J. Chem. Thermodynamics 64 (2013) 159–166

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J. Chem. Thermodynamics

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Study of thermodynamic and transport properties of binary liquidmixtures of n-decane with hexan-2-ol, heptan-2-ol and octan-2-olat T = 298.15 K. Experimental results and application of thePrigogine–Flory–Patterson theory

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⇑ Corresponding author. Address: P. G. Department of Chemistry, Jalna EducationSociety’s R. G. Bagdia Arts, S. B. Lakhotia Commerce, R. Benzonji Science College,Jalna 431 203, Maharashtra, India. Mobile: +91 9421650049; fax: +91 2482230566.

E-mail addresses: marvind22@yahoo.co.in (A.R. Mahajan), mirgane_chem@yahoo.co.in (S.R. Mirgane).

1 Tel.: +91 9422722292.

Aravind R. Mahajan ⇑, Sunil R. Mirgane 1

P.G. Department of Chemistry, J.E.S. College, Jalna, 431203 Maharastra, India

a r t i c l e i n f o

Article history:Received 30 September 2012Received in revised form 25 April 2013Accepted 9 May 2013Available online 20 May 2013

Keywords:n-Decane2-AlkanolsPFP theoryMcAllister’s multibody interaction model

a b s t r a c t

Densities and viscosities of binary mixtures of n-decane with hexan-2-ol, heptan-2-ol and octan-2-olhave been measured over the entire range of composition at T = 298.15 K and at atmospheric pressure.From the experimental values of density and viscosity, the excess molar volumes (VE

m) and excess Gibbsenergy of activation of viscous flow (G⁄E) have been calculated. These results were fitted to Redlich–Kisterpolynomial equations to estimate the binary coefficients and standard errors. Jouyban–Acree model isused to correlate the experimental values of density, viscosity and ultrasonic velocity at T = 298.15 K.The results of the viscosity-composition are discussed in the light of various viscosity semi-empiricalequations. The experimental results have been used to test the applicability of the Prigogine–Flory–Patt-erson (PFP) theory. The values of Dlng have also been analysed using Bloomfield and Dewan model. Theexperimental and calculated quantities are used to study the nature of mixing behaviour between themixtures.

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1. Introduction

Accurate knowledge of thermodynamic properties of organicliquid mixtures has relevance in understanding the molecularinteractions between the components of the mixture, in develop-ing new theoretical models, and also in carrying out engineeringapplications in the process industry.

In recent years, measurements of thermodynamic and transportproperties have been adequately employed in understanding thenature of molecular systems and physico-chemical behaviour inliquid mixtures. The non-rectilinear behaviour of above-mentionedproperties of liquid mixtures with changing mole fractions isattributed to the difference in size of the molecules and strengthof interactions [1].

Literature surrey reveals that, the effect of molecular size,shape, chain length and degree of molecular association of2-alkanols, on the volumetric, viscometric and acoustic propertiesof binary mixtures containing acetonitrile [2], acetophenone [3],

methylbenzene [4] and methylcyclohexane [5] have been reportedearlier.

In this paper, we report accurate data on densities and viscosi-ties for binary liquid mixtures of an n-decane with hexan-2-ol,heptan-2-ol at T = 298.15 K over entire composition range. Usingthese data, excess molar volume, VE

m and excess Gibbs energy ofactivation of viscous flow G⁄E have been calculated. This work willalso provide a test of various semi-empirical equations to correlateviscosity of binary mixtures.

The calculated results are discussed in terms of intermolecularinteractions between n-decane and alkane-2-ol at T = 298.15 K.

2. Experimental

The sources, CAS number, initial mole fraction purity, purifica-tion method, analysis method and final mole fraction purity ofthe pure chemicals are summarized in table 1.

The water content was determined by a Fischer titration. Priorto use, all liquids were stored over 0.4 nm molecular sieves to re-duce the water content and were degassed. The binary mixturesof varying composition were prepared by mass in special air-tightbottles. The masses were recorded on a Metler balance to an accu-racy of ± 1 � 10�5 g. Care was taken to avoid evaporation and con-tamination during mixing. The estimated uncertainty in molefraction was < 1 � 10�4.

TABLE 1The provenance, CAS number, maximum water content mass%, initial mole fraction purity, purification method, .analysis method and final mole fraction purity of the purechemicals.

