Measurement and prediction of thermophysical properties of binary mixtures of dicyclopentadiene with methylcyclohexane, toluene, and p-xylene

Journal Pre-proof Measurement and prediction of thermophysical properties of binary mixtures of dicyclopentadiene with methylcyclohexane, toluene, and p-xylene ´ Ahmed Amin Touazi, Saeda Didaoui, Kamel Khimeche, Mokhtar Benziane

PII:

S0040-6031(20)30060-5

DOI:

https://doi.org/10.1016/j.tca.2020.178536

Reference:

TCA 178536

To appear in:

Thermochimica Acta

Received Date:

23 January 2020

Accepted Date:

28 January 2020

Please cite this article as: Touazi AA, Didaoui S, Khimeche K, Benziane M, Measurement and prediction of thermophysical properties of binary mixtures of dicyclopentadiene with methylcyclohexane, toluene, and p-xylene, Thermochimica Acta (2020), doi: https://doi.org/10.1016/j.tca.2020.178536

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Measurement and prediction of thermophysical properties of binary mixtures of dicyclopentadiene with methylcyclohexane, toluene, and pxylene Ahmed Amin Touazia,*, Saéda Didaouib,*, Kamel Khimechea, Mokhtar Benzianec a

Ecole Militaire Polytechnique EMP, BP 17 Bordj-El-Bahri, Alger, Algérie. Faculté de chimie, USTHB, BP.32 El-Alia, 16111 Bab-Ezzouar, Alger, Algérie. c Ecole Supérieure du Matériel, ESM. BP 188 Beau-Lieu, Alger. Algérie. b

Corresponding Authors: [email protected] (Saeda Didaoui), [email protected] (Ahmed Amin Touazi).

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Flash point. density and viscosity of high density fuel with additives were measured. Flash point data were fitted by UNIFAC and ASOG models. PFP theory was applied to estimate excess molar volume. Several correlations were used to predict viscosity. NRTL, UNIQUAC and Heil models were employed to correlate the excess Gibbs energy.

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    

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Research Highlights

Abstract

Flash point. density and viscosity of three binary mixtures containing dicyclopentadiene

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(DCPD) with methylcyclohexane, toluene and p-xylene were measured in the present work. The experimental data of flash points were compared with the values calculated by Le Chatelier modified equation. Activity coefficients were estimated by the UNIFAC, UNIFAC

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Dortmund and ASOG models. Also, excess molar volumes, viscosity deviation and excess Gibbs energy of activation of viscous flow were calculated from data of density and viscosity.

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E Prigogine-Flory-Patterson theory was applied to predict Vm . Empirical models were used to

predict the viscosity data. NRTL, UNIQUAC and Heil models were applied to calculate G*E. The findings have been employed to examine structural effects and molecular interactions which are dominant between compound molecules. The obtained experimental results showed weak molecular interactions and theory study demonstrated that UNIFAC, PFP, Eyring_NRTL, Lobe, and NRTL were the best models found to fit the flash point, excess molar volume, viscosity and excess free Gibbs energy.

Keywords: Dicyclopentadiene, Excess molar volume, Viscosity, Excess Gibbs energy, Molecular interaction Nomenclature: DCPD: Dicyclopentadiene PFP: Prigogine-Flory- Patterson. NRTL: Non Random To Liquids UNIFAC: UNIquac Functional-group Activity Coefficients UNQUAC: UNiversal QUAsi-Chemical ASOG: Analytical Solution of Group method JP: Jet Propelled

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RJ: RamJet.

1. Introduction

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Since the last century and up to the present day the military industry has made considerable efforts for the development of high-density fuels. The good results are obtained by the use of fuels based on naphthenic compounds derived from petroleum refining.

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Nevertheless, nearly all airplane nowadays are weight-limited on take off so a reduction in fuel volume and the use of a high-density fuel is a good solution[1, 2]. The high energy

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density fuel has many applications to launch cruise missiles and rockets (JP9, JP10, RJ4, RJ5, and RJ6)[3, 4]. Aircraft fuels are regarded as flammable products and therefore its implementation, filling, storage and distribution in tanks requires specific preventive

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measures. The flash point is one of the most important variables used to characterize fire and explosion hazard of liquids, for that storage jet fuel must be below its flash point[5, 6].

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Knowing that flash point is the lowest temperature at which the vapors emitted by the fuel mixed with the air produces a flame that extinguishes as soon[7, 8]. DCPD was used as fuel for aircraft and missiles, but the elevated viscosity leads to spray problems during

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injection[9]. In order to regulate this problem, hydrocarbon components with low viscosity were chosen as additives. Prior investigations on dicyclopentadiene are essentially concentrated on the isomerization to exo to manufacture high volumetric density fuel named exo-tetrahydrodicyclopentadiene usually referred to as JP-10 or producing new polymers via ring opening metathesis polymerization. Few studies have shown that its exothermic behavior is qualitatively based on

tricyclopentadiene-based products, also used as high-density volumetric fuel for the production of efficient fuels, in cases where the volume of the tank is limited [9]. Methylcyclohexane, toluene, and p-xylene are natural constituents of crude oil and important component of gasoline, kerosene and diesel. They have numerous commercial and industrial applications and are organic solvents in paints, glues and as important additives of fuels. The following to our study of thermophysical and thermodynamic properties about binary mixtures containing the high-density jet fuel[10]. Three compounds with a cyclic structure like methylcyclohexane, toluene, and p-xylene allow having more thermal stability than the nalkanes with the same or lower carbon number. Also, they have high volatility, low viscosity and they are important compounds found in jet fuel composition. For all these, factors were chosen as additives for DCPD. The structure effect of DCPD molecule with cyclic paraffin

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and aromatic hydrocarbons (proximity, steric hindrance effects) offers a serious test for the predictive potential of thermodynamic theories of mixtures[11].

Data on flash point, density, and viscosity of binary mixtures of dicyclopentadiene (DCPD) + methylcyclohexane, toluene, and p-xylene at 288.15, 293.15, 298.15, 303.15, 308.15, 313.15,

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318.15K and atmospheric pressure (0.1012 MPa) have been measured experimentally. From these results, the excess molar volumes, viscosity deviations and excess free energy of

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activation of flow viscosity have been derived. This study can be used to analyze and discuss the nature and strength of intermolecular interactions in binary mixtures and geometrical

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effects in the systems[7, 12, 13].

