9243 0.802 – – 0.7386

1.4285 1.4267 1.4240 1.4221 1.4205

1.43047 1.42817 – – –

N,N-DMA

293.15 298.15 303.15 308.15 313.15

1.0839 1.0968 1.1097 1.1190 1.1255

66.6719 69.0911 71.5617 73.3692 74.6488

90.5331 91.6859 93.0769 94.0008 94.4799

0.9623 0.9602 0.9360 0.9268 0.9221

0.9615 0.96633 0.93169 – 0.9232

0.9481 0.9237 0.8788 0.8264 0.7689

– 0.927 0.8710 – 0.766

1.4361 1.4342 1.4320 1.4300 1.4285

– 1.4384 1.4356 – –

Ref. [32].

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By applying the condition of linearity with composition

Z obs ¼ xA Z A þ xAB Z AB

Z cal ¼ ð4Þ

where xA, xAB, ZA and ZAB and Zobs are the mole fraction of A, mole fraction of associate AB, physical properties (viscosity and refractive index) of A and physical properties (viscosity and refractive index) of associate AB and observed physical properties respectively. The component AB can not be obtained in its pure form. Here, the equilibrium reaction is not complete by definition i.e. there are also molecules of non-associated components in the mixtures. Hence, Eq. (4) takes the form as;

Z obs ¼ ½xA Z A þ xB Z B þ xAB Z AB h

ð5Þ

where h is a temperature dependent adjustable parameter which changes with the changing temperature conditions. The general idea of this model can be, however, exploited as;

K as ¼

½AB ðC A  ½ABÞðC B  ½ABÞ

ð6Þ

where CA and CB are initial molar concentrations of the components. One can take any value of Kas and calculate the equilibrium value of [AB] for every composition of the mixture as well as [A] = CA  [AB] and [B] = CB  [AB]. Replacing molar concentration by activities for concentrated solution, Eq. (6) becomes,

K as ¼

aAB ðaA  aAB ÞðaB  aAB Þ

ð7Þ

where aA, aB and aAB are the activity of component A, component B and associate, AB respectively. Taking equimolar activities which are equal to;

a0A ¼ aA  aAB

and a0B ¼ aB  aAB

where a0A and a0B are the activities of [A] and [B] in equimolar quantities respectively. From Eq. (7) one can obtain the value of Kas as;

K as ¼

aAB aAB ¼ aA aB  aA aAB  aB aAB þ a2AB a0A  a0B

ð8Þ

Now, assuming any value of viscosity and refractive index in the pure components A, B and ZAB, it is possible to compare the viscosities and refractive indices calculated using Eq. (5) with the experimental values. On changing both the adjustable parameters Kas and ZAB gradually, one can get different values of the sum of squares of deviations,

S ¼ RðZ obs  Z cal Þ2

ð9Þ

where Zobs and Zcal are the observed and calculated equilibrium properties respectively. The minimum value of S can be obtained theoretically by a pair of the fitted parameters. But we found that for some Kas and ZAB, the value of S is high and changes rapidly, and for others, it is low and changes slowly when changing the fitted parameters. In such cases, the value of ZAB should not be much lower than the lowest observed viscosity and refractive index of the system or much higher than the highest one. Quantitatively, it should be reasonable to accept the pair of adjustable parameters Kas and ZAB which has the physical sense and which reproduces the experimental physical property satisfactorily. 3.2. Corrected model of Ramaswami and Anbanthan On inspecting the results obtained from Ramaswamy and Anbananthan model, Glisnki suggested the equation assuming additivity with the volume fraction, / of the components derived by Natta and Baccardedda [20], as;

Z1 Z2 /1 Z 2 þ /2 Z 1

ð10Þ

where Zcal is the theoretical physical properties of binary liquid mixture, /1, /2 are the volume fractions of components 1 and 2 and Z1 and Z2 are the physical properties of pure component liquids. The numerical procedure and determination of association constant, Kas, were similar to that described before and the advantage of this method as compared with the earlier one was that the data on densities of liquid mixture are not necessary except those of pure components needed to calculate the volume fractions. 3.3. Prigogine–Flory–Patterson model Theories [21] relate the viscosities of liquids either to the activation energy required for the molecule to overcome the attractive forces of its neighbors (absolute rate theory) or the probability of an empty site near a molecule into which a neighboring molecule can jump (free volume theory). Macedo and Litovitz [22] made the hypothesis that these two effects are combined so that the probabilities for viscous flow is taken as the product of the probabilities for acquiring sufficient activation energy and the occurrence of an empty site. Similar assumptions are made for solutions. The theory is applicable to the mixtures of the molecules of different sizes and lays particular stress on contribution of equation of state to the thermodynamic excess functions. The form of such equation for viscous flow is given as;

g ¼ X exp½DG– =RT þ cv  =V f 

ð11Þ

Here v is the characteristic volume which must be available for a molecular segment jumping to its new site, Vf is the free volume per segment in the mixture and is equal to v  v⁄, c is a factor of the order unity, DG– is the free energy of activation per mole, R is gas constant T is absolute temperature and X is a frequency factor respectively. A bridge can be formed to the thermodynamic functions of mixing by assuming a simple relationship between free energy of activation DG–, and the residual Gibbs free energy of mixing DGRM according to Roseveare et al. [21] as; ⁄

DG– ¼

2 X

R xi DG– i  aDGM

ð12Þ

i¼1

where DGRM is the residual free energy of mixing, a is a constant of order unity and DG– i is the activation free energy of ith component liquid. The residual free energy of mixing DGRM can be expanded in terms of enthalpy and entropy contributions as;

DGRM ¼ DHM  T DSRM

ð13Þ

DSRM

where DHM and are the enthalpy of mixing per mole and residual entropy per mole respectively. By substituting the value of DG– in Eq. (11) we get,

ln g ¼

2 X

(

xi ln gi  DGRM =RT þ v  ð1  v f Þ 

i¼1

2 X

!)

xi =V fi

ð14Þ

i¼1

The value of DGRM for binary liquid mixture can be evaluated as detailed out by Flory et al. [6–8] as;

! # e 1=3  1Þ 1 1 ðV 1 e þ 3 T 1 ln ¼  e1 V e e 1=3  1Þ V ðV ! " # e 1=3  1Þ ðV 1 1   2 e þ 3 T 2 ln þ x2 P 2 V 2  e 1=3  1Þ e2 V e ðV V "

DGRM

x1 P1 V 1

þ

x1 P1 V 1 h2 X 12 e1 V

ð15Þ

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R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11

By substituting the value of DGRM in Eq. (14), we obtain the final expression for the dynamic viscosity of binary liquid mixture as;

4. Results and discussion

 e 1  1= v e 1Þ ln g ¼ x1 ln gi þ x2 ln g2  x1 P 1 v 1 fð1= v n o 1=3 þ 3 Te 1 ln ðv~ 1  1Þ=ðv~ 1=3  1Þ þ x2 P 2 v 2 fð1=v~ 2  1=v~ Þ n o i  1Þ=ðv~ 1=3  1Þ þ x1 v 1 h2 X 12 =v~ 1 =RT þ 3T~ 2 ln ðv~ 1=3 2