Chemical name CASnumber

Water content(mass%)

Source Initial molefraction purity

Purificationmethod

Analysismethod

Final molfraction purity

n-Decane 124-65-9 0.03 S.D. Fine Chemicals >0.992 F.G.Da G.C.b >0.995Hexan-2-ol 626-93-7 0.02 E-Merck >0.993 F.G.Da G.C.b >0.996Heptan-2-ol 543-49-7 0.02 E-Merck >0.991 F.G.Da G.C.b >0.994Octan-2-ol 123-96-6 0.004 E-Merck >0.994 F.G.Da G.C.c >0.996

a Fractional glass distillation.b Gas–liquid chromatography, HP6980 using FID detector.c Gas–liquid chromatography, DB Wax using FID detector.

TABLE 2Comparison of experimental densities (q) and viscosities (g) of pure liquids withliterature values at T = 298.15 K.

Pure liquids q � 10�3/kg �m�3 g/mPa � s

Experimental Literature Experimental Literature

n-Decane 0.72635 0.7267a 0.845 0.861b,c

Hexane-2-ol 0.81084 0.8105d 4.105 4.104d

Heptane-2-ol 0.81374 0.81372e 5.088 5.089e

Octane-2-ol 0.81705 0.81708f 6.429 6.435f

a Baraigi et al. [11].b Gonazalez et al. [12].c Gonazalez et al. [14].d Iloukhani et al. [2].e Almasi et al. [3].f Hasan et al. [4].

160 A.R. Mahajan, S.R. Mirgane / J. Chem. Thermodynamics 64 (2013) 159–166

The densities of the solutions were measured using a singlecapillary pycnometer made up of borosil glass with a bulb of 8cm3 and capillary with internal diameter of 0.1 cm was chosenfor the present work. The detailed pertaining to calibration, exper-imental set up and operational procedure has been previouslydescribed [6–10]. .An average of triplicate measurement was takeninto account. The reproducibility of density measurementwas ± 1 � 10�5 g cm�3.

The dynamic viscosities were measured using an Ubbelohdesuspended level viscometer [6–10] calibrated with conductivitywater. An electronic digital stop watch with readability of ± 0.01s was used for the flow time measurements. At least three repeti-tions of each data point reproducible to ± 0.05 s were obtained, andthe results were averaged. Since all flow times were greater than300 s and capillary radius (0.1 mm) was far less than its length(50 to 60) mm, the kinetic energy and end corrections, respectively,were found to be negligible. The uncertainties in dynamic viscosi-ties are of the order ± 0.003 mPa s. A thermostatically controlled,well-stirred water bath whose temperature was controlledto ± 0.01 K was used for density and viscosity measurement.

Standard uncertainties u are U(x1) = 0.0002, and the combinedexpanded uncertainty Uc is Uc(q) = 1 � 10�3 kg �m3 andUc(g) = 0.003 mPa � s with 0.95 level of confidence (k � 2).

The purity of the samples and accuracy of data were checked bycomparing the measured densities and viscosities of the pure com-pounds with the literature values, which are given in table 2. Thusour results obtained are in good agreement with those listed in theliterature [11–14].

3. Results

Experimental values of densities (q) and viscosities (g) of mix-tures at T = 298.15 K are listed as a function of mole fraction in ta-ble 3. The density values have been used to calculate excess molarvolumes (VE

m) using the following equation

VEm=m3 �mol�1 ¼ ðx1M1 þ x2M2Þ=q12 � ðx1M1=q1Þ � ðx2M2=q2Þ;

ð1Þ

where q12 is the density of the mixture and x1M1, q1, and x2, M2, q2

are the mole fraction, the molar mass, and the density of purecomponents 1and 2, respectively.

Excess Gibbs energy of activation of viscous flow G⁄E for binarymixtures can be calculated as

G�E ¼ RT lnðgt=g2t2Þ � x1 lnðg1t1=g2t2Þ½ �; ð2Þ

where t is the molar volume of the mixture and ti is the molar vol-ume of the pure component, R is the gas constant, T is the absolutetemperature, and g is the dynamic viscosity of the mixture, respec-tively. gi is the dynamic viscosity of the pure component i and x1 themole fraction in component.

The excess molar volumes and excess Gibbs energy of activationof viscous flow were fitted to a Redlich–Kister [15] equation of thetype

Y ¼ x1x2

Xn

iaiðx1 � x2Þi; ð3Þ

where Y is either VEm, or G⁄E and n is the degree of polynomial.

