Densities, speeds of sound, refractive indices, excess and partial molar properties of polyethylene glycol 200 + methyl acrylate or ethyl acrylate or n-butyl acrylate binary mixtures at temperatures from 293.15 to 318.15 K

Accepted Manuscript Densities, speeds of sound, refractive indices, excess and partial molar properties of polyethylene glycol 200 + methyl acrylate or ethyl acrylate or n-butyl acrylate binary mixtures at temperatures from 293.15 to 318.15 K

Neha Chaudhary, Anil Kumar Nain PII: DOI: Reference:

S0167-7322(18)33443-3 doi:10.1016/j.molliq.2018.09.020 MOLLIQ 9626

To appear in:

Journal of Molecular Liquids

Received date: Revised date: Accepted date:

4 July 2018 2 September 2018 4 September 2018

Please cite this article as: Neha Chaudhary, Anil Kumar Nain , Densities, speeds of sound, refractive indices, excess and partial molar properties of polyethylene glycol 200 + methyl acrylate or ethyl acrylate or n-butyl acrylate binary mixtures at temperatures from 293.15 to 318.15 K. Molliq (2018), doi:10.1016/j.molliq.2018.09.020

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ACCEPTED MANUSCRIPT Densities, speeds of sound, refractive indices, excess and partial molar properties of polyethylene glycol 200 + methyl acrylate or ethyl acrylate or n-butyl acrylate binary mixtures at temperatures from 293.15 to 318.15 K Neha Chaudhary and Anil Kumar Nain*

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Department of Chemistry, Dyal Singh College (University of Delhi), New Delhi – 110 003, India

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MA

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*Corresponding author: Tel.: 91-9810081160; Fax: 91-11-24365606 E-mail address: [email protected]

ACCEPTED MANUSCRIPT Abstract The densities, , speeds of sound, u and refractive indices, nD of binary mixtures of polyethylene glycol 200 with methyl acrylate, ethyl acrylate, n-butyl acrylate, including those of pure liquids, over the entire composition range were measured at temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric pressure. Using the

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experimental data, the excess molar volume, VmE , excess molar isentropic compressibility,

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E Ks,m , excess speed of sound, u E , deviations in refractive index,  nD , deviations in molar

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refraction, RM have been calculated. The partial molar volumes and compressibilities,

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excess partial molar volumes and compressibilities over the whole composition range, and at infinite dilution have also been calculated. The excess properties were correlated by the

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Redlich–Kister polynomial equation. The variations of these parameters with composition and temperature are discussed in terms of intermolecular interactions in these mixtures.

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Moreover, the values of ultrasonic speeds for these mixtures were also calculated by using

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scaled particle theory and the results are compared with the experimentally measured values.

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Keywords: Polyethylene glycol 200; Alkyl acrylates; Density; Speed of sound; Refractive index; excess properties; Intermolecular interactions; Scaled particle theory.

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ACCEPTED MANUSCRIPT 1. Introduction The physicochemical properties of pure components and their liquid mixtures, such as density, speed of sound, viscosity, refractive indices, heat capacity, activity coefficients at infinite dilution and excess molar volume and liquid-liquid equilibria are required for developing reliable predictive models for understanding the interaction occurring among the

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molecules in liquid mixtures [14]. The mixing of two or more different solvents give rise to

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excess properties of solution with non-ideal behavior. The deviations from ideality of

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thermodynamic properties of liquid mixture, undergoing specific interactions are due to difference in the molecular size, shape and structure [5]. The density, speed of sound and

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refractive index data of liquid mixtures are useful in the study of intermolecular interaction that occur between solute-solvent, solute-solute interactions and solvent-solvent interaction

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[6,7].

Polyethylene glycols (PEGs) have low vapour pressure and low toxicity and they are

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highly biodegradable polymers. PEGs have received great attention as a class of chemical

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substances which are widely used in industrial applications [8]. PEGs are important because

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of presence of both good proton acceptor as well as proton donor groups [9] and are used in variety of industrial and pharmaceutical applications, viz., in the cleaning of exhaust air and gas streams, textile fields, processed foods, lubricants, humectants, cosmetics and drugs [10,11]. Acrylates are very important industrial chemicals and are widely used commercially for production of technically important special type highly latex and polymeric compounds [12]. The double bonds of acrylates are very reactive so they easily form the polymers which are highly used in industry [13]. Alkyl acrylates are frequently used in many applications such as leather, textiles, adhesives, paints, antioxidant agents, inks, amphoteric surfactants, paper, detergents, surface coatings, etc. [14]. Therefore, the study of intermolecular

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ACCEPTED MANUSCRIPT interactions of PEG 200 with alkyl acrylate (methyl acrylate, ethyl acrylate and n-butyl acrylate) mixtures would be interesting owing to their industrial applications. This work reports experimental densities, , speeds of sound, u and refractive indices, nD data for binary mixtures of PEG 200 with methyl acrylate (MA), ethyl acrylate (EA), n-butyl acrylate (n-BA), including those of pure liquids, over the entire composition range at

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temperatures (293.15, 298.15, 303.15, 308.15, 313.15 and 318.15) K and atmospheric

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E pressure. From the experimental data, the excess properties, viz., VmE , Ks,m , u E ,  nD and

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RM have been calculated. The partial molar volumes, Vm,1 and Vm,2 , excess partial molar

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E E volumes Vm,1 and Vm,2 of the components over whole composition range and at infinite

dilution ; the partial molar compressibilities, K s,m,1 and K s,m,2 , and excess partial molar E

MA

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isentropic compressibilities, K s,m,1 and K s,m,2 over the whole composition range and at

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infinite dilution have also been calculated. The variations of these parameters with the

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composition and temperature have been discussed in terms of intermolecular interactions prevailing in these mixtures. The values of ultrasonic speeds have also been calculated

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theoretically for these mixture by using scaled particle theory and compared with the experimental findings. 2. Experimental 2.1. Materials

The polyethylene glycol 200 (Thomas Baker, India, mass fraction purity > 0.99), methyl acrylate (CDH, India, mass fraction purity > 0.99), ethyl acrylate (Spectrochem, India, mass fraction purity > 0.99), n-butyl acrylate (CDH, India, mass fraction purity > 0.99) used in the study were purified by using the methods described in the literature [15,16]. The water content of the purified chemicals was estimated by Karl Fischer titration using Karl Fisher coulometer (890 KF Titrando, Metrohm, USA). The purities and other specification of

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ACCEPTED MANUSCRIPT chemicals are listed in Table 1. Prior to use, all the chemicals were stored over 0.4 nm molecular sieves for 72 h to remove water content, if any, and were degassed at low pressure. The mixtures were prepared by mass and were kept in special airtight stopper glass bottles to avoid evaporation. The weighing was done by using an electronic balance (Model: GR-202, AND, Japan) with a precision of 0.01 mg. The uncertainty in the mole fraction was

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estimated to be less than 1 × 104.

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2.2 Apparatus and Procedure

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The densities of pure liquids and their binary mixtures were measured by using a singlecapillary pycnometer (made of Borosil glass) having a bulb capacity of ~10 cm 3. The

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capillary with graduated marks had uniform bore and could be closed with a well-fitted cap. The marks on the capillary were calibrated by using triply distilled water. The uncertainty in

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density measurement was found within 0.02 kg·m3. The ultrasonic speeds in pure liquids

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and in their binary mixtures were measured using a single-crystal variable-path

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multifrequency ultrasonic interferometer (Mittal Enterprises, India, Model: M81S) operating at 3 MHz. The uncertainty in ultrasonic speed measurements was within 0.5 m·s1. The

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refractive indices of pure liquids and their binary mixture were measured using a thermo stated Abbe refractometer. The values of refractive index were obtained using sodium D light. The temperature of the test liquids between the prisms of refractometer during the measurements was maintained to an accuracy of 0.01 K by circulating water through the jacket around the prisms from an electronically controlled thermostatic water bath and the temperature was measured with a digital thermometer connected with the prism jacket. The uncertainty in refractive index measurements was within 0.0001. The temperature of the test liquids during the measurements was maintained to an uncertainty of 0.01 K in an electronically controlled thermostatic water bath (JULABO, Model: ME-31A, Germany).

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ACCEPTED MANUSCRIPT The reliability of experimental measurements of ρ, u and nD was ascertained by comparing the experimental data of pure liquids with the corresponding literature [1741] values at all the investigated temperatures. This comparison is given in Table 2 and the agreement between the experimental and the literature values is found satisfactory. 3. Results and Discussion

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The experimental values of densities, , speeds of sound, u and refractive indices, nD for

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the binary mixtures of PEG 200 with MA, EA and n-BA over the entire composition range,

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expressed in mole fraction, x1 of PEG 200 at different temperatures are given in Tables 35. 3.1. Excess properties

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E The excess molar volume, VmE , excess molar isentropic compressibility, Ks,m , excess

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speed of sound, u E , deviations in refractive index,  nD , deviations in molar refractions,

RM have been calculated by using the following relations [4245]

E id Ks,m  Ks,m  Ks,m

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uE  u  ( id ksid )1/ 2

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(1)

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VmE  Vm  ( x1Vm,1  x2Vm,2 )

(2) (3)

1/ 2

 nD  nD  1 (nD,1 )2  2 (nD,2 )2 

(4)

RM  RM  [ x1RM,1  x2 RM,2 ]

(5)

where Vm is the molar volume,  is volume fraction, the superscript 1 and 2 refer to pure PEG200 and acrylates, respectively, and superscript ‘id’ represents ideal mixture. The values id id of Vm, K s,m ,  , s, Ks,m ,  and RM have been calculated by using the following relations

[44,45] Vm  ( x1M1  x2 M 2 ) / 

(6)

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ACCEPTED MANUSCRIPT K s,m   sV

(7)

s 1/ u2

(8)

 id  x11  x2 2

(9)

2

i  xiVm,i /  xiVm,i

(10)

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i 1

(11)

 n2  1  RM   2D  Vm n  2  D 

(12)

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 x1 (Vm,1 p,1 )2 x2 (Vm,2 p,2 ) 2 (Vmid pid ) 2  id Ks,m  x1Ks,m,1  x2 Ks,m,2  T     C C Cpid  p,1 p,2 

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where M is the molar mass and p is the isobaric expansivity, Cp is the molar isobaric heat

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capacity. The values of Vmid ,  pid and Cpid are calculated by using following relations

Vmid  x1Vm,1  x2Vm,2

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Cpid  x1Cp,1  x2Cp,2

(14)

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pid  1p,1  2p,2

(13)

(15)

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The values of p are calculated from the temperature dependence of the density data of pure liquids by using the relation, (–1/)(/T)p) and Cp values for the pure liquids at few required temperatures have been calculated using group contribution method [46]. The values E of VmE , Ks,m , u E ,  nD and RM have been fitted to a Redlich-Kister type polynomial

equation [47] polynomial equation; j

Y  x1 (1  x1 ) Ai 1  2 x1  E

i

(16)

i 0

E where Y E is VmE or Ks,m or u E or  nD or RM . The volume fraction,  has been used in

place of x for fitting of  sE and  nD . The value of coefficients, Ai were evaluated by using

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ACCEPTED MANUSCRIPT the method of least squares regression, with all points weighted equally. The optimal number of Ai coefficients has been determined statistically by performing F-test. The standard deviations,  of fit have been calculated by using the relation E E    YCalc.  YExpt.  