Table 1 presents the comparison of experimental densities, dynamic viscosities and refractive indices of acetonitrile, formamide, NMA, DMF and DMA with literature values at 293.15, 298.15, 303.15, 308.15 and 313.15 K. Coefficients of the Redlich–Kister polynomials and their standard deviations (r) for viscosity and refractive index are presented in Table 2. Parameters of McAllister three body and four body interaction model and standard deviations for viscosities and refractive indices are presented in Tables 3 and 4. Table 5 presents the comparison of average deviation (AD) from various theoretical models used in this work. Values of mole fraction (x1), density of the mixture (q) experimental physical properties (gexp and nexp), theoretical physical properties obtained from various models, g(Eq. (16)), g(Eq. (5)), g(Eq. (10)), and n(Eq. (18)), n(Eq. (5)), n(Eq. (10)) for acetonitrile + formamide, acetonitrile + NMA, acetonitrile + DMF and acetonitrile + DMA over the whole composition range at five temperatures were recorded in Table 6. Relations between association phenomenons in liquids were analyzed earlier [27] by considering van der Waals equation which was based only on simple averaged geometrical derivations without analyzing the system in terms of equilibrium. The association phenomenons have been related usually the deviation of different quantities from additivity. Ramaswamy and Anbananthan derived the model based on the assumption of linearity of acoustic impedance with the mole fractions of components which was corrected and tested [11] for the prediction of associational behavior from sound velocity data. The quantities analyzed were refractive index, molar volume, viscosity, intermolecular free length and many other [15–19,28]. The physical properties such as viscosity, surface tension, sound velocity, free energy, and refractive index can be predicted well with this model. Prediction of viscosity and refractive index from this approach is our first attempt. The results of fittings obtained from the model were utilized properly. The basic doubt regarding this model except the assumption of linearity of viscosity and refractive index with mole fraction is that these liquids have poor tendency to form dimmers. The calculations were performed using a computer

þ 1=fðv~  1Þ  x1 =ðv~ 1  1Þ  x2 =ðv~ 2  1Þ

ð16Þ

The values of reduced and characteristic parameters in Eq. (16) are obtained by the procedure as detailed out by Flory [6], Abe and Flory [7], and Flory et al. [8] and others [23–25] and notations used have their usual significance. 3.4. Lorentz–Lorentz relation Lorentz–Lorentz (L–L) [5] relation has widest application during the evaluation of refractive indices of mixture and density of pure components as well as density of the mixture and represented in terms of specific refraction as:

 2   2   2  n 1 1 n  1 w1 n  1 w2 ¼ 12 þ 22 2 n þ2 q n1 þ 2 q1 n2 þ 2 q2

ð17Þ

This relation can be used in another form, where / is taken into consideration,

  2   2   2 n 1 n1  1 n2  1 / / þ ¼ 1 n2 þ 2 n21 þ 2 n22 þ 2 2

ð18Þ

here n, n1, n2, q, q1, q2, w1, w2 are the refractive indices of mixture and pure components, 1.2, density of mixture, density of pure components, 1.2, weight fraction of pure components, 1.2, respectively and /1, /2 are the volume fractions of pure components which is obtained by the relation [26] as:

xi v i /i ¼ P xi v i

ð19Þ

where xi, vi are the mole fraction and molar volume of the ith component.

Table 2 Coefficients of the Redlich–Kister equation and standard deviations (r) for dynamic viscosities and refractive indexes of binary liquid mixtures at various temperatures. Viscosity (Dg/m Pa s)

Refractive index (Dn) a1

a2

a3

(r)

a0

a1

a2

a3

(r)

3.1701 3.1632 2.6741 2.0784 2.3229

1.8712 0.7940 1.1674 1.4471 4.5681

6.8920 10.2145 11.9986 13.6920 5.9900

0.6440 0.8327 1.0105 1.1726 1.6384

0.0385 0.0455 0.0654 0.0449 1.3919

0.0166 0.0104 0.0285 0.0408 3.1690

0.0393 0.0563 0.1012 0.0097 12.8875

0.1120 0.1200 0.1118 0.2526 19.0309

0.0606 0.0740 0.0580 0.0617 0.5562

Acetonitrile + NMA 293.15 4.1889 298.15 4.0509 303.15 4.6082 308.15 5.1816 313.15 8.9919

7.4616 8.8224 7.6271 8.5019 1.4651

12.2001 14.7111 16.2804 17.2466 3.6885

18.2377 24.2105 24.4327 29.3852 0.1919

1.4274 1.4430 1.5493 1.6631 2.1670

0.1003 0.1013 0.0908 0.0780 0.0769

0.0108 0.0045 0.0743 0.0401 0.0173

0.0341 0.1662 0.0905 0.1145 0.0678

0.1447 0.2093 0.1345 0.0272 0.1458

0.0760 0.0674 0.0543 0.0564 0.0583

Acetonitrile + DMF 293.15 0.2213 298.15 0.3119 303.15 0.3716 308.15 0.5250 313.15 1.3309

0.0189 0.0924 0.1916 0.2681 2.4799

0.2069 0.0634 0.1009 0.0864 0.3005

0.7605 0.5789 0.2400 0.2984 9.6102

0.0865 0.1157 0.1175 0.1563 0.4153

0.0892 0.1126 0.0991 0.0696 0.0779

0.0070 0.0308 0.0320 0.0537 0.0702

0.0155 0.0464 0.0456 0.1569 0.0363

0.0953 0.0322 0.1129 0.0315 0.1714

0.0749 0.0804 0.0604 0.0557 0.0642

Acetonitrile + DMA 293.15 0.2950 298.15 0.7187 303.15 0.8263 308.15 0.6879 313.15 1.7913

0.5366 2.9035 2.7546 3.2466 0.1858

1.6253 9.7217 9.1740 7.6681 9.5379

0.8254 7.0938 7.3906 5.8533 20.3185

0.1030 0.3382 0.3439 0.3466 0.5520

0.1195 0.0782 0.3527 0.1022 0.0642

0.0050 0.0744 2.5839 0.0288 0.2209

0.0218 0.1537 2.3181 0.1285 0.0637

0.1844 0.1188 8.8068 0.0165 0.3853

0.0811 0.0748 0.0852 0.0725 0.0626

T

a0

Acetonitrile + formamide 293.15 2.7294 298.15 3.3838 303.15 3.8870 308.15 4.4916 313.15 5.9431

5

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 Table 3 Parameters of McAllister three body and four body interaction models and standard deviations (r) for dynamic viscosities of binary liquid mixtures at various temperatures. McAllister three body (g/m Pa s)

McAllister four body (g/m Pa s)

Component

Temperature

b

(r)

Acetonitrile + formamide

293.15 298.15 303.15 308.15 313.15

6.3047 5.6181 5.4960 5.0060 4.0534

1.9907 2.4121 2.6860 3.3268 4.7869

0.1492 0.1897 0.2296 0.2384 0.3421

3.9953 3.5698 3.9134 3.2778 3.3434

2.4531 2.6765 2.2533 2.9014 2.2323

2.7933 3.0623 3.6689 3.7401 5.8728

0.1077 0.1500 0.1600 0.1965 0.2487

Acetonitrile + NMA

293.15 298.15 303.15 308.15 313.15

36.5865 35.7563 35.5126 33.5257 30.5538

0.9316 0.9725 1.0636 1.2355 1.8102

0.5110 0.5044 0.5496 0.5103 0.5253

43.6982 40.5831 46.1787 38.2883 31.9775

0.2585 0.2999 0.2217 0.3266 0.4913

14.7182 13.6061 18.4335 15.3849 16.1991

0.2232 0.2134 0.2199 0.1909 0.3381

Acetonitrile + DMF

293.15 298.15 303.15 308.15 313.15

0.5694 0.5928 0.6013 0.6060 0.4841

0.9262 0.9196 0.9093 0.9697 0.3087

0.1491 0.0258 0.0220 0.0336 1.0318

0.4546 0.4892 0.5009 0.4693 2.5562

1.0544 0.9544 0.9202 1.1118 0.0087

0.6914 0.7391 0.7480 0.6918 5.3663

0.0260 0.0260 0.0221 0.0320 0.6780

Acetonitrile + DMA

293.15 298.15 303.15 308.15 313.15

0.8209 0.6306 1.3938 1.6916 1.6593

0.9045 1.4473 0.7203 0.5838 0.5699

0.0164 1.1463 0.0224 0.0486 0.0313

0.6959 0.2144 1.2229 1.7698 1.5738

0.8836 9.7934 0.6841 0.3961 0.4908

0.9105 0.2333 1.0117 1.2701 1.0301

0.1176 1.0121 0.0176 0.0228 0.0128

a

a

b

(r)

c

Table 4 Parameters of McAllister three body and four body interaction models and standard deviations (r) for refractive index of binary liquid mixtures at various temperatures. Component