Coefficients ai was obtained by fitting equation (3) to experimentalresults using a least-squares regression method. In each case, theoptimum number of coefficients is ascertained from an examinationof the variation in standard deviation (r).

r was calculated using the relation

rðYÞ ¼PðYexpt � YcalcÞ2

N � n

" #1=2

; ð4Þ

where N is the number of data points and n is the number ofcoefficients. The calculated values of the coefficients ai along withthe standard deviations (r are given in table 4.

4. Discussion

The variation in excess molar volumes, VEm with mole fraction of

the binary mixtures of n-decane with hexan-2-ol, heptan-2-ol andoctan-2-ol T = 298.15 K are displayed in figure 1. The VE

m curve forthe mixture show positive deviation over the entire compositionrange.

Generally VEm can be considered as arising from three types of

interactions between component molecules of liquid mixtures[5,16–20]: (i) physical interactions consisting of mainly of disper-sion forces or weak dipole–dipole interaction making a positivecontribution, hereby the contraction volume, (ii) chemical orspecific interactions, which include charge transfer,forming ofH-bonds and other complex forming interactions,resulting in anegative contribution, (iii) structural contribution due to differ-ences in size and shape of the component molecules of themixtures,due to fitting of component molecules into each other’sstructure, hereby reducing the volume of the mixtures, resultingin a negative contribution .

TABLE 3Densities (q), viscosities (g), excess molar volumes (VE

m) and excess Gibbs energy ofactivation of viscous flow (G⁄E) of binary mixtures at T = 298.15 K.a

�1 q �10�3

(kg �m�3)VE

m �106

(m3 �mol�1)

g (mPa � s) G⁄E

(J �mol�1)

n-Decane(1) + hexane-2-ol (2)0.0000 0.81084 0.000 4.105 00.0555 0.80294 0.135 3.569 �1120.0999 0.79723 0.197 3.170 �2210.1554 0.79050 0.267 2.725 �3670.1998 0.78543 0.317 2.410 �4900.2556 0.77942 0.372 2.062 �6500.2999 0.77491 0.410 1.821 �7800.3555 0.76955 0.448 1.561 �9390.3998 0.76552 0.471 1.384 �10620.4554 0.76072 0.490 1.198 �12010.4998 0.75710 0.499 1.076 �12930.5554 0.75279 0.499 0.952 �13810.5997 0.74954 0.491 0.875 �14190.6555 0.74566 0.470 0.802 �14210.6999 0.74272 0.445 0.760 �13850.7555 0.73925 0.402 0.725 �12910.7998 0.73662 0.359 0.708 �12000.8555 0.73348 0.292 0.699 �9900.8999 0.73111 0.230 0.698 �6000.9555 0.72829 0.138 0.703 �4001.0000 0.72635 0.000 0.845 0

n-Decane(1) + heptan-2-ol (2)0.0000 0.81374 0.000 5.080 00.0552 0.80687 0.069 4.250 �2330.0999 0.80155 0.120 3.732 �3010.1555 0.79515 0.183 3.152 �4030.1999 0.79026 0.229 2.740 �4970.2554 0.78436 0.282 2.283 �6320.2999 0.77983 0.319 1.962 �7550.3554 0.77440 0.356 1.614 �9270.3998 0.77024 0.378 1.375 �10780.4555 0.76523 0.396 1.122 �12850.4998 0.76141 0.401 0.954 �14610.5555 0.75680 0.398 0.782 �16900.5999 0.75327 0.386 0.673 �18710.6554 0.74904 0.361 0.570 �20800.6999 0.74579 0.333 0.510 �22230.7553 0.74187 0.289 0.461 �22800.8000 0.73884 0.246 0.440 �22000.8555 0.73520 0.187 0.432 �20000.8998 0.73239 0.135 0.438 �12500.9553 0.72898 0.067 0.457 �8001.0000 0.72635 0.000 0.845 0

