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

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Experimental Thermal and Fluid Science

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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 2011Received in revised form 23 July 2011Accepted 25 August 2011Available online 6 September 2011

Keywords:ViscosityRefractive indexAssociational behaviorRamaswamy and Anbananthan (RS)Prigogine–Flory–Patterson (PFP)DensityMcAllister

0894-1777/$ - see front matter � 2011 Elsevier Inc. Adoi:10.1016/j.expthermflusci.2011.08.005

⇑ Corresponding author. Tel.: +91 0512 2560070, m+91 2563842.

E-mail address: rajeevshukla47@rediffmail.com (R1 Address: Department of Chemistry, VSSD College,

India.2 Present address: Department of Chemistry, PSIT, K3 Present address: Department of Chemistry, PSAT, K

a b s t r a c t

Densities, viscosities and refractive indices were measured for the binary liquid mixtures formed byformamide, 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 concentra-tion range. Lorentz–Lorentz (L–L) relation, Prigogine–Flory–Patterson model (PFP), model devised byGlinski and Ramaswamy and Anbananthan (RS) models were used to study the associational behaviorof weakly interacting liquids from viscosity and refractive index data. These non-associated and associ-ated models were compared and also tested for different systems. The measured properties were fitted toRedlich–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, viscos-ities and refractive indices of binary liquid mixture can be better understood from these models andinteractions and association constant can be well predicted. The associated processes yield fair agreementbetween theory and experiment as compared to non-associated processes.

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1. Introduction

Density, viscosity and refractive index are important basic dataused in process simulation, equipment design, solution theory andmolecular dynamics [1,2]. A better understanding of viscosity is ofconsiderable physico-chemical interest and is essential in design-ing calculations involving heat transfer, mass transfer and fluidflow. Knowledge of viscosity is widely used in processing and prod-uct formulations [3] in many industrial applications. The solventschosen in the present work have technical and industrial impor-tance. Roy et al. [4] measured densities and viscosities of binaryliquid mixtures of formamide with 2-methoxy ethanol, acetophe-non, acetonitrile, 1,2-dimethoxy ethane and dimethyl surfoxideat 298.15, 308.15 and 318.15 K over the entire composition rangeat 0.1 m Pa and obtained the values of excess molar volume, VE, vis-cosity 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 formam-ide, N-methyl acetamide (NMA), di-methylformamide (DMF) anddi-methylacetamide (DMA) with acetonitrile at (T = 293.15,

ll rights reserved.

obile: +91 9838516217; fax:

.K. Shukla).Nawabgang, Kanpur 208 002,

anpur, India.anpur, India.

298.15, 303.15, 308.15 and 313.15) K and atmospheric pressureover the whole concentration range. These data were analyzed interms of Lorentz–Lorentz (L–L) relation [5], Prigogine–Flory–Patt-erson model (PFP) [6–10], model devised by Glinski [11] and themodel of Ramaswamy and Anbananthan (RS) [12]. RS and modeldevised by Glinski (associated) are based on the association con-stant as an adjustable parameter where as PFP model (non-associ-ated) is based on the additivity of liquids. For that purpose, weselected the liquids containing poor interacting properties havingimmense sense of technological significance in chemical indus-tries. From these results, deviation in viscosity, Dg and deviationin refractive index, Dn were calculated and fitted to the Redlich–Kister type polynomial equation [13] to derive the binary coeffi-cients and the standard errors. An attempt has also been made tocorrelate the experimental properties with the McAllister equation[14] which is based on Eyring’s theory of absolute reaction ratesand for liquids, the free energy of activation for viscosity are addi-tive on a number fraction and that interactions of like and unlikemolecules. The mixing behavior of such liquid mixtures containingacetonitrile is interesting due to presence of cyano group coupledwith amide linkage resulting interactions in the liquid mixtures.

The association phenomenon has been related usually to thedifferent quantity from additivity and the model [12] is simpleaveraged geometrical derivations in terms of equilibrium. Theassociational behavior of liquids and their correlation with molec-ular interactions has also been made using different liquid models.This is our first attempt to correlate all the models (associated and

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

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

2. Experimental section

2.1. Materials

High purity and AR grade samples of formamide, N-methylace-tamide, di-methyl formamide and di-methyl acetamide and aceto-nitrile used in this experiment were obtained from Merck Co., Inc.,Germany and purified by distillation in which the middle fractionwas collected. The liquids were stored in dark bottles over0.4 nm molecular sieves to reduce water content and were par-tially degassed with a vacuum pump. The purity of each compoundwas checked by gas chromatography and the results indicated thatthe mole fraction purity was higher than 0.99. All the materialswere used without further purification. The purity of chemicalsused was confirmed by comparing the densities and viscositieswith those reported in the literature as shown in Table 1.

2.2. Apparatus and procedure

Before each series of experiments, we calibrated the instrumentat atmospheric pressure with doubly distilled water. The uncer-tainty in the density measurement was within ±6.7 kg m�3 of thepublished values. The densities of the pure components and theirmixtures were measured with the bi-capillary pyknometer. The li-quid mixtures were prepared by mass in an air tight stopped bottleusing an electronic balance model SHIMADZUAX-200 accurate towithin ±0.1 mg. The average uncertainty in the composition ofthe mixtures was estimated to be less than ±0.0001. All molarquantities were based on the IUPAC relative atomic mass table.

The viscosities of pure liquids and the mixtures were measuredat atmosphere pressure and at different temperatures using CanonUbbelohde suspended-level viscometer. The viscometer was im-mersed in a well stirred water bath (Raga Industries) with temper-ature control to ±0.01 K. The flow time was recorded with a digitalstopwatch capable of measuring time to within ±0.01 s. Each

Table 1Comparison of density, viscosity and refractive index with literature data for pure compo

Compound T a � 10�3 K bT � 1012 Pa V/cm3 mole�1 qex

Acetonitrile 293.15 1.2762 108.8470 51.5379 0.7298.15 1.2943 113.5441 52.5540 0.7303.15 1.3151 119.1053 53.0841 0.7308.15 1.3300 123.1860 53.5551 0.7313.15 1.3420 126.5467 53.9776 0.7

Formamide 293.15 0.9431 43.9231 39.7879 1.1298.15 0.9515 45.1146 39.8937 1.1303.15 0.9570 45.8963 40.0355 1.1308.15 0.9594 46.2463 40.1784 1.1313.15 0.9656 47.1502 40.5145 1.1

NMA 293.15 1.1095 71.5118 76.4404 0.9298.15 1.1224 74.0374 76.8502 0.9303.15 1.1349 76.5384 76.9311 0.9308.15 1.1440 78.3887 77.2074 0.9313.15 1.1364 76.8504 77.7246 0.9

N,N-DMF 293.15 1.0844 66.7696 76.5260 0.9298.15 1.0899 67.7959 76.9287 0.9303.15 1.0970 69.1223 77.5984 0.9308.15 1.1108 71.7621 78.1126 0.9313.15 1.1187 73.3117 78.3807 0.9

N,N-DMA 293.15 1.0839 66.6719 90.5331 0.9298.15 1.0968 69.0911 91.6859 0.9303.15 1.1097 71.5617 93.0769 0.9308.15 1.1190 73.3692 94.0008 0.9313.15 1.1255 74.6488 94.4799 0.9

a Ref. [32].

experiment was repeated four times at each temperature for allcomposition and results were averaged. The viscosity g of the li-quid was then calculated from the following relationship

m ¼ g=q ¼ kðt ��Þ 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 constantand the Hagen Bach correction factor respectively. The calibrationof the viscometer was carried out with doubly distilled water anddoubly distilled benzene. Care was taken to reduce evaporationduring the measurements. The estimated uncertainty in viscositymeasurements was within ±0.001 m Pa s and reproducible to±9.8 � 10�3 m Pa s.

Refractive indices were measured using a thermostatically con-trolled Abbe refractometer model, Atago-3T. For every sample, themeasurements were repeated three times and mean value were ta-ken in each calculation. The uncertainty in the refractive indexmeasurements was accurate to ±0.0001.

3. Modeling

3.1. Ramaswami and Anbananthan model

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

Aþ B ¼ AB ð2Þ

and the association constant Kas can be defined as;

Kas ¼½AB�½A�½B� ð3Þ

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

nents at 293.15, 298.15, 303.15, 308.15 and 313.15 K.

p/g cm3 qa/g cm3 gexp/m Pa s glita/m Pa s nExp nlit

a

865 0.7822 0.3699 – 1.3409 1.34411811 0.77649 0.3426 0.3410 1.3402 1.34163733 0.77125 0.3201 0.3240 1.3392 –665 – 0.3408 – 1.3283 –605 – 0.3348 – 1.3260 –

320 1.1339 3.7542 3.7640 1.4409 1.44754290 1.12915 3.3220 3.302 1.4370 1.44682250 – 2.9663 – 1.4359 –210 – 2.6531 – 1.4280 –117 – 2.4039 – 1.4250 –

563 – 3.3712 – 1.4279 –512 – 3.3643 – 1.4270 –502 0.9520 3.3512 3.35 1.4261 –468 0.94604 3.2310 3.23 1.4250 1.4253405 – 3.1020 3.012 1.4230 –

551 0.94873 0.9224 0.9243 1.4285 1.43047501 0.94387 0.8006 0.802 1.4267 1.42817419 0.9412 0.7399 – 1.4240 –357 – 0.7214 – 1.4221 –325 0.9310 0.7204 0.7386 1.4205 –

623 0.9615 0.9481 – 1.4361 –602 0.96633 0.9237 0.927 1.4342 1.4384360 0.93169 0.8788 0.8710 1.4320 1.4356268 – 0.8264 – 1.4300 –221 0.9232 0.7689 0.766 1.4285 –

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 3

By applying the condition of linearity with composition

Zobs ¼ xAZA þ xABZAB ð4Þ

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

Zobs ¼ ½xAZA þ xBZB þ xABZAB�h ð5Þ

where h is a temperature dependent adjustable parameter whichchanges with the changing temperature conditions.

The general idea of this model can be, however, exploited as;

Kas ¼½AB�

ðCA � ½AB�ÞðCB � ½AB�Þ 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 forconcentrated solution, Eq. (6) becomes,

Kas ¼aAB

ðaA � aABÞðaB � aABÞð7Þ

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

a0A ¼ aA � aAB and a0B ¼ aB � aAB

where a0A and a0B are the activities of [A] and [B] in equimolar quan-tities respectively.

From Eq. (7) one can obtain the value of Kas as;

Kas ¼aAB

aAaB � aAaAB � aBaAB þ a2AB

¼ aAB

a0A � a0Bð8Þ

Now, assuming any value of viscosity and refractive index in thepure components A, B and ZAB, it is possible to compare the viscos-ities and refractive indices calculated using Eq. (5) with the exper-imental values. On changing both the adjustable parameters Kas

and ZAB gradually, one can get different values of the sum ofsquares of deviations,

S ¼ RðZobs � ZcalÞ2 ð9Þ

where Zobs and Zcal are the observed and calculated equilibriumproperties respectively.

The minimum value of S can be obtained theoretically by a pairof 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 islow and changes slowly when changing the fitted parameters. Insuch cases, the value of ZAB should not be much lower than thelowest observed viscosity and refractive index of the system ormuch higher than the highest one. Quantitatively, it should be rea-sonable to accept the pair of adjustable parameters Kas and ZAB

which has the physical sense and which reproduces the experi-mental physical property satisfactorily.

3.2. Corrected model of Ramaswami and Anbanthan

On inspecting the results obtained from Ramaswamy and Anba-nanthan model, Glisnki suggested the equation assuming additiv-ity with the volume fraction, / of the components derived byNatta and Baccardedda [20], as;

Zcal ¼Z1Z2

/1Z2 þ /2Z1ð10Þ

where Zcal is the theoretical physical properties of binary liquidmixture, /1, /2 are the volume fractions of components 1 and 2and Z1 and Z2 are the physical properties of pure component liquids.

The numerical procedure and determination of association con-stant, Kas, were similar to that described before and the advantageof this method as compared with the earlier one was that the dataon densities of liquid mixture are not necessary except those ofpure components needed to calculate the volume fractions.

3.3. Prigogine–Flory–Patterson model

Theories [21] relate the viscosities of liquids either to the acti-vation energy required for the molecule to overcome the attractiveforces of its neighbors (absolute rate theory) or the probability ofan empty site near a molecule into which a neighboring moleculecan jump (free volume theory). Macedo and Litovitz [22] made thehypothesis that these two effects are combined so that the proba-bilities for viscous flow is taken as the product of the probabilitiesfor acquiring sufficient activation energy and the occurrence of anempty site. Similar assumptions are made for solutions. The theoryis applicable to the mixtures of the molecules of different sizes andlays particular stress on contribution of equation of state to thethermodynamic excess functions. The form of such equation forviscous flow is given as;

g ¼ X exp½DG–=RT þ cv�=Vf � ð11Þ

Here v⁄ is the characteristic volume which must be available for amolecular segment jumping to its new site, Vf is the free volumeper segment in the mixture and is equal to v � v⁄, c is a factor ofthe order unity, DG– is the free energy of activation per mole, R isgas constant T is absolute temperature and X is a frequency factorrespectively.

A bridge can be formed to the thermodynamic functions of mix-ing by assuming a simple relationship between free energy of acti-vation DG–, and the residual Gibbs free energy of mixing DGR

M

according to Roseveare et al. [21] as;

DG– ¼X2

i¼1

xiDG–i � aDGR

M ð12Þ

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 DGR

M can be expanded interms of enthalpy and entropy contributions as;

DGRM ¼ DHM � TDSR

M ð13Þ

where DHM and DSRM are the enthalpy of mixing per mole and resid-

ual entropy per mole respectively. By substituting the value of DG–

in Eq. (11) we get,

lng ¼X2

i¼1

xi ln gi � DGRM=RT þ v� ð1� v f Þ �

X2

i¼1

xi=Vfi

!( )ð14Þ

The value of DGRM for binary liquid mixture can be evaluated as

detailed out by Flory et al. [6–8] as;

DGRM ¼ x1P�1V�1

1eV 1

� 1eV !

þ 3eT 1 lnðeV 1=3

1 � 1ÞðeV 1=3 � 1Þ

" #

þ x2P�2V�21eV 2

� 1eV !

þ 3eT 2 lnðeV 1=3

2 � 1ÞðeV 1=3 � 1Þ

" #

þ x1P�1V�1h2X12eV 1

ð15Þ

4 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;

ln g ¼ x1 ln gi þ x2 ln g2 � x1P�1v�1fð1=ev 1 � 1=ev 1Þ�

þ 3eT 1 ln ð~v1=31 � 1Þ=ð~v1=3 � 1Þ

n oþ x2P2v�2fð1=~v2 � 1=~vÞ

þ 3~T2 ln ð~v1=32 � 1Þ=ð~v1=3 � 1Þ

n oþ x1v�1h2X12=~v1

i=RT

þ 1=fð~v � 1Þ � x1=ð~v1 � 1Þ � x2=ð~v2 � 1Þ ð16Þ

The values of reduced and characteristic parameters in Eq. (16)are obtained by the procedure as detailed out by Flory [6], Abe andFlory [7], and Flory et al. [8] and others [23–25] and notations usedhave their usual significance.

3.4. Lorentz–Lorentz relation

Lorentz–Lorentz (L–L) [5] relation has widest application duringthe evaluation of refractive indices of mixture and density of purecomponents as well as density of the mixture and represented interms of specific refraction as:

n2 � 1n2 þ 2

� �1q¼ n2

1 � 1n2

1 þ 2

� �w1

q1þ n2

2 � 1n2

2 þ 2

� �w2

q2ð17Þ

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

n2 � 1n2 þ 2

� �¼ n2

1 � 1n2

1 þ 2

� �/1 þ

n22 � 1

n22 þ 2

� �/2 ð18Þ

here n, n1, n2, q, q1, q2, w1, w2 are the refractive indices of mixtureand pure components, 1.2, density of mixture, density of pure com-ponents, 1.2, weight fraction of pure components, 1.2, respectivelyand /1, /2 are the volume fractions of pure components which is ob-tained by the relation [26] as:

/i ¼xiv iP

xiv ið19Þ

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

Table 2Coefficients of the Redlich–Kister equation and standard deviations (r) for dynamic visco

Viscosity (Dg/m Pa s)

T a0 a1 a2 a3 (r)

Acetonitrile + formamide293.15 2.7294 3.1701 �1.8712 �6.8920 0.644298.15 3.3838 3.1632 �0.7940 �10.2145 0.832303.15 3.8870 2.6741 1.1674 �11.9986 1.010308.15 4.4916 2.0784 1.4471 �13.6920 1.172313.15 5.9431 �2.3229 4.5681 �5.9900 1.638

Acetonitrile + NMA293.15 4.1889 7.4616 12.2001 �18.2377 1.427298.15 4.0509 8.8224 14.7111 �24.2105 1.443303.15 4.6082 7.6271 16.2804 �24.4327 1.549308.15 5.1816 8.5019 17.2466 �29.3852 1.663313.15 8.9919 1.4651 3.6885 �0.1919 2.167

Acetonitrile + DMF293.15 0.2213 �0.0189 �0.2069 �0.7605 0.086298.15 0.3119 �0.0924 �0.0634 �0.5789 0.115303.15 0.3716 �0.1916 �0.1009 �0.2400 0.117308.15 0.5250 �0.2681 �0.0864 �0.2984 0.156313.15 1.3309 �2.4799 0.3005 9.6102 0.415

Acetonitrile + DMA293.15 0.2950 0.5366 �1.6253 0.8254 0.103298.15 0.7187 2.9035 �9.7217 7.0938 0.338303.15 0.8263 2.7546 �9.1740 7.3906 0.343308.15 0.6879 3.2466 �7.6681 5.8533 0.346313.15 1.7913 �0.1858 �9.5379 20.3185 0.552

4. Results and discussion

Table 1 presents the comparison of experimental densities, dy-namic 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–Kisterpolynomials and their standard deviations (r) for viscosity andrefractive index are presented in Table 2. Parameters of McAllisterthree body and four body interaction model and standard devia-tions for viscosities and refractive indices are presented in Tables3 and 4. Table 5 presents the comparison of average deviation(AD) from various theoretical models used in this work. Values ofmole fraction (x1), density of the mixture (q) experimental physicalproperties (gexp and nexp), theoretical physical properties obtainedfrom 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 compo-sition range at five temperatures were recorded in Table 6.

Relations between association phenomenons in liquids wereanalyzed earlier [27] by considering van der Waals equation whichwas based only on simple averaged geometrical derivations with-out analyzing the system in terms of equilibrium. The associationphenomenons have been related usually the deviation of differentquantities from additivity. Ramaswamy and Anbananthan derivedthe model based on the assumption of linearity of acoustic imped-ance with the mole fractions of components which was correctedand tested [11] for the prediction of associational behavior fromsound velocity data. The quantities analyzed were refractive index,molar volume, viscosity, intermolecular free length and manyother [15–19,28]. The physical properties such as viscosity, surfacetension, sound velocity, free energy, and refractive index can bepredicted well with this model.

Prediction of viscosity and refractive index from this approachis our first attempt. The results of fittings obtained from the modelwere utilized properly. The basic doubt regarding this model ex-cept the assumption of linearity of viscosity and refractive indexwith mole fraction is that these liquids have poor tendency to formdimmers. The calculations were performed using a computer

sities and refractive indexes of binary liquid mixtures at various temperatures.

Refractive index (Dn)

a0 a1 a2 a3 (r)

0 0.0385 0.0166 0.0393 �0.1120 0.06067 0.0455 0.0104 0.0563 �0.1200 0.07405 0.0654 �0.0285 �0.1012 0.1118 0.05806 0.0449 �0.0408 0.0097 0.2526 0.06174 1.3919 �3.1690 �12.8875 19.0309 0.5562

4 0.1003 0.0108 �0.0341 0.1447 0.07600 0.1013 0.0045 �0.1662 0.2093 0.06743 0.0908 0.0743 �0.0905 �0.1345 0.05431 0.0780 0.0401 �0.1145 �0.0272 0.05640 0.0769 0.0173 �0.0678 0.1458 0.0583

5 0.0892 0.0070 0.0155 0.0953 0.07497 0.1126 0.0308 0.0464 0.0322 0.08045 0.0991 �0.0320 �0.0456 0.1129 0.06043 0.0696 0.0537 �0.1569 �0.0315 0.05573 0.0779 0.0702 0.0363 �0.1714 0.0642

0 0.1195 0.0050 �0.0218 0.1844 0.08112 0.0782 0.0744 0.1537 �0.1188 0.07489 0.3527 �2.5839 �2.3181 8.8068 0.08526 0.1022 0.0288 0.1285 0.0165 0.07250 0.0642 0.2209 0.0637 �0.3853 0.0626

Table 3Parameters of McAllister three body and four body interaction models and standard deviations (r) for dynamic viscosities of binary liquid mixtures at various temperatures.

Component Temperature McAllister three body (g/m Pa s) McAllister four body (g/m Pa s)

a b (r) a b c (r)

Acetonitrile + formamide 293.15 6.3047 1.9907 0.1492 3.9953 2.4531 2.7933 0.1077298.15 5.6181 2.4121 0.1897 3.5698 2.6765 3.0623 0.1500303.15 5.4960 2.6860 0.2296 3.9134 2.2533 3.6689 0.1600308.15 5.0060 3.3268 0.2384 3.2778 2.9014 3.7401 0.1965313.15 4.0534 4.7869 0.3421 3.3434 2.2323 5.8728 0.2487

Acetonitrile + NMA 293.15 36.5865 0.9316 0.5110 43.6982 0.2585 14.7182 0.2232298.15 35.7563 0.9725 0.5044 40.5831 0.2999 13.6061 0.2134303.15 35.5126 1.0636 0.5496 46.1787 0.2217 18.4335 0.2199308.15 33.5257 1.2355 0.5103 38.2883 0.3266 15.3849 0.1909313.15 30.5538 1.8102 0.5253 31.9775 0.4913 16.1991 0.3381

Acetonitrile + DMF 293.15 0.5694 0.9262 0.1491 0.4546 1.0544 0.6914 0.0260298.15 0.5928 0.9196 0.0258 0.4892 0.9544 0.7391 0.0260303.15 0.6013 0.9093 0.0220 0.5009 0.9202 0.7480 0.0221308.15 0.6060 0.9697 0.0336 0.4693 1.1118 0.6918 0.0320313.15 0.4841 0.3087 1.0318 2.5562 0.0087 5.3663 0.6780

Acetonitrile + DMA 293.15 0.8209 0.9045 0.0164 0.6959 0.8836 0.9105 0.1176298.15 0.6306 1.4473 1.1463 0.2144 9.7934 0.2333 1.0121303.15 1.3938 0.7203 0.0224 1.2229 0.6841 1.0117 0.0176308.15 1.6916 0.5838 0.0486 1.7698 0.3961 1.2701 0.0228313.15 1.6593 0.5699 0.0313 1.5738 0.4908 1.0301 0.0128

Table 4Parameters 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 1.3844 1.4289 0.0029 0.3515 3.1291 0.5709 0.0546298.15 1.3829 1.4324 0.0032 1.3811 1.3899 1.4440 0.0028303.15 1.3827 1.4326 0.0032 1.3814 1.3885 1.4448 0.0028308.15 1.3889 1.4019 0.0048 1.3935 1.3577 1.4312 0.0037313.15 1.3720 1.3980 0.0026 1.3510 1.4023 1.3941 0.0022

Acetonitrile + NMA 293.15 1.4300 1.4562 0.0473 1.3487 1.5770 1.3435 0.0447298.15 1.4498 1.4261 0.0022 1.4050 1.4563 1.4040 0.0015303.15 1.4364 1.4355 0.0042 1.3834 1.4847 1.3881 0.0025308.15 1.4296 1.4300 0.0042 1.3805 1.4721 1.3884 0.0030313.15 1.4281 1.4223 0.0008 1.3969 1.4160 1.4213 0.0008

Acetonitrile + DMF 293.15 1.4537 1.4300 0.0033 1.4301 1.4081 1.4456 0.0027298.15 1.4661 1.4342 0.0023 1.4389 1.4166 1.4480 0.0013303.15 1.4389 1.4405 0.0018 1.4066 1.4338 1.4326 0.0046308.15 1.4242 1.4218 0.0045 1.3726 1.4710 1.3808 0.0026313.15 1.4306 1.4257 0.0018 1.3994 1.4176 1.4240 0.0018

Acetonitrile + DMA 293.15 1.4634 1.4365 0.0021 1.4648 1.4366 1.4500 0.0020298.15 1.4572 1.4264 0.0032 1.4714 1.3989 1.4662 0.0015303.15 1.4868 1.3932 0.0496 1.5610 1.2492 1.5670 0.0479308.15 1.4609 1.4318 0.0035 1.4778 1.3959 1.4743 0.0008313.15 1.4452 1.4032 0.0039 1.4322 1.4451 1.3982 0.0035

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 5

program which allows fittings easily both the adjustable parame-ters simultaneously, or the parameters were changed manually.

We constructed the data sheet in a computer program, withassociation constant Kas and CA,B as the fitted parameters (CA,B

is the viscosity and refractive index of pure components A andB) means a hypothetical liquid having only the associate A–B.On changing these parameters, the equilibrium concentrationsof species [A], [B] and [AB] will change and the viscosity andrefractive index can be computed. The difference between exper-imental and theoretical values for viscosities and refractive indi-ces is used to obtain the sum of squares of deviations. It isassumed that in solution three components are formed insteadof two (pure A, pure B and associate, AB). The values of viscosityin pure associate can be treated as a fitted one with the value ofKas.

Values of thermal expansion coefficient (a) and isothermalcompressibility (bT) needed in the PFP model were obtained from

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

bT ¼1:71� 10�3

T4=9u2q4=3and a ¼ 75:6� 10�3

T1=9u1=2q1=3ð20Þ

The mixing function, Dg; Dn were represented mathematicallyby the Redlich–Kister equation [11] for correlating the experimen-tal data as:

y ¼ xið1� x1ÞXp

i¼0

aið2x1 � 1Þi ð21Þ

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

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

Temperature Kas � 104 gab/m Pa s

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

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

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

g(Eq. (23))/m Pa s

g(Eq. (24))/m Pa s

n(Eq.

(18))

n(Eq.

(5))

n(Eq.

(10))

n(Eq.

(23))

n(Eq.

(24))

Acetonitrile + formamide293.15 1.3000 3.6500 0.6051 0.4434 1.5515 0.1302 0.0966 0.0180 0.0081 0.0140 0.0021 0.3865298.15 1.0000 3.3190 0.6948 0.5987 1.5434 0.1643 0.1294 0.0169 0.0099 0.0159 0.0023 0.0019303.15 1.2000 2.6962 0.7917 0.8585 1.5750 0.1983 0.1383 0.0152 0.0105 0.0166 0.0024 0.0020308.15 1.1200 2.6490 0.8440 0.8793 1.5514 0.1943 0.1615 0.0056 0.0370 0.0164 0.0042 0.0029313.15 1.1100 0.3347 0.9562 1.0432 1.6435 0.3057 0.2017 0.0075 0.0051 0.0108 0.0020 0.0018

Acetonitrile + NMA293.15 1.4000 3.3498 1.5491 1.0510 1.7481 0.4308 0.2047 0.0063 0.0137 0.0288 0.0212 0.0242298.15 1.5000 3.3013 1.5504 1.0590 1.0590 0.4318 0.1993 0.0043 0.0105 0.0097 0.0018 0.0012303.15 1.6000 2.8999 1.5722 1.1531 1.7372 0.4553 0.1937 0.0066 0.0095 0.0085 0.0036 0.0022308.15 1.7000 2.6000 1.6282 1.2226 1.7249 0.4360 0.1687 0.0077 0.0073 0.0061 0.0032 0.0023313.15 1.8000 2.3038 1.7452 1.3840 1.8088 0.4353 0.2904 0.0061 0.0084 0.0072 0.0006 0.0006

Acetonitrile + DMF293.15 1.1800 0.6998 0.2354 0.0407 0.0776 0.1313 0.0225 0.0059 0.0172 0.0121 0.0028 0.0020298.15 1.1900 0.7596 0.2499 0.0491 0.0828 0.0212 0.0221 0.0061 0.0221 0.0173 0.0020 0.0011303.15 1.2100 0.7235 0.2647 0.0533 0.0878 0.0178 0.0165 0.0050 0.0157 0.0110 0.0017 0.0032308.15 1.3200 0.6805 0.2637 0.0725 0.1047 0.0259 0.0255 0.0129 0.0083 0.0055 0.0036 0.0023313.15 1.3300 0.6389 0.1562 0.0827 0.1119 0.1486 0.1675 0.0058 0.0141 0.0091 0.0016 0.0014

Acetonitrile + DMA293.15 1.3400 0.9971 0.3341 0.0430 0.1266 0.0123 0.0792 0.0035 0.0220 0.0139 0.0019 0.0016298.15 1.3500 0.9378 0.3702 0.0927 0.1713 0.1241 0.1060 0.0042 0.0189 0.0111 0.0025 0.0014303.15 1.3600 0.8777 0.3945 0.1232 0.1924 0.0182 0.0127 0.0204 0.0333 0.0255 0.0240 0.0265308.15 1.3700 0.8123 0.4006 0.1472 0.2087 0.0390 0.0179 0.0074 0.0226 0.0149 0.0030 0.0006313.15 1.3800 0.7562 0.1127 0.1479 0.2000 0.0259 0.0107 0.0053 0.0145 0.0080 0.0033 0.0030

Table 6Experimental 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.

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. (18)) n(Eq. (5)) n(Eq. (10))

Acetonitrile + formamideT = 293.15 K0.1225 1.1258 3.4824 3.3065 3.2518 1.5487 1.4387 1.4455 1.4286 1.42460.2390 1.0992 3.1358 2.8633 2.8692 1.1705 1.4298 1.4405 1.4169 1.41050.3499 1.0835 2.9998 2.3923 2.5050 0.8898 1.4105 1.4401 1.4058 1.39810.4557 1.0405 2.8654 1.9402 2.1575 0.7242 1.4058 1.4264 1.3952 1.38710.5567 1.0102 2.4568 1.5350 1.8258 0.6149 1.3978 1.4181 1.3851 1.37730.6533 0.9705 2.0265 1.1893 1.5085 0.5373 1.3848 1.4050 1.3755 1.36850.7456 0.9403 1.8564 0.9057 1.2054 0.4795 1.3735 1.3958 1.3663 1.36060.8340 0.9015 1.3547 0.6798 0.9150 0.4347 1.3625 1.3822 1.3574 1.35340.9187 0.8503 0.5852 0.5040 0.6369 0.3990 1.3501 1.3623 1.3490 1.3468

T = 298.15 K0.1225 1.1015 3.4810 3.0468 2.9594 1.6612 1.4387 1.4334 1.4251 1.42100.2390 1.0825 3.1300 2.6683 2.6146 1.1259 1.4290 1.4331 1.4138 1.40720.3499 1.0657 2.9901 2.2046 2.2864 0.8616 1.4104 1.4333 1.4030 1.39520.4557 1.0345 2.8644 1.8405 1.9733 0.7039 1.4054 1.4262 1.3928 1.38450.5567 0.9985 2.4561 1.4667 1.6744 0.5992 1.3975 1.4163 1.3830 1.37510.6533 0.9624 2.0264 1.1435 1.3886 0.5246 1.3846 1.4057 1.3737 1.36660.7456 0.9351 1.8505 0.8758 1.1154 0.4688 1.3731 1.3988 1.3648 1.35900.8340 0.8792 1.3540 0.6606 0.8538 0.4255 1.3622 1.3775 1.3562 1.35210.9187 0.8492 0.5004 0.4920 0.6031 0.3909 1.3499 1.3683 1.3480 1.3459

T = 303.15 K0.1225 1.0998 3.4715 2.7846 2.4088 1.4808 1.4380 1.4337 1.4240 1.41990.2390 1.0735 3.1258 2.4840 2.1355 1.0364 1.4289 1.4304 1.4127 1.40600.3499 1.0538 2.9002 1.8352 1.8753 0.8061 1.4101 1.4295 1.4020 1.39400.4557 1.0258 2.8568 1.7572 1.6271 0.6651 1.4050 1.4242 1.3917 1.38330.5567 0.9802 2.4500 1.4112 1.3901 0.5699 1.3970 1.4098 1.3820 1.37390.6533 0.9594 2.0000 1.1058 1.1635 0.5013 1.3840 1.4067 1.3726 1.36550.7456 0.9256 1.8222 0.8492 0.9469 0.4496 1.3729 1.3968 1.3637 1.35790.8340 0.8728 1.3455 0.6408 0.7395 0.4092 1.3619 1.3772 1.3552 1.35100.9187 0.8402 0.4987 0.4766 0.5408 0.3767 1.3489 1.3667 1.3470 1.3448

T = 308.15 K0.1225 1.0856 3.4054 2.5500 2.3657 1.4489 1.4199 1.4208 1.3998 1.41140.2390 1.0568 3.1025 2.3180 2.0882 1.0120 1.4105 1.4158 1.3772 1.39700.3499 1.0215 2.8971 1.7204 1.8233 0.7863 1.4099 1.4073 1.3594 1.38460.4557 0.9856 2.8401 1.6834 1.5719 0.6484 1.3904 1.3979 1.3458 1.37360.5567 0.9508 2.4459 1.3634 1.3343 0.5553 1.3801 1.3883 1.3359 1.3639

6 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. (18)) n(Eq. (5)) n(Eq. (10))

0.6533 0.9256 1.9982 1.0746 1.1104 0.4883 1.3700 1.3827 1.3293 1.35520.7456 0.8809 1.7059 0.8280 0.9000 0.4379 1.3675 1.3675 1.3255 1.34740.8340 0.8405 1.3054 0.6256 0.7022 0.3984 1.3599 1.3538 1.3243 1.34040.9187 0.8028 0.4057 0.4650 0.5162 0.3667 1.3480 1.3409 1.3253 1.3341

T = 313.15 K0.1225 1.0807 3.3901 2.3469 2.1504 1.3681 1.4123 1.4196 1.4128 1.40850.2390 1.0559 3.9570 2.1623 1.9093 0.9704 1.4058 1.4163 1.4013 1.39430.3499 1.0158 2.8897 1.8998 1.6798 0.7601 1.3945 1.4056 1.3903 1.38190.4557 0.9758 2.8304 1.6042 1.4609 0.6299 1.3854 1.3942 1.3798 1.37100.5567 0.9365 2.4358 1.3099 1.2519 0.5413 1.3789 1.3825 1.3698 1.36140.6533 0.8905 1.8758 1.0395 1.0520 0.4772 1.3687 1.3672 1.3602 1.35280.7456 0.8726 1.6889 0.8054 0.8611 0.4286 1.3555 1.3643 1.3511 1.34500.8340 0.8405 1.2568 0.6112 0.6782 0.3906 1.3482 1.3545 1.3424 1.33800.9187 0.7992 0.3944 0.4558 0.5029 0.3599 1.3302 1.3398 1.3340 1.3317

Acetonitrile + NMAT = 303.15 K0.2733 0.9357 1.6113 3.4724 2.5406 1.0468 1.4157 1.4199 1.4097 1.40940.4481 0.9235 1.1728 3.1358 2.0185 0.7268 1.4083 1.4100 1.3951 1.39590.5757 0.8895 0.8708 2.9898 1.6373 0.5942 1.3903 1.4013 1.3835 1.38500.6808 0.8764 0.6899 2.8654 1.3234 0.5166 1.3829 1.3976 1.3740 1.37530.7614 0.8658 0.5955 2.4468 1.0826 0.4696 1.3769 1.3845 1.3662 1.36730.8282 0.8465 0.5316 2.0265 0.8830 0.4366 1.3668 1.3756 1.3595 1.36040.8821 0.8351 0.4708 1.8464 0.7220 0.4132 1.3607 1.3612 1.3539 1.35450.9290 0.8252 0.4315 1.3547 0.5819 0.3948 1.3554 1.3599 1.3489 1.34920.9685 0.8051 0.3960 0.5752 0.4639 0.3805 1.3453 1.3501 1.3446 1.4974

T = 303.15 K0.2733 0.9305 1.5808 3.471 2.4987 2.4987 1.4160 1.4135 1.4082 1.40840.4481 0.9197 1.1503 3.13 1.9849 1.9848 1.4102 1.4089 1.3938 1.39490.5757 0.8807 0.8538 2.9801 1.6098 1.6097 1.3903 1.4002 1.3824 1.38400.6808 0.8704 0.6763 2.8644 1.3009 1.3008 1.3850 1.3921 1.3731 1.37440.7614 0.8595 0.5838 2.4361 1.0639 1.0639 1.3794 1.3801 1.3654 1.36650.8282 0.8405 0.5211 2.0264 0.8676 0.8675 1.3698 1.3701 1.3588 1.35970.8821 0.8305 0.4616 1.8405 0.7091 0.7091 1.3648 1.3589 1.3532 1.35390.9290 0.8205 0.4230 1.354 0.5713 0.5712 1.3598 1.3500 1.3484 1.34870.9685 0.8015 0.3882 0.4904 0.4551 0.4551 1.3504 1.3489 1.3442 1.3442

T = 303.15 K0.2733 0.9108 1.4204 3.4615 2.2076 0.9702 1.4064 1.4130 1.4060 1.40750.4481 0.8998 1.0525 3.1258 1.7608 0.6803 1.4012 1.4075 1.3921 1.39400.5757 0.8712 0.7901 2.8002 1.4346 0.5585 1.3871 1.3995 1.3810 1.38320.6808 0.8652 0.6320 2.8568 1.1660 0.4867 1.3844 1.3899 1.3719 1.37370.7614 0.8501 0.5502 2.4200 0.9599 0.4430 1.3771 1.3788 1.3644 1.36590.8282 0.8357 0.4947 2.0000 0.7892 0.4124 1.3702 1.3655 1.3580 1.35910.8821 0.8256 0.4404 1.8122 0.6514 0.3906 1.3654 1.3501 1.3526 1.35340.9290 0.7958 0.4056 1.3455 0.5315 0.3734 1.3509 1.3468 1.3479 1.34830.9685 0.7853 0.3736 0.4887 0.4306 0.3600 1.3459 1.3423 1.3438 1.3438

T = 308.15 K0.2733 0.9007 1.2959 3.3954 1.9848 0.9250 1.4023 1.4100 1.4043 1.40630.4481 0.8795 0.8669 3.1025 1.5893 0.6549 1.3923 1.4023 1.3905 1.39290.5757 0.8654 0.6639 2.8871 1.3006 0.5399 1.3857 1.3925 1.3795 1.38210.6808 0.8556 0.5437 2.8401 1.0629 0.4716 1.3813 1.3899 1.3706 1.37250.7614 0.8456 0.4729 2.4199 0.8805 0.4299 1.3768 1.3726 1.3631 1.36480.8282 0.8298 0.4256 1.9982 0.7294 0.4006 1.3693 1.3600 1.3568 1.35800.8821 0.8198 0.3937 1.6959 0.6075 0.3797 1.3646 1.3490 1.3515 1.35230.9290 0.7902 0.3701 1.3054 0.5014 0.3632 1.3503 1.3460 1.3468 1.34720.9685 0.7805 0.3529 0.3957 0.4120 0.3503 1.3458 1.3422 1.3427 1.3428

T = 313.15 K0.2733 0.8798 1.1538 3.3801 1.765733 0.883648 1.3910 1.4089 1.4007 1.40230.4481 0.8697 0.7800 3.957 1.4215314 0.633758 1.3851 1.3982 1.3854 1.38730.5757 0.8556 0.6045 2.8797 1.1702744 0.525312 1.3774 1.3865 1.3731 1.37540.6808 0.8425 0.5015 2.8304 0.9633236 0.460418 1.3703 1.3748 1.3632 1.36490.7614 0.8346 0.4416 2.4158 0.8046 0.4205 1.3659 1.3645 1.3549 1.35640.8282 0.8194 0.4022 1.8758 0.6730 0.3924 1.3580 1.3556 1.3479 1.34890.8821 0.8008 0.3761 1.6889 0.5669 0.3723 1.3485 1.3489 1.3419 1.34270.9290 0.7824 0.3572 1.2568 0.4746 0.3564 1.3393 1.3400 1.3368 1.33710.9685 0.7615 0.3439 0.3844 0.3968 0.3440 1.3290 1.3356 1.3322 1.3322

Acetonitrile + DMFT = 293.15 K0.2142 0.9391 0.9752 0.7599 0.7069 0.6399 1.4189 1.4211 1.4097 1.41410.3802 0.9297 0.2975 0.6899 0.6357 0.5544 1.4128 1.4196 1.3951 1.40170.5126 0.9158 0.2482 0.6122 0.5789 0.5010 1.4047 1.4032 1.3835 1.39080.6206 0.8957 0.2314 0.5988 0.5326 0.4645 1.3936 1.3956 1.3740 1.38120.7104 0.8748 0.2319 0.5123 0.4941 0.4380 1.3823 1.3855 1.3662 1.3726

(continued on next page)

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 7

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. (18)) n(Eq. (5)) n(Eq. (10))

0.7863 0.8569 0.2437 0.4995 0.4615 0.4178 1.3727 1.3799 1.3595 1.36490.8513 0.8354 0.2642 0.3815 0.4336 0.4020 1.3615 1.3700 1.3539 1.35800.9075 0.8253 0.2923 0.3765 0.4095 0.3892 1.3559 1.3653 1.3489 1.35180.9567 0.7902 0.3276 0.3699 0.3884 0.3787 1.3385 1.3512 1.3446 1.3461

T = 298.15 K0.2142 0.9342 0.9531 0.7545 0.6791 0.6183 1.4182 1.4256 1.4082 1.41240.3802 0.9272 0.2712 0.6855 0.6123 0.5381 1.4143 1.4199 1.3938 1.40010.5126 0.9215 0.2249 0.6100 0.5589 0.4877 1.4112 1.4102 1.3824 1.38930.6206 0.8901 0.2096 0.5955 0.5154 0.4530 1.3951 1.4036 1.3731 1.37990.7104 0.8721 0.2109 0.5102 0.4792 0.4278 1.3859 1.3924 1.3654 1.37150.7863 0.8504 0.2230 0.4955 0.4486 0.4085 1.3749 1.3824 1.3588 1.36390.8513 0.8344 0.2436 0.3801 0.4225 0.3933 1.3668 1.3756 1.3532 1.35720.9075 0.8248 0.2718 0.3762 0.3998 0.3811 1.3620 1.3654 1.3484 1.35110.9567 0.7899 0.3073 0.3609 0.3800 0.3710 1.3448 1.3522 1.3442 1.3455

T = 303.15 K0.2142 0.9304 0.9512 0.7401 0.6563 0.5974 1.4181 1.4199 1.4060 1.41010.3802 0.9255 0.2472 0.6804 0.5916 0.5198 1.4157 1.4165 1.3921 1.39810.5126 0.9192 0.2036 0.6089 0.5400 0.4710 1.4125 1.4033 1.3810 1.38770.6206 0.8892 0.1900 0.5901 0.4979 0.4375 1.3973 1.3945 1.3719 1.37850.7104 0.8706 0.1925 0.5066 0.4629 0.4131 1.3880 1.3822 1.3644 1.37030.7863 0.8584 0.2056 0.4901 0.4333 0.3945 1.3819 1.3755 1.3580 1.36300.8513 0.8261 0.2273 0.3799 0.4080 0.3798 1.3659 1.3654 1.3526 1.35640.9075 0.8259 0.2570 0.3745 0.3861 0.3680 1.3659 1.3524 1.3479 1.35050.9567 0.7853 0.2948 0.3599 0.3669 0.3582 1.3460 1.3499 1.3438 1.3451

T = 308.15 K0.2142 0.9280 0.8853 0.7365 0.6084 0.5612 1.4184 1.4022 1.4043 1.40830.3802 0.9234 0.2342 0.6345 0.5518 0.4937 1.4163 1.4065 1.3905 1.39650.5126 0.9065 0.1947 0.6804 0.5067 0.4505 1.4079 1.3964 1.3795 1.38610.6206 0.8801 0.1831 0.5835 0.4700 0.4205 1.3947 1.3825 1.3706 1.37700.7104 0.8647 0.1864 0.5021 0.4394 0.3984 1.3871 1.3765 1.3631 1.36890.7863 0.8561 0.1999 0.4865 0.4135 0.3815 1.3830 1.3654 1.3568 1.36170.8513 0.8248 0.2219 0.3745 0.3914 0.3681 1.3675 1.3524 1.3515 1.35520.9075 0.8234 0.2516 0.3705 0.3723 0.3573 1.3669 1.3499 1.3468 1.34940.9567 0.7805 0.2891 0.3545 0.3555 0.3483 1.3459 1.3401 1.3427 1.3440

T = 313.15 K0.2142 0.9255 0.8024 0.7302 0.5788 0.5384 1.4158 1.4138 1.4007 1.40510.3802 0.9199 0.8529 0.6365 0.5272 0.4771 1.4119 1.4035 1.3854 1.39180.5126 0.9002 0.9007 0.6756 0.4861 0.4374 1.4010 1.3937 1.3731 1.38030.6206 0.8751 0.8237 0.5800 0.4526 0.4096 1.3876 1.3813 1.3632 1.37010.7104 0.8615 0.7250 0.4989 0.4247 0.3890 1.3801 1.3764 1.3549 1.36110.7863 0.8502 0.6242 0.4812 0.4011 0.3731 1.3738 1.3642 1.3479 1.35310.8513 0.8227 0.5312 0.3705 0.3809 0.3606 1.3597 1.3521 1.3419 1.34600.9075 0.8207 0.4500 0.3624 0.3635 0.3504 1.3582 1.3456 1.3368 1.33950.9567 0.7798 0.3809 0.3501 0.3482 0.3419 1.3379 1.3330 1.3322 1.3336

Acetonitrile + DMAT = 293.15 K0.2453 0.9591 1.1481 0.8914 0.8439 0.7046 1.4324 1.4298 1.4127 1.42030.4223 0.9512 0.2338 0.7989 0.7327 0.5812 1.4266 1.4200 1.3958 1.40670.5562 0.9421 0.1883 0.7011 0.6486 0.5132 1.4203 1.4156 1.3831 1.39490.6610 0.9159 0.1776 0.6582 0.5828 0.4702 1.4055 1.4025 1.3731 1.38440.7452 0.8856 0.1842 0.5799 0.5299 0.4405 1.3891 1.3945 1.3651 1.37510.8144 0.8653 0.2024 0.5124 0.4864 0.4188 1.3779 1.3801 1.3585 1.36680.8722 0.8529 0.2302 0.4973 0.4501 0.4022 1.3707 1.3748 1.3530 1.35930.9212 0.8355 0.2672 0.4015 0.4193 0.3892 1.3613 1.3614 1.3483 1.35260.9634 0.8159 0.3136 0.3985 0.3928 0.3786 1.3509 1.3543 1.3443 1.3464

T = 298.15 K0.2453 0.9358 1.1025 0.8865 0.8011 0.6774 1.4253 1.4287 1.4111 1.41860.4223 0.9256 0.2196 0.8001 0.6982 0.5628 1.4189 1.4123 1.3945 1.40520.5562 0.9145 0.1775 0.7798 0.6204 0.4989 1.4121 1.4065 1.3820 1.39350.6610 0.8995 0.1683 0.7114 0.5595 0.4582 1.4034 1.3945 1.3722 1.38320.7452 0.8755 0.1755 0.6014 0.5106 0.4300 1.3904 1.3899 1.3643 1.37400.8144 0.8504 0.1940 0.5864 0.4704 0.4093 1.3770 1.3800 1.3578 1.36590.8722 0.8348 0.2220 0.5123 0.4368 0.3935 1.3685 1.3742 1.3524 1.35850.9212 0.8119 0.2591 0.4456 0.4083 0.3810 1.3566 1.3612 1.3478 1.35190.9634 0.7999 0.3058 0.4012 0.3838 0.3709 1.3501 1.3500 1.3439 1.3459

T = 303.15 K0.2453 0.9248 1.0533 0.8254 0.7491 0.6412 1.4247 1.4274 1.4094 1.41680.4223 0.9016 0.1975 0.7987 0.6555 0.5366 1.4113 1.4113 1.3931 1.40370.5562 0.8908 0.1596 0.7565 0.5847 0.4776 1.4046 1.4000 1.3808 1.39220.6610 0.8705 0.1521 0.7065 0.5293 0.4398 1.3931 1.3936 1.3712 1.38210.7452 0.8559 0.1600 0.6531 0.4848 0.4134 1.3848 1.3835 1.3635 1.37320.8144 0.8391 0.1787 0.5734 0.4482 0.3941 1.3754 1.3742 1.3572 1.3652

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. (18)) n(Eq. (5)) n(Eq. (10))

0.8722 0.8069 0.2068 0.5236 0.4176 0.3792 1.3586 1.3699 1.3519 1.35800.9212 0.7909 0.2443 0.4985 0.3917 0.3675 1.3500 1.3600 1.3474 1.35150.9634 0.7854 0.2918 0.4041 0.3694 0.3579 1.3467 1.4990 1.3435 1.3455

T = 308.15 K0.2453 0.9158 1.0111 0.8297 0.7072 0.6123 1.4228 1.4298 1.4076 1.41500.4223 0.9016 0.1816 0.6965 0.6213 0.5159 1.4141 1.4158 1.3916 1.40200.5562 0.8759 0.1469 0.7512 0.5562 0.4610 1.3996 1.4056 1.3794 1.39070.6610 0.8669 0.1407 0.7023 0.5054 0.4255 1.3939 1.3998 1.3699 1.38070.7452 0.8498 0.1491 0.6725 0.4645 0.4008 1.3843 1.3901 1.3623 1.37190.8144 0.8257 0.1679 0.6102 0.4309 0.3825 1.3712 1.3822 1.3560 1.36390.8722 0.8067 0.1960 0.5789 0.4028 0.3684 1.3610 1.3721 1.3507 1.35680.9212 0.7895 0.2336 0.5001 0.3790 0.3573 1.3517 1.3641 1.3463 1.35040.9634 0.7759 0.2815 0.4101 0.3585 0.3482 1.3444 1.3512 1.3425 1.3445

T = 313.15 K0.2453 0.9098 0.9641 0.7457 0.6624 0.5833 1.4191 1.4056 1.4038 1.41180.4223 0.8890 0.9964 0.7249 0.5855 0.4968 1.4057 1.4026 1.3861 1.39740.5562 0.8654 0.9324 0.7005 0.5274 0.4467 1.3966 1.3912 1.3727 1.38490.6610 0.8566 0.8287 0.6972 0.4819 0.4140 1.3847 1.3854 1.3622 1.37390.7452 0.8442 0.7179 0.6624 0.4453 0.3910 1.3765 1.3792 1.3537 1.36410.8144 0.8198 0.6151 0.5879 0.4153 0.3739 1.3626 1.3687 1.3468 1.35540.8722 0.7908 0.5256 0.5465 0.3902 0.3608 1.3468 1.3501 1.3410 1.34760.9212 0.7828 0.4500 0.4879 0.3690 0.3503 1.3415 1.3489 1.3361 1.34050.9634 0.7742 0.3869 0.4065 0.3506 0.3418 1.3360 1.3300 1.3319 1.3341

R.K. Shukla et al. / Experimental Thermal and Fluid Science 37 (2012) 1–11 9

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

r ¼Xm

i¼1

ðyexpi� ycali

Þ2=ðm� pÞ" #1=2

ð22Þ

where m is the number of experimental points and p is the numberof adjustable parameters. For viscosity, the r values lie between0.08 and 2.16 m Pa s and the largest r value corresponds to aceto-nitrile + NMA mixture at 313.15 K and for refractive index, the rvalues lie between 0.05 and 0.55 and the largest r value corre-sponds to acetonitrile + formamide mixture at 313.15 K. In boththe cases, largest standard deviation occurs at higher temperatures.

McAllister multi-body interaction model [14] is widely used forcorrelating the viscosity of liquid mixtures with mole fraction. Thethree body model is defined as:

ln g ¼ x31 ln g1 þ 3x2

1x2 ln aþ 3x1x22 ln bþ x3

2 ln g2

� ½lnðx1 þ x2M2=M1Þ� þ 3x21x2½lnð2þM2=M1Þ=3�

þ 3x1x22 ln½ð1þ 2M2=M1Þ=3� þ x3

2 lnðM2=M1Þ� ð23Þ

and the four body model is given by,

ln g ¼ x41 ln g1 þ 4x3

1x2 ln aþ 6x21x2

2 ln bþ 4x1x32 ln c þ x4

2 ln g2

� lnðx1 þ x2M2=M1Þ� þ 4x31x2 ln½ð3þM2=M1Þ=4�

þ 6x21x2

2 ln½ð1þM2=M1Þ=2� þ 4x1x32

� ln½ð1þ 3M2=M1Þ=4� þ x42 lnðM2=M1Þ� 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 purecomponents 1 and 2 respectively; a–c are adjustable parametersthat are characteristic of the system. In the above Eqs. (22) and(23) the coefficient a–c have been calculated using the least squaresprocedure. The estimated parameters of the viscosity equations andthe standard deviations, r, between the calculated and experimen-tal values are given in Table 3. It is observed that the four bodymodel of the McAllister equation correlated the mixture viscosityto a significantly higher degree of accuracy for all of the systemsthan does the three body model. Furthermore, the values of theMcAllister parameters have shown a decreasing tendency with rise

in temperature. Generally, McAllister’s models are adequate in cor-relating the systems having small deviations. These equations havealso been utilized for the prediction of refractive index successfully.

With the increase of mole fraction (x2), the values of dynamicviscosities and refractive index obtained from all the models de-crease at all temperatures except at few places. The average devi-ation (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, 0.24and 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 0.40at 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 at298.15 K), (0.86, 1.15, 0.05 and 0.12 at 303.15 K), (0.88, 1.22, 0.07and 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 0.17at 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 at313.15 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 at303 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 estimatederror 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 acetoni-trile + formamide and acetonitrile + NMA mixture at all tempera-tures can be ascribed as unusual behavior of these solvents andhigher overall average estimated error in PFP model (Eq. (16))can be explained as the model was developed for nonelectrolytec-meric spherical chain molecules and the systems under investi-gation have interacting and associating properties. Moreover, theexpression [20] used for the computation of a and bT are alsoempirical in nature.

Similarly, the overall average deviation in refractive index ob-tained from Eqs. (18), (5), (10), (23) and (24) for all the systemsare 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 and0.002) and (0.008, 0.022, 0.014, 0.007, 0.009)] respectively. Thetheoretical findings are very close to experimental data showingthe success of all the theoretical models.

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

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

T = 293.15 K

0.000.200.400.600.801.001.20

0.00 0.20 0.40 0.60 0.80 1.00x1

visc

osity

/ mPa

s

T = 303.15 K

0.000.200.400.600.801.001.20

0.00 0.20 0.40 0.60 0.80 1.00x1

visc

osity

/ mPa

s

Fig. 1. Plot of dynamic viscosity g, with mole fraction x1 for x acetonitrile+(1 � x) DMA atviscosity from McAllister four body model (Eq. (24)), N, viscosity from Ramaswamy modfrom the model devised by Glinski (Eq. (10)).

T = 293.15 k

0.000.200.400.600.801.001.201.401.60

0.00 0.20 0.40 0.60 0.80 1.00x1

Ref

ract

ive

inde

x

Ref

ract

ive

inde

x

T = 308.15k

0.000.200.400.600.801.001.201.401.60

0.00 0.20 0.40 0.60 0.80 1.00x1

Ref

ract

ive

inde

x

Ref

ract

ive

inde

x

Fig. 2. Plot of refractive index n, with mole fraction x1 for x acetonitrile+(1 � x) DMA atrelation (Eq. (18)), �, refractive index from McAllister four body model (Eq. (24)), N, refthree body model (Eq. (23)) and d, refractive index from the model devised by Glinski

as compared to others because of non- associated processes. Butthe trend in all the figures is almost similar and positive. Very closevalues of McAllister three and four body interaction models withthe experimental data confirms the success of other experimentalfindings.

T = 308.15 K

0.000.200.400.600.801.001.20

0.00 0.20 0.40 0.60 0.80 1.00x1

visc

osity

/ mPa

s

T = 313.15 K

0.00

0.20

0.40

0.60

0.80

1.00

1.20

0.00 0.20 0.40 0.60 0.80 1.00x1

visc

osity

/ mPa

s

313.15: �, viscosity from PFP model (Eq. (16)), j experimental dynamic viscosity, �,el (Eq. (5)), x, viscosity from McAllister three body model (Eq. (23)) and d, viscosity

T = 303.15 k

0.00

0.20

0.40

0.60

0.80

1.00

1.20

1.40

1.60

0.00 0.20 0.40 0.60 0.80 1.00x1

T = 313.15 k

0.000.200.400.600.801.001.201.401.60

0.00 0.20 0.40 0.60 0.80 1.00x1

313.15: j, experimental refractive index, � refractive index from Lorentz–Lorentzractive index from Ramaswamy model (Eq. (5)), x, refractive index from McAllister(Eq. (10)).

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

The Ramaswamy and Anbananthan model based on associatedprocesses gives more reliable results and helpful in deducing theinternal structure of associates through the fitted values of viscos-ity and refractive index in a hypothetical pure associate and ob-served dependence of concentration on composition of a mixture.The Prigogine–Flory–Patterson (PFP) model based on non-associ-ated processes has been applied to associated molecules for thefirst time and satisfactory findings are obtained up to some extent.However, there is every possibility to improve the results. In gen-eral, still modifications are needed in order to interpret the associ-ational behavior and interactions in liquid mixture.

Acknowledgments

Authors are extremely thankful to UGC, New Delhi for financialsupport (Grant-34-332/2008) and Department of Chemistry, VSSDCollege, for cooperation.

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