Journal of Molecular Liquids 193 (2014) 249–255

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Journal of Molecular Liquids

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Volumetric, refractive and FT-IR behaviour of β-pinene with o, m,p-cresol at 303.15, 308.15 and 313.15 K

Jasmin Bhalodia, Sangita Sharma ⁎Department of Chemistry, Hemchandracharya North Gujarat University, Patan 384265, India

⁎ Corresponding author. Tel.: +91 02766 220932x364.E-mail address: sangitamem2000@gmail.com (S. Shar

0167-7322/$ – see front matter © 2013 Elsevier B.V. All rihttp://dx.doi.org/10.1016/j.molliq.2013.12.037

a b s t r a c t

a r t i c l e i n f o

Article history:Received 15 September 2013Received in revised form 3 December 2013Accepted 17 December 2013Available online 7 January 2014

Keywords:DensityExcess molar volumeRefractive indexMolar refractionMixing rulesFT-IR spectroscopy

Density (ρ) and refractive index (nD) of binarymixtures ofβ-pinenewith o,m, p-cresol have beenmeasured overthe entire composition range expressed bymole fraction (x1) and volume fraction (ϕ1) of theβ-pinene at 303.15,308.15 and 313.15 K at atmospheric pressure. The FT-IR measurements were carried out at 298.15 K. From theexperimental data, excess molar volume (VE), deviation in refractive index (ΔnD) and deviation in molarrefraction (ΔRm) have been calculated and fitted to the Redlich–Kister polynomial equation. The excess or deviationparameters were plotted against mole fraction or volume fraction of the β-pinene over whole composition range.The observed negative or positive values of excess or deviation parameters were explained on the basis of theintermolecular interactions present in these mixtures. A comparative study of mixing rules namely Arago–Biot,Dale–Gladstone, Lorentz–Lorenz, Eykeman, Weiner, Heller, Newton, Oster and Eyring–John has been carried outto test their validity for these binaries over entire mole fraction of β-pinene at three temperatures. Comparison ofvariousmixing rules has been expressed in terms of average deviation. The FT-IR study reveals that complex forma-tion becomes maximum at 0.3 mole fraction of β-pinene, which is also supported by the VE and ΔnD data. Theposition and pattern of intensity of\OH bands as per FT-IR data strongly supports the conclusion that molecularassociation through H-bonding has taken place.

© 2013 Elsevier B.V. All rights reserved.

1. Introduction

Excess thermodynamic properties ofmixtures are useful in the studyof molecular interactions [1]. Thermodynamic properties derived fromthe measurements of density and refractive indexes for binary mixtureare useful in understanding the nature and type of molecular interac-tions between component molecules. With knowledge of variousthermodynamic properties and molecular interactions in the mixtureof β-pinene with self associated molecules like alcohol, cresols help usin designing an efficient industrial process and also in understandinginter and intra molecular interactions. The studies on interaction arerequired not only intrinsically but also in supercritical extraction withcarbon dioxide of essential oils of aromatic plants where alcohols (eth-anol or methanol) have been proposed as a modifier that can improvethe extraction process. The liquids used in the present study areimportant due to their various industrial applications. β-Pinene is oneof the most common compounds found in a number of essential oils.

o-Cresol is mostly used as an intermediate for the production ofpesticides, epoxy resins, dyes and pharmaceuticals, and also as a compo-nent of disinfectants and cleaning agents. o-Cresol is readily biodegrad-able and has a low bio- or geo-accumulation potential. In 90% of the

ma).

ghts reserved.

uses, cresols are organic intermediates in manufacturing of phenolic andepoxy resins, plasticizers, herbicides, rubber and plastic antioxidants,dyes, deodorizing and odour-enhancing compounds, fragrances andpharmaceuticals [2]. m-Cresol is used in disinfectants, textile scouringagents, surfactants and as intermediates in the manufacture ofsalicylaldehyde, coumarin and herbicides [3].

In our earlier paper [4], the results of our research programme onexcess properties of β-pinene + aromatic hydrocarbons have beenreported. To understand more about the interactions, the study hasbeen extended to mixture of β-pinene with o, m, p-cresol at 303.15 to313.15 K. As far as literature review is concerned, no data is availablefor these mixtures. So density and refractive index have been measuredover the whole composition range for the mixture of β-pinene with o,m, p-cresol at temperature 303.15, 308.15 and 313.15 K. From the exper-imental density and refractive index, excess molar volume, deviation inrefractive index and deviation molar refraction has been calculated. Theresults are discussed in terms of mentioned molecular interactions. Thustreatment of this class of mixtures offers a particular challenge in orderto describe interaction occurring in their solution and also to test theoret-ical models.