Moreover, extensive information about structural phenomena of liquid mixtures is of very important in the development of predictive models. The experimental data of flash points

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were compared with the theoretical values calculated by Le Chatelier modified equation [14]. Activity coefficients were calculated by the UNIFAC[15], UNIFAC_ Dortmund[16] and ASOG[17] models. Excess molar volume values were fitted by using the PFP theory[18]. and

kinematic

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Dynamic

Eyring_UNIQUAC[20],

viscosity

data

Eyring_Wilson[21],

were

correlated

models

and

by

Eyring_NRTL[19],

Lobe[22]

Heric[23]

and

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McAllister[24] equations. Semi predictive models were proposed to predict NRTL[25], UNIQUAC[26] and Heil[27] models were tested to predict experimental excess Gibbs free energy of activation of viscous flow. 2. Materials And Methods 2.1. Materials The reactants in this investigation, DCPD, methylcyclohexane, toluene, and p-xylene, were used as received from a supplier, without any further purification and their structures are

represented in Fig. 1. The purities and the water contents were provided by suppliers. Also, the purity was calculated by Gas Chromatography (PERKIN ELMER, GCMS CLARUS SQ8S) and the water contents were measured in our laboratory using a Coulometric Karl Kischer Titrator (71000 GR), in Table1 the corresponding information is exhibited. It should be noted that DCPD is pure 99% at solid-state. In this study present, purity of only 95% at the liquid state and the presence of trace impurities can slightly affect the measurement of physical properties. The dicyclopentadiene (DCPD) has two isomers endo and exo and the determination of composition of mixture by using Gas Chromatograph method (PERKIN ELMER, GCMS CLARUS SQ8S) was reported 94.84% of endo-dicyclpentadiene and the chromatogram was presented in Fig 2.

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The supplementary analysis was performed with NMR spectroscopy apparatus to confirm the isomer of dicyclopentadiene by using a Bruker. The 13C and 1H NMR spectrums obtained of dicyclopentadiene were shown in Figs 3 and 4 respectively. The experimental and theoretical values of 13C and 1H NMR of endo-dicyclopentadiene were compared in Tables 2 and 3 .

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2.2. Apparatus and procedure

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endo isomerisation with purity superior than 94%.

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The comparison confirmed that our sample dicyclopentadiene (DCPD) used in this study have

A closed cup analyzed (ERAFLASH Eralytics, temperature stability 0.1 °C, Austria) was

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used to measure the flash point of pure components and their corresponding mixtures. The mole fraction of each reactant was weighed by using an analytical balance (OHAUS model EX224M, sensitivity 0.0001 g, Switzerland). A sample volume of 2 mL was prepared and put

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in the analyzed cup. The procedure was performed according to the standard test method ASTM D56.

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Simultaneously measurement of density and viscosity of pure reactant and their binary

mixtures were performed by using a digital Stabinger viscometer (SVM 3000, Reproducibility: 0.02°C, 0.0005 g.cm-3, 0.0035 mPa.s, Austria) in the temperature range [288.15-318.15] K and atmospheric pressure. The followed procedure in the present study was similar to that used in the previous investigation[10].

The observed values of flash point, density and dynamic viscosity of pure reactants have been compared with the literature values in Table 4, which showed that the measurements agree with the literature values. 3. Results and discussion 3.1. Flash-point The experimental data of flash point measured by ERAFLASH of three binary mixtures were shown in Table 5. The flash point for a mixture can be predicted by the Le Chatelier modified equation[14], and a model for estimating activity coefficients: ∑ 𝑖=1

𝑥𝑖 𝛾𝑖 𝑃𝑖𝑠𝑎𝑡 𝑠𝑎𝑡 𝑃𝑖,𝑓𝑝

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2

=1

(1)

Where xi is the mole fraction of the flammable substance, γi is the activity coefficient and 𝑃𝑖𝑠𝑎𝑡 is the vapor pressure of the flammable substance at the temperature of the mixture flash

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𝑠𝑎𝑡 point. 𝑃𝑖,𝑓𝑝 is the vapor pressure of component i at its flash point.

estimated using the Antoine equation: log 𝑃𝑖𝑠𝑎𝑡 𝐵𝑖 𝑇 + 𝐶𝑖

(2)

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= 𝐴𝑖 −

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The saturated vapor pressure variation with temperature for a pure substance, i, can be

Where Ai, Bi, and Ci are the parameters of compound i, and shown in Table 6.

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3.1.1. Prediction of flash point by Activity coefficient models In this study, the activity coefficients, 𝛾𝑖 , were estimated by UNIFAC, UNIFAC Dortmund and ASOG models.

∅𝑖 𝑍 𝜃𝑖 ∅𝑖 + ( ) 𝑞𝑖 ln + 𝑙𝑖 − ∑ 𝑥𝑗 𝑙𝑗 𝑥𝑖 2 ∅𝑖 𝑥𝑖

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ln 𝛾𝑖 = ln

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UNIFAC[15]

𝑗

+ ∑ 𝑣𝑘,𝑖 (ln Г𝑘 − ln Г𝑘,𝑖 )

(3)

𝑘

UNIFAC Dortmund[16] ln 𝛾𝑖 = 1 −

∅′ 𝑖 ∅′ 𝑖 𝑍 ∅𝑖 ∅𝑖 + ln − ( ) 𝑞𝑖 (1 − + ln ) 𝑥𝑖 𝑥𝑖 2 𝜃𝑖 𝜃𝑖 + ∑ 𝑣𝑘,𝑖 (ln Г𝑘 − ln Г𝑘,𝑖 ) 𝑘

(4)

ASOG model[17] 𝑣𝑖 𝑣𝑖 ln 𝛾𝑖 = ln +1− ∑𝑗 𝑣𝑗 𝑥𝑗 ∑𝑗 𝑣𝑗 𝑥𝑗 + ∑ 𝑣𝑘,𝑖 (ln Г𝑘 − ln Г𝑘,𝑖 )

(5)

𝑘

Raoult's law[28] For the activity coefficients of the liquid phase are equal to unity, the solution was ideal and the equation (1) was modified. 2

𝑥𝑖 𝑃𝑖𝑠𝑎𝑡 𝑥1 𝑃1𝑠𝑎𝑡 𝑥2 𝑃2𝑠𝑎𝑡 ∑ 𝑠𝑎𝑡 = 𝑠𝑎𝑡 + 𝑠𝑎𝑡 𝑃𝑖,𝑓𝑝 𝑃1,𝑓𝑝 𝑃2,𝑓𝑝 𝑖=1

=1

(6)

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The estimated activity coefficients were subsequently used to predict the corresponding flash points. It is well known that these parameters are obtained by regression of the experimental data for such binary mixtures and are listed in Table 5.