Temperature

McAllister three body (n)

McAllister four body (n)

a

b

(r)

a

b

c

(r)

Acetonitrile + formamide

293.15 298.15 303.15 308.15 313.15

1.3844 1.3829 1.3827 1.3889 1.3720

1.4289 1.4324 1.4326 1.4019 1.3980

0.0029 0.0032 0.0032 0.0048 0.0026

0.3515 1.3811 1.3814 1.3935 1.3510

3.1291 1.3899 1.3885 1.3577 1.4023

0.5709 1.4440 1.4448 1.4312 1.3941

0.0546 0.0028 0.0028 0.0037 0.0022

Acetonitrile + NMA

293.15 298.15 303.15 308.15 313.15

1.4300 1.4498 1.4364 1.4296 1.4281

1.4562 1.4261 1.4355 1.4300 1.4223

0.0473 0.0022 0.0042 0.0042 0.0008

1.3487 1.4050 1.3834 1.3805 1.3969

1.5770 1.4563 1.4847 1.4721 1.4160

1.3435 1.4040 1.3881 1.3884 1.4213

0.0447 0.0015 0.0025 0.0030 0.0008

Acetonitrile + DMF

293.15 298.15 303.15 308.15 313.15

1.4537 1.4661 1.4389 1.4242 1.4306

1.4300 1.4342 1.4405 1.4218 1.4257

0.0033 0.0023 0.0018 0.0045 0.0018

1.4301 1.4389 1.4066 1.3726 1.3994

1.4081 1.4166 1.4338 1.4710 1.4176

1.4456 1.4480 1.4326 1.3808 1.4240

0.0027 0.0013 0.0046 0.0026 0.0018

Acetonitrile + DMA

293.15 298.15 303.15 308.15 313.15

1.4634 1.4572 1.4868 1.4609 1.4452

1.4365 1.4264 1.3932 1.4318 1.4032

0.0021 0.0032 0.0496 0.0035 0.0039

1.4648 1.4714 1.5610 1.4778 1.4322

1.4366 1.3989 1.2492 1.3959 1.4451

1.4500 1.4662 1.5670 1.4743 1.3982

0.0020 0.0015 0.0479 0.0008 0.0035

program which allows fittings easily both the adjustable parameters simultaneously, or the parameters were changed manually. We constructed the data sheet in a computer program, with association constant Kas and CA,B as the fitted parameters (CA,B is the viscosity and refractive index of pure components A and B) means a hypothetical liquid having only the associate A–B. On changing these parameters, the equilibrium concentrations of species [A], [B] and [AB] will change and the viscosity and refractive index can be computed. The difference between experimental and theoretical values for viscosities and refractive indices is used to obtain the sum of squares of deviations. It is assumed that in solution three components are formed instead of two (pure A, pure B and associate, AB). The values of viscosity in pure associate can be treated as a fitted one with the value of Kas. Values of thermal expansion coefficient (a) and isothermal compressibility (bT) needed in the PFP model were obtained from

the following expression due to unavailability of experimental data. The values of a and bT obtained from such expression have already been tested in many cases by us [28] and others [29–31].

bT ¼

1:71  103 T 4=9 u2

q

4=3

and a ¼

75:6  103 T 1=9 u1=2 q1=3

ð20Þ

The mixing function, Dg; Dn were represented mathematically by the Redlich–Kister equation [11] for correlating the experimental data as:

y ¼ xi ð1  x1 Þ

p X

ai ð2x1  1Þi

ð21Þ

i¼0

where y refers to Dg, Dn, x1 is the mole fraction and ai is the coefficients. The values of coefficients ai were determined by a multiple regression analysis based on the least squares method and are summarized along with the standard deviations between

6

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11

Table 5 Comparison of average deviation values obtained from various liquid state models. Kas  104

gab/

g(Eq. (16))/

g(Eq. (5))/

g(Eq. (10))/

g(Eq. (23))/

g(Eq. (24))/

n(Eq.

n(Eq.

n(Eq.

n(Eq.

n(Eq.

m Pa s

m Pa s

m Pa s

m Pa s

m Pa s

m Pa s

(18))

(5))

(10))

(23))

(24))

Acetonitrile + formamide 293.15 1.3000 298.15 1.0000 303.15 1.2000 308.15 1.1200 313.15 1.1100

3.6500 3.3190 2.6962 2.6490 0.3347

0.6051 0.6948 0.7917 0.8440 0.9562

0.4434 0.5987 0.8585 0.8793 1.0432

1.5515 1.5434 1.5750 1.5514 1.6435

0.1302 0.1643 0.1983 0.1943 0.3057

0.0966 0.1294 0.1383 0.1615 0.2017

0.0180 0.0169 0.0152 0.0056 0.0075

0.0081 0.0099 0.0105 0.0370 0.0051

0.0140 0.0159 0.0166 0.0164 0.0108

0.0021 0.0023 0.0024 0.0042 0.0020

0.3865 0.0019 0.0020 0.0029 0.0018

Acetonitrile + NMA 293.15 1.4000 298.15 1.5000 303.15 1.6000 308.15 1.7000 313.15 1.8000

3.3498 3.3013 2.8999 2.6000 2.3038

1.5491 1.5504 1.5722 1.6282 1.7452

1.0510 1.0590 1.1531 1.2226 1.3840

1.7481 1.0590 1.7372 1.7249 1.8088

0.4308 0.4318 0.4553 0.4360 0.4353

0.2047 0.1993 0.1937 0.1687 0.2904

0.0063 0.0043 0.0066 0.0077 0.0061

0.0137 0.0105 0.0095 0.0073 0.0084

0.0288 0.0097 0.0085 0.0061 0.0072

0.0212 0.0018 0.0036 0.0032 0.0006

0.0242 0.0012 0.0022 0.0023 0.0006

Acetonitrile + DMF 293.15 1.1800 298.15 1.1900 303.15 1.2100 308.15 1.3200 313.15 1.3300

0.6998 0.7596 0.7235 0.6805 0.6389

0.2354 0.2499 0.2647 0.2637 0.1562

0.0407 0.0491 0.0533 0.0725 0.0827

0.0776 0.0828 0.0878 0.1047 0.1119

0.1313 0.0212 0.0178 0.0259 0.1486

0.0225 0.0221 0.0165 0.0255 0.1675

0.0059 0.0061 0.0050 0.0129 0.0058

0.0172 0.0221 0.0157 0.0083 0.0141

0.0121 0.0173 0.0110 0.0055 0.0091

0.0028 0.0020 0.0017 0.0036 0.0016

0.0020 0.0011 0.0032 0.0023 0.0014

Acetonitrile + DMA 293.15 1.3400 298.15 1.3500 303.15 1.3600 308.15 1.3700 313.15 1.3800