The complex formation in binary mixtures is interpreted in terms ofH-bonding and their FT-IR stretching frequencies. FT-IR is a powerfultool in studying inter and intra molecular association by examiningthe position of the\OH band, bandwidth and intensity of first overtoneband.

Table 2Mole fraction (x1), density (ρ) and excess molar volume (VE) for the mixture at 303.15,308.15 and 313.15 K.

x1 ρ/(g cm−3) VE/(cm3 mol−1)

T/K = 303.15 308.15 313.15 303.15 308.15 313.15

β-Pinene (1) + o-cresol (2)0.0683 1.0173 1.0121 1.0070 0.186 0.207 0.2350.1430 0.9981 0.9931 0.9882 0.351 0.379 0.4090.2204 0.9799 0.9752 0.9703 0.490 0.523 0.554

250 J. Bhalodia, S. Sharma / Journal of Molecular Liquids 193 (2014) 249–255

2. Experimental

2.1. Materials

The chemicals (β-pinene) used for this investigation have beenimported fromSigma-Aldrich (Germany) having purity (99.90%) and cre-sols were procured from S.D. Fine (India) with quoted purities (99.00%).These chemicals have been used without any further treatment. Therespective literature survey has been done for each component of binarymixture and the results are given in Table 1. The experimental values ofdensity and refractive index are given in Table 1 are very close to litera-ture values [1–14].

2.2. Apparatus and procedure

The densities of the pure liquids and the mixtures were measuredwith a bulb volume 10 cm3 capillary pycnometer. Double distilledwater was used as calibrating substance. A thermostatically controlled,well-stirred water bath whose temperature was controlled to ±0.01 Kwas used for all the density measurements. Binary mixtures were pre-pared by mass, using an electronic analytical balance (Reptech RA-2012) with a precision of ±0.0001 g. The uncertainty in mole fractionwas estimated to be ±0.0001. The uncertainty of the density measure-ments was estimated to be ±0.01%.

Refractive indices for the sodium D-line were measured with athermostated Abbe's refractometer SER. No. 995033 at 303.15, 308.15and 313.15 K. The temperature was controlled by waterbath. Theerror in refractive index measurements was less than 0.0001 units.Calibration of the instruments was done bymeasuring the refractive in-dices of double-distilled water and toluene at a known temperature.Water was circulated into the prism of the refractometer using acirculating pump connected with a constant temperature waterbath tomaintain the temperature. The sample mixtures were directly injectedinto the prism assembly of the instrument by means of an airtighthypodermic syringe. When the liquid mixture attained the constanttemperature, the refractive index measurements were made. Anaverage of triplet measurements was taken into consideration for eachof the mixtures.

FT-IR measurements of β-pinene with aromatic hydrocarbons werestudied onALPHAFT-IR Spectrometer (Bruker, Germany). A spectroscopiccell equipped with a KBr optical Window was used to carry out spectralanalysis. The samples were prepared by mixing of β-pinene with cresolsin the 1:1 ratios. The spectra were corrected from the water vapour and

Table 1Comparison of experimental densities (ρ) and refractive indices (nD) of pure liquids withliterature values at 303.15, 308.15 and 313.15 K.

Pure liquid T/K ρ/(g cm−3) nD

Experimental Literature Experimental Literature

β-Pinene 303.15 0.8616 0.86195 [5] 1.4721 1.4728 [6]0.86231 [7]

308.15 0.8586 0.8580 [6] 1.4707 1.4705 [6]313.15 0.8548 0.85487 [8] 1.4687 1.4685 [6]

0.85483 [7]o-Cresol 303.15 1.0365 1.0369 [9] 1.5375 1.5410 [9]

1.0487 [1]308.15 1.0313 1.0316 [9] 1.5351 1.5386 [10]

1.03273 [10] 1.5370 [9]313.15 1.0263 1.0260 [11] 1.5325 –

1.0391 [10]m-Cresol 303.15 1.0264 1.0261 [12] 1.5327 1.5350 [9]

308.15 1.0214 1.02164 [13] 1.5307 1.5320 [9]313.15 1.0163 1.0160 [11] 1.5291 –

p-Cresol 303.15 1.0262 1.0263 [9] 1.5293 1.5340 [9]308.15 1.0220 1.02198 [14] 1.5272 1.5310 [9]

1.0224 [9]313.15 1.0180 1.0168 [11] 1.5250 –

1.01805 [14]

CO2 contributions and accumulated over the spectral range 4000 cm−1

to 500 cm−1, with a nominal resolution of 2 cm−1 and 4 scans at298.15 K.

3. Results and discussion

Comparison of experimental and literature values of pure compo-nents at 303.15, 308.15 and 313.15 K are given in Table 1. The valuesare in good agreement.