The average absolute deviations (AAD) between the experimental and predicted values were

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presented in Table 6. AAD is given by: ADD =∑

exp

|Ti

predict

− Ti

|

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n

N

i

(7)

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The measured flash points of studied binary mixtures were compared with the predicted values from the activity coefficient of UNIFAC, UNIFAC_Dortmund, ASOG models and from ideal solution Raoult's law were shown in Fig.5. The flash point predicted values by

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Landolt-Börnstein databases of Antoine's coefficients were deferred with the experimental data. Average absolute deviations values (ADD) of flash point calculated were varied between

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9 to 11.5 %.

All-flash point values predicted by Antoine coefficients estimated for DCPD were agreed with the experimental data. Average absolute deviations values (ADD) of flash point obtained

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were varied between 0.66 to 5.96 %. However, the calculated values based on the UNIFAC model were found to be better than those based on the ASOG model and Raoult's law. We concluded that results obtained by used Antoine coefficients of Landolt-Börnstein databases were less attractive than results obtained by Antoine coefficients estimated for DCPD. Except unavailability of the density and viscosity literature data for DCPD. The graphically comparison between the density and viscosity experimental and literature data of (methylcyclohexane, toluene and p-xylene) were performed and shown in Figs.6 and 7.

The graphically comparison between experimental and literature density data for methylcyclohexane, toluene and p-xylene was displayed in Fig. 6. Except density value at 318.1K was little bite greater than literature value, all density values obtained at temperature studies were stackable with literature values. The density standard deviation calculated of methylcyclohexane, toluene and p-xylene were presented respectively: 0.067%, 0.015%, and 0.02%. The graphically comparison between experimental and literature viscosity data for methylcyclohexane, toluene and p-xylene was exposed in Fig.7. For methylcyclohexane, except viscosity value at 318.1K was lower than literature value, all density values obtained at temperature studies were stackable with literature values. For toluene, experimental values viscosity were greater than literature values from 288.15 to 308.15K, contrariwise, were lower

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at 313.15 and 318.15K. For p-xylene, experimental values viscosity were stackable with literature values from 288.15 to 308.15K, and little bite lower at 313.15 and greater at 318.15K. The viscosity standard deviation calculated of methylcyclohexane, toluene and p-

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xylene were presented respectively: 1.28%, 1.46%, and 1.46%. 3.2. Excess molar volumes

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Density values, 𝜌, of three mixtures at various temperatures were listed as a function of mole fraction in Table 7. The density data have been used to calculated excess molar volumes, 𝑉𝑚𝐸 , 2

𝑉𝑚𝐸

1 = ∑ 𝑥i 𝑀i [( ) 𝜌 𝑖=1

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1 − ( )] 𝜌𝑖

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by means of equation (8):

(8)

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Where xi and Mi represent the mole fraction and molar mass of pure components i. ρ and 𝜌𝑖 are the densities of binary mixtures and pure components i, respectively.

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E Fig.8 has displayed the variation of excess molar volumes, Vm versus the mole fraction x1 for E those three binary mixtures at different temperatures. The positive values of, Vm , in the 1st and

2nd binary mixtures and the negative ones of the 3rd binary mixture indicate that the volume expansion in 1st (DCPD + methylcyclohexane) mixture was greater than those in 2nd (DCPD + toluene) mixture. This result can be attributed to the physical effect from the dispersion forces and non-specific physical interactions. The volume contraction in 3rd (DCPD + p-xylene) mixture can be ascribed to structural effect due to the packing of components attributed to the differences molar volume and free volume of molecules.

The values of 𝑉𝑚𝐸 at equimolar composition for all binary mixtures vary according to the sequence: 3rd binary (DCPD + p-xylene) < 2nd binary (DCPD + toluene) < 1st binary (DCPD + methylcyclohexane).

The Redlich–Kister equation is as follow: 𝑛

𝑌 = 𝑥1 𝑥2 ∑ 𝐴𝑖 (𝑥1 𝑖=0

− 𝑥2 )𝑖

(9)

where Y is either 𝑉𝑚𝐸 or G*E and n is the degree of the polynomial. 𝑥1 and 𝑥2 are the mole fractions of components, Ai , the polynomial coefficient obtained by a linear least-squares fitting procedure. In each case, the optimum number of coefficients was

σ(Y) = (

Yexp −Ycal 2 ∑( ) Yexp

N−m

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ascertained from an examination of the variation of the standard deviation 𝜎 with: 1 2

) ×

(10)

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100

In which N is the number of results and m, the number of parameters retained in Eq. (9).

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The values adopted for the coefficient Ai and standard deviation σ for 𝑉𝑚𝐸 or G*E were summarized respectively in Table 8.