0.9971 0.9378 0.8777 0.8123 0.7562

0.3341 0.3702 0.3945 0.4006 0.1127

0.0430 0.0927 0.1232 0.1472 0.1479

0.1266 0.1713 0.1924 0.2087 0.2000

0.0123 0.1241 0.0182 0.0390 0.0259

0.0792 0.1060 0.0127 0.0179 0.0107

0.0035 0.0042 0.0204 0.0074 0.0053

0.0220 0.0189 0.0333 0.0226 0.0145

0.0139 0.0111 0.0255 0.0149 0.0080

0.0019 0.0025 0.0240 0.0030 0.0033

0.0016 0.0014 0.0265 0.0006 0.0030

Temperature

Table 6 Experimental densities (q), experimental viscosities, theoretical dynamic viscosities from Ramaswamy and Anbananthan (Eq. (5)), Prigogine–Flory–Patterson models (Eq. (16)), model devised by Glinski (Eq. (10)), experimental refractive indices, theoretical refractive indices from Ramaswamy and Anbananthan (Eq. (5)), Lorenz–Lorenz relation (Eq. (17)), model devised by Glinski (Eq. (10)) of Binary liquid mixtures at various temperatures.

qmix/g cm3

gexp/m Pa s

g(Eq. (16))/m Pa s

g(Eq. (5))/m Pa s

g(Eq. (10))/m Pa s

nexp

n(Eq.

Acetonitrile + formamide T = 293.15 K 0.1225 1.1258 0.2390 1.0992 0.3499 1.0835 0.4557 1.0405 0.5567 1.0102 0.6533 0.9705 0.7456 0.9403 0.8340 0.9015 0.9187 0.8503

3.4824 3.1358 2.9998 2.8654 2.4568 2.0265 1.8564 1.3547 0.5852

3.3065 2.8633 2.3923 1.9402 1.5350 1.1893 0.9057 0.6798 0.5040

3.2518 2.8692 2.5050 2.1575 1.8258 1.5085 1.2054 0.9150 0.6369

1.5487 1.1705 0.8898 0.7242 0.6149 0.5373 0.4795 0.4347 0.3990

1.4387 1.4298 1.4105 1.4058 1.3978 1.3848 1.3735 1.3625 1.3501

1.4455 1.4405 1.4401 1.4264 1.4181 1.4050 1.3958 1.3822 1.3623

1.4286 1.4169 1.4058 1.3952 1.3851 1.3755 1.3663 1.3574 1.3490

1.4246 1.4105 1.3981 1.3871 1.3773 1.3685 1.3606 1.3534 1.3468

T = 298.15 K 0.1225 0.2390 0.3499 0.4557 0.5567 0.6533 0.7456 0.8340 0.9187

1.1015 1.0825 1.0657 1.0345 0.9985 0.9624 0.9351 0.8792 0.8492

3.4810 3.1300 2.9901 2.8644 2.4561 2.0264 1.8505 1.3540 0.5004

3.0468 2.6683 2.2046 1.8405 1.4667 1.1435 0.8758 0.6606 0.4920

2.9594 2.6146 2.2864 1.9733 1.6744 1.3886 1.1154 0.8538 0.6031

1.6612 1.1259 0.8616 0.7039 0.5992 0.5246 0.4688 0.4255 0.3909

1.4387 1.4290 1.4104 1.4054 1.3975 1.3846 1.3731 1.3622 1.3499

1.4334 1.4331 1.4333 1.4262 1.4163 1.4057 1.3988 1.3775 1.3683

1.4251 1.4138 1.4030 1.3928 1.3830 1.3737 1.3648 1.3562 1.3480

1.4210 1.4072 1.3952 1.3845 1.3751 1.3666 1.3590 1.3521 1.3459

T = 303.15 K 0.1225 0.2390 0.3499 0.4557 0.5567 0.6533 0.7456 0.8340 0.9187

1.0998 1.0735 1.0538 1.0258 0.9802 0.9594 0.9256 0.8728 0.8402

3.4715 3.1258 2.9002 2.8568 2.4500 2.0000 1.8222 1.3455 0.4987

2.7846 2.4840 1.8352 1.7572 1.4112 1.1058 0.8492 0.6408 0.4766

2.4088 2.1355 1.8753 1.6271 1.3901 1.1635 0.9469 0.7395 0.5408

1.4808 1.0364 0.8061 0.6651 0.5699 0.5013 0.4496 0.4092 0.3767

1.4380 1.4289 1.4101 1.4050 1.3970 1.3840 1.3729 1.3619 1.3489

1.4337 1.4304 1.4295 1.4242 1.4098 1.4067 1.3968 1.3772 1.3667

1.4240 1.4127 1.4020 1.3917 1.3820 1.3726 1.3637 1.3552 1.3470

1.4199 1.4060 1.3940 1.3833 1.3739 1.3655 1.3579 1.3510 1.3448

T = 308.15 K 0.1225 0.2390 0.3499 0.4557 0.5567

1.0856 1.0568 1.0215 0.9856 0.9508

3.4054 3.1025 2.8971 2.8401 2.4459

2.5500 2.3180 1.7204 1.6834 1.3634

2.3657 2.0882 1.8233 1.5719 1.3343

1.4489 1.0120 0.7863 0.6484 0.5553

1.4199 1.4105 1.4099 1.3904 1.3801

1.4208 1.4158 1.4073 1.3979 1.3883

1.3998 1.3772 1.3594 1.3458 1.3359

1.4114 1.3970 1.3846 1.3736 1.3639

X1

(18))

n(Eq.

(5))

n(Eq.

(10))

7

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 Table 6 (continued) X1

qmix/g cm3

gexp/m Pa s

g(Eq. (16))/m Pa s

g(Eq. (5))/m Pa s

g(Eq. (10))/m Pa s

nexp

n(Eq.

0.6533 0.7456 0.8340 0.9187

0.9256 0.8809 0.8405 0.8028

1.9982 1.7059 1.3054 0.4057

1.0746 0.8280 0.6256 0.4650

1.1104 0.9000 0.7022 0.5162

0.4883 0.4379 0.3984 0.3667

1.3700 1.3675 1.3599 1.3480

1.3827 1.3675 1.3538 1.3409

1.3293 1.3255 1.3243 1.3253

1.3552 1.3474 1.3404 1.3341

T = 313.15 K 0.1225 0.2390 0.3499 0.4557 0.5567 0.6533 0.7456 0.8340 0.9187

1.0807 1.0559 1.0158 0.9758 0.9365 0.8905 0.8726 0.8405 0.7992

3.3901 3.9570 2.8897 2.8304 2.4358 1.8758 1.6889 1.2568 0.3944

2.3469 2.1623 1.8998 1.6042 1.3099 1.0395 0.8054 0.6112 0.4558

2.1504 1.9093 1.6798 1.4609 1.2519 1.0520 0.8611 0.6782 0.5029

1.3681 0.9704 0.7601 0.6299 0.5413 0.4772 0.4286 0.3906 0.3599

1.4123 1.4058 1.3945 1.3854 1.3789 1.3687 1.3555 1.3482 1.3302

1.4196 1.4163 1.4056 1.3942 1.3825 1.3672 1.3643 1.3545 1.3398

1.4128 1.4013 1.3903 1.3798 1.3698 1.3602 1.3511 1.3424 1.3340

1.4085 1.3943 1.3819 1.3710 1.3614 1.3528 1.3450 1.3380 1.3317

Acetonitrile + NMA T = 303.15 K 0.2733 0.9357 0.4481 0.9235 0.5757 0.8895 0.6808 0.8764 0.7614 0.8658 0.8282 0.8465 0.8821 0.8351 0.9290 0.8252 0.9685 0.8051