Experimentally measured values of density of mixture of β-pinenewith cresols as function of mole fraction of β-pinene at 303.15, 308.15and 313.15 K are listed in Table 2. Excess molar volumes are calculatedby using following equation

VE ¼ Vm−X2i¼1

Vixi ð1Þ

where Vi represents the molar volume and xi the mole fraction of ithcomponent. The quantity Vm refers to the molar volume of the mixturewhich can be calculated from the mixture density ρm and the compo-nent molecular weights, M1 andM2 as

Vm ¼ M1x1 þM2x2ð Þρm

: ð2Þ

Experimentally measured values of refractive indices, nD of mixtureof β-pinene + o, m, p-cresol at different temperatures as a function ofvolume fraction are given in Table 3. Deviation in refractive index, ΔnDand molar refraction, ΔRm are calculated by using following equations

ΔnD ¼ nD exp−nD1ϕ1−nD2

ϕ2 ð3Þ

ΔRm ¼ Rm−Rm1ϕ1−Rm2

ϕ2 ð4Þ

0.3055 0.9617 0.9573 0.9526 0.603 0.634 0.6690.3975 0.9441 0.9399 0.9353 0.654 0.684 0.7120.4974 0.9276 0.9236 0.9193 0.554 0.589 0.6070.6062 0.9111 0.9074 0.9032 0.443 0.468 0.4830.7252 0.8946 0.8911 0.8870 0.312 0.333 0.3480.8559 0.8781 0.8749 0.8709 0.170 0.177 0.186

β-Pinene (1) + m-cresol (2)0.0689 1.0081 1.0063 0.9984 0.169 0.190 0.1940.1428 0.9904 0.9894 0.9808 0.320 0.343 0.3740.2221 0.9730 0.9728 0.9636 0.457 0.485 0.5240.3076 0.9560 0.9570 0.9469 0.544 0.587 0.6340.3999 0.9395 0.9400 0.9307 0.587 0.628 0.6800.4999 0.9238 0.9242 0.9154 0.508 0.548 0.5950.6086 0.9084 0.9080 0.9004 0.384 0.414 0.4520.7272 0.8930 0.8918 0.8853 0.250 0.276 0.3050.8571 0.8773 0.8771 0.8701 0.125 0.143 0.152

β-Pinene (1) + p-cresol (2)0.0689 1.0083 1.0041 0.9998 0.151 0.171 0.2080.1428 0.9906 0.9864 0.9821 0.305 0.340 0.3740.2222 0.9730 0.9688 0.9647 0.460 0.505 0.5370.3076 0.9560 0.9520 0.9477 0.556 0.600 0.6490.3999 0.9394 0.9356 0.9313 0.603 0.645 0.6950.4999 0.9239 0.9202 0.9159 0.508 0.545 0.6050.6086 0.9084 0.9048 0.9007 0.393 0.429 0.4680.7272 0.8929 0.8895 0.8855 0.256 0.285 0.3100.8571 0.8773 0.8742 0.8702 0.130 0.137 0.162

Table 3Volume fraction (ϕ1), refractive index (nD), deviation in refractive index (ΔnD) and deviation in molar refraction (ΔRm) for the mixture at 303.15, 308.15 and 313.15 K.

ϕ1 nD ΔnD ΔRm/(cm3 mol−1)

T/K = 303.15 308.15 313.15 303.15 308.15 313.15 303.15 308.15 313.15

β-Pinene (1) + o-cresol (2)0.1000 1.5276 1.5256 1.5232 −0.0034 −0.0031 −0.0029 −0.4823 −0.4619 −0.44740.2000 1.5191 1.5172 1.5151 −0.0053 −0.0050 −0.0046 −0.8312 −0.8094 −0.78240.3000 1.5114 1.5095 1.5073 −0.0065 −0.0063 −0.0061 −1.1339 −1.1168 −1.09900.4000 1.5040 1.5022 1.5001 −0.0073 −0.0071 −0.0069 −1.3413 −1.3251 −1.30390.5000 1.4971 1.4954 1.4934 −0.0077 −0.0075 −0.0072 −1.4624 −1.4464 −1.42250.6000 1.4912 1.4896 1.4877 −0.0071 −0.0069 −0.0065 −1.4755 −1.4572 −1.43440.7000 1.4858 1.4843 1.4826 −0.0059 −0.0057 −0.0052 −1.3524 −1.3357 −1.30230.8000 1.4811 1.4797 1.4778 −0.0041 −0.0039 −0.0037 −1.0613 −1.0440 −1.02710.9000 1.4764 1.4751 1.4731 −0.0022 −0.0020 −0.0020 −0.6274 −0.6119 −0.6065