n-Decane(1) + octan-2-ol (2)0.0000 0.81705 0 6.429 00.0554 0.81077 0.036 5.222 �1880.0998 0.80583 0.071 4.638 �3060.1554 0.79974 0.119 3.972 �4710.1999 0.79499 0.158 3.491 �6170.2554 0.7892 0.205 2.951 �8180.2999 0.78467 0.239 2.564 �9930.3555 0.77916 0.275 2.136 �12270.3998 0.7749 0.298 1.836 �14260.4554 0.76969 0.318 1.509 �16810.4999 0.76564 0.326 1.284 �18870.5555 0.76074 0.326 1.046 �21330.5998 0.75694 0.318 0.889 �23090.6555 0.7523 0.298 0.73 �24760.7000 0.7487 0.274 0.63 �25000.7554 0.74432 0.236 0.538 �24000.7998 0.74091 0.2 0.487 �23620.8554 0.73674 0.149 0.45 �22810.8999 0.73347 0.106 0.438 �16500.9554 0.72948 0.052 0.445 �12001.0000 0.72635 0 0.845 0

a Standard uncertainties U are U(x1) = 0.0002, and the combined expanded uncer-tainty Uc is Uc(q) = 1 � 10�3 kg �m�3 and Uc(g) = 0.003 mPa � s with 0.95 level ofconfidence (k � 2).

TABLE 4Coefficients ai of equation (3) and corresponding standard deviation (r) of equation(4).

System a0 a1 a2 a3 r

n-Decane(1) + hexane-2-ol (2)

VEm/(m3 �mol�1) 2.033 0.152 �0.5406 1.9 0.007

G⁄E/(J �mol�1 ) �1122.23 �259.1 �784 �1153 7.3

n-Decane(1) + heptan-2-ol (2)

VEm/(m3 �mol�1) 1.61 0.062 �0.443 0.276 0.001

G⁄E/(J �mol�1 ) �1183 �809 �34.431 �516 5.4

n-Decane(1) + octan-2-ol (2)

VEm/(m3n �mol�1) 1.129 0.1677 �0.462 0.1437 0.0023

G⁄E/(J �mol�1) �1119.18 �30.22 �45.44 �741 9.2

A.R. Mahajan, S.R. Mirgane / J. Chem. Thermodynamics 64 (2013) 159–166 161

The large positive VEm values (figure 1) for n of n-decane with

hexan-2-ol, heptan-2-ol and octan-2-ol mixture are attributed to

the breaking up of three-dimensional H-bonded network of al-kane-2-ol due to the addition of solute, which is not compensatedby the weak interactions between unlike molecules. The VE

m valuesfor binary mixtures of n-decane with alkane-2-ol are in the orderoctan-2-ol > heptan-2-ol > hexan-2-ol.

The G⁄E values of all binary systems are shown in table 3. Figure2 depicts the variation of G⁄E with mole fraction of the binary mix-tures of n-decane with hexan-2-ol, heptan-2-ol and octan-2-olT = 298.15 K.The values of G⁄E for all binary mixtures are negativeover entire mole fraction. The negative values of G⁄E may be dueto (i) the mutual loss of dipolar association, and (ii) the differencesin size and shape of unlike molecules. These results support thefact that the breaking up of three-dimensional H-bonded networkof alkane-2-ol due to the addition of solute. According to Meyeret al. [17] negative values of G⁄E correspond to the existence of sol-ute–solute association.

5. Theoretical analysis

5.1. Prigogine–Flory–Patterson (PFP) theory

The Prigogine–Flory–Patterson (PFP) theory [18–20] has beencommonly employed to estimate and analyse excess thermody-namic functions theoretically. This theory has been described indetails by Patterson and co-workers [21,22]. According to PFP the-ory, VE

m can be separated into three factors: (1) an interactionalcontribution, VE

mðint:Þ (2) a free volume contribution, VEmðfvÞ and

(3) an internal pressure contribution, VEmðP

�Þ. The expression forthese three contributions are given as VE

m

VEmðintÞ ¼ ½ð~t1=3 � 1Þ~t2=3wh2=ð4=3~t�1=3 � 1ÞP�1v12�; ð5Þ

VEmðfvÞ ¼ �½ð~t1 � ~t2Þ2ð14=9~t�1=3 � 1Þw1w2�=½ð14=9~t�1=3 � 1Þ~t;