1.6113 1.1728 0.8708 0.6899 0.5955 0.5316 0.4708 0.4315 0.3960

3.4724 3.1358 2.9898 2.8654 2.4468 2.0265 1.8464 1.3547 0.5752

2.5406 2.0185 1.6373 1.3234 1.0826 0.8830 0.7220 0.5819 0.4639

1.0468 0.7268 0.5942 0.5166 0.4696 0.4366 0.4132 0.3948 0.3805

1.4157 1.4083 1.3903 1.3829 1.3769 1.3668 1.3607 1.3554 1.3453

1.4199 1.4100 1.4013 1.3976 1.3845 1.3756 1.3612 1.3599 1.3501

1.4097 1.3951 1.3835 1.3740 1.3662 1.3595 1.3539 1.3489 1.3446

1.4094 1.3959 1.3850 1.3753 1.3673 1.3604 1.3545 1.3492 1.4974

T = 303.15 K 0.2733 0.4481 0.5757 0.6808 0.7614 0.8282 0.8821 0.9290 0.9685

0.9305 0.9197 0.8807 0.8704 0.8595 0.8405 0.8305 0.8205 0.8015

1.5808 1.1503 0.8538 0.6763 0.5838 0.5211 0.4616 0.4230 0.3882

3.471 3.13 2.9801 2.8644 2.4361 2.0264 1.8405 1.354 0.4904

2.4987 1.9849 1.6098 1.3009 1.0639 0.8676 0.7091 0.5713 0.4551

2.4987 1.9848 1.6097 1.3008 1.0639 0.8675 0.7091 0.5712 0.4551

1.4160 1.4102 1.3903 1.3850 1.3794 1.3698 1.3648 1.3598 1.3504

1.4135 1.4089 1.4002 1.3921 1.3801 1.3701 1.3589 1.3500 1.3489

1.4082 1.3938 1.3824 1.3731 1.3654 1.3588 1.3532 1.3484 1.3442

1.4084 1.3949 1.3840 1.3744 1.3665 1.3597 1.3539 1.3487 1.3442

T = 303.15 K 0.2733 0.4481 0.5757 0.6808 0.7614 0.8282 0.8821 0.9290 0.9685

0.9108 0.8998 0.8712 0.8652 0.8501 0.8357 0.8256 0.7958 0.7853

1.4204 1.0525 0.7901 0.6320 0.5502 0.4947 0.4404 0.4056 0.3736

3.4615 3.1258 2.8002 2.8568 2.4200 2.0000 1.8122 1.3455 0.4887

2.2076 1.7608 1.4346 1.1660 0.9599 0.7892 0.6514 0.5315 0.4306

0.9702 0.6803 0.5585 0.4867 0.4430 0.4124 0.3906 0.3734 0.3600

1.4064 1.4012 1.3871 1.3844 1.3771 1.3702 1.3654 1.3509 1.3459

1.4130 1.4075 1.3995 1.3899 1.3788 1.3655 1.3501 1.3468 1.3423

1.4060 1.3921 1.3810 1.3719 1.3644 1.3580 1.3526 1.3479 1.3438

1.4075 1.3940 1.3832 1.3737 1.3659 1.3591 1.3534 1.3483 1.3438

T = 308.15 K 0.2733 0.4481 0.5757 0.6808 0.7614 0.8282 0.8821 0.9290 0.9685

0.9007 0.8795 0.8654 0.8556 0.8456 0.8298 0.8198 0.7902 0.7805

1.2959 0.8669 0.6639 0.5437 0.4729 0.4256 0.3937 0.3701 0.3529

3.3954 3.1025 2.8871 2.8401 2.4199 1.9982 1.6959 1.3054 0.3957

1.9848 1.5893 1.3006 1.0629 0.8805 0.7294 0.6075 0.5014 0.4120

0.9250 0.6549 0.5399 0.4716 0.4299 0.4006 0.3797 0.3632 0.3503

1.4023 1.3923 1.3857 1.3813 1.3768 1.3693 1.3646 1.3503 1.3458

1.4100 1.4023 1.3925 1.3899 1.3726 1.3600 1.3490 1.3460 1.3422

1.4043 1.3905 1.3795 1.3706 1.3631 1.3568 1.3515 1.3468 1.3427

1.4063 1.3929 1.3821 1.3725 1.3648 1.3580 1.3523 1.3472 1.3428

T = 313.15 K 0.2733 0.4481 0.5757 0.6808 0.7614 0.8282 0.8821 0.9290 0.9685

0.8798 0.8697 0.8556 0.8425 0.8346 0.8194 0.8008 0.7824 0.7615

1.1538 0.7800 0.6045 0.5015 0.4416 0.4022 0.3761 0.3572 0.3439

3.3801 3.957 2.8797 2.8304 2.4158 1.8758 1.6889 1.2568 0.3844

1.765733 1.4215314 1.1702744 0.9633236 0.8046 0.6730 0.5669 0.4746 0.3968

0.883648 0.633758 0.525312 0.460418 0.4205 0.3924 0.3723 0.3564 0.3440

1.3910 1.3851 1.3774 1.3703 1.3659 1.3580 1.3485 1.3393 1.3290

1.4089 1.3982 1.3865 1.3748 1.3645 1.3556 1.3489 1.3400 1.3356

1.4007 1.3854 1.3731 1.3632 1.3549 1.3479 1.3419 1.3368 1.3322

1.4023 1.3873 1.3754 1.3649 1.3564 1.3489 1.3427 1.3371 1.3322

Acetonitrile + DMF T = 293.15 K 0.2142 0.9391 0.3802 0.9297 0.5126 0.9158 0.6206 0.8957 0.7104 0.8748

0.9752 0.2975 0.2482 0.2314 0.2319

0.7599 0.6899 0.6122 0.5988 0.5123

0.7069 0.6357 0.5789 0.5326 0.4941

0.6399 0.5544 0.5010 0.4645 0.4380

1.4189 1.4128 1.4047 1.3936 1.3823

1.4211 1.4196 1.4032 1.3956 1.3855

1.4097 1.3951 1.3835 1.3740 1.3662

1.4141 1.4017 1.3908 1.3812 1.3726

(18))

n(Eq.

(5))

n(Eq.

(10))

(continued on next page)

8

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11

Table 6 (continued) X1

qmix/g cm3

gexp/m Pa s

g(Eq. (16))/m Pa s

g(Eq. (5))/m Pa s

g(Eq. (10))/m Pa s

nexp

n(Eq.