β-Pinene (1) + m-cresol (2)0.1000 1.5246 1.5229 1.5215 −0.0020 −0.0018 −0.0016 −0.4106 −0.4875 −0.37760.2000 1.5172 1.5156 1.5142 −0.0034 −0.0031 −0.0028 −0.7418 −0.8414 −0.69460.3000 1.5103 1.5088 1.5072 −0.0042 −0.0039 −0.0038 −0.9935 −1.1194 −0.94850.4000 1.5036 1.5021 1.5006 −0.0049 −0.0046 −0.0043 −1.1842 −1.3557 −1.12660.5000 1.4972 1.4958 1.4943 −0.0052 −0.0049 −0.0046 −1.2956 −1.4478 −1.23100.6000 1.4917 1.4903 1.4887 −0.0046 −0.0044 −0.0042 −1.2983 −1.4490 −1.24160.7000 1.4866 1.4852 1.4835 −0.0037 −0.0035 −0.0033 −1.1846 −1.3062 −1.13990.8000 1.4815 1.4801 1.4783 −0.0027 −0.0026 −0.0025 −0.9550 −1.0464 −0.92170.9000 1.4766 1.4753 1.4735 −0.0016 −0.0014 −0.0012 −0.5722 −0.7028 −0.5399

β-Pinene (1) + p-cresol (2)0.1000 1.5220 1.5201 1.5181 −0.0016 −0.0014 −0.0013 −0.3981 −0.3863 −0.36650.2000 1.5153 1.5135 1.5115 −0.0026 −0.0024 −0.0022 −0.7126 −0.6955 −0.67840.3000 1.5089 1.5072 1.5053 −0.0032 −0.0030 −0.0028 −0.9516 −0.9305 −0.90980.4000 1.5027 1.5011 1.4992 −0.0037 −0.0035 −0.0033 −1.1301 −1.1078 −1.08330.5000 1.4967 1.4952 1.4933 −0.0040 −0.0037 −0.0035 −1.2348 −1.2111 −1.18750.6000 1.4913 1.4898 1.4879 −0.0037 −0.0035 −0.0033 −1.2544 −1.2361 −1.21030.7000 1.4860 1.4846 1.4827 −0.0033 −0.0031 −0.0029 −1.1708 −1.1496 −1.13050.8000 1.4812 1.4798 1.4780 −0.0023 −0.0022 −0.0020 −0.9399 −0.9243 −0.90200.9000 1.4766 1.4753 1.4734 −0.0012 −0.0010 −0.0009 −0.5531 −0.5398 −0.5249

0.0 0.2 0.4 0.6 0.8 1.00.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

x1

303.15 K

VE (

cm3 .m

ol-1

)

Fig. 1. Excess molar volume (VE) plotted against mole fraction (x1) for binary mixtures β-pinene + o-cresol (■), + m-cresol (●) and β-pinene + p-cresol (▲) at T = 303.15 K.

251J. Bhalodia, S. Sharma / Journal of Molecular Liquids 193 (2014) 249–255

where ϕ1, ϕ2, nD1, nD2, Rm1 and Rm2 (cm3 mol−1) are volume fraction,refractive index, molar refraction of components 1 and 2 which can beobtained as

ϕi ¼xiViX2i¼1

xiVi

ð5Þ

Rmi¼ n2

Di−1

n2Diþ 2

Vi ð6Þ

Vi ¼Mi

ρið7Þ

where Vi, xi,Mi and ϕi are molar volume, mole fraction, molar mass andvolume fraction respectively.

The deviation function of VE, ΔnD and ΔRm are fitted in the Redlich–Kister polynomial [15] using the following equation. These values areplotted against the mole fraction and volume fraction of β-pinene asshown in Figs. 1, 2 and 3.

YE ¼ x1 1−x1ð ÞXni¼0

Ai 2x1−1ð Þi ð8Þ

where YE = (VE, ΔnD and ΔRm) and x1 is the mole fraction or volumefraction (ϕ1) of the first component. The co-efficient Ai was calculatedby unweighted least square method. In each case, the optimum num-bers of coefficient are ascertained from the examination of the variationin standard deviation in YE of Eq. (8). The standard deviation (σ) wascalculated using the following equation:

σ Yð Þ ¼X

YEexp−YE

cal

� �2N−pð Þ

264

375

12

ð9Þ

where, Y expE is the experimentally derived excess (or deviation) func-

tion. Y calE is the calculated value of the respective functions. N is the

number of experimental points and p is the number of co-efficientsused for fitting the data. The estimated values of Ai and σ for YE versusx1 are shown in Table 4. In all the cases, the best fit was obtained byusing only three fitting coefficients.