ð6Þ

E � ~ ~ � � � � VmðP Þ ¼ ½ðt1 � t2ÞðP1 þ P2Þw1w2Þ�=ðP1w1 þ P2w2Þ�: ð7Þ

Thus, the excess molar volume VEm is given as

VEm=ðx1V1 þ x2V2Þ ¼ VE

mðintÞ � VEmðfvÞ þ VE

mðP�Þ; ð8Þ

where w, h and P⁄ represent the contact energy fraction, surface sitefraction, and characteristic pressure, respectively, and are calcu-lated as

w1 ¼ ð1� w2Þ ¼ U1P�1=ðU1P�1 þU2P�2Þ; ð9Þ

h2 ¼ ð1� h1Þ ¼ U2= U1ðV�2=V�1Þ� �

; ð10Þ

P� ¼ T~t2a=jT : ð11Þ

/

FIGURE 1. Plot of excess molar volumes (VEm) against mole fraction of n-decane with (s) hexane-2-ol; (h) heptane-2-ol; and octane-2-ol (4) at T = 298.15 K. The

corresponding dotted (---) curves have been derived from PFP theory. The corresponding solid curves have been derived experimental results.

/

FIGURE 2. Plot of excess Gibbs energy of activation of viscous flow (G⁄E) against mole fraction of n-decane with (s) hexane-2-ol; (h) heptane-2-ol; and octane-2-ol (4) atT = 298.15 K.

162 A.R. Mahajan, S.R. Mirgane / J. Chem. Thermodynamics 64 (2013) 159–166

TABLE 5Flory parameters of the pure compounds T = 298.15 K.

Components 106V⁄/(m3 �mol�1) 106P⁄/(J �m�3) T⁄/K

n-Decane 155.6091 453 5091Hexane-2-ol 102.532 476 5517Heptane-2-ol 115.6 512 5415Octan-2-ol 129.979 535 5563

A.R. Mahajan, S.R. Mirgane / J. Chem. Thermodynamics 64 (2013) 159–166 163

The details of the notations and terms used in equations (5)–(9)may be obtained from the literature [18–24]. The other parameterspertaining to pure liquids and the mixtures are obtained from theFlory theory [18,25] while a and jT values are taken from the liter-ature [26–30]. Flory parameters of the pure compounds are givenin table 5.The interaction parameter v12 required for the calcula-tion of VE

m using PFP theory has been derived by fitting the VEm

expression to the experimental equimolar value of VEm for each sys-

tem under study.The values of v12, h2, three PFP contributions interactional, free

volume, and P⁄ effect, and experimental and calculated (using PFPtheory) VE

m values at near equimolar composition are presented intable 6. Study of the data presented in table 6 reveals that theinteractional and free volume contributions are positive, whereasP⁄ contributions are negative for all the three systems under inves-tigation. For these binary mixtures, it is only the interactional con-tribution that dominates over the remaining two contributions.The P⁄ contribution, which depends both on the differences ofinternal pressures and differences of reduced volumes of the com-ponents has little significance for the studied binary mixtures ascompared to other two.

Furthermore, in order to check whether v12, derived fromnearly equimolar VE

m values can predict the correct compositiondependence, VE

m has been calculated theoretically using v12 overthe entire composition range. The theoretically calculated valuesare plotted in figure 1 for comparison with the experimental re-sults. Figure 1 show that the PFP theory is quite successful in pre-dicting the trend of the dependence of VE

m on composition for thepresent systems.

In order to perform a numerical comparison of the estimationcapability of the PFP theory, we calculated the standard percentagedeviations (r %) using the relation

r% ¼X

100 ðExpt� TheorÞ=Expt ðn� 1Þh i1=2

; ð12Þ

where n represents the number of experimental data points.

5.2. Semi-empirical models for analysing viscosity of liquid mixtures

Several empirical and semi-empirical relations have been usedto represent the dependence of viscosity on concentration of com-ponents in binary liquid mixtures and these are classified accord-ing to the number of adjustable parameters used to account forthe deviation from some average [31,32].We will consider heresome of the most commonly used semi-empirical models for

TABLE 6Calculated values of the three contributions to the excess molar volume from the PFP the

Component v12 �106 (J �m�3) VE � 106/(m3 mol�1)

Experimental

n-Decane(1) + hexane-2-ol (2) 19.36 0.499n-Decane(1) + hexane-2-ol (2) 19.36 0.499n-Decane(1) + heptan-2-ol (2) 17.75 0.401n-Decane(1) + octan-2-ol (2) 12.57 0.326

analysing viscosity of liquid mixtures based on one, two and threeparameters. An attempt has been made to check the suitability ofequations for experimental data fits by taking into account thenumber of empirical adjustment coefficients.