0.7863 0.8513 0.9075 0.9567

0.8569 0.8354 0.8253 0.7902

0.2437 0.2642 0.2923 0.3276

0.4995 0.3815 0.3765 0.3699

0.4615 0.4336 0.4095 0.3884

0.4178 0.4020 0.3892 0.3787

1.3727 1.3615 1.3559 1.3385

1.3799 1.3700 1.3653 1.3512

1.3595 1.3539 1.3489 1.3446

1.3649 1.3580 1.3518 1.3461

T = 298.15 K 0.2142 0.3802 0.5126 0.6206 0.7104 0.7863 0.8513 0.9075 0.9567

0.9342 0.9272 0.9215 0.8901 0.8721 0.8504 0.8344 0.8248 0.7899

0.9531 0.2712 0.2249 0.2096 0.2109 0.2230 0.2436 0.2718 0.3073

0.7545 0.6855 0.6100 0.5955 0.5102 0.4955 0.3801 0.3762 0.3609

0.6791 0.6123 0.5589 0.5154 0.4792 0.4486 0.4225 0.3998 0.3800

0.6183 0.5381 0.4877 0.4530 0.4278 0.4085 0.3933 0.3811 0.3710

1.4182 1.4143 1.4112 1.3951 1.3859 1.3749 1.3668 1.3620 1.3448

1.4256 1.4199 1.4102 1.4036 1.3924 1.3824 1.3756 1.3654 1.3522

1.4082 1.3938 1.3824 1.3731 1.3654 1.3588 1.3532 1.3484 1.3442

1.4124 1.4001 1.3893 1.3799 1.3715 1.3639 1.3572 1.3511 1.3455

T = 303.15 K 0.2142 0.3802 0.5126 0.6206 0.7104 0.7863 0.8513 0.9075 0.9567

0.9304 0.9255 0.9192 0.8892 0.8706 0.8584 0.8261 0.8259 0.7853

0.9512 0.2472 0.2036 0.1900 0.1925 0.2056 0.2273 0.2570 0.2948

0.7401 0.6804 0.6089 0.5901 0.5066 0.4901 0.3799 0.3745 0.3599

0.6563 0.5916 0.5400 0.4979 0.4629 0.4333 0.4080 0.3861 0.3669

0.5974 0.5198 0.4710 0.4375 0.4131 0.3945 0.3798 0.3680 0.3582

1.4181 1.4157 1.4125 1.3973 1.3880 1.3819 1.3659 1.3659 1.3460

1.4199 1.4165 1.4033 1.3945 1.3822 1.3755 1.3654 1.3524 1.3499

1.4060 1.3921 1.3810 1.3719 1.3644 1.3580 1.3526 1.3479 1.3438

1.4101 1.3981 1.3877 1.3785 1.3703 1.3630 1.3564 1.3505 1.3451

T = 308.15 K 0.2142 0.3802 0.5126 0.6206 0.7104 0.7863 0.8513 0.9075 0.9567

0.9280 0.9234 0.9065 0.8801 0.8647 0.8561 0.8248 0.8234 0.7805

0.8853 0.2342 0.1947 0.1831 0.1864 0.1999 0.2219 0.2516 0.2891

0.7365 0.6345 0.6804 0.5835 0.5021 0.4865 0.3745 0.3705 0.3545

0.6084 0.5518 0.5067 0.4700 0.4394 0.4135 0.3914 0.3723 0.3555

0.5612 0.4937 0.4505 0.4205 0.3984 0.3815 0.3681 0.3573 0.3483

1.4184 1.4163 1.4079 1.3947 1.3871 1.3830 1.3675 1.3669 1.3459

1.4022 1.4065 1.3964 1.3825 1.3765 1.3654 1.3524 1.3499 1.3401

1.4043 1.3905 1.3795 1.3706 1.3631 1.3568 1.3515 1.3468 1.3427

1.4083 1.3965 1.3861 1.3770 1.3689 1.3617 1.3552 1.3494 1.3440

T = 313.15 K 0.2142 0.3802 0.5126 0.6206 0.7104 0.7863 0.8513 0.9075 0.9567

0.9255 0.9199 0.9002 0.8751 0.8615 0.8502 0.8227 0.8207 0.7798

0.8024 0.8529 0.9007 0.8237 0.7250 0.6242 0.5312 0.4500 0.3809

0.7302 0.6365 0.6756 0.5800 0.4989 0.4812 0.3705 0.3624 0.3501

0.5788 0.5272 0.4861 0.4526 0.4247 0.4011 0.3809 0.3635 0.3482

0.5384 0.4771 0.4374 0.4096 0.3890 0.3731 0.3606 0.3504 0.3419

1.4158 1.4119 1.4010 1.3876 1.3801 1.3738 1.3597 1.3582 1.3379

1.4138 1.4035 1.3937 1.3813 1.3764 1.3642 1.3521 1.3456 1.3330

1.4007 1.3854 1.3731 1.3632 1.3549 1.3479 1.3419 1.3368 1.3322

1.4051 1.3918 1.3803 1.3701 1.3611 1.3531 1.3460 1.3395 1.3336

Acetonitrile + DMA T = 293.15 K 0.2453 0.9591 0.4223 0.9512 0.5562 0.9421 0.6610 0.9159 0.7452 0.8856 0.8144 0.8653 0.8722 0.8529 0.9212 0.8355 0.9634 0.8159

1.1481 0.2338 0.1883 0.1776 0.1842 0.2024 0.2302 0.2672 0.3136

0.8914 0.7989 0.7011 0.6582 0.5799 0.5124 0.4973 0.4015 0.3985

0.8439 0.7327 0.6486 0.5828 0.5299 0.4864 0.4501 0.4193 0.3928

0.7046 0.5812 0.5132 0.4702 0.4405 0.4188 0.4022 0.3892 0.3786

1.4324 1.4266 1.4203 1.4055 1.3891 1.3779 1.3707 1.3613 1.3509

1.4298 1.4200 1.4156 1.4025 1.3945 1.3801 1.3748 1.3614 1.3543

1.4127 1.3958 1.3831 1.3731 1.3651 1.3585 1.3530 1.3483 1.3443

1.4203 1.4067 1.3949 1.3844 1.3751 1.3668 1.3593 1.3526 1.3464

T = 298.15 K 0.2453 0.4223 0.5562 0.6610 0.7452 0.8144 0.8722 0.9212 0.9634

0.9358 0.9256 0.9145 0.8995 0.8755 0.8504 0.8348 0.8119 0.7999

1.1025 0.2196 0.1775 0.1683 0.1755 0.1940 0.2220 0.2591 0.3058

0.8865 0.8001 0.7798 0.7114 0.6014 0.5864 0.5123 0.4456 0.4012

0.8011 0.6982 0.6204 0.5595 0.5106 0.4704 0.4368 0.4083 0.3838

0.6774 0.5628 0.4989 0.4582 0.4300 0.4093 0.3935 0.3810 0.3709

1.4253 1.4189 1.4121 1.4034 1.3904 1.3770 1.3685 1.3566 1.3501

1.4287 1.4123 1.4065 1.3945 1.3899 1.3800 1.3742 1.3612 1.3500

1.4111 1.3945 1.3820 1.3722 1.3643 1.3578 1.3524 1.3478 1.3439

1.4186 1.4052 1.3935 1.3832 1.3740 1.3659 1.3585 1.3519 1.3459

T = 303.15 K 0.2453 0.4223 0.5562 0.6610 0.7452 0.8144

0.9248 0.9016 0.8908 0.8705 0.8559 0.8391

1.0533 0.1975 0.1596 0.1521 0.1600 0.1787

0.8254 0.7987 0.7565 0.7065 0.6531 0.5734

0.7491 0.6555 0.5847 0.5293 0.4848 0.4482

0.6412 0.5366 0.4776 0.4398 0.4134 0.3941

1.4247 1.4113 1.4046 1.3931 1.3848 1.3754

1.4274 1.4113 1.4000 1.3936 1.3835 1.3742

1.4094 1.3931 1.3808 1.3712 1.3635 1.3572

1.4168 1.4037 1.3922 1.3821 1.3732 1.3652

(18))

n(Eq.

(5))

n(Eq.

(10))

9

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 Table 6 (continued) X1

qmix/g cm3

gexp/m Pa s

g(Eq. (16))/m Pa s

g(Eq. (5))/m Pa s

g(Eq. (10))/m Pa s

nexp

n(Eq.