3.1. Excess molar volume

Excess molar volumes are positive on the whole composition rangefor the investigated mixtures (Fig. 1). The variation of VE with tempera-ture is within the uncertainty range of magnitude. The maxima areobserved at 0.3775, 0.3762 and 0.3772 for all o, m and p-cresol binary

0.0 0.2 0.4 0.6 0.8 1.0-0.008

-0.007

-0.006

-0.005

-0.004

-0.003

-0.002

-0.001

0.000n D

1

303.15 K

Fig. 2. Deviation in refractive index (ΔnD) plotted against mole fraction (ϕ1) for binarymixtures β-pinene + o-cresol (■), + m-cresol (●) and β-pinene + p-cresol (▲) atT = 303.15 K.

Table 4Coefficients of the Redlich–Kister equation and standard deviation for excess molarvolume (V E), deviation in refractive index (ΔnD) and deviation in molar refraction(ΔRm) for β-pinene (1) + o, m, p-cresol (2).

Function A0 A1 A2 A3 A4 σ

β-Pinene (1) + o-cresol (2)T = 303.15 K

VE/cm3 mol−1 2.302 −1.788 −0.849 1.434 1.076 0.017ΔnD −0.031 0.002 0.009 0.009 −0.015 0.000ΔRm/(cm3 mol−1) −5.877 −1.418 0.134 0.637 −0.896 0.007

T = 308.15 KVE/cm3 mol−1 2.428 −1.813 −0.858 1.235 1.179 0.016ΔnD −0.030 0.002 0.009 0.008 −0.011 0.000ΔRm/(cm3 mol−1) −5.811 −1.412 0.212 0.572 −0.690 0.007

T = 313.15 KVE/cm3 mol−1 2.533 −1.916 −0.994 1.176 1.731 0.021ΔnD −0.029 0.004 0.014 0.003 −0.019 0.000ΔRm −5.724 −1.344 0.479 0.362 −1.050 0.009

β-Pinene (1) + m-cresol (2)T = 303.15 K

VE/cm3 mol−1 2.069 −1.795 −0.964 1.305 1.004 0.009ΔnD −0.020 0.003 0.009 −0.001 −0.014 0.000ΔRm/(cm3 mol−1) −5.165 −1.138 −0.180 0.031 −0.448 0.004

T = 308.15 KVE/cm3 mol−1 2.239 −1.868 −1.241 1.368 1.590 0.011ΔnD −0.019 0.002 0.008 0.001 −0.010 0.000ΔRm/(cm3 mol−1) −5.851 −0.829 1.118 −0.995 −3.596 0.012

T = 313.15 KVE/cm3 mol−1 2.412 −1.983 −0.967 1.405 0.913 0.011ΔnD −0.018 0.002 0.006 0.002 −0.003 0.000ΔRm/(cm3 mol−1) −4.916 −1.190 −0.445 0.089 0.249 0.003

β-Pinene (1) + p-cresol (2)T = 303.15 K

VE/cm3 mol−1 2.103 −1.883 −0.884 1.675 0.594 0.012ΔnD −0.016 −0.001 0.002 0.006 −0.003 0.000ΔRm/(cm3 mol−1) −4.940 −1.348 −0.745 0.428 0.323 0.002

T = 308.15 KVE/cm3 mol−1 2.254 −1.922 −0.633 1.426 0.202 0.013ΔnD −0.015 −0.001 −0.000 0.006 0.004 0.000ΔRm/(cm3 mol−1) −4.849 −1.368 −0.743 0.474 0.437 0.001

T = 313.15 KVE/cm3 mol−1 2.489 −2.020 −1.375 1.493 1.721 0.013ΔnD −0.016 −0.001 0.002 0.006 0.001 0.000ΔRm/(cm3 mol−1) −4.749 −1.332 −0.799 0.375 0.752 0.002

252 J. Bhalodia, S. Sharma / Journal of Molecular Liquids 193 (2014) 249–255

mixtures respectively. All curves obtained are symmetrical with respectto mole fraction. VE values are given in Table 2. The magnitude of VE isthe resultant of several effects broadly categorized as [16]

(i) Dominance of similar molecules (cresols) on mixing gives apositive contribution to VE

(ii) Non-specific physical interaction between dissimilar moleculesalso gives a positive contribution to VE

(iii) Specific interaction between dissimilar molecules (H-bondingetc.) gives a negative contribution to VE

(iv) Interstitial accommodation due to difference in molar volumeand free volume between unlike liquids also gives a negativecontribution to VE

In the present case, the positive contributions observed for all binarymixtures may be due to contribution of factors (i) and (ii).

The variation of VE with temperature for all the binaries can beexplained on the combined effect of following factors

(i) Difference inmolar volumes of dissimilar components is loweredwith rise of temperature

(ii) Weakening of specific interaction between dissimilar molecules(iii) Increases in kinetic energy of component molecules.