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3.2.1. Prediction of excess molar volume by Prigogine-Flory-Patterson (PFP) theory The Prigogine-Flory-Patterson (PFP) theory is given by: ̅ 1⁄3 −1) ̅𝑉 2⁄3 𝛹𝑖 𝜃𝑗 (𝜒𝑖𝑗 /𝑃𝑖∗ ) (𝑉 ] ̅ −1⁄3 −1) ((4⁄3)𝑉

̅̅̅1 −𝑉 ̅2 )(𝑃1∗ +𝑃2∗ )𝛹1 𝛹2 (𝑉 𝑃2∗ 𝛹1 +𝑃1∗ 𝛹2

]

𝐼𝐼𝐼

𝐼

+ [−

̅1 −𝑉 ̅2 )2 ((14⁄9)𝑉 ̅ −1⁄3 −1)𝛹1 𝛹2 (𝑉 ] ̅ −1⁄3 −1)𝑉 ̅ ((4⁄9)𝑉

𝐼𝐼

+

(11)

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[

=[

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𝐸 𝑉𝑖𝑗 ∗ 𝑋𝑖 𝑉𝑖 +𝑋𝑗 𝑉𝑗∗

𝐸 𝐸 (I): 𝑉𝑖𝑛𝑡 interactional contribution, (II): 𝑉𝑓𝑣 free volume contribution and (III): 𝑉𝑃𝐸∗ internal

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pressure contribution.

The interaction parameter 𝜒𝑖𝑗 of PFP theory represents the intermolecular interaction that exists between components of binary mixtures. Graphical comparison between experimental and theoretical 𝑉𝑚𝐸 values with those calculated from PFP theory at a range of temperature T/K= 288.15 to 318.15 was exhibited in Fig. 8. Excess molar volumes values are positive for mixtures of DCPD with methylcyclohexane and toluene, except for p-xylene. The VE values at equimolar concentrations of DCPD and

additives follow the order p-xylene < toluene < methylcyclohexane. The VE values of DCPD with methylcyclohexane are larger than those corresponding to aromatic compounds (toluene and p-xylene). More positive values are obtained with a cyclic chain of methylcyclohexane than aromatic chain of toluene. These VE values can be explained by dispersion forces are predominant. Also, we can note the presence of double liaison in the structure of molecules of DCPD, toluene, and p-xylene, that favorite attraction phenomena between (DCPD + p-xylene) contrariwise (DCPD + toluene) when we are observed lower expansion of volume. Here it worth to mention the effect of the position of second CH3 group of p-xylene gave negative VE values were positive values obtained for the toluene compared to the aromatics.

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We conclude that the PFP theory is quite successful in predicting the VE for aromatic compounds that naphthenic compound, with standard deviation values, obtained less than 2.6 % for toluene, 8.5% for p-xylene and up 22% for methylcyclohexane.

The values of the interaction parameter, 𝜒12 , were listed in Table 9. There are positives for 1st

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binary mixture, indicating weak intermolecular specific interactions and negatives for 2nd binary mixture and 3rd binary mixture which suggest a strong intermolecular specific

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interaction. The interaction parameter χ12 calculated by PFP model follow the order toluene < p-xylene < methylcyclohexane. As well, the absolute values of parameter interaction (χ12 )

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increase with temperature increase for three binary mixtures.

𝐸 For the 1st and the 3rd binary mixture, an interactional contribution 𝑉𝑖𝑛𝑡 was responsible to

decide of the sign and magnitude of the excess molar volume, for 2nd binary mixture, an

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internal pressure contribution, 𝑉𝑃𝐸∗ was dominated to decide the sign and magnitude of the excess molar volume.

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However, the comparison between the experimental and the theoretical values of excess molar volume calculated by PFP theory was made by calculating standard deviation, σ, the

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applicability of PFP theory has given good agreement with experimental excess molar volume for the both 2nd and 3rd binary mixtures, the 2nd binary mixture was given lower standard deviation than 3rd binary mixture. The PFP theory of 1st binary mixture was yielded greater deviations.

Viscosity deviation The viscosity deviation, ∆ for binary mixtures was expressed achieved by equation (12):

∆ = 2

− ∑ 𝑥𝑖 𝑖

(12)

𝑖=1

Where xi is the mole fraction of component i in the mixture.  and 𝑖 are the dynamic viscosities of the mixture and pure components i, respectively. The variation of viscosity deviation, ∆ with the mole fraction x1 for those three binary mixtures at different temperatures is shown in Fig 9. The same behaviour has been observed for binary mixtures of DCPD with methylcyclohexane, toluene, and p-xylene. ∆ values were negatives and become more negative when the temperature decreases. The values and

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magnitude of ∆ depend on the size and shape of compounds in addition to intermolecular forces, may be ascribed to the presence of weak intermolecular interactions[29].

The experimental dynamic and kinematic viscosity were discussed below on tested of various semi-predictive models and correlations.

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3.3. Prediction of dynamic viscosity

ln( 𝑉) = 𝑥1 ln(1 𝑉1 ) + 𝑥2 ln(2 𝑉2 )

𝜏12 𝑒𝑥𝑝 (−𝛼𝜏12 ) ] 𝑥2 + 𝑥1 𝑒𝑥𝑝 (−𝛼𝜏12 )

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∆g 𝑖𝑗 ) 𝑅𝑇

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𝜏𝑖𝑗 =(

(13)

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+

𝜏21 𝑒𝑥𝑝 (−𝛼𝜏21 ) 𝑥1 + 𝑥2 𝑒𝑥𝑝 (−𝛼𝜏21 )

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+ 𝑥1 𝑥2 [

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Eyring-NRTL model[19]:

∆g 𝑖𝑗 is the interaction parameters and α is the non-randomness parameter equal 0.3. Eyring-UNIQUAC model[20]:

(14)

ln( 𝑉) = 𝑥1 ln(1 𝑉1 ) + 𝑥2 ln(2 𝑉2 ) + 𝑥1 ln

1  𝜃1 𝜃2 + 𝑥2 ln 2 + 5 (𝑞1 𝑥1 ln + 𝑞2 𝑥2 ln ) 𝑥1 𝑥2 𝑥1 𝑥2

− 𝑞1 𝑥1 ln(𝜃1 + 𝜃2 𝜏12 ) − 𝑞2 𝑥2 ln(𝜃2 + 𝜃1 𝜏21 )

(15)

𝜏𝑖𝑗 = 𝑒𝑥𝑝 (−

∆𝑢𝑖𝑗 ) 𝑅𝑇

(16)

respectively, and ∆𝑢𝑖𝑗 represents the interaction parameters. Eyring-Wilson model[21]:

𝑉1 𝜆21 𝑒𝑥𝑝 (− )) 𝑉2 𝑅𝑇

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+ 𝑥2 ln (𝑥2

(17)

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+ 𝑥1

𝑉2 𝜆12 𝑒𝑥𝑝 (− )) 𝑉1 𝑅𝑇

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ln( 𝑉) = 𝑥1 ln(1 𝑉1 ) + 𝑥2 ln(2 𝑉2 ) + 𝑥1 ln (𝑥1 + 𝑥2

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𝑞𝑖 , is the surface area parameter, 𝜃𝑖 and 𝑖 are the surface area and volume fraction,

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where 𝜆𝑖𝑗 is the interaction parameters. 3.4. Prediction of kinematic viscosity

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Lobe equation[22]:

𝜈2

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𝜈 = 𝛷1 𝜈1 exp [𝛷2 𝛼12 ln ( )] 𝜈1

𝜈2 + 𝛷2 𝜈2 exp [𝛷1 𝛼21 𝑙𝑛 ( )] 𝜈1

(18)

Where 𝛷1 and 𝛷2 are the volume fractions of the components, 𝛼12 and 𝛼21 represent interaction parameters. Heric equation[23]:

ln(𝜈) = 𝑥1 ln(𝜈1 ) + 𝑥2 ln(𝜈2 ) + 𝑥1 ln(𝑀1 ) + 𝑥2 ln(𝑀2 ) − ln(𝑥1 𝑀1 + 𝑥2 𝑀2 ) + 𝑥1 𝑥2 [𝛾12 + 𝛾21 (𝑥1 − 𝑥2 )]

(19)

where 𝛾12 and 𝛾21 represent the interaction parameters. McAllister model[24]: ln(𝜈) = 𝑥13 ln(𝜈1 ) + 𝑥23 ln(𝜈2 ) + 3𝑥12 𝑥2 ln(𝜈12 ) + 3𝑥22 𝑥1 ln(𝜈21 ) − ln (𝑥1 + 𝑥2

𝑀2 ) 𝑀1

+ 𝑥23 ln (

𝑀2 ) 𝑀1

(20)

where 𝜈12 and 𝜈21 represent the interaction parameters.

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2 𝑀2 1 2𝑀2 + 3𝑥12 𝑥2 ln ( + ) + 3𝑥22 𝑥1 ln ( + ) 3 3𝑀1 3 3𝑀1

The obtained results using the models and correlations to predict dynamic and kinetic

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viscosities were shown in Figs 10 and 11. These graphs displayed a comparison between experimental and theoretical values of viscosity at 298.15 K. Fitting parameters derived from

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the viscosity correlations and the corresponding standard deviations at all temperature investigated were listed in Table 10. An examination of correlations Eyring_NRTL and

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Eyring_Wilson have given good agreement with the dynamic viscosity experimental values than Eyring_UNIQUAC. It was found that both of Heric equation and McAllister model have the same standard errors at each temperature and Lobe equation has given good agreement

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with the kinematic viscosity experimental values than Heric correlation and McAllister model.

From the results given in Table 10, we can conclude that the models and correlations with

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two interaction parameters used in this study give the good description with standard deviation low than 5% for (Eyring_NRTL, Eyring_Wilson, Lobe, Heric and Mc Allister) for

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all mixtures investigated expect Eyring_UNIQUAC model the results gave less attractive for third mixture (DCPD + p-xylene) with Standard deviation up12%. Thereby, the interaction parameters (gij, uij, λij, αij, γij and Zij) which can assume both positive and negative values, are characteristic of each mixture; they represent a measure of the strength of the intermolecular interactions between unlike molecules and are not dependent on the mixture composition. Positive and negative values obtained of interaction

parameters (gij, uij, αij and γij) reflect the behaviour of binary mixture that deviate from Raoult's law except (λij and Zij) values were all positive at all temperatures investigated. 3.5. Excess Gibbs free energy of activation of viscous flow The experimental excess Gibbs free energy of activation of viscous flow 𝐺 ∗𝐸 for binary mixtures were derived from equation (21): 𝐺 ∗𝐸 = R𝑇 [ln( 𝑉) 2

− ∑ 𝑥𝑖 ln(𝑖 𝑉𝑖 )]

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(21)

𝑖=1

Where xi is the mole fractions, 𝑉, 𝑉𝑖 the molar volumes and , 𝑖 the dynamic viscosities of the mixture and pure components i, respectively. R is the gas constant, T is the absolute

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temperature.

Three binary mixtures containing DCPD and (methylcyclohexane, toluene, and p-xylene)

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were displayed in Figs 12-14 in which we observed that G*E values were negatives for all binary, further supporting the presence of weak intermolecular interactions.

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3.5.1. Prediction of Excess Gibbs free energy of activation of viscous flow by semi-empirical models

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NRTL model [25]: 𝐸 𝐺𝑚 𝜏21 𝐺21 = 𝑥1 𝑥2 ( 𝑅𝑇 𝑥1 + 𝑥2 𝐺21

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𝜏12 𝐺12 ) 𝑥2 + 𝑥1 𝐺12

(22)

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+

UNIQUAC model [26]: 𝐺𝐸 𝛷1 𝛷2 𝜃1 𝜃2 = 𝑥1 ln + 𝑥2 ln + 5 [𝑞1 𝑥1 ln + 𝑞2 𝑥2 ln ] − 𝑞1 𝑥1 ln(𝜃1 + 𝜃2 τ21 ) 𝑅𝑇 𝑥1 𝑥2 𝛷1 𝛷2 −𝑞2 𝑥2 ln(𝜃2 + 𝜃1 τ12 )

(23)

Heil model [27]: 𝐺𝐸 = −[𝑥1 ln(𝑥1 + 𝑥2 𝛬21 ) + 𝑥2 ln(𝑥2 + 𝛬12 𝑥1 )] 𝑅𝑇 + 𝑥1 𝑥2 [

𝜏21 𝛬12 𝜏12 𝛬21 + ] 𝑥1 + 𝑥2 𝛬21 𝑥2 + 𝛬12 𝑥1

(24)

The results of fitting parameters and standard deviations derived by using NRTL, UNIQUAC and Heil models to predict excess Gibbs free energy of activation of viscous flow at all temperatures investigated were given in Table 11. It is clearly seen that semi predictive models used were only suitable with 2nd binary mixture by given smaller standard deviation than other binary mixtures.