0.8722 0.9212 0.9634

0.8069 0.7909 0.7854

0.2068 0.2443 0.2918

0.5236 0.4985 0.4041

0.4176 0.3917 0.3694

0.3792 0.3675 0.3579

1.3586 1.3500 1.3467

1.3699 1.3600 1.4990

1.3519 1.3474 1.3435

1.3580 1.3515 1.3455

T = 308.15 K 0.2453 0.4223 0.5562 0.6610 0.7452 0.8144 0.8722 0.9212 0.9634

0.9158 0.9016 0.8759 0.8669 0.8498 0.8257 0.8067 0.7895 0.7759

1.0111 0.1816 0.1469 0.1407 0.1491 0.1679 0.1960 0.2336 0.2815

0.8297 0.6965 0.7512 0.7023 0.6725 0.6102 0.5789 0.5001 0.4101

0.7072 0.6213 0.5562 0.5054 0.4645 0.4309 0.4028 0.3790 0.3585

0.6123 0.5159 0.4610 0.4255 0.4008 0.3825 0.3684 0.3573 0.3482

1.4228 1.4141 1.3996 1.3939 1.3843 1.3712 1.3610 1.3517 1.3444

1.4298 1.4158 1.4056 1.3998 1.3901 1.3822 1.3721 1.3641 1.3512

1.4076 1.3916 1.3794 1.3699 1.3623 1.3560 1.3507 1.3463 1.3425

1.4150 1.4020 1.3907 1.3807 1.3719 1.3639 1.3568 1.3504 1.3445

T = 313.15 K 0.2453 0.4223 0.5562 0.6610 0.7452 0.8144 0.8722 0.9212 0.9634

0.9098 0.8890 0.8654 0.8566 0.8442 0.8198 0.7908 0.7828 0.7742

0.9641 0.9964 0.9324 0.8287 0.7179 0.6151 0.5256 0.4500 0.3869

0.7457 0.7249 0.7005 0.6972 0.6624 0.5879 0.5465 0.4879 0.4065

0.6624 0.5855 0.5274 0.4819 0.4453 0.4153 0.3902 0.3690 0.3506

0.5833 0.4968 0.4467 0.4140 0.3910 0.3739 0.3608 0.3503 0.3418

1.4191 1.4057 1.3966 1.3847 1.3765 1.3626 1.3468 1.3415 1.3360

1.4056 1.4026 1.3912 1.3854 1.3792 1.3687 1.3501 1.3489 1.3300

1.4038 1.3861 1.3727 1.3622 1.3537 1.3468 1.3410 1.3361 1.3319

1.4118 1.3974 1.3849 1.3739 1.3641 1.3554 1.3476 1.3405 1.3341

the experimental and fitted values of the respective function in Table 2. The standard deviation is defined by.

r¼

" #1=2 m X ðyexpi  ycali Þ2 =ðm  pÞ

ð22Þ

i¼1

where m is the number of experimental points and p is the number of adjustable parameters. For viscosity, the r values lie between 0.08 and 2.16 m Pa s and the largest r value corresponds to acetonitrile + NMA mixture at 313.15 K and for refractive index, the r values lie between 0.05 and 0.55 and the largest r value corresponds to acetonitrile + formamide mixture at 313.15 K. In both the cases, largest standard deviation occurs at higher temperatures. McAllister multi-body interaction model [14] is widely used for correlating the viscosity of liquid mixtures with mole fraction. The three body model is defined as:

ln g ¼ x31 ln g1 þ 3x21 x2 ln a þ 3x1 x22 ln b þ x32 ln g2  ½lnðx1 þ x2 M 2 =M1 Þ þ 3x21 x2 ½lnð2 þ M2 =M 1 Þ=3 þ 3x1 x22 ln½ð1 þ 2M2 =M 1 Þ=3 þ x32 lnðM2 =M 1 Þ

ð23Þ

and the four body model is given by,

ln g ¼ x41 ln g1 þ 4x31 x2 ln a þ 6x21 x22 ln b þ 4x1 x32 ln c þ x42 ln g2  lnðx1 þ x2 M 2 =M1 Þ þ 4x31 x2 ln½ð3 þ M 2 =M 1 Þ=4 þ 6x21 x22 ln½ð1 þ M 2 =M1 Þ=2 þ 4x1 x32  ln½ð1 þ 3M 2 =M 1 Þ=4 þ x42 lnðM 2 =M 1 Þ

ð24Þ

where g is the viscosity of the mixture and x1, g1, M1, x2, g2 and M2 are the mole fractions, viscosities, and molecular weights of pure components 1 and 2 respectively; a–c are adjustable parameters that are characteristic of the system. In the above Eqs. (22) and (23) the coefficient a–c have been calculated using the least squares procedure. The estimated parameters of the viscosity equations and the standard deviations, r, between the calculated and experimental values are given in Table 3. It is observed that the four body model of the McAllister equation correlated the mixture viscosity to a significantly higher degree of accuracy for all of the systems than does the three body model. Furthermore, the values of the McAllister parameters have shown a decreasing tendency with rise

(18))

n(Eq.

(5))

n(Eq.

(10))

in temperature. Generally, McAllister’s models are adequate in correlating the systems having small deviations. These equations have also been utilized for the prediction of refractive index successfully. With the increase of mole fraction (x2), the values of dynamic viscosities and refractive index obtained from all the models decrease at all temperatures except at few places. The average deviation (AD) in dynamic viscosity obtained from Eqs. (16), (5), (10), (23) and (24) for all the systems are found to be [(0.61, 1.55, 0.24 and 0.33 at 293.15 K), (0.69, 1.55, 0.25 and 0.37 at 298.15 K), (0.79, 1.57, 0.26 and 0.39 at 303.15 K), (0.24, 1.63, 0.26 and 0.40 at 308.15 K), (0.95, 1.74, 0.16 and 0.11at 313.15 K)], [(0.44, 1.05, 0.04 and 0.04 at 293.15 K), (0.60, 1.06, 0.05 and 0.09 at 298.15 K), (0.86, 1.15, 0.05 and 0.12 at 303.15 K), (0.88, 1.22, 0.07 and 0.15 at 308.15 K), (1.04, 1.38, 0.08 and 0.15 at 313.15 K)] and [(1.55, 1.75, 0.08 and 0.13 at 293.15 K), (1.54, 1.06, 0.08 and 0.17 at 298.15 K), (1.58, 1.74, 0.09 and 0.19 at 303.15 K), (1.55, 1.72, 0.10 and 0.21 at 308.15 K), (1.64, 1.81, 0.11 and 0.20 at 313.15 K)] and [(0.10, 0.20, 0.02 and 0.08 at 293.15 K), (0.13, 0.20, 0.02 and 0.11 at 298.15 K), (0.14, 0.19, 0.02 and 0.01 at 303 K), (0.16, 0.17, 0.03, and 0.02 at 308.15 K), (0.20, 0.29, 0.17, and 0.01 at 313.15 K)] respectively. The overall average estimated error in dynamic viscosity obtained from (Eqs. (16), (5), (10), (23) and (24)) for all the systems are found to be [(0.77, 0.75, 1.57, 0.20 and 0.15), (1.60, 1.17, 161, 0.44 and 0.21), (0.23, 0.06, 0.08, 0.07 and 0.05) and (0.32, 0.11, 0.18, 0.04 and 0.05) ] respectively. Higher deviation values of dynamic viscosities in acetonitrile + formamide and acetonitrile + NMA mixture at all temperatures can be ascribed as unusual behavior of these solvents and higher overall average estimated error in PFP model (Eq. (16)) can be explained as the model was developed for nonelectrolyte c-meric spherical chain molecules and the systems under investigation have interacting and associating properties. Moreover, the expression [20] used for the computation of a and bT are also empirical in nature. Similarly, the overall average deviation in refractive index obtained from Eqs. (18), (5), (10), (23) and (24) for all the systems are found to be [(0.012, 0.014, 0.014, 0.003 and 0.08), (0.006, 0.009, 0.011, 0.006 and 0.006), (0.007, 0.015, 0.010, 0.002 and 0.002) and (0.008, 0.022, 0.014, 0.007, 0.009)] respectively. The theoretical findings are very close to experimental data showing the success of all the theoretical models.