In the present case, there is a substantial increase in VE values withincrease in temperature for all the binaries. This may be also due to

0.0 0.2 0.4 0.6 0.8 1.0-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

0.0

1

Rm

(cm

3 .mol

-1)

Fig. 3. Deviation in molar refractive index (ΔRm) plotted against mole fraction (ϕ1) for bi-nary mixtures β-pinene + o-cresol (■), +m-cresol (●) and β-pinene + p-cresol (▲) atT = 303.15 K.

the contribution of factors (ii) and (iii) as explained above. The VE

values has observed the following sequence

o‐cresolNm‐cresolNp‐cresol

3.2. Refractive index deviation

The refractive index, nD of amaterial is defined as the velocity of lightin a vacuum to the velocity in thematerial and therefore for a liquid, it isgreater than water. The refractive index is a thermodynamic propertyand it is a state function which for a pure liquid and liquid mixture de-pends on temperature and pressure.

It is well known that in the case of liquids when refractive index of aliquid can bemeasured accurately andprecisely, therewould be interestin theoretical and empirical correlation of this propertywith theproper-ties that are otherwise more difficult to measure directly [17].

It is clear from Figs. 2 and 3 that ΔnD and ΔRm values are negativeover whole composition range.

ΔnD is negatively correlated with ΔVm/R and VE is directly interpret-able as a sign reversed measure of deviation of reduced free volumefrom ideality [18].

There are small negative values of ΔnD which are related to increaseinmolar volume. Large positive VE values and small negativeΔnD valueson mixing attributes to presence of non specific interaction betweencomponent molecules.

Table 5Average deviation in the refractive index (nD) from nine mixing relations for β-pinene(1) + o, m, p-cresol(2) binary mixtures at 303.15, 308.15 and 313.15 K.

Mixing rule 303.15 K 308.15 K 313.15 K

β-Pinene (1) + o-cresol (2)A–B −0.004500 −0.004318 −0.004100G–D −0.004500 −0.004318 −0.004100L–L −0.004260 −0.004086 −0.003873WR −0.006364 −0.006128 −0.005878Heller −0.004244 −0.004070 −0.003856Newton −0.004713 −0.004525 −0.004303Eyring–John −0.004393 −0.004215 −0.003998Eykman −0.004437 −0.004257 −0.004039Oster −0.004637 −0.004451 −0.004230

β-Pinene (1) + m-cresol (2)A–B −0.002936 −0.002733 −0.002573G–D −0.002936 −0.002733 −0.002573L–L −0.002731 −0.002532 −0.002369WR −0.004537 −0.004302 −0.004167Heller −0.002717 −0.002519 −0.002355Newton −0.003120 −0.002913 −0.002755Eyring–John −0.002845 −0.002643 −0.002481Eykman −0.002882 −0.002680 −0.002518Oster −0.003054 −0.002848 −0.002689

β-Pinene (1) + p-cresol (2)A–B −0.002327 −0.002177 −0.002023G–D −0.002327 −0.002177 −0.002023L–L −0.002144 −0.001999 −0.001846WR −0.003754 −0.003570 −0.003408Heller −0.002133 −0.001987 −0.001834Newton −0.002491 −0.002337 −0.002182Eyring–John −0.002246 −0.002097 −0.001943Eykman −0.002279 −0.002130 −0.001975Oster −0.002432 −0.002279 −0.002124

253J. Bhalodia, S. Sharma / Journal of Molecular Liquids 193 (2014) 249–255

Large negative ΔRm values are observed for the binary mixture overentire composition range and at different temperatures. Deviation inmolar refraction is a measure of strength of interactions between soluteand solvent in the mixture. It is sensitive to function of wavelength,temperature and solution composition. Negative ΔRm suggest for weakinteraction.

In general, the positive deviation in ΔnD values on basis of volumefraction indicates for the presence of significant interaction in mixtureswhereas negative deviation in Δn values indicate presence of weakinteractions [19].

The observed trend in ΔnD values are

β‐pineneþ o‐cresol b β‐pineneþm‐cresol b β‐pineneþ p‐cresol:

The observed trend in ΔRm values are

β‐pineneþ o‐cresol b β‐pineneþm‐cresol b β‐pineneþ p‐cresol:

ΔnD andΔRm values increasewith increase of temperature for all thebinaries indicating that interactions between unlike molecules weakenwith rise of temperature. This further supports our earlier conclusionthat VE and ΔnD values are opposite in sign and are in agreement withthe view proposed by Brocco et al. [18].

3.3. Refractive index mixing rules

The refractive index of a liquid mixture can be predicated fromdensity together with the refractive indices and densities of purecomponents by using various mixing rules available in literature[20].