2

1/ 2

 n  j 

(17)

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where n is the number of experimental data points and j is the number of Ai coefficients considered (j+1 in the present study). The coefficients, Ai and corresponding standard

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E deviations,  of fit for the mixtures are listed in Table 6. The variations of VmE , Ks,m , uE ,

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 nD and RM with composition along with smoothed values from Eq. (16) at studied

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temperatures are shown graphically in Figs. 17, respectively.

The sign and magnitude of excess functions resulting on mixing of the components is the

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result of several effects that can operate in the same or in the opposite direction [48]. The

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magnitude VmE depends upon the expansion and contraction of volume of liquids due to

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mixing. The factors that are mainly responsible for volume expansion and contraction, i.e.

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positive or negative values VmE are due to chemical, physical and structural effects of components in mixture. The chemical contributions which involves the breaking the associates that are present in the pure liquids, resulting in positive values. The physical contributions comprise of dispersion forces and non-specific physical interactions, also result in positive values VmE . The chemical contributions also involve the strong specific interactions such as formation of H-bonding, charge transfer complexes, and strong dipole-dipole of between the component molecules of the mixture leads to negative values. The structural contributions are due to the changes of interstitial accommodation (favorable/unfavorable) of the molecules of one component into other molecules of second component resulting in negative/positive VmE values.

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ACCEPTED MANUSCRIPT Figure 1 indicates that the VmE values are negative for PEG 200 + MA/EA/n-BA binary mixtures over the entire mole fraction range and at each investigated temperature. The molecules of PEG 200 are associated through hydrogen bonding in pure state, mixing of acrylates with PEG 200 would induce mutual dissociation of the hydrogen bonds present in pure PEG with subsequent formation of new strong hydrogen bonds between the terminal

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hydrogen atom of hydroxyl group of PEG and carbonyl group of acrylates molecules, leading

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to contraction in volume of mixture, which results in negative VmE values. The values of VmE

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for these mixtures follows the order: MA < EA < n-BA (Fig. 2), which indicates that the order of interaction between PEG 200 and acrylates molecules follows: MA > EA > n-BA,

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this due to fact that as the size of alkyl group in acrylates molecules increases from methyl to

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butyl, the closer approach of PEG 200 and acrylate molecules becomes increasingly difficult due to steric hindrance, which results in decreased in interaction between unlike molecules,

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E leading to expansion in volume. The Vm values become more negative with increase in

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temperature, which may be attributed to increased physical interactions as a result of greater interstitial accommodation of smaller acrylates molecules into the voids created by the larger

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PEG 200 molecules due to increase in free volume between PEG 200 molecules. The results presented in Fig. 3 indicates that values are negative for the systems over the E

entire mole fraction range and temperature. The observed negative Ks,m values confirms the specific interaction (hydrogen bonding) in these systems through a better interstitial accommodation of smaller molecules of acrylates into the voids created by PEG 200 molecules, leading to increase in free volume and decrease in compressibility of the mixture, E E which results in negative Ks,m values. In case of higher alkyl group the magnitude of Ks,m

values increase and follows the sequence MA < EA < n-BA (Fig. 4). The plausible interpretation for the observed order may be the steric hindrance caused by bulkier alkyl

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ACCEPTED MANUSCRIPT group in acrylates. With the increase in size of alkyl group from methyl to butyl, the closer approach of PEG 200 and acrylate molecules becomes increasingly difficult due to steric hindrance, which results in decreased in interaction between unlike molecules, leading to E increase in compressibility. These trends in values of Ks,m further support the conclusions

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E drawn from the variations of Vm values.

A perusal of Fig. 5 indicates that the values of u E are positive over entire composition

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range for the binary mixtures of PEG 200 + MA/EA/n-BA at the investigated temperatures.

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E The magnitude of u plays an important role in describing molecular rearrangements as a

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result of molecular interactions occurring in liquid mixture. In general, positive deviations in

u E indicate the presence of significant interactions and negative deviations in u E indicate

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weak interactions between the component molecules in the mixtures [49,50]. The observed E positive values of u indicates that the molecular order originating from the mixing process

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is larger than the one from ideal behavior. These binary mixtures indicate significant

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interactions involving formation of hydrogen bonding interactions between the component

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E molecules of the mixture. The values u of these mixtures follows the order: MA > EA > n-

BA, which indicate the order of interactions between PEG 200 and acrylates molecules in the same sequence.

The deviations in refractive index,  nD represents the electronic perturbation due to mixing of molecules and is a measure of the quantity of interaction. From Fig. 6, it can be observed that the values of  nD for these binary mixtures are positive over the whole composition range. The magnitudes of  nD at equimolar composition of these mixtures follow the order: MA > EA > n-BA. The strength of intermolecular interactions is indicated by the magnitude of  nD . The intermolecular interactions are more prominent in the

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ACCEPTED MANUSCRIPT mixtures with higher  nD . In general, the positive deviations in  nD values are considered due to presence of significant interactions in the mixtures, whereas negative deviations in   nD values indicate weak interactions between the components of the mixture. The

observed positive  nD values are due to the hydrogen bonds formed between the unlike

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molecules of PEG 200 and acrylates in mixing process, which are stronger than the breaking

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up of self-associations. Also, the  nD values are found opposite to the sign of excess molar

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volumes VmE for all the three binary mixtures (Figs. 2 and 6), which agrees with the view proposed by Brocos et al. [51,52]. This further reinforces our earlier conclusions regarding

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the intermolecular interactions from the variations of VmE values of these mixtures.

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Figure 7 indicates that the deviations in molar refraction, RM are positive for binary mixtures (PEG 200 + MA/EA/BA) over the entire composition range for and temperatures.

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The observed positive RM values indicate that significant interactions are prevailing

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between unlike molecules in these mixture leads to more efficient packing in the mixture than in pure liquids. The magnitude of RM follows the sequence MA > EA > n-BA. This trend

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can be interpreted as the weakening of interactions on moving from MA to n-BA, which is due to increase in the free volume of the mixture. 3.2. Partial molar properties

The partial molar properties (partial molar volume and partial molar compressibility),

Y m,1 of component 1 (PEG 200) and Y m,2 of component 2 (acrylate) in these mixtures over entire composition range were calculated by using the following relations [53]





(18)





(19)

* Y m,1  Y E  Ym,1  x2 Y E / x1

* Y m,2  Y E  Ym,2  x1 Y E / x1

T, p

T, p

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ACCEPTED MANUSCRIPT * * where Y is Vm or Ks; Ym,1 and Ym,2 are the molar properties for pure components, PEG 200

and acrylates, respectively. The derivative, (Y E / x1 )T,p in Eqs. (18) and (19) was obtained by differentiation of the Eq. (16), which leads to the following equations for Y m,1 and Y m,2 n

n

i 0

i 1

n

n

i 0

i 1

* Y m,1  Ym,1  x22  Ai (1  2 x1 )i  2 x1 x22  Ai (1  2 x1 )i 1

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(20)

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* Y m,2  Ym,2  x12  Ai (1  2 x1 )i  2 x12 x2  Ai (1  2 x1 )i 1

E

(21)

E

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By using the values of excess partial molar properties, Y m,1 and Y m,2 over the whole

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composition range were calculated by using the following relations [54] E

* Y m,1  Y m,1  Ym,1 E

MA

* Y m,2  Y m,2  Ym,2

(22)

E

(23)

E

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The values of V m,1 , V m,2 , V m,1 and V m,2 as functions of mole fraction, x1 of PEG 200 for the

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three systems at investigated temperatures are listed in Tables S1S6 given as supplementary E

E

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material. The variations of V m,1 and V m,2 with mole fraction, x1 of PEG 200 for these systems at 298.15 K are presented in Fig. 8, respectively. A close perusal of Tables S4S6 E

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and Fig. 7 indicates that the values of V m,1 and V m,2 are negative over the whole composition range for binary mixtures under study. This suggests that the volumes of each component in the mixture are less than their respective molar volumes in the pure state, i.e., there is E

decrease in volume on mixing PEG 200 with acrylates. In general, the negative V m,1 and E

V m,2 values indicate the presence of significant solute-solvent interactions between unlike E

E

molecules, whereas the positive V m,1 and V m,2 values indicate presence of solutesolute/solvent-solvent (or weak solute-solvent) interactions [55] between like molecules in

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ACCEPTED MANUSCRIPT E

E

the mixture. The negative value of V m,1 and V m,2 at equimolar composition follow the order MA > EA > n-BA, which indicates that the order of interaction in this same order. E

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The values of Ks,m,1 , Ks,m,2 , K s,m,1 and K s,m,2 as functions of mole fraction, x1 of PEG 200 for the three systems at investigated temperatures are listed in Tables S7S12 given as E

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supplementary material. The values of excess partial molar compressibilities, K s,m,1 and E

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K s,m,2 as with mole fraction, x1 of PEG 200 for these systems at 298.15 K have been shown

E

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graphically in Fig. 9. A close perusal of Tables S1012 and Fig. 9 indicates that the values of E

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K s,m,1 and K s,m,2 are negative for all the investigated binary mixtures over the whole composition range. This suggests the presence of significant solute-solvent interactions E

E

MA

between the molecules in the mixture. In general, the negative K s,m,1 and K s,m,2 values indicate the presence of significant solute-solvent interactions between unlike molecules, E

E

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whereas the positive K s,m,1 and K s,m,2 values indicate presence of solute-solute/solventsolvent (or weak solute-solvent) interactions [55] between like molecules in the mixture. The E

E

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observed negative K s,m,1 and K s,m,2 values indicate significant PEG 200-acrylates interactions.