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Conclusions

The flash points of binary mixtures containing DCPD with methylcyclohexane, toluene, and p-xylene, were measured by ERAFLASH closed cup tester. The experimental data were compared with values calculated by using Le Chatelier modified equation. The activity

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coefficients were estimated by the UNIFAC, UNIFAC_Dortmund and the ASOG models. All the predictions agree with the experimental data. However, the calculated values based on the

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UNIFAC model were found to be better than those based on the UNIFAC_Dortmund and ASOG. Density and viscosity data of three binary mixtures were measured over a temperature

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range between (288.15 to 318.15) K by using Digital viscosimeter SVM 3000. The measurements were used to calculate excess thermodynamic properties. Based on the results obtained by using PFP theory, it can be concluded that good fit of the experimental excess

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molar volume values of 2nd and 3rd binary mixtures and worst fit of 1st binary mixture at all temperatures investigated. From the standard deviations obtained by using dynamic and kinematic viscosity correlations, Eyring_NRTL, Eyring_Wilson, and Lobe have given good

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agreement with viscosity data at all temperature studies. Finally, models were proposed to correlate excess Gibbs free energy of activation of viscous flow; NRTL, UNIQUAC and Heil

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models have given satisfactory fit of experimental G*E values for 2nd binary mixture and poorest fit of 1st and 3rd binary mixtures at all temperature studies.

Conflict of Interest



All authors have participated in (a) conception and design, or analysis and interpretation of the data; (b) drafting the article or revising it critically for important intellectual content; and (c) approval of the final version.



This manuscript has not been submitted to, nor is under review at, another journal or other publishing venue.



The authors have no affiliation with any organization with a direct or indirect financial interest in the subject matter discussed in the manuscript.

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Acknowledgments The authors are grateful for the financial support of this research from Ecole Militaire

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Polytechnique (Doctoral Training Program).

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Figures captions Figure 1. Structures of used compounds. Figure 2. Chromatogram of dicyclopentadiene obtained by Gas Chromatography. Figure 3. 13C-NMR spectrum of dicyclopentadiene. Figure 4. 1H-NMR spectra of dicyclopentadiene. Figure 5. Comparison of the flash point prediction curves with experimental data against mole fraction. x1 of (a) DCPD + methylcyclohexane. (b) DCPD + toluene. (c) DCPD + p-

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xylene (, Exp.; ▬, UNIFAC; ▬▬, UNIFAC estimated ; ▬, UNIFAC Dortmund; ▬▬, UNIFAC Dortmund estimated; ▬, ASOG; ▬▬, ASOG estimated; ▬ , Raoult's law; ▬▬ , Raoult's law estimated).

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Figure 6. Comparison between experimental () and literature (, [9];, [34]; , [35];, [36]; ,[37];,[39];,[40];,[42];,[43];,[44]) density data of studied pure compounds

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(a; methylcyclohexane, b; toluene, c; p-xylene).

Figure 7. Comparison between experimental () and literature (, [9];, [34]; , [35];,

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[36]; ,[37];,[39];,[40];,[42];,[43];,[45];,[46]) viscosity data of studied pure

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compounds (a; methylcyclohexane, b; toluene, c; p-xylene). Figure 8. Variation of excess molar volume (𝑉𝑚𝐸 ) against mole fraction, x1 of (a) DCPD +

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methylcyclohexane, (b) DCPD + toluene, (c) DCPD + p-xylene at different temperatures (, 288.15K ; , 293.15 K; , 298.15K; , 303.15K; , 308.15 K; , 313.15K; , 318.15K;

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▬,▬, ▬, ▬, ▬, ▬ , ▬, PFP). Figure 9. Variation of viscosity deviation () against mole fraction. x1 of DCPD for (a) 1st binary, (b) 2nd binary and (c) 3rd binary at different temperatures (, 288.15 K; , 293.15 K; , 298.15 K; , 303.15 K; , 308.15 K; , 313.15 K; , 318.15 K).

Figure 10. Variation of experimental and theoretical dynamic viscosity () against mole fraction, x1 of DCPD for (a) 1st binary, (b) 2nd binary and (c) 3rd binary at different temperatures (, Exp; ▬, Eyring_NRTL, ▬; Eyring_UNIQUAC, ▬; Eyring_Wilson) at 298.15 K. Figure 11. Variation of experimental and theoretical kinetic viscosity () against mole fraction, x1 of DCPD for (a) 1st binary, (b) 2nd binary and (c) 3rd binary at different temperatures temperatures (, Exp; ▬, Lobe ▬; Heric, ▬; Mc Allister) at 298.15 K.

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Figure 12. Variation of excess free Gibbs energy (G*E) against mole fraction, x1 of endo DCPD for 1st binary mixture (DCPD + methylcyclohexane) at different temperatures (, 288.15 K; , 303.15 K; , 318.15 K; ▬, ▬ , ▬, semi-predictive models of: (a) NRTL; (b)

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UNIQUAC; (c) Heil).

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Figure 13. Variation of excess free Gibbs energy (G*E) against mole fraction, x1 of endoDCPD for 2nd binary mixture (DCPD + toluene) at different temperatures (, 288.15 K; ,

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303.15 K; , 318.15 K; ▬, ▬ , ▬, semi-predictive models of: (a) NRTL; (b) UNIQUAC; (c) Heil).

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Figure 14. Variation of excess free Gibbs energy (G*E) against mole fraction, x1 of endoDCPD for 3rd binary mixture (DCPD + p-xylene) at different temperatures (, 288.15 K; ,

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Heil).