Here, we present nine mixing rules to calculate the refractive indexof the present systems and compare them with experimentallymeasured values.

Arago–Biot (A–B) [21]

nD ¼ nD1ϕ1 þ nD2

ϕ2: ð10Þ

Dale–Glastone (D–G) [22]

nD−1 ¼ nD1−1

� �ϕ1 þ nD2

−1� �

ϕ2: ð11Þ

Lorentz–Lorenz (L–L) [23]

n2D−1

n2D þ 2

¼ n2D1−1

n2D1

þ 2

!ϕ1 þ

n2D2−1

n2D2 þ 2

!ϕ2: ð12Þ

Eykman (Eyk) [24]

n2D−1

n2D þ 0:4

¼ n2D1−1

n2D1

þ 0:4

!ϕ1 þ

n2D2−1

n2D2 þ 0:4

!ϕ2: ð13Þ

Weiner (WR) [25]

n2D−n2

D1

n2D þ 2n2

D1

!¼ ϕ2

n2D2−n2

D1

n2D2

þ 2n2D1

!: ð14Þ

Heller (Hr) [26]

nD−nD1

nD1

¼ 32

nD2−nD1

� �2−1

nD2−nD1

� �2 þ 2

0B@

1CAϕ2: ð15Þ

Newton (Nw) [27]

n2D1−1 ¼ n2

D1−1

� �ϕ1 þ n2

D2−1

� �ϕ2: ð16Þ

Oster (Os) [28]

n2D−1

� �2n2

D þ 1� �n2D

24

35V ¼

n2D1−1

� �2n2

D1þ 1

� �n2D1

24

35x1V1

þn2D2−1

� �2n2

D2þ 1

� �n2D2

24

35x2V2: ð17Þ

Eyring–John (E–J) [29]

nD ¼ nD1ϕ21 þ 2 nD1

nD2

� �1=2ϕ1ϕ2 þ nD2

ϕ22: ð18Þ

In all these equations, nD is refractive index of mixture, nD1 is refrac-tive index of pure component-1, nD2 is refractive index of purecomponent-2, ϕ1 is volume fraction of pure component-1 and ϕ2 isvolume fraction of pure component-2.

The predicted refractive indexes of binary mixtures at each temper-ature studied were compared with experimentally measured valuesand the results are presented in Table 5 in terms of average deviation.The deviation between theoretically calculated and experimentallyobserved values of refractive indexes can further be reduced by takinginto consideration the concept of excess volume and volume additivityas suggested earlier [4].

A close look at Table 5 reveals that allmixing rules show good agree-ment for present binary systems. The values of average deviationobtained for Arago–Biot and Dale–Glasston are similar for the presentsystem as expected because equation of Dale–Glasston gets reduced to

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tra

nsm

ittan

ce [

%]

Wavenumber (cm-1)

4000 3500 3000 2500 2000 1500 1000 500

Fig. 5. Experimental IR transmittances spectra at 298.15 K for β-pinene ( ), m-cresol(—) and β-pinene + m-cresol (—).

254 J. Bhalodia, S. Sharma / Journal of Molecular Liquids 193 (2014) 249–255

Arago–Biot if volume additivity is assumed. Heller relation showssmallest deviation. In fact Dale–Glasston equation formulated for vol-ume additivity is a limiting case of Heller's equation. However, Weinerequation shows relatively larger deviation for binary mixtures. Weinerequation is based on the assumption that molecules of both compo-nents are spherically symmetrical. It is also clear that average deviationvalues become larger as temperature increases as expected.

3.4. FT-IR study

It is assumed that the possible molecular interactions will alterthe spectroscopic characteristics of the binary mixtures as comparedto pure components (Figs. 4 to 6). In order to investigate theprime \OH bonded complex and intermolecular association betweenβ-pinene + cresols, the spectra was recorded near 1:1 molar volumeand 0.39 mole fraction of β-pinene at 298.15 K. The test is focused onaromatic C\H stretching at 3070 cm−1 and aromatic ring stretchingat 1475 cm−1 for cresols. The frequencies of o-, m-, and p-cresol at754; 776; 853; and 815 cm−1 respectively are obtained due to substitu-tion on phenyl ring.