°

°

The values of partial molar properties, Y m,1 and Y m,2 of PEG 200 and acrylates at infinite dilution were calculated by using equations (18)(21), and the excess partial molar °E

°E

properties, Y m,1 and Y m,2 at infinite dilution were calculated by using the equations (22) and °E

°

E

(23) substituting Y m,i and Y m,i in place of Y m,i and Y m,i , respectively. °

°E

E

°

* * The values of V m,1 , Vm,1 , V m,1 , V m,2 , Vm,2 and V m,2 for all the three binary systems at

the investigated temperatures are listed in Table 7. A close perusal of Table 7 that the values

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ACCEPTED MANUSCRIPT of

°E

E

V m,1 and V m,2 are negative for all the three binary systems at each investigated

temperature. This suggests that the molar volumes of each component in the mixtures are less than their respective molar volumes in the pure state, i.e., there is a contraction in volume on E

°E

mixing PEG 200 with acrylates. The values of V m,1 and V m,2 decreases with increase in

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temperature of mixture, further supports the observed trends for VmE values for these binary systems.

E

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E

°

°

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* * The variations of K s,m,1 , Ks,m,1 , K s,m,1 , K s,m,2 , Ks,m,2 and K s,m,2 for the binary mixtures

E

E

at each investigated temperature are listed in Table 8. The values of K s,m,1 and K s,m,2 are

E

E

K s,m,1 and K s,m,2 is MA < EA < n-BA. This order reflects the order of interactions in

MA

of

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negative for all the binary mixtures of PEG 200 and alkyl acrylates. The order of magnitude

these systems. The compressibility can be analyzed in terms of structural and geometrical

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factors [56,57]. The structural compressibility results from the breakdown of associated

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structure while geometrical compressibility is due to the simultaneous compression of the

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molecules leading to contraction in volume and decrease in the average intermolecular E

E

distance. The observed values of K s,m,1 and K s,m,2 indicate that the geometrical E

E

compressibility factor dominates in these mixtures. Also, K s,m,1 and K s,m,2 values decrease with increase in temperature leading to compression in volume of the mixture. These trends E further support the conclusions drawn from the variations of  sE , u E and Ks,m values for

these binary mixtures. 3.4. Scaled particle theory The theoretical speed of sound in binary mixtures may be estimated based on some empirical, semi-empirical and statistical models such as CFT, FLT, Nomoto relation, van

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ACCEPTED MANUSCRIPT Deal-Vangeal relation, etc. for the mixtures [58]. However, all these theoretical models have a common drawback is that the shapes of the participating molecules have not been taken into consideration [59]. SPT is the only theoretical model developed that considers the shape of participating molecules of mixtures [60]. The elementary idea of the SPT is an insertion of an additional scaled particle of a variable size into a fluid. This process is equivalent to a

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formation of cavity, which is free of any other fluid particles. The important point of the SPT

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theory described in consists of a derivation of the excess chemical potential of a scaled

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particle, which is equal to a work required to create the corresponding cavity in fluid [61]. SPT is a statistical model which assumes liquids molecules as hard spheres. Macroscopic

for the work of cavity formation [62].

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parameters such as ultrasonic speed are evaluated by equating them with the relation obtained

MA

In SPT, seven different shapes, such as spherical, cube, tetrahedral, disc A, disc B, disc C and disc D, of the participating components are considered and when the correct shapes are

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assigned to participating components, the theoretical speed of sound estimated based on

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model will give values close to the experimental values [63]. The equation of state of fluid in

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SPT, p 1      N kBT   3

(24)

Where ρN is number density NA/Vo, where Vo is the non-ideal volume of the mixture, η=VH.ρN, VH being hard core volume of the molecule and the other quantities have usual meanings [64]. The equation of state for mixture of hard convex molecules (not necessarily spherical) is given by

AB N p 1   Ν kBT 1  V N  1  V  N





2



B 2C N

   V Ν 

3

Where A=  xi Ri , B   xi Si , C   xi Ri2 ,V   xV i Hi

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(25)

ACCEPTED MANUSCRIPT Ri, Si and VHi are the mean radius of curvature, surface area and volume, respectively, of a molecule of species i, ρN is number density of mixture molecule, xi is the mole fraction. The values of R, S, VH for various shapes are given in Table S13 given as supplementary material. The pressure derivative is related to speed of sound through the following equation,

 dp  2  u  d  T



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(26)

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where ρ is molecular density and γ (= Cp/Cv) is the ratio of specific heats. The values of Cv have been calculated using the following thermodynamic relation [65]

𝐶𝑣

=

𝑇 𝑠

SC

𝐶𝑃

(27)

NU

where T is the isothermal compressibility. Combining equations (25) and (26), we get

MA

N N2 Mu 2 1 2   2 AB  B C 3 4  RT 1  V N 2 1  V N  1  V N 

(28)

D

Equation (28) is used to evaluate the speed of sound in binary mixtures theoretically. For pure

η= VH. ρN. 2

AC CE P

Mu 2 1   X  1   4  RT 1  

TE

liquids, Eq. (28) is modified by introducing dimensionless shape parameters, X=RS/VH and

(29)

Its solution is obtained as [65]

  K  K 2  L 1

(30)

Where K=1+L(X1)/2 and L=  RT / Mu 2 . The obtained values of η are listed in Table S14 given as supplementary material. The mean radius and surface area of a molecule can be written as R=YV1/3 and S=ZR2

(31)

16

ACCEPTED MANUSCRIPT Where Y and Z are the parameters related to shape of the molecule. Different values of X, Y and Z can be calculated for the different shapes as listed in Table S15 given as supplementary material. The deviations of calculated speed of sound obtained using SPT from the experimental speeds for all mole fractions, for each system at the temperature 298.15 K for various shape

calc

 uexpt 

RI

u

uexpt

(32)

SC

du 

PT

combinations of constituent molecules are calculated by using the equation [65]

Where ucalc and uexpt are the theoretical and experimental speeds of sound, respectively. The

NU

absolute values of deviations are summed up for all the mole fractions for a particular binary mixture giving Σdu. In this paper, theoretical speeds of sound of the mixtures are estimated

with experimental speeds of sound.

MA

by assigning the above said seven shapes to the participating molecules and compared them

D

In the present investigation, the theoretical speeds of sound based on SPT is computed for

TE

the PEG 200 + alkyl acrylates mixtures by considering different shapes, viz., sphere, cube,

AC CE P

tetrahedron, disc A, disc B, disc C and disc D for both the participating components. Hence for a binary mixture there are 49 combinations of shapes at a particular temperature. By assigning these seven shapes to each of the component molecules, theoretical speeds of sound were calculated. Further, the deviation of theoretical speed of sound from experimentally observed values is determined by sum deviation. The minimum deviation is observed when the participating molecules are assigned correct shapes. The theoretically predicted speeds of sound considering shapes for which minimum deviations were obtained for the binary mixture of PEG 200 with MA/EA/n-BA at 298.15 K are provided in Table 9. The minimum deviation (0.2715) for theoretically calculated speed of sound for PEG 200 + MA molecules is obtained when the molecules are assigned the shapes of disc B and disc C

17

ACCEPTED MANUSCRIPT respectively. Similarly, in case of PEG 200 + EA, when the shape of participating molecules is assumed to be disc C and disc B, the theoretical ultrasonic speeds closely agrees well with the experimental values at 298.15 K with a deviation of 0.2868. In case of PEG 200 + n-BA, the minimum deviation (0.2325) is obtained when the disc C and disc D shape are considered for the participating species. The scaled particle theory (SPT) predicted the speeds of sound

PT

for these mixtures satisfactorily and reasonably well.

RI

3.5. Prediction of refractive index

SC

The refractive indices of the investigated mixtures have been predicted from pure component data in term of average percentage deviation by employing semi-empirical mixing

NU

rules proposed by Arago and Biot (A-B) [67], Gladstone and Dale (G-D) [68], Lorentz and Lorentz (L-L) [69], Heller (H) [70], Eykman (EK) [71] and Weiner (W) [72] mixing rules.

MA

The deviations between predicted and experimental values have been expresses in terms of average percentage deviations (APDs) calculated by using the following relation

D

 1  (nDExpt.  nDCalc. ) APD   100 Expt. m nD 

TE

(32)

AC CE P

Where m is the number of data points. The values of average percentage deviations (APDs) at each investigated temperature are presented in Table 10. A close perusal of Table 10 revealed that the APDs in theoretically calculated refractive indices by using these correlating equations are between 0.175 to 0.414 for PEG 200 + MA, 0.120 to 0.405 for PEG 200 + EA and 0.065 to 0.186 for PEG 200 + n-BA mixtures. It is observed that EK relation predicts the refractive indices values best, followed by A-B and GD relations and then by Weiner and then by L-L and Heller relations for all the three systems under study. The APDs for these mixtures follow the order: MA > EA > n-BA, indicating that the interactions in these mixtures follow the same order: MA > EA > n-BA, which further supports our earlier conclusion regarding interactions in these mixtures derived from

18

ACCEPTED MANUSCRIPT excess and partial molar properties of these systems. Also, The APDs for these mixtures increase with increase in temperature suggesting increased interactions between the unlike molecules leading to a decrease in volume and compressibility, as observed in trends of

AC CE P

TE

D

MA

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SC

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PT

excess properties also.

19

ACCEPTED MANUSCRIPT 4. Conclusion The present study reported the densities, , speeds of sound, u and refractive indices, nD of the binary mixtures of PEG 200 with MA/EA/n-BA over whole composition range at six different temperatures. From the experimental data, various physicochemical parameters, viz.,

PT

E E , u E , nD and Rm of the mixtures; Vm,1 and Vm,2 , Ks,m,1 and Ks,m,2 , Vm,1 and VmE , Ks,m E E E ° °  ° and Ks,m,1 and Ks,m,2 over whole composition range; Vm,1 and Vm,2 ; Ks,m,1 and Ks,m,2 ; Vm,2

SC

RI

°E °E E °E and Vm,2 and Ks,m,1 and Ks,m,2 of the components infinite dilution have been calculated. Vm,1

The results have been discussed in terms of intermolecular interactions in these mixtures. The

NU

results indicate that the presence of strong interactions through strong hydrogen bonding between the unlike molecules of PEG 200 and MA/MA/n-BA molecules. The results

MA

indicated that the dipole-dipole interactions in these systems follow the order: MA > MA > nBA. The scaled particle theory was found successful in predicting the u values over whole

D

composition range and at 298.15 K. The refractive indices of the mixtures were predicted

TE

from pure component data by using various mixing rules, the predicted nD values compared

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well with the experimental findings.

20

ACCEPTED MANUSCRIPT References [1]

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[10] D. S. Soane, Polymer Applications for Biotechnology, Prentice Hall: Englewood Cliffs,

MA

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[11] B.V.K Naidu, K.C Rao, M.C.S Subha, J. Chem. Eng. Data 47 (2002) 379–382. [12] J.A. Dean, Lange's handbook of chemistry, McGraw Hill, New York, 1956.