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303.15 K; , 318.15 K; ▬, ▬ ,▬, semi-predictive models of: (a) NRTL;( b) UNIQUAC; (c)

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Figure 1

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315

pr

Tflash point (K)

320

310

300

0,2

Jo ur

na l

Pr

0,0

e-

305

0,4

0,6

x1

0,8

1,0

oo

f

Figure 6

0,780

(a)

0,775

pr

3

Density, (g/cm )

0,770 0,765

0,755

Pr

0,750

e-

0,760

290

295

300

305

310

315

320

310

315

320

Temperature/K

na l

0,745 285

0,875 0,870

3

Density,(g/cm )

0,865

Jo ur

(b)

0,860 0,855 0,850 0,845

0,840 285

290

295

300

305

Temperature/K

(c)

f

0,870

oo

0,865

3

Density, (g/cm )

0,860

pr

0,855 0,850

0,840 0,835 285

e-

0,845

290

295

300

305

310

315

320

310

315

320

Figure 7

na l

Pr

Temperature/K

0,80 0,75

Viscosity, mPa.s)

(a)

Jo ur

0,85

0,70 0,65 0,60 0,55 0,50 285

290

295

300

305

Temperature/K

f

0,66

(b)

oo

0,64 0,62

0,58 0,56 0,54

pr

Viscosity, mPa.s)

0,60

0,52 0,50

0,46 0,44 285

e-

0,48

290

295

300

305

310

315

320

310

315

320

Pr

Temperature/K

0,75

na l

(c)

Viscosity, mPa.s)

Jo ur

0,70

0,65

0,60

0,55

0,50

0,45 285

290

295

300

305

Temperature/K

oo

f

Figure 8

5,5

(a)

5,0 4,5

pr

4,0

(cm /mol)

3,5 3,0

1,5 1,0

Pr

0,5

e-

m

2,0

V

E

3

2,5

0,0 0,0

0,4

0,6

0,8

1,0

0,6

0,8

1,0

x1

0,28

na l

(b)

0,2

0,24

(c)

0,12

m

E

3

(cm /mol)

0,16

V

Jo ur

0,20

0,08 0,04 0,00 0,0

0,2

0,4

x1

f

0,00

oo

-0,05 -0,10 -0,15

-0,25 -0,30

pr

m

V

E

3

(cm /mol)

-0,20

-0,35 -0,40

-0,50 -0,55 0,0

e-

-0,45

0,2

0,4

0,6

Jo ur

na l

Pr

x1

0,8

1,0

oo

f

Figure 9 0,0 -0,2 -0,4

(a)

pr

-0,6

-1,0 -1,2 -1,4 -1,6

0,2

0,4

Pr

-1,8 0,0

e-

(mPa.s)

-0,8

0,6

0,8

1,0

0,6

0,8

1,0

x1

na l

0,0 -0,2

(b)

-0,4 -0,6

(mPa.s)

Jo ur

-0,8 -1,0 -1,2 -1,4 -1,6

-1,8 0,0

0,2

0,4

x1

f

0,0

oo

-0,2

(c)

-0,4 -0,6

-1,0

pr

(mPa.s)

-0,8

-1,2 -1,4

-1,8 0,0

e-

-1,6

0,2

0,4

0,6

Jo ur

na l

Pr

x1

0,8

1,0

oo

f

Figure 10

4,0 3,5

(a)

pr

3,0

2,0 1,5 1,0

Pr

0,5

e-

(mPa.s)

2,5

0,2

0,4

0,6

0,8

1,0

0,6

0,8

1,0

x1

na l

0,0 0,0

4,0 3,5

(b)

3,0

(mPa.s)

Jo ur

2,5 2,0 1,5 1,0 0,5

0,0 0,0

0,2

0,4

x1

(c)

f

4,0

oo

3,5 3,0

2,0

pr

(mPa.s)

2,5

1,5

0,5

0,2

Jo ur

na l

Pr

0,0 0,0

e-

1,0

0,4

0,6

x1

0,8

1,0

oo

f

Figure 11

4,5 4,0 3,5

(a)

pr

2,5

2

(m /s)

3,0

1,5 1,0

Pr

0,5

e-

2,0

0,2

0,4

0,6

0,8

1,0

0,6

0,8

1,0

x1

na l

0,0 0,0

4,5 4,0 3,5 3,0 2,5

2

(m /s)

Jo ur

(b)

2,0 1,5 1,0 0,5 0,0 0,0

0,2

0,4

x1

f

4,5

oo

4,0

(c)

3,5

2,5

pr

2

(m /s)

3,0

2,0 1,5

0,5

0,2

Jo ur

na l

Pr

0,0 0,0

e-

1,0

0,4

0,6

x1

0,8

1,0

oo

f

Figure 12

0 -100

pr

-200

(a)

-400 -500 -600 -700

Pr

-800 0,0

e-

*E

G (J/mol)

-300

0,4

0,6

0,8

1,0

0,6

0,8

1,0

x1

na l

0,2

0

-100

(b)

-200

*E

G (J/mol)

Jo ur

-300 -400 -500 -600 -700

-800 0,0

0,2

0,4

x1

f

0

(c)

oo

-100 -200

-400

pr

*E

G (J/mol)

-300

-500

-700 -800 0,0

e-

-600

0,2

0,4

0,6

Jo ur

Figure 13

na l

Pr

x1

0,8

1,0

f

0

oo

-100 -200 -300

pr

*E

G (J/mol)

(a)

-400

-600 -700 0,0

e-

-500

0,2

0,4

0,6

0,8

1,0

0,6

0,8

1,0

Pr

x1

0

-200

Jo ur

*E

G (J/mol)

(b)

na l

-100

(c)

-300 -400 -500 -600

-700 0,0

0,2

0,4

x1

f

0

oo

-100

-300

pr

*E

G (J/mol)

-200

-400

-600 -700 0,0

e-

-500

0,2

0,4

0,6

Jo ur

Figure 14

na l

Pr

x1

0,8

1,0

f

0

oo

-100 -200 -300

pr

*E

G (J/mol)

(a)

-400

-600 -700 0,0

e-

-500

0,2

0,4

0,6

0,8

1,0

0,6

0,8

1,0

Pr

x1

0

na l

-100 -200 -300

Jo ur

*E

G (J/mol)

(b)

(c)

-400 -500 -600 -700

-800 0,0

0,2

0,4

x1

f

0

oo

-100

-300

pr

*E

G (J/mol)