10

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11

T = 308.15 K

T = 293.15 K

1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00

as compared to others because of non- associated processes. But the trend in all the figures is almost similar and positive. Very close values of McAllister three and four body interaction models with the experimental data confirms the success of other experimental findings.

0.20

0.40

0.60

0.80

1.00

viscosity/ mPa s

viscosity/ mPa s

Plot of dynamic viscosity and refractive index obtained from various models with mole fraction at various temperatures are presented in Figs. 1 and 2. In all the cases, theoretical dynamic viscosity and refractive index computed from various models agree well with the experimental value except for PFP model and L–L relation

1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00

0.20

0.40

x1

1.20 1.00

0.20

0.40

0.80

1.00

0.60

0.80

1.00

T = 313.15 K

1.20

viscosity/ mPa s

viscosity/ mPa s

T = 303.15 K

0.80 0.60 0.40 0.20 0.00 0.00

0.60

x1

0.80

1.00 0.80 0.60 0.40 0.20 0.00 0.00

1.00

0.20

0.40

x1

0.60

x1

Fig. 1. Plot of dynamic viscosity g, with mole fraction x1 for x acetonitrile+(1  x) DMA at 313.15: , viscosity from PFP model (Eq. (16)), j experimental dynamic viscosity, , viscosity from McAllister four body model (Eq. (24)), N, viscosity from Ramaswamy model (Eq. (5)), x, viscosity from McAllister three body model (Eq. (23)) and d, viscosity from the model devised by Glinski (Eq. (10)).

1.60

T = 303.15 k

1.40

Refractive index

1.20

Refractive index

T = 293.15 k 1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00 0.00

1.00 0.80 0.60 0.40 0.20

0.20

0.40

0.60

0.80

0.00 0.00

1.00

0.20

0.40

x1 T = 308.15k

0.80

1.00

T = 313.15 k

1.40 1.20

Refractive index

Refractive index

1.60

0.60

x1

1.00 0.80 0.60 0.40 0.20 0.00 0.00

0.20

0.40

0.60

x1

0.80

1.00

1.60 1.40 1.20 1.00 0.80 0.60 0.40 0.20 0.00

0.00

0.20

0.40

0.60

0.80

1.00

x1

Fig. 2. Plot of refractive index n, with mole fraction x1 for x acetonitrile+(1  x) DMA at 313.15: j, experimental refractive index,  refractive index from Lorentz–Lorentz relation (Eq. (18)), , refractive index from McAllister four body model (Eq. (24)), N, refractive index from Ramaswamy model (Eq. (5)), x, refractive index from McAllister three body model (Eq. (23)) and d, refractive index from the model devised by Glinski (Eq. (10)).

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11

The Ramaswamy and Anbananthan model based on associated processes gives more reliable results and helpful in deducing the internal structure of associates through the fitted values of viscosity and refractive index in a hypothetical pure associate and observed dependence of concentration on composition of a mixture. The Prigogine–Flory–Patterson (PFP) model based on non-associated processes has been applied to associated molecules for the first time and satisfactory findings are obtained up to some extent. However, there is every possibility to improve the results. In general, still modifications are needed in order to interpret the associational behavior and interactions in liquid mixture. Acknowledgments Authors are extremely thankful to UGC, New Delhi for financial support (Grant-34-332/2008) and Department of Chemistry, VSSD College, for cooperation. References [1] L.C. Want, H.S. Xu, J.H. Zhao, C.Y. Song, F.A. Wang, J. Chem. Thermodyn. 37 (2005) 477–483. [2] A. Mchaweh, A. Alsaygh, Kh. Nabrifar, M.A. Moshfeghiam, Fluid Phase Equilib. 224 (2004) 57–167. [3] K. Baker, D. Garbe, H. Surburg, Common Fragrance and Flavor Materials: Preparation Properties and Uses, fourth ed., Wiley VCH, Weinheim, Germany, 2001. [4] Mahendra Nath Roy, B.K. Sarkar, R. Chand, J. Chem. Eng. Data 52 (2007) 1630– 1637.

[5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32]

11

H.A. Lorentz, Ann. Phys. 9 (1880) 641–665. P.J. Flory, J. Am. Chem. Soc. 82 (1965) 1833–1838. A. Abe, P.J. Flory, J. Am. Chem. Soc. 82 (1965) 1838–1845. P.J. Flory, R.A. Orwoll, A. Vrij, J. Am. Chem. Soc. 86 (1964) 515–3520. J. Prigogine, A. Bellemans, A. Mathod, Molecular Theory of Solutions, NorthHolland, Amsterdam, 1957. D. Patterson, A.K. Rastogi, J. Phys. Chem. 74 (1970) 1067–1071. J. Glinski, J. Chem. Phys. 118 (2003) 2301–2307. Ramaswamy, D. Anbananthan, Acustica 48 (1981) 281–282. O. Redlich, A.T. Kister, Indust. Eng. Chem. 40 (1948) 345–348. R.A. McAllister, AIChE J. 6 (1960) 427–431. A. Ali, K. Tewari, A.K. Nain, V. Chakravorty, Phys. Chem. Liq. 38 (2000) 459. P.S. Nikam, V.M. Kapade, M. Hasan, Indian J. Pure Appl. Phys. 38 (2000) 170. A. Rodrignez, J. Canosa, J. Tojo, J. Chem. Eng. Data 46 (2001) 1506. A. Ali, A. Kumar Nain, Indian J. Pure Appl. Phys. 39 (2001) 421. P.S. Nikam, B.S. Jagdale, A.B. Sawant, M. Hasan, Indian J. Pure Appl. Phys. 39 (2001) 433. G. Natta, M. Baccaredda, Atti Accad. Naz. Lincci. 4 (1948) 360. W.E. Roseveare, R.E. Powell, H. Eyring, J. Appl. Phys. 12 (1941) 669–679. P.B. Macedo, T.A. Litovitz, J. Chem. Phys. 42 (1965) 245–256. R.K. Shukla, A. Kumar, K. Srivastava, N. Singh, J. Solution Chem. 36 (2007) 1103–1116. R.K. Shukla, S. Dwivedi, P. Awasthi, J. Phys. Chem. Liq. 44 (2006) 431–440. R.K. Shukla, S. Dwivedi, A.N. Dubey, J. Mol. Liq. 133 (2007) 33–38. M.I. Aralaguppi, C. Jadar, T.M. Aminabhavi, J. Chem. Eng. Data 44 (1999) 441. W.S. chaafts, Ann. Phys. (Leipzig) 40 (1940) 393. R.K. Shukla, N. Awasthi, A. Kumar, A. Shukla, V.K. Pandey, J. Mol. Liq. 158 (2011) 20–28. R. Dey, N.K. Soni, R.K. Mishra, D.K. Dwivedi, J. Pure Appl. Ultrason. 28 (2006) 20–28. J.D. Pandey, Richa Verma, Chem. Phys. 270 (2001) 429–438. J.D. Pandey, R. Dey, M. Upadhyaya, Acoust. Lett. 21 (1996) 120. J.A. Riddick, W.B. Bunger, T.K. Sakano, Organic Solvents Techniques of Chemistry, fourth ed., Wiley, New York, 1986.