TE

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D

[13] B.B. Wayland, G. Poszmik, S.L. Mukerjee, M. Fryd, J. Am. Chem. Soc. 116 (1994)

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[15] A.I. Vogel, Text Book of Practical Organic Chemistry, 5th ed., Longman Green, London, 1989.

[16] J.A. Riddick, W.B. Bunger, T. Sakano, Organic Solvents: Physical Properties and Methods of Purification, 4 th ed., Wiley-Interscience, New York, 1986. [17] S. Ottani, D. Vitalini, F. Comelli, C. Castellari, J. Chem. Eng. Data 47 (2002) 1197– 1204.

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ACCEPTED MANUSCRIPT [23] R. Francesconi, A. Bigi, K. Rubini, F. Comelli, J. Chem. Eng. Data 52 (2007) 2020– 2025. [24] J.M. Vuksanovi´, E.M. Živković, I. R. Radovi´, B. D. Djordjevi´, S. P. Šerbanović, M. Lj. Kijevcanin, Fluid Phase Equilibria 345 (2013) 28–44. [25] N. V. Živković, S. S. Šerbanović, M. Lj. Kijevčanin, E. M. Živković, J. Chem. Eng. Data 58 (2013) 3332−3341.

PT

[26] A.K. Nain, S. Ansari, A. Ali, J Solution Chem 43 (2014) 1032–1054. [27] A. Ali, S. Ansari, A.K. Nain, J. Mol. Liq. 178 (2013) 178–184.

[28] A.K. Nain, P. Droliya, J. Chem. Thermodynamics 105 (2017) 317–326.

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[29] J.A. Riddick, W.B. Bunger, T. Sakano, Organic Solvents: Physical Properties and

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Methods of Purification, 4th ed., Wiley-Interscience, New York, 1986. [30] L. Lomba, B. Giner, C. Lafuente, S. Martín, H. Artigas, J. Chem. Eng. Data 58 (2013)

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1193–1202.

[31] N.V. Sastry, M.K. Valand, Phys. Chem. Liq. 38 (2000) 61–72. [32] J. George, N.V. Sastry, S.R. Patel, M.K. Valand, J. Chem. Eng. Data 47 (2002) 262–

MA

269.

[33] J. Wisniak, R.D. Peralta, R. Infante, J. Solution Chem. 34 (2005) 171–183.

D

[34] J. Wisniak, L.E. Sandoval, R.D. Peralta, R. Infante, G. Cortez, L.E. Elizalde, H. Soto, J.

TE

Solution Chem. 36 (2007) 135–152. [35] R.D. Peralta, R. Infante, G. Cortez, R.R. Ramirez, J. Wisniak, J. Chem. Thermodyn.35 (2003) 239–250.

AC CE P

[36] W. Liau, M. Tang, Y. Chen, J. Chem. Eng. Data 43 (1998) 826–829. [37] R.D. Peralta, R. Infante, G. Cortez, J. Wisniak, J. Solution Chem. 33 (2004) 339–351. [38] A.K. Nain, J.Chem. Thermodyn. 59 (2013) 49–64. [39] A. Ali, F. Nabi, M. Tariq, Int. J. Thermophys. 30 (2009) 464–474. [40] P. Bahadur, N.V. Sastry, Int. J.Thermophys. 24 (2003) 447–462. [41] V.V. Sergeev, Yu. Ya. Van-Chin-Syan, Russian J. Appl Chem. 85 (2012) 689−691. [42] A. Yadav, A. Guha, A. Pandey, M. Pal, S. Trivedi, S. Pandey, J. Chem. Thermodyn. 116 (2018) 67–75. [43] P. Brocos, A. Pineiro, R. Bravo, A. Amigo, Phys. Chem. Chem. Phys. 5 (2003) 550– 557. [44] G.C. Benson, O. Kiyohara, J. Chem. Thermodyn. 11 (1979) 1061–1064. [45] G. Douheret, M.I. Davis, J.C.R. Reis, M.J. Blandamer, Chem. Phys. Chem. 2 (2001).

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ACCEPTED MANUSCRIPT [46] R.C. Reid, J.M. Prausnitz, B.E. Poling, The Properties of Gases and Liquids, 4th Edn., McGraw Hill Inc., New York, 1987, 139. [47] J. Wisnaik, G. Cortez, R.D. Peralta, R. Infante, L.E. Elizalde, T.A. Amaro, O. Gracia, H. Soto, J. Chem. Thermodyn. 40 (2008) 1671–1683. [48] A. Rodriguez, J. Canosa, J. Tojo, J. Chem. Thermodyn. 35 (2003) 1321–1333. [49] F. Kawaizumi, M. Ohno, Y. Miyahara, Bull. Chem. Soc. Jpn. 50 (1977) 2229–2233.

PT

[50] O. Prakash, S. Sinha, Acustica 54 (1984) 223–225.

[51] P. Brocos, A. Pineiro, R. Bravo, A. Amigo, Phys. Chem. Chem. Phys. 5 (2003) 550–

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557.

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[52] A. Pineiro, P. Brocos, A. Amigo, M. Pintos, R. Bravo, Phys. Chem. Liq. 38 (2000), 251260.

NU

[53] S.V. Latha, G.L. Flower, K.R. Reddy, C.V.N. Rao, A. Ratnakar, J. Mol. Liq. 209 (2015) 153–160.

[54] F. Chen, J. Wu, Z. Wang, J. Mol. Liq. 140 (2008) 6–9.

MA

[55] J.E. Desnoyers, G. Perron, J. Solution Chem. 26 (1997) 749755. [56] L. Hall, Phys. Rev. 73 (1948) 775784.

D

[57] B. Hawrylak, K. Gracie, R. Palepu, J. Solution Chem. 27 (1998) 1731.

TE

[58] H. Reiss, H.L. Frisch, J.L. Lebowitz, J. Chem. Phys. 31 (1959) 369–380. [59] A. Ali, A.K. Nain, N. Kumar, M. Ibrahim, Chinese J. Chem. 21 (2003) 253–260.

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[60] M. Kalidoss, R. Srinivasamoorthy, S. Edwin Gladson, Acust. Acta Acust. 83 (1997) 776–779.

[61] S.M Latifi, H. Modarress, Phy. Chem. Liq. 48 (2010) 117–126. [62] H. Reiss, Adv. Chem. Phy. 9 (1965) 1- 9. [63] K. Rajagopala, S. Chenthilnath, Thermochimica Acta 498 (2010) 45–53. [64] S. Ghosh, K.N. Pande, Y.D. Wankhade, Ind. J. Pure Appl. Phys. 42 (2004) 729–734. [65] D.R. Gaskell, Introduction to the thermodynamics of materials, 5th Edition, Taylor & Francis, New York, 2008. [66] R.M. Gibbons, Mol. Phy. 17 (1969) 8186. [67] D.F.J. Arago, J.B. Biot, Mem. Acad. Fr. (1806) 7–11. [68] D. Dale, F. Gladstone, Philos. Trans. Roy. Soc. Lond. 148 (1858) 887–890. [69] H.A. Lorentz, Theory of Electrons, Leipzig, 1906. [70] W.J. Heller, J. Phys. Chem. 69 (1965) 1123–1129.

23

ACCEPTED MANUSCRIPT [71] I. Prigogine, Molecular Theory of Solutions, North-Holland, Amsterdam, 1957.

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TE

D

MA

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SC

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[72] O. Weiner, Berichte (Leipzig) 62 (1910) 256–260.

24

ACCEPTED MANUSCRIPT Figure captions E Fig. 1. Plots of excess molar volume, Vm vs. mole fraction, x1 of PEG 200 for (a) PEG 200 +

MA, (b) PEG 200 + EA and (c) PEG 200 + n-BA binary mixtures at temperatures, T/K = 293.15, ; At T/K = 298.15, ■; T/K = 303.15, ▲; T/K = 308.15, ●; T/K = 313.15, □; T/K = 318.15, ∆. The points represent experimental values and lines represent values calculated

PT

from Eq. (16). E Fig. 2. Plots of excess molar volume, Vm vs. mole fraction, x1 of PEG 200 for PEG 200 +

RI

MA/EA/n-BA binary mixtures at temperature, T/K = 298.15, MA, ; EA, ■; n-BA, ▲. The

SC

points represent experimental values and lines represent values calculated from Eq. (16). E Fig. 3. Plots of excess molar compressibility, Ks,m vs. mole fraction, x1 of PEG 200 for (a)

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PEG 200 + MA, (b) PEG 200 + EA and (c) PEG 200 + n-BA binary mixtures at temperatures, T/K = 293.15, ; At T/K = 298.15, ■; T/K = 303.15, ▲; T/K = 308.15, ●; T/K = 313.15, □; T/K = 318.15, ∆. The points represent experimental values and lines represent

MA

values calculated from Eq. (16).

E Fig. 4. Plots of excess molar compressibility, Ks,m vs. mole fraction, x1 of PEG 200 for PEG

D

200 + MA/EA/n-BA binary mixtures at temperature, T/K = 298.15, MA, ; EA, ■; n-BA, ▲.

TE

The points represent experimental values and lines represent values calculated from Eq. (16). Fig. 5. Plots of excess speed of sound, u E vs. mole fraction, x1 of PEG 200 for PEG 200 +

AC CE P

MA/EA/n-BA binary mixtures at temperature, T/K = 298.15, MA, ; EA, ■; n-BA, ▲. The points represent experimental values and lines represent values calculated from Eq. (16). Fig. 6. Plots of deviations in refractive index,  nD vs. volume fraction, 1 of PEG 200 for PEG 200 + MA/EA/n-BA binary mixtures at temperature, T/K = 298.15, MA, ; EA, ■; nBA, ▲. The points represent experimental values and lines represent values calculated from Eq. (16). Fig. 7. Plots of deviation in molar refraction, RM vs. mole fraction, x1 of PEG 200 for PEG 200 + MA/EA/n-BA binary mixtures at temperature, T/K = 298.15, MA, ; EA, ■; n-BA, ▲. The points represent experimental values and lines represent values calculated from Eq. (16).