-200

-400

-600 -700 0,0

e-

-500

0,2

0,4

0,6

Jo ur

na l

Pr

x1

0,8

1,0

CAS N°

Supplier

Purity supplier

Purity

oo

Compound

f

Table 1 Specifications of the used chemicals

(% mass)

(% mass) by GC

Water content%

Water content%

(% mass)

(% mass) by Karl Fisher

by supplier

77-73-6

Sigma Aldrich

>95%

94.85%

< 0.003%

0.003%

methylcyclohexane C7H14

108-87-2

Sigma Aldrich

≥99.8%

99%

max 0.005%

0.002%

toluene C7H8

108-83-3

Sigma Aldrich

≥99.5%

99%

max 0.012%

0.005%

p-xylene C8H10

106-42-3

Sigma Aldrich

≥99%

99%

< 0.002%

0.002%

Jo ur

na l

Pr

e-

pr

DCPD C10H12

Table 2 Comparison of experimental and theoretical 13C NMR chemical shifts of the endo-DCPD H- atom number

Experimental data for DCPD 34.69 132.04 131.99 54.82 45.20 136.00 132.37 46.22 41.22 50.35

34.70 132.06 132.06 54.80 45.17 136 132.41 46.21 41.18 50.34

Jo

ur

na

lP

re

-p

ro of

C1 C2 C3 C3,a C4 C5 C6 C7 C7,a C8

Theoretical data for endo-isomer[30]

Table 3 Comparison of experimental and theoretical 1H NMR chemical shifts of the endo-DCPD Experimental data for DCPD 1.635 2.178 5.509 5.513 3.235 2.784 5.953 6.00 2.908 2.737 1.31 1.51

Theoretical data for endo-isomer [30] 1.62 2.18 5.50 5.50 3.21 2.79 5.93 5.99 2.88 2.72 1.30 1.47

Jo

ur

na

lP

re

-p

ro of

H- atom number H1x H1y H2 H3 H3a H4 H5 H6 H7 H7a H8a H8s

Table 4 Flash point TFP, density ρ and dynamic viscosity  of pure liquids at p = 0.1012 MPa with the corresponding values available in the literature.

Ref.

320.05

318.70

[31]

288.15

318.15

[32]

f

oo

Lit.

Lit.

Ref.

Exp.

Lit.

0.9858

-

-

5.0683

-

293.15

0.9815

0.9890

[33]

4.4632

4.0000

[33]

298.15

0.9772

-

-

3.9180

-

-

303.15

0.9729

-

-

3.4564

-

-

308.15

0.9685

-

-

3.1260

-

-

313.15

0.9641

-

-

2.8104

-

-

318.15

0.9597

-

-

2.5390

-

-

[34]

288.15

0.7741

0.7734

[35]

0.7823

0.7840

[36]

293.15

0.7698

0.7693

[37]

0.7298

0.729

[37]

0.76935

[38]

0.735

[38]

0.7650

[36]

0.6850

[36]

0.76496

[37]

0.681

[37]

0.76505

[38]

0,692

[38]

0.76065

[9]

0.627

[9]

0.76065

[37]

0.637

[37]

0.76071

[38]

0.651

[38]

0.75629

[9]

0.581

[9]

e-

pr

Exp.

Pr

DCPD

Exp.

270.15

Jo ur

methylcyclohexane

 (mPa.s)

ρ (g/cm3)

T(K)

TFP (K)

na l

Compounds

268.55

298.15

303.15

308.15

0.7655

0.7611

0.7568

[36]

0.6819

0.6389

0.5998

Ref.

[37]

0.598

[36]

0.75629

[38]

0.562

[37]

0.615

[38]

0.554

[9]

0.549

[37]

0.549

[38]

313.15

0.7524

0.7480

277.15

277.50

[39]

[9]

0.75193

[37]

0.75193

[38]

0.5641

0.5314

0.74758

288.15

0.8713

0.871501

[40]

0.6373

0.62506

[40]

293.15

0.8667

0.866859

[40]

0.6003

0.59610

[40]

0.8620

0.86221

[40]

0.5666

0.56703

[40]

0.8620

[41]

0.5590

[41]

0.85754

[40]

0.54003

[40]

0.8572

[41]

0.5260

[41]

0.8575

[44]

0.5253

[44]

0.85286

[40]

0.51279

[40]

0.8526

[41]

0.4980

[41]

0.8529

[44]

0.4933

0.848164

[40]

0.8479

[44]

0.84342

[35]

0.84344

[40]

298.15

na l

303.15

Jo ur

0.75637

Pr

toluene

e-

pr

318.15

oo

f

0.7563

308.15

313.15

318.15

0.8574

0.8527

0.8482

0.8434

0.8435

0.5357

0.5069

0.4807

0.48657 0.4717

0.4571

0.46203 0.4491

[44] [40] [44] [40] [44]

[44] 300.15

[42]

288.15

0.865253

0.8607

0.8565

e-

298.15

Jo ur

na l

Pr

303.15

308.15

313.15

318.15

0.8521

0.8478

[43]

0.7025

0.701

[43]

0.6517

0.650

[43]

0.6083

0.6100

[35]

0.611

[43]

0.5700

[35] [43]

0.86552

[45]

0.860917

[43]

0.86117

[45]

0.8567

[35]

0.856617

[43]

0.85682

[45]

0.8523

[35]

0.852255

[43]

0.576

0.8520

[44]

0.5726

0.85247

[45]

0.8480

[35]

0.8477

[44]

0.84812

[45]

0.8432

[44]

0.84377

[45]

0,8387

[44]

0.83942

[45]

0.486

0.8395

[46]

0.4919

pr

293.15

0.8652

f

303.15

oo

p-xylene

0.8431

0.8396

0.5753

0.5364

0.5390 0.5374

0.5094

0.5178

0.5049

0.4882

[44]

[35] [44]

[44]

[44] [46] [47]

Jo ur

na l

Pr

e-

pr

oo

f

Standard and relative standard uncertainties u, ur are u(x) =0.012, u(T)= ± 0.02 K, u (P) = 0.0005 MPa, ur (ρ) = 0.25