The equation of Grunberg-Nissan, Tamara and Kurata Hindet al., and Katti and Chaudhari has one adjustable parameter.

Gruenberg-Nissan provided the following empirical equationcontaining one adjustable parameter [33] .The equation is

lng12 ¼ x1 ln g1 þ x2 ln g2 þ x1x2G12; ð13Þ

where G12 may be regarded as a parameter proportional to theinterchange energy also an approximate measure of the strengthof the interaction between the components .

The one-parameter equation due to Tamura and Kurata [34] isgave the equation of the form

gm ¼ x1g1U1 þ x2gU2 þ 2ðx1x2U1U2Þ1=2T12; ð14Þ

where U1 and U2 re the volume fractions of components 1 and 2,respectively; T12 is Tamura and Kurata constant.

Hind et al. [35] proposed the following equation

gm ¼ x21g1 þ x2

2g2 þ 2x1x2H12; ð15Þ

where H12 is attributed to unlike pair interactions.Katti and Chaudhari [36] derived the following equation

lngm ¼ x1 ln gm01 þ x2 lngnu0

2 þ x1x2Wvis=RT; ð16Þ

where Wvis is an interaction term and ti is the molar volume of purecomponent i.Heric [37] expression is

lngm ¼ x1 lng1 þ x2 ln g2 þ x1 ln g1 þ x2 ln g2 þ lnðx1g1

þ x2g2Þ þ d12; ð17Þ

where d2 = a12x1x2 is a term representing departure from a non-interacting system and a12 = a21 is the interaction parameter.Either a12 or a21 can be expressed as a linear function ofcomposition:

a12 ¼ b012 þ b0012ðx1 � x2Þ: ð18Þ

From an initial guess of the values of coefficients b’12 and b’’12

the values of a12 are computed.Heric and Brewer [38] equation is

ln m ¼ x1 ln m1 þ x2 ln m2 þ x1 ln M1 þ x2 ln M2 � ln½x1M1

þ x2M2� þ x1x2½a12þ a21ðx1 � x2Þ�: ð19Þ

The M1 and M2 are molar mass of components 1 and 2 and a12

and a21 are interaction parameters and other terms involved havetheir usual meaning. a12 and a21 are parameters, which can be cal-culated from the least-squares method.

McAllister’s multibody interaction model [39] was widely usedto correlate kinematic viscosity (m) data. The two-parameterMcAllister equation based on Eyring’s [40] theory of absolute reac-tion rates taken into account interaction of both like and unlikemolecules by two dimensional three-body model. The three-bodyinteraction model is

ory with interaction parameter at T = 298.15 K.

at x = 0.5 Calculated contribution

PEP VE � 106 (int) VE � 106 (fv) VE � 106 (p⁄)

0.498 0.596 0.042 �0.0550.498 0.596 0.042 �0.0550.398 0.537 0.025 �0.1090.328 0.5999 0.0544 �0.2183

164 A.R. Mahajan, S.R. Mirgane / J. Chem. Thermodynamics 64 (2013) 159–166

ln num ¼ x31 ln m1 þ 3x2

1x2 ln Z12 þ 3x1x22 ln Z21 þ x3

2 ln m2

� ln½x1 þ ðx2M2Þ=M1� þ 3x21x2 ln½2=3þM2=ð3M1Þ�

þ 3x1x22 ln½1=3þ 2M2=ð3M1Þ�x3

2 lnðM2=M1Þ ð20Þ

and the four body model was given by

ln num ¼ x41 ln m1þ 4x3

1x2 ln Z1112 þ 6x21x2

2 ln Z1122 þ 4x1x32

� ln Z2221 þ x42 ln m2 � ln½x1 þ x2ðM2=M1Þ� þ 4x3

1x2

� ln½3þ ðM2=M1Þ=4� þ 6x21x2

2 ln½1þ ðM2=M1Þ=2�þ 4x1x3

2 ln½1þ ð3M2=M1Þ=4� þ x42 lnðM2=M1Þ; ð21Þ

where Z12, Z21, Z1112, Z1122 and Z2221 are interaction parameters andMi and mi are the molar mass and kinematic viscosity of pure com-ponent i, respectively.