25

ACCEPTED MANUSCRIPT E E Fig. 8. Variations of excess partial molar volumes, (a) Vm,1 and (b) Vm,2 of PEG 200 and

MA/EA/n-BA vs. mole fraction, x1 of PEG 200 for binary mixtures at temperature, T/K = 298.15. PEG 200 + MA, ; PEG 200 + EA, ■; PEG 200 + n-BA, ▲. E

E

Fig. 9. Variations of excess partial molar volumes, (a) K s,m,1 and (b) K s,m,2 of PEG 200 and MA/EA/n-BA vs. mole fraction, x1 of PEG 200 for binary mixtures at temperature, T/K =

AC CE P

TE

D

MA

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SC

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PT

298.15. PEG 200 + MA, ; PEG 200 + EA, ■; PEG 200 + n-BA, ▲.

26

ACCEPTED MANUSCRIPT

Source

PEG 200 (25322-68-3)

Thomas Baker, > 0.99 India

Fractional distillation

> 0.998

< 70

GCb

Methyl acrylate (96-33-3)

CDH, India

> 0.99

Fractional distillation

> 0.995

< 40

GC

Ethyl acrylate (140-88-5)

Spectrochem, India

> 0.99

Fractional distillation

> 0.996

< 60

GC

n-Butyl acrylate (141-32-2)

CDH, India

> 0.99

Fractional distillation

< 60

GC

> 0.994

SC

GC = Gas chromatography

NU

Karl-Fischer titration

b

Purification Final method Mass fraction purity

AC CE P

TE

D

MA

a

Initial mass fraction Purity

27

Water Analysis contenta/ method ppm

PT

Chemical name (CAS number)

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Table 1 Specification of chemicals

ACCEPTED MANUSCRIPT Table 2 Comparison of Experimental values of density, , speed of sound, u, and refractive index, nD of pure liquids with the corresponding values available in the literature at the temperatures, T/K = (293.15 – 318.15) and pressure, p = 101 kPa

PEG 200 293.15

1124.34

298.15

1120.36

303.15

1116.39

308.15

1112.41

1124.8 [21] 1127.0 [22] 1124.8 [23] 1124.31 [25] 1120.98 [17] 1120.96 [18] 1122.4 [20] 1120.7 [21] 1120.34 [24] 1120.34 [25] 1121.12 [26] 1120.98 [27] 1117.01 [17] 1116.30 [19] 1116.6 [21] 1117.0 [22] 1116.9 [23] 1116.36 [24] 1116.37 [25] 1117.18 [26] 1117.2 [27] 1112.39 [25] 1113.21 [26]

313.15

1108.44

Literature

1622.3

1.4601

1.4600 [25]

1.4584

1.4585 [17] 1.4585 [18] 1.4580 [20] 1.4582 [21] 1.4586 [24] 1.4582 [25] 1.4588 [26] 1.4588 [27] 1.4570 [17] 1.4564 [19] 1.4565 [25] 1.4575 [26] 1.4575 [27]

1608.4

1608.6 [20] 1607.3 [26]

PT

Literature

nD Expt

1596.2

MA

Expt

u /m·s−1 Expt Literature

RI

 /kg·m−3

SC

T/K

1596.3 [26]

1.4566

1585.1 [26]

1.4549

NU

Liquid

1108.42 [25] 1109.23 [26] 1108.98 [27] 1104.45 1104.43 [25] 953.51[28] 953.50 [29] 955.313 [30]

1574

AC CE P

Methyl acrylate

TE

D

1585.2

1563.4 1204.7

947.56[28] 949.174 [30] 947.50 [31] 949.2 [39] 941.61[28] 943.005 [30] 943.4 [39]

1183.4

308.15

935.66[28] 936.797 [30] 935.60 [31] 935.62 [32] 937.7 [39] 929.71[28] 930.548 [30] 932.0 [39]

1139.1

923.76[28] 924.254 [30] 925.18 [32]

1118.3

318.15 293.15

298.15

303.15

313.15

318.15

1.4532

1162.2

1117.8

28

1190.33 [30] 1204.6 [38] 1194.5 [39] 1168.97 [30] 1183.6 [38] 1172.1 [39] 1147.56 [30] 1162.2 [38] 1145.6 [39] 1126.66 [30] 1139.1 [38] 1140.0[32,40] 1105.67 [30] 1117.8 [38] 1122.1 [39] 1084.76 [30] 1095.7 [38] 1095.0 [40]

1.4547 [25] 1.4,561 [26] 1.4561 [27] 1.4530 [25] 1.4547[27]

1.4515 1.4030

1.4513 [25]

1.4002

1.400245 [30] 1.4000 [39]

1.3975

1.397495 [30] 1.3979 [39]

1.3948

1.394766 [30] 1.3954 [39]

1.3920

1.391997 [30]

1.3893

1.38923 [30] 1.3944 [39]

ACCEPTED MANUSCRIPT Table 2 Continued

308.15

313.15 318.15 293.15 298.15

303.15 308.15

313.15

318.15

AC CE P

n-Butyl acrylate

1190.4 1166.5

1180.55 [30] 1159.47 [30] 1095.1 [39] 1167.5 [39]

1.4062 1.4036

1144.1

1138.59 [30] 1145.1 [39] 1117.84 [30] 1118.7 [39]

1.4010

1097.23 [30] 1095.1 [39] 1076.72 [30] 1224.69 [30]

1.3956

1204.94 [30] 1207.5 [39]

1.4163

1185.38 [30] 1185.1 [39] 1165.95 [30] 1159.3 [39]

1.4140

1146.1

1146.68 [30] 1135.1 [39]

1.4089

1.408939 [30] 1.4069[39]

1126.6

1127.55 [30]

1.4065

1.406467 [30]

1120.7

1098.1 1077.7 1222.3 1202.6

MA

303.15

921.76 [28] 921.899 [30] 915.95 [28] 915.95 [28] 916.121 [30] 915.963 [33] 915.946 [34] 915.93 [35] 916.2 [39] 910.14 [28] 910.319 [30] 910.6 [39] 904.33 [28] 904.487 [30] 904.60 [31] 904.9 [39] 898.52 [28] 898.626 [30] 899.8 [39] 892.71 [28] 892.732 [15] 898.85 [28] 899.095 [30] 898.60 [36] 894.10 [28] 894.111 [30] 894.10 [31] 893.98 [37] 894.1 [39] 889.35 [28] 889.111 [30] 889.2 [39] 884.60 [28] 884.111 [30] 884.60 [31] 884.4 [39] 879.85 [28] 879.097 [30] 789.04 [36] 879.0 [39] 875.10 [28] 874.067 [30]

D

293.15 298.15

TE

Ethyl acrylate

Literature

nD Expt

PT

Expt

u /m·s−1 Expt Literature

RI

 /kg·m−3

SC

T/K

NU

Liquid

1184.6 1165.1

29

1.3982

1.3928 1.4186

1.4114

Literature

1.403568 [30] 1.4049 [39]

1.400924 [30] 1.4032 [39] 1.398201 [30] 1.4014 [39] 1.395505 [30] 1.3999 [39] 1.392789 [30] 1.4198 [36] 1.4188 [41] 1.416316 [30] 1.4119 [39]

1.413855 [30] 1.4102 [39] 1.411405 [30] 1.4084 [39]

ACCEPTED MANUSCRIPT Table 3 Densities, /kg m3 as a function of mole fraction, x1 of PEG 200 for PEG 200 + MA/EA/n-BA binary mixtures at the temperatures, T/K = (293.15 – 318.15) and pressure, p = 100 kPa x1

T/K 293.15

298.15

303.15

308.15

313.15

318.15

947.56 973.00 995.34 1013.72 1030.02 1046.66 1061.10 1070.86 1079.60 1088.25 1096.04 1102.80 1108.97 1114.86 1120.36

941.61 967.38 989.97 1008.57 1025.06 1041.90 1056.52 1066.38 1075.21 1084.00 1091.87 1098.72 1104.93 1110.88 1116.39

935.66 961.74 984.60 1003.42 1020.08 1037.12 1051.91 1061.90 1070.87 1079.74 1087.71 1094.62 1100.92 1106.89 1112.41

929.71 956.12 979.26 998.27 1015.12 1032.32 1047.28 1057.38 1066.50 1075.48 1083.56 1090.54 1096.90 1102.90 1108.44

923.76 950.50 973.93 993.15 1010.17 1027.53 1042.65 1052.87 1062.08 1071.23 1079.40 1086.47 1092.90 1098.90 1104.45

898.52 922.67 944.88 965.56 984.57 1002.17 1018.36 1032.44 1045.52 1057.71 1069.08 1079.20 1088.73 1098.89 1108.44

892.71 917.08 939.45 960.32 979.47 997.22 1013.55 1027.78 1040.98 1053.27 1064.74 1074.96 1084.58 1094.84 1104.45

PEG 200 + EA

910.14 933.87 955.72 976.07 994.75 1012.05 1027.96 1041.79 1054.62 1066.56 1077.70 1087.62 1096.97 1106.97 1116.39

D

915.95 939.48 961.14 981.30 999.84 1016.97 1032.74 1046.43 1059.14 1070.96 1082.00 1091.82 1101.08 1111.00 1120.36

TE

921.76 945.09 966.55 986.54 1004.92 1021.91 1037.53 1051.09 1063.67 1075.37 1086.30 1096.03 1105.20 1115.04 1124.34

AC CE P

0.0000 0.0725 0.1450 0.2185 0.2920 0.3660 0.4400 0.5095 0.5790 0.6485 0.7180 0.7840 0.8500 0.9250 1.0000

RI

SC

NU

953.51 978.62 1000.70 1018.86 1034.98 1051.41 1065.70 1075.34 1083.96 1092.51 1100.20 1106.90 1113.02 1118.85 1124.34

MA

0.0000 0.0770 0.1539 0.2254 0.2968 0.3797 0.4626 0.5259 0.5891 0.6589 0.7287 0.7956 0.8625 0.9313 1.0000

30

PT

PEG 200 + MA

904.33 928.26 950.30 970.82 989.66 1007.10 1023.16 1037.10 1050.05 1062.11 1073.38 1083.40 1092.84 1102.93 1112.41

ACCEPTED MANUSCRIPT Table 3 Continued x1

T/K 293.15

298.15

303.15

308.15

313.15

318.15

894.10 914.19 933.60 950.94 967.75 985.61 1002.89 1018.57 1033.78 1049.42 1064.57 1078.94 1092.89 1106.83 1120.36

889.35 909.51 928.99 946.38 963.25 981.17 998.52 1014.26 1029.52 1045.22 1060.42 1074.84 1088.84 1102.82 1116.39

884.60 904.82 924.37 941.82 958.75 976.74 994.15 1009.94 1025.26 1041.00 1056.27 1070.73 1084.78 1098.80 1112.41

879.85 900.14 919.75 937.26 954.25 972.30 989.77 1005.62 1021.00 1036.80 1052.12 1066.63 1080.72 1094.79 1108.44

875.10 895.46 915.15 932.72 949.75 967.87 985.40 1001.31 1016.74 1032.60 1047.96 1062.53 1076.66 1090.77 1104.45