The free\OH band due to stretching at 3418 cm−1 and bending at1329 cm−1 is obtained for o-cresol. Similarly, these two frequencies areobtained at 3321; 1339; 3324; and 1362 cm−1 for m-cresol andp-cresol respectively. Some of the frequencies show shift which areshown in Table 6. A change in IR frequencies is observed from 5 to64 cm−1 in the mixtures with respect to cresols. The shift in the fre-quency indicates that there is specific interaction between β-pineneand cresols. It is well established that for less intensive H-bonding, asharper and less intense band is observed at higher frequency but dueto extensive bonding, broad band appears at lower frequency. The\OH stretching due to free \OH group appear as a sharp bandat 3650–3590 cm−1 but \OH stretching due to intermolecular H-bonding shows broader bandwhich shifts its position to lower frequen-cy appears in the range of 3550–3200 cm−1. In the present study,\OHband shift towards higher frequency and this indicates for the weaken-ing of intramolecular association through intermolecular H-bonding.

Thus, the pattern, position and intensity of\OH band as per IR datastrongly support the conclusion that the molecular association throughH-bonding is maximum at the 0.39 mole fraction of β-pinene for allthese selected binaries and is a weak intermolecular association whencompared to intra molecular association in pure components. The re-sults are the same as explained by Awasthi and Shukla [30]. If Δνshows shift towards higher frequency (positive shift), there is weak-ened intermolecular association between unlike molecules and nega-tive values of Δν i.e. shift towards lower frequency indicates for strongassociation between unlike molecules. Here, β-pinene + cresol mix-tures show positive Δν values with respect to cresols that indicate

4000 3500 3000 2500 2000 1500 1000 500

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tra

nsm

ittan

ce [

%]

Wavenumber (cm-1)

Fig. 4. Experimental IR transmittances spectra at 298.15 K for β-pinene ( ), o-creso l(—) and β-pinene + o-cresol (—).

weakening in intramolecular hydrogen bonded association in cresolsand formation of new H-bonding type of interaction with β-pinenebut this H-bonding is of lower in order as compared to pure compo-nents. The cross bonding between unlike molecules decrease in theorder of o-cresol N m-cresol N p-cresol.

The intensity of\OHabsorption in the range of 3550–3200 cm−1 inthe spectrum of mixture of β-pinene with m-cresol shows less absorp-tion as compared to other selected mixtures. The IR spectrum is relatedto the change in dipole that occurs during the vibration. Consequently,vibrations that produce a large change in dipole (e.g. C_O stretch) re-sult in a more intense absorption than those that result in a relativelymodest change in dipole (e.g. C_C). The overall spectrum is compositeof a group of frequencies, with band intensities in part related to contri-bution of each functional group and each group has its own unique con-tribution based on molar extinction coefficient. The weak interactionsbetween β-pinene with m-cresol results in structure which may leadto less change in dipole moment and lower extinction coefficient value.

4. Conclusion

The positive VE, negative ΔnD and ΔRm values over whole composi-tion range at all temperatures are indicating of weak interactions be-tween component molecules. The values of VE, ΔnD and ΔRm increasewith increase of temperature in all the binarymixtures. The nine refrac-tive index rules namely Arago–Biot, Dale–Gladstone, Lorentz–Lorenz,Eykeman, Weiner, Heller, Newton, Oster and Eyring–John providedexcellent agreement for presently studied binary mixtures. Hellerrelation showed least deviation while Wiener showed relatively larger

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Tra

nsm

ittan

ce [

%]

Wavenumber (cm-1)

4000 3500 3000 2500 2000 1500 1000 500

Fig. 6. Experimental IR transmittances spectra at 298.15 K for β-pinene ( ), p-cresol (—)and β-pinene + p-cresol (—).

Table 6Shift of bands for equimolar solutions of β-pinene (1) + o, m, p-cresol (2) binary mixtures at 298.15 K in FT-IR spectroscopy.

Mixture ν\OH stretching νC\H

aromatic stretchingν_CH2

olefinic stretchingν_CH2

olefinic symmetricstretching

ν_CH2

wagging exocyclic bondν\CH3

geminal methylgroup

β-Pinene – – 3070 2982 875 1382 1366o-Cresol 3418 3033 – – – – –

m-Cresol 3321 3040 – – – – –

p-Cresol 3324 3024 – – – – –

β-Pinene + o-cresol 3423 3033 3069 2978 874 1382 1365β-Pinene + m-cresol 3346 3040 3070 2978 874 1382 1365β-Pinene + p-cresol 3388 3023 3070 2979 876 1382 1365Shift of β-pinene + o-cresol 5 0 −1 −4 −1 0 −1Shift of β-pinene + m-cresol 25 0 0 −4 −1 0 −1Shift of β-pinene + p-cresol 64 −1 0 −3 −2 0 −1

255J. Bhalodia, S. Sharma / Journal of Molecular Liquids 193 (2014) 249–255

deviation. Positive shift in IR frequencies of mixtures with respect topure cresols indicate weakening of intermolecular association in cresolsand development of new weak interactions with β-pinene.

Acknowledgements

The authors thank the UGC (New Delhi) for financial assistance.

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