The correlating ability of each of equations (13)–(21) was testedand their adjustable parameters and standard deviations (r):

r ¼ ð1=ðn� kÞX

100ðgexptl � gcalcdÞ=gexptlÞ2

h i1=2; ð22Þ

where n represents the number of data points and k is the numberof numerical coefficients is given in table 7. According to Fort andMoore [41] and Ramamurthy [42], system exhibits strong interac-tion if the G12 is positive; if it is negative they show weak interac-tion. On this basis we can say that there is weak interaction inthe system studied.

Interaction parameter Wvis shows almost same trend as that ofG12.In fact one could say that the parameter G12 and Wvis exhibit al-most similar behaviour, which is not unlikely in view of logarith-mic nature of both equation.

Tamara and Kurata and Hind et al., represent the binary mixturesatisfactory as compared to Gruenberg-Nissan and Katti andChaudhari. Use of a three parameter equation reduces the r valuessignificantly below that of two parameters equation. From thisstudy, it can be concluded that the correlating ability significantlyimproves for these non-ideal systems as number of adjustable

TABLE 7Adjustable parameters of equations (13)–(21) and standard deviations of binarymixture viscosities for {x1 n-decane + (1 � x1) alkane-2-ol} at T = 298.15 K.

Equation System including n-decane + alkane-2-ol

Hexane-2-ol Heptane-2-ol Octane-2-ol

Grunberg–NissanG12 �2.253 �3.724 �3.226R 1.124 3.597 2.904

Tamura and KurataT12 0.005 �0.925 �1.117R 0.355 1.766 1.884

Hind et al.H12 �3.75 �1.266 �1.409R 0.964 1.956 1.145

Katti and ChaudhariWvis �2.173 �3.665 �3.198R 1.134 2.602 3.905

Herc and Brewera12 �2.26 �4.248 �3.936a21 �2.912 �5.406 �5.529R 0.461 2.001 2.449

McAllister’s three-bodyZ12 0.467 0.081 0.094Z21 2.272 5.225 4.068R 0.463 1.03 1.449

McAllister’s four-bodyZ1112 0.481 0.059 0.511Z1122 2.157 8.543 1.897Z2221 2.591 1.976 1.998R 0.325 0.397 1.865

parameter is increased. From table 7, it is clear that McAllister’sfour-body interaction model is suitable for correlating the kine-matic viscosities of the binary mixtures studied.

5.3. Bloomfield and Dewan model

There are different expressions available in the literature to cal-culate g. Here, the Bloomfield and Dewan [43] model has been ap-plied to compare calculated Dlng values using experimental datafor each binary mixture by the following relation

D ln g ¼ ln g� ðx1 ln g1 þ x2 ln g2Þ: ð23Þ

Bloomfield and Dewan [43] developed the expression from thecombination of the theories of free volumes and absolute reactionrate

D ln g ¼ f ðmÞ � DGR=RT; ð24Þ

where f(t) is the characteristic function of the free volume definedby

f ð~tÞ ¼ 1=ð~t� 1Þx1=ð~t1 � 1Þ � x2=ð~t2 � 1Þ ð25Þ

and DGR is the residual energy of mixing, calculated with the fol-lowing expression

DGR ¼ DGE þ RTfx1 lnðx1=U1Þ þ x2 lnðx2=U2Þg; ð26Þ

where U1 and U2 are segment fraction defined by

U2 ¼ 1�U1 ¼ x2=½x2 þ x1ðr1=r2Þ�; ð27Þ

where r1 and r2 are in the ratio of respective molar core volumes V1⁄

and V2⁄.

The excess energy can be obtained from the statistical theory ofliquid mixtures proposed by Flory and co-workers [18,19] and isgiven by

DGE ¼ x1P�1V�1½1=ð~t1 � x1 lnfð~t1=31 � 1Þ=ð~t1=3 � 1Þg

þ x2P�2V�2½1=ð~t2 � x2 lnfð~t1=32 � 1Þ=ð~t1=3 � 1Þg�

þ ðx1h2V�1v12Þ=~t; ð28Þ

where the various symbols used have their usual meanings.Using the v12 values from fitting values of VE

m and the values ofthe parameters for the pure liquid components, we have calculatedDGR and f(t) and finally Dlng, according to the Bloomfield and De-wan relationship, which is compared with the experimental values.Figure 3 shows that the good agreement between the estimatedand experimental curves occurs for given binary systems.