RI

SC

NU

TE

D

MA

898.85 918.86 938.21 955.49 972.24 990.03 1007.26 1022.89 1038.04 1053.63 1068.72 1083.04 1096.95 1110.85 1124.34

AC CE P

0.0000 0.0730 0.1459 0.2131 0.2802 0.3538 0.4274 0.4963 0.5651 0.6381 0.7110 0.7823 0.8535 0.9268 1.0000

31

PT

PEG 200 + n-BA

ACCEPTED MANUSCRIPT Table 4 Speeds of sound, u/m s1 as function of mole fraction, x1 of PEG 200 for PEG 200 + MA/EA/n-BA mixtures at the temperatures, T/K = (293.15 – 318.15 and pressure, p = 101 kPa x1

T/K 293.15

298.15

303.15

308.15

313.15

318.15

0.0000 1204.7 0.0770 1244.3 0.1539 1287.2 0.2254 1325.3 0.2968 1361.6 0.3797 1401.6 0.4626 1439.2 0.5259 1466.4 0.5891 1492.2 0.6589 1519.1 0.7287 1544.3 0.7956 1566.9 0.8625 1588.0 0.9313 1608.1 1.0000 1622.3 PEG 200 + EA

1183.4 1223.4 1267.0 1305.7 1342.6 1383.2 1421.5 1449.2 1475.5 1502.9 1528.7 1551.8 1573.5 1594.1 1608.4

1162.2 1202.7 1246.9 1286.2 1323.8 1365.2 1404.2 1432.5 1459.4 1487.5 1514.0 1537.8 1560.1 1581.5 1596.2

1139.1 1180.1 1225.0 1265.0 1303.3 1345.6 1385.7 1414.7 1442.5 1471.6 1499.0 1523.9 1547.2 1569.7 1585.2

1117.8 1159.1 1204.6 1245.1 1284.0 1327.1 1368.0 1397.7 1426.1 1456.0 1484.4 1510.1 1534.4 1557.8 1574.0

1095.7 1137.3 1183.2 1224.3 1263.8 1307.7 1349.5 1380.0 1409.2 1440.1 1469.4 1496.2 1521.6 1546.2 1563.4

0.0000 0.0725 0.1450 0.2185 0.2920 0.3660 0.4400 0.5095 0.5790 0.6485 0.7180 0.7840 0.8500 0.9250 1.0000

1166.5 1193.1 1221.5 1250.4 1280.3 1311.5 1343.4 1374.1 1405.3 1437.3 1469.9 1501.4 1533.3 1570.6 1608.4

1098.1 1125.4 1153.7 1184.0 1215.3 1248.3 1282.2 1315.2 1349.0 1383.8 1419.8 1454.5 1490.1 1531.8 1574.0

1077.7 1105.0 1133.6 1164.1 1195.7 1229.1 1263.5 1297.5 1331.9 1367.6 1404.1 1440.1 1476.8 1519.8 1563.4

RI

SC

NU

MA 1144.1 1171.1 1199.2 1221.7 1259.0 1290.9 1323.3 1354.5 1386.6 1419.0 1453.1 1485.6 1518.0 1557.4 1596.2

D

TE

AC CE P

1190.4 1216.9 1244.5 1273.5 1294.0 1303.5 1364.8 1394.9 1425.3 1456.4 1487.1 1501.7 1549.4 1585.8 1622.3

32

PT

PEG 200 + MA

1120.7 1147.9 1176.1 1206.0 1239.9 1269.3 1302.5 1334.6 1367.6 1401.7 1436.5 1470.7 1504.6 1544.4 1585.2

ACCEPTED MANUSCRIPT Table 4 Continued x1

T/K 293.15

298.15

303.15

308.15

313.15

318.15

1202.6 1218.1 1235.4 1253.4 1272.9 1296.4 1322.2 1348.4 1376.7 1409.0 1443.8 1480.4 1519.3 1562.4 1608.4

1184.6 1200.4 1218.0 1236.1 1255.9 1279.7 1305.8 1332.3 1361.0 1393.8 1429.0 1466.0 1505.7 1549.4 1596.2

1165.1 1181.2 1199.1 1217.4 1237.5 1261.7 1288.2 1315.2 1344.3 1377.7 1413.9 1451.8 1492.5 1537.2 1585.2

1146.1 1162.5 1180.6 1199.1 1219.4 1243.9 1270.7 1298.0 1327.6 1361.7 1398.7 1437.5 1479.3 1525.0 1574.0

1126.6 1143.3 1161.7 1180.4 1200.9 1225.6 1252.7 1280.4 1310.6 1345.5 1383.3 1423.3 1466.1 1513.2 1563.4

RI

SC

NU

MA

TE

D

1222.3 1237.4 1254.5 1272.2 1291.6 1314.9 1340.3 1366.2 1394.1 1426.1 1460.4 1496.2 1534.6 1577.0 1622.3

AC CE P

0.0000 0.0730 0.1459 0.2131 0.2802 0.3538 0.4274 0.4963 0.5651 0.6381 0.7110 0.7823 0.8535 0.9268 1.0000

33

PT

PEG 200 + n-BA

ACCEPTED MANUSCRIPT

Table 5 Refractive index, nD as function of mole fraction, x1 PEG 200 of for PEG 200 + MA/EA/n-BA binary mixtures at the temperatures, T/K = (293.15 – 318.15) and pressure, p = 101 kPa T/K 293.15

298.15

303.15

308.15

313.15

318.15

1.4002 1.4108 1.4197 1.4267 1.4327 1.4384 1.4430 1.4460 1.4484 1.4507 1.4526 1.4542 1.4557 1.4571 1.4584

1.3975 1.4083 1.4174 1.4246 1.4307 1.4365 1.4412 1.4442 1.4467 1.4490 1.4509 1.4525 1.4540 1.4553 1.4566

1.3948 1.4058 1.4151 1.4225 1.4287 1.4347 1.4395 1.4425 1.4450 1.4473 1.4493 1.4508 1.4523 1.4537 1.4549

PT

x1

1.3920 1.4033 1.4128 1.4203 1.4267 1.4328 1.4377 1.4408 1.4433 1.4457 1.4476 1.4492 1.4506 1.4520 1.4532

1.3893 1.4009 1.4105 1.4182 1.4247 1.4309 1.4359 1.4390 1.4416 1.4440 1.4460 1.4476 1.4490 1.4503 1.4515

1.3982 1.4060 1.4130 1.4194 1.4250 1.4300 1.4344 1.4380 1.4413 1.4441 1.4467 1.4489 1.4509 1.4530 1.4549

1.3956 1.4036 1.4107 1.4172 1.4229 1.4280 1.4325 1.4362 1.4395 1.4424 1.4450 1.4472 1.4492 1.4513 1.4532

1.3928 1.4010 1.4083 1.4149 1.4207 1.4259 1.4305 1.4343 1.4377 1.4407 1.4433 1.4455 1.4475 1.4496 1.4515

1.4036 1.4110 1.4178 1.4239 1.4293 1.4341 1.4383 1.4418 1.4449 1.4477 1.4502 1.4524 1.4544 1.4565 1.4584

TE

1.4062 1.4134 1.4201 1.4261 1.4314 1.4361 1.4402 1.4436 1.4467 1.4494 1.4519 1.4541 1.4561 1.4582 1.4601

AC CE P

0.0000 0.0725 0.1450 0.2185 0.2920 0.3660 0.4400 0.5095 0.5790 0.6485 0.7180 0.7840 0.8500 0.9250 1.0000

D

PEG 200 + EA

SC

NU

1.4030 1.4133 1.4220 1.4289 1.4347 1.4403 1.4448 1.4477 1.4501 1.4523 1.4542 1.4558 1.4573 1.4587 1.4601

MA

0.0000 0.0770 0.1539 0.2254 0.2968 0.3797 0.4626 0.5259 0.5891 0.6589 0.7287 0.7956 0.8625 0.9313 1.0000

RI

PEG 200+MA

1.4010 1.4086 1.4155 1.4217 1.4272 1.4321 1.4364 1.4399 1.4431 1.4459 1.4484 1.4506 1.4526 1.4547 1.4566

34

ACCEPTED MANUSCRIPT Table 5 Continued x1 T/K 293.15

298.15

303.15

308.15

313.15

318.15

1.4163 1.4206 1.4248 1.4285 1.4319 1.4354 1.4387 1.4416 1.4443 1.4470 1.4496 1.4519 1.4541 1.4563 1.4584

1.4140 1.4184 1.4227 1.4264 1.4299 1.4335 1.4369 1.4398 1.4425 1.4452 1.4478 1.4501 1.4523 1.4545 1.4566

1.4114 1.4160 1.4204 1.4242 1.4278 1.4315 1.4349 1.4379 1.4407 1.4434 1.4460 1.4484 1.4506 1.4528 1.4549

1.4089 1.4137 1.4182 1.4221 1.4258 1.4295 1.4330 1.4360 1.4389 1.4417 1.4443 1.4467 1.4489 1.4511 1.4532

1.4065 1.4115 1.4161 1.4201 1.4238 1.4276 1.4311 1.4342 1.4371 1.4400 1.4426 1.4450 1.4473 1.4494 1.4515

RI

SC

NU

TE

D

MA

1.4186 1.4228 1.4269 1.4305 1.4338 1.4373 1.4405 1.4434 1.4460 1.4487 1.4513 1.4536 1.4558 1.4580 1.4601

AC CE P

0.0000 0.0730 0.1459 0.2131 0.2802 0.3538 0.4274 0.4963 0.5651 0.6381 0.7110 0.7823 0.8535 0.9268 1.0000

35

PT

PEG 200 + n-BA

ACCEPTED MANUSCRIPT Table 6 Coefficients, Ai from Eq. (16) for various excess properties and standard deviations,  for PEG 200 + MA/EA/n-BA mixtures at the temperatures, T/K = (293.15 – 318.15) A3

A4

A5

1.0483 1.0030 0.9629 0.9187 0.7387 0.4783

0.0830 0.0683 0.0840 0.0756 0.0222 0.0355

-0.1537 -0.1629 -0.1904 -0.2249 -0.0978 0.0974

-0.2059 -0.2243 -0.2377 -0.2639 -0.2941 -0.3243

0.4725 0.5329 0.6138 0.6635 0.7288 0.7882



0.0039 0.0039 0.0047 0.0054 0.0059 0.0064

0.1581 0.1556 0.1491 0.1525 0.1586 0.1586

-0.5672 -0.6336 -0.6776 -0.7146 -0.7653 -0.7951

0.0042 0.0046 0.0047 0.0050 0.0051 0.0053

-0.5458 -0.6108 -0.6383 -0.7140 -0.7916 -0.8104

-0.5106 -0.5410 -0.4474 -0.6093 -0.5605 -0.5543

0.6172 0.6432 0.5331 0.5767 0.6957 0.6711

-0.2504

0.1511

0.0020 0.0028 0.0025 0.0033 0.0026 0.0017

0.5048 0.4889 0.4835 0.5313 0.5187 0.5071

-0.1540 -0.1817 -0.1197 -0.2521 -0.3194 -0.2766

-0.0395 -0.0471 -0.0399 -0.1359 -0.0636 -0.0362

0.0853 0.1959 0.0450 0.1905 0.2353 0.1780

0.0013 0.0018 0.0022 0.0023 0.0019 0.0017

MA

0.1680 0.1308 0.0880 0.0339 -0.0086 -0.0619

TE

10−2 · uE /m·s−1 293.15 2.9545 298.15 2.9986 303.15 3.0412 308.15 3.0773 313.15 3.1146 318.15 3.1453 2 10 ·  nD 293.15 2.5603 298.15 2.6981 303.15 2.8355 308.15 2.9853 313.15 3.1225 318.15 3.2423 6 10 · ΔRm/(m3·mol−1) 293.15 0.9349 298.15 1.0131 303.15 1.0882 308.15 1.1714 313.15 1.2576 318.15 1.3204

SC

NU

0.0014 0.0010 0.0017 0.0008 0.0010 0.0009

AC CE P

PEG 200 + MA 106 · VmE /m3·mol−1 293.15 -3.1341 -0.3139 298.15 -3.2840 -0.3101 303.15 -3.4341 -0.3157 308.15 -3.5901 -0.2965 313.15 -3.7315 -0.2743 318.15 -3.8786 -0.2739 E 14 5 −1 −1 10 · Ks,m /m ·N ·mol 293.15 -2.8118 -0.8365 298.15 -2.9969 -0.8960 303.15 -3.1890 -0.9692 308.15 -3.3954 -1.0449 313.15 -3.6114 -1.1313 318.15 -3.8406 -1.2254

A2

PT

A1

RI

A0

D

T/K

36

-0.1849

ACCEPTED MANUSCRIPT Table 6 Continued

0.3158 0.2448 0.2123 0.1223 0.0738 0.0870

0.1145 0.1069 0.1162 0.1612 0.1215 0.1053

0.0476 0.0843 0.0742 0.1120 0.1029

-0.2618 -0.2717 -0.2721 -0.2898 -0.2772 -0.2615

0.1762 0.2179 0.2028 0.1862 0.1576 0.1070

0.2099 0.1879 0.1827 0.1756 0.1162



0.0005 0.0006 0.0007 0.0006 0.0005 0.0011 0.0020 0.0019 0.0023 0.0021 0.0014 0.0012

0.1103 0.1722 0.1942 0.2089 0.1970 0.2522

0.0109 0.0376 -0.0064 -0.0254 -0.0283 -0.0239

0.0986 0.0435 0.0519 0.0730 0.0952 0.0530

1.8450 1.8422 1.8351 1.8327 1.8416 1.8525

0.0012 0.0005 0.0011 0.0010 0.0009 0.0008

0.2814 0.2492 0.2417 0.2065 0.1770 0.1188

0.0402 -0.0217 -0.0711 -0.0853 -0.1503 -0.0943

-0.2556 -0.1767 -0.1188 -0.0630 0.0117 0.1382

-0.1239 -0.0445

0.0014 0.0009 0.0012 0.0015 0.0010 0.0013

-0.3898 -0.3431 -0.3317 -0.2987 -0.2492 -0.0219

-0.2275

TE

-0.0060 -0.0782 -0.1270 -0.1686 -0.2536 -0.3053

A5

PT

A4

D

-0.0803 -0.1671 -0.2270 -0.3079 -0.3808 -0.4558

AC CE P

10−2 · uE /m·s−1 293.15 1.8450 298.15 1.8422 303.15 1.8351 308.15 1.8327 313.15 1.8416 318.15 1.8525 2 10 ·  nD 293.15 0.6994 298.15 0.7599 303.15 0.8251 308.15 0.8910 313.15 0.9545 318.15 1.0202 6 10 · ΔRm/(m3·mol−1) 293.15 1.6321 298.15 1.7184 303.15 1.8211 308.15 1.9124 313.15 2.0003 318.15 2.0864

A3

RI

PEG200 + EA 106· VmE /m3·mol−1 293.15 -2.1053 -0.5410 298.15 -2.2058 -0.5423 303.15 -2.3152 -0.5494 308.15 -2.4088 -0.5796 313.15 -2.5189 -0.5692 318.15 -2.6337 -0.5854 E 14 5 −1 −1 10 · Ks,m /m ·N ·mol 293.15 -2.1325 -0.6956 298.15 -2.2574 -0.7302 303.15 -2.4069 -0.7481 308.15 -2.5642 -0.7716 313.15 -2.7338 -0.7946 318.15 -2.8831 -0.8196

A2

SC

A1

NU

A0

MA

T/K

0.1659 0.2227

37

-0.2747

0.0870

0.0018 0.0012 0.0017 0.0021 0.0013 0.0016

ACCEPTED MANUSCRIPT Table 6 Continued

0.0281 0.0093 0.0006 0.0026 -0.0034 -0.0282

0.0169

-0.0489 -0.0497 -0.0610 -0.0837 -0.1441 -0.2441

-0.0205 -0.0383 -0.0633 -0.0495 -0.0409 -0.0550

A5

PT

-0.0066

RI

-0.0188

0.0542

0.0297

0.2164 0.2407 0.2398 0.2840 0.3450 0.4288

-0.0459 -0.0542 -0.0510 -0.0814 -0.1251 -0.1586

-0.0241

0.0775 0.0735 0.0609 0.0685 0.0538 0.0548

-0.0284 0.0049 -0.2008 -0.1912 -0.0274 0.0820

-0.1200 -0.1077 -0.0655 -0.0429 0.0438 0.0902

-0.2212 -0.3217 -0.0611

0.1062 0.1090 0.1282 0.1372 0.1201 0.1140

0.0317 0.0390 -0.1568 -0.1210 -0.0020 0.0741

-0.0905 -0.0760 -0.0925 -0.0662 0.0325 0.0934

-0.2049 -0.2599

TE

-0.4373 -0.4626 -0.4933 -0.5234 -0.5496 -0.5773

A4

AC CE P

10−2 · uE /m·s−1 293.15 0.7693 298.15 0.7834 303.15 0.8058 308.15 0.8189 313.15 0.8279 318.15 0.8341 2 10 ·  nD 293.15 0.8900 298.15 0.9776 303.15 1.0792 308.15 1.1733 313.15 1.2601 318.15 1.3449 6 10 · ΔRm/(m3·mol−1) 293.15 0.4409 298.15 0.4993 303.15 0.5706 308.15 0.6345 313.15 0.6968 318.15 0.7541

A3

SC

PEG 200 + n-BA 106· VmE /m3·mol−1 293.15 -1.3907 -0.2398 298.15 -1.4751 -0.2464 303.15 -1.5590 -0.2485 308.15 -1.6472 -0.2570 313.15 -1.7339 -0.2614 318.15 -1.8318 -0.2642 E 14 5 −1 −1 10 · Ks,m /m ·N ·mol 293.15 -1.0849 0.0326 298.15 -1.1646 0.0427 303.15 -1.2529 0.0590 308.15 -1.3414 0.0724 313.15 -1.4288 0.0873 318.15 -1.5203 0.1030

A2

NU

A1

MA

A0

D

T/K

38

0.0322 0.0304 0.0397 0.0251

-0.1697 -0.1763

-0.1298 -0.1252



0.0006 0.0006 0.0006 0.0010 0.0008 0.0007 0.0006 0.0007 0.0003 0.0007 0.0009 0.0006 0.0005 0.0005 0.0003 0.0005 0.0007 0.0004 0.0029 0.0019 0.0023 0.0017 0.0019 0.0024 0.0024 0.0018 0.0019 0.0014 0.0015 0.0020

ACCEPTED MANUSCRIPT E

°

E

°

* * Table 7 The values of V m,1 , Vm,1 , V m,1 , V m,2 , Vm,2 and V m,2 of the components for PEG 200 + MA/EA/n-BA binary mixtures at the temperatures, T/K = (293.15 – 318.15)

T/K

°

106· V m,1

E

°

E

* 106· Vm,1

106· V m,1

106· V m,2

* 106· Vm,2

106· V m,2

169.877 170.481 171.087 171.699 172.314 172.937

-2.470 -2.686 -2.893 -3.117 -3.343 -3.541

88.279 88.652 88.999 89.464 89.760 90.131

90.287 90.854 91.429 92.010 92.599 93.195

-2.009 -2.202 -2.430 -2.546 -2.838 -3.064

169.877 170.481 171.087 171.699 172.314 172.937

-2.168 -2.312 -2.462 -2.593 -2.790 -3.027

107.303 107.866 108.410 109.149 109.533 110.086

108.618 109.307 110.005 110.712 111.428 112.153

-1.315 -1.441 -1.596 -1.563 -1.895 -2.067

141.454 142.131 142.813 143.528 144.197 144.886

142.593 143.351 144.116 144.890 145.673 146.463

-1.140 -1.219 -1.303 -1.362 -1.476 -1.577

(m3·mol−1)

167.709 168.169 168.625 169.106 169.524 169.910

PEG 200 + n-BA

D

169.877 170.481 171.087 171.699 172.314 172.937

TE

168.292 168.769 169.274 169.798 170.315 170.794

-1.585 -1.712 -1.814 -1.902 -1.999 -2.143

AC CE P

293.15 298.15 303.15 308.15 313.15 318.15

MA

293.15 298.15 303.15 308.15 313.15 318.15

NU

PEG 200 + EA

RI

167.407 167.795 168.194 168.582 168.972 169.395

SC

293.15 298.15 303.15 308.15 313.15 318.15

39

PT

PEG 200 + MA

ACCEPTED MANUSCRIPT 

E

E



* * Table 8 The values K s,m,1 , Ks,m,1 , K s,m,1 , K s,m,2 , Ks,m,2 and K s,m,2 of the components for PEG 200 + MA/EA/n-BA binary mixtures at the temperatures, T/K = (293.15 – 318.15)