5.3.1. The Jouyban and Acree modelThe Jouyban–Acree model [44,45] was introduced to correlate

the physicochemical properties of the solution in mixed solventsincluding the dielectric constants, viscosity solvatochromic param-eter, and density, speed of sound and more recently molar vol-umes. The model uses the physicochemical properties of themono-solvents as input data and a number of curve-fitting param-eters representing the effects of solvent–solvent interactions in thesolution. It is basically derived for representing the solvent effectson the solubility of non-polar solutes in nearly ideal binary solventmixtures at isothermal conditions. The proposed equation is

ln ym;T ¼ f1 ln y1;T þ f2 ln y2;T þ f1f2R½Ajðf1 � f2Þj=T�; ð29Þ

where ym, T, y1,T and y2,T is density, or viscosity of the mixture andsolvents 1 and 2 at temperature T, respectively, f1 and f2 are the vol-ume fractions of solvents in case of density, and mole fraction incase of viscosity, and Aj are the model constants.

/

FIGURE 3. Plot of Dln g against mole fraction of n-decane with (s) hexane-2-ol; (h) heptane-2-ol; and octane-2-ol (4) at T = 298.15 K. The corresponding dotted (---) curveshave been derived from Bloomfield and Dewan model. The corresponding solid curves have been derived experimental results.

TABLE 8Parameters of Jouyban–Acree model and average percentage deviation for densitiesand viscosities at of binary mixtures at T = 298.15 K.

System A0 A1 A2 APD

Densityn-Decane(1) + hexane-2-ol (2) �16.812 1.275 �4.12 0.175n-Decane(1) + heptan-2-ol (2) �11.498 2.104 �1.91 0.154n-Decane(1) + octan-2-ol (2) �9.0926 1.0266 0.6448 0.1183

Viscosityn-Decane(1) + hexane-2-ol (2) �5.123 9.236 �3.125 0.812n-Decane(1) + heptan-2-ol (2) �6.321 8.123 �2.158 0.913n-Decane(1) + octan-2-ol (2) �4.2926 11.2857 �2.7614 0.7668

A.R. Mahajan, S.R. Mirgane / J. Chem. Thermodynamics 64 (2013) 159–166 165

The correlating ability of the Jouyban–Acree model was testedby calculating the average percentage deviation (APD) betweenthe experimental and calculated density and speed of sound as

APD ¼ ð100=NÞR½ðjyexptl � ycalcdjÞ=yexptlÞ�; ð30Þ

where N is the number of data points in each set. The optimumnumbers of constants Aj, in each case, were determined from theexamination of the average percentage deviation value.

The constants Aj calculated from the least squares analysis arepresented in table 8 along with the average percentage deviation(APD). The proposed model provides reasonably accurate calcula-tions for the density and viscosity of binary liquid mixtures atT = 298.15 K and the model could be used in data modelling.

6. Conclusions

Densities and viscosities for the binary liquid mixture of n-dec-ane with hexan-2-ol, heptan-2-ol and octan-2-ol were measured atthe temperature of 288.15 K over the whole range of compositions.The positive VE

m and negative G⁄E for n-decane with hexan-2-ol,

heptan-2-ol and octan-2-ol mixtures suggest that the rupture ofhydrogen bonded chain of the dipolar interaction between soluteand alkan-2-ol exceed the intermolecular interaction throughdipole–dipole and hydrogen bonding between n-decane andalkan-2-ol molecules. This behaviour is characteristic for systemscontaining an associated component.

All of the selected correlative models are capable of represent-ing the volumetric and the viscometric behaviour of the mixturewith a higher or lower degree of accuracy. McAllister’s four-bodyinteraction model is suitable for correlating the kinematicviscosities of the binary mixtures studied. Also the Prigogine–Flory–Patterson (PFP) theory shows that the good agreementbetween the estimated and experimental curves occurs for givenbinary systems. The Jouyban–Acree model and the Bloomfield andDewan relationship show that the good agreement between theestimated and experimental values occurs for given binarysystems.

Acknowledgments

Authors are thankful to Prof. B.R. Arbad, Dr. B.A.M. Universityfor their valuable suggestions and discussion. Authors are alsothankful to Principal Dr. R.S. Agarwal, J.E.S. College, Jalna for thefacilities provided.

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at http://dx.doi.org/10.1016/j.jct.2013.05.014.

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JCT 13-95