T/K



1014· K s,m,1

* 1014· Ks,m,1

E



E

1014· K s,m,1

1014· K s,m,2

* 1014· Ks,m,2

1014· K s,m,2

5.741 5.882 6.015 6.142 6.275 6.406

-3.382 -3.584 -3.782 -4.041 -4.308 -4.602

3.871 3.989 4.117 4.301 4.468 4.676

6.524 6.847 7.189 7.579 7.971 8.403

-2.654 -2.858 -3.071 -3.278 -3.503 -3.728

5.741 5.882 6.015 6.142 6.275 6.406

-3.086 -2.853 -3.263 -3.537 -3.724 -3.927

6.729 6.941 7.536 7.724 8.108 8.504

8.316 8.770 9.234 9.747 10.284 10.817

-1.587 -1.829 -1.697 -2.023 -2.176 -2.312

9.527 9.867 10.238 10.618 10.985 11.404

10.618 11.086 11.548 12.066 12.604 13.187

-1.092 -1.219 -1.310 -1.448 -1.619 -1.783

(m5·N−1·mol−1)

2.654 3.029 2.752 2.605 2.550 2.479

PEG 200 + n-BA

D

5.741 5.882 6.015 6.142 6.275 6.406

TE

4.673 4.672 4.697 4.740 4.748 4.719

-1.067 -1.210 -1.318 -1.402 -1.526 -1.687

AC CE P

293.150 298.150 303.150 308.150 313.150 318.150

MA

293.15 298.15 303.15 308.15 313.15 318.15

NU

PEG 200 + EA

RI

2.359 2.298 2.233 2.102 1.967 1.804

SC

293.15 298.15 303.15 308.15 313.15 318.15

40

PT

PEG 200 + MA

ACCEPTED MANUSCRIPT Table 9 Speeds of sound values computed using SPT for different behavioural shapes along with minimum deviation, σ and experimentally measured values and for PEG 200 + MA/EA/n-BA binary mixture at temperature, T/K = 298.15 ucal

0.5891 0.6589 0.7287 0.7956 0.8625 0.9313 1.0000

1593.5 1502.9 1528.7 1551.8 1573.5 1594.1 1608.4 Σdu

1522.1 1544.3 1562.6 1576.8 1588.0 1598.7 1609.0 0.2715

D

TE

AC CE P

PT

uexp

0.5790 0.6485 0.7180 0.7840 0.8500 0.9250 1.0000

1406.3 1438.3 1470.9 1502.5 1534.7 1571.9 1608.4 Σdu

1476.3 1502.4 1526.3 1547.1 1566.6 1587.9 1608.9 0.2868

0.5651 0.6381 0.7110 0.7823 0.8535 0.9268 1.0000

1376.7 1409.0 1443.8 1480.4 1519.3 1562.4 1608.4 Σdu

1410.2 1440.8 1472.5 1504.3 1537.4 1572.5 1608.9 0.2325

MA

PEG 200 + MA (Disc B + Disc C) 0.0000 1183.4 1183.8 0.0770 1223.4 1263.2 0.1539 1267.0 1337.6 0.2254 1305.7 1401.4 0.2968 1342.6 1457.1 0.3797 1383.2 1511.9 0.4626 1421.5 1553.2 0.5259 1449.2 1576.7 PEG 200 + EA (Disc C+ Disc B) 0.0000 1167.9 1167.1 0.0725 1211.3 1193.4 0.1450 1255.2 1221.0 0.2185 1298.5 1250.0 0.2920 1340.3 1280.0 0.3660 1379.5 1311.2 0.4400 1416.0 1343.2 0.5095 1447.5 1374.0 PEG 200 + BA (Disc C+ Disc D) 0.0000 1202.6 1203.2 0.0730 1218.1 1226.8 0.1459 1235.4 1251.4 0.2131 1253.4 1274.8 0.2802 1272.9 1299.1 0.3538 1296.4 1326.5 0.4274 1322.2 1354.7 0.4963 1348.4 1381.9

x1

RI

ucal

SC

uexp

NU

x1

41

ACCEPTED MANUSCRIPT Table 10 Average percentage deviations (APDs) in theoretically calculated refractive indices by using Arago-Biot (A-B), Gladstone-Dale (G-D), Lorentz-Lorentz (L-L), Heller (H), Eykman (EK), and Weiner (W) relations for PEG 200 + MA/EA/n-BA binary mixtures at the temperatures, T/K = (293.15 – 318.15) T/K

Average percentage deviations (APDs) A-B

G-D

L-L

H

EK

W

0.304 0.324 0.343 0.361 0.380 0.397

0.315 0.335 0.356 0.373 0.392 0.408

0.318 0.338 0.358 0.376 0.395 0.414

0.175 0.189 0.202 0.214 0.227 0.239

0.308 0.328 0.347 0.365 0.384 0.402

0.203 0.215 0.229 0.242 0.255 0.270

0.215 0.229 0.243 0.257 0.270 0.285

0.325 0.346 0.365 0.374 0.395 0.405

0.120 0.129 0.139 0.149 0.158 0.169

0.206 0.219 0.233 0.247 0.260 0.275

0.121 0.135 0.141 0.158 0.172 0.185

0.065 0.074 0.081 0.092 0.103 0.113

0.117 0.128 0.139 0.152 0.166 0.179

0.203 0.215 0.229 0.242 0.255 0.270

PEG 200 + n-BA

D

0.115 0.126 0.136 0.149 0.163 0.177

TE

0.115 0.126 0.136 0.149 0.163 0.177

AC CE P

293.15 298.15 303.15 308.15 313.15 318.15

MA

293.15 298.15 303.15 308.15 313.15 318.15

NU

PEG 200 + EA

RI

0.304 0.324 0.343 0.361 0.380 0.397

SC

293.15 298.15 303.15 308.15 313.15 318.15

0.123 0.134 0.145 0.158 0.172 0.186

42

PT

PEG 200 + MA

ACCEPTED MANUSCRIPT

106  VmE /(m3 mol1)

0.0

(a)

-0.2 -0.4 -0.6 -0.8

0.0

0.2

0.4

PT

-1.0 0.6

0.8

RI

x1 0.0

SC

(b)

-0.2

NU

-0.3 -0.4 -0.5 -0.6 -0.7

0.4

0.6

AC CE P

0.8

1.0

0.8

1.0

x1

TE

0.0

106  VmE /(m3 mol1)

0.2

D

0.0

MA

106  VmE /(m3 mol1)

-0.1

-0.1

1.0

(c)

-0.2 -0.3 -0.4 -0.5

0.0

0.2

0.4

0.6

x1

Fig. 1

43

ACCEPTED MANUSCRIPT 0.0

PT

-0.4

RI

-0.6

SC

106  VmE /(m3 mol1)

-0.2

-1.0 0.2

0.4

0.6

x1

Fig. 2

AC CE P

TE

D

MA

0.0

NU

-0.8

44

0.8

1.0

ACCEPTED MANUSCRIPT 0.0 -0.2 -0.4 -0.6 -0.8

PT

1014.Ks,mE/(m 5 N1 mol1)

(a)

-1.0 0.0

0.2

0.4

0.6

0.8

SC

0.0

(b)

NU

-0.2

-0.4

-0.6

-0.8 0.2

0.4

0.6

0.8

1.0

x1

-0.1

AC CE P

1014.Ks,mE/(m 5 N1 mol1)

0.0

TE

D

0.0

MA

1014.Ks,mE/(m 5 N1 mol1)

1.0

RI

x1

(c)

-0.2

-0.3

-0.4

0.0

0.2

0.4

0.6

x1

Fig. 3

45

0.8

1.0

ACCEPTED MANUSCRIPT 0.0

-0.1

-0.3

PT

-0.4

-0.5

RI

1014. Ks,mE/(m5 N1 mol1)

-0.2

SC

-0.6

-0.8 0.2

0.4

0.6

x1

AC CE P

TE

D

MA

0.0

NU

-0.7

Fig. 4

46

0.8

1.0

ACCEPTED MANUSCRIPT 0.8

0.7

0.6

PT

0.4

0.3

RI

102. uE/(m s1)

0.5

SC

0.2

NU

0.1

0.0 0.2

0.4

0.6

x1

Fig. 5

AC CE P

TE

D

MA

0.0

47

0.8

1.0

ACCEPTED MANUSCRIPT

0.8

0.7

0.6

PT

0.4

RI

102. nD

0.5

SC

0.3

NU

0.2

0.1

0.2

0.4

0.6

1

Fig. 6

AC CE P

TE

D

0.0

MA

0.0

48

0.8

1.0

ACCEPTED MANUSCRIPT 0.30

PT

0.20

0.15

RI

106. Rm/(m3 mol1)

0.25

SC

0.10

0.00 0.2

0.4

0.6

x1

AC CE P

TE

D

MA

0.0

NU

0.05

Fig. 7

49

0.8

1.0

ACCEPTED MANUSCRIPT 0.0

-0.5

-1.0

PT

-1.5

-2.0

RI

106  Vm,1E /(m3 mol1)

(a)

-3.0 0.0

0.2

0.4

0.6

0.8

1.0

NU

x1

MA

0.0

(b)

D

-0.5

TE

-1.0

-1.5

AC CE P

106  Vm,2E /(m3 mol1)

SC

-2.5

-2.0

-2.5

0.0

0.2

0.4

0.6

x1

Fig. 8

50

0.8

1.0

ACCEPTED MANUSCRIPT 0.0 -0.5

(a)

-1.5 -2.0

PT

1014 Ks,m,1E/(m5 N1 mol1)

-1.0

-2.5

RI

-3.0

SC

-3.5 -4.0 0.2

0.4

0.6

0.8

1.0

NU

0.0

x1

MA

0.0

D TE

-1.0

-1.5

(b)

AC CE P

1014 KSm,2 /(m5 N1 mol1)

-0.5

-2.0

-2.5

-3.0

0.0

0.2

0.4

0.6

x1

Fig. 9

51

0.8

1.0

ACCEPTED MANUSCRIPT Graphical Abstract

0.0

RI

PT

-0.3

SC

-0.6

-0.9 0.0

0.2

NU

106 . VmE/(m3 mol3)

MA EA n-BA

0.4

0.6

0.8

1.0

TE

D

MA

x1

AC CE P

Excess molar volume, VmE as function of mole fraction, x1 of PEG 200 for PEG 200 + MA/EA/n-BA binary mixtures at 298.15 K

52

ACCEPTED MANUSCRIPT Research Highlights

Study reports new density data of PEG 200 + alkyl acrylate mixtures



Study reports new speed of sound data of PEG 200 + alkyl acrylate mixtures



Study reports new refractive index data of PEG 200 + alkyl acrylate mixtures



Correlates excess properties with interactions in these mixtures



The scaled particle theory (SPT) is used to predict theoretical speed of sound

AC CE P

TE

D

MA

NU

SC

RI

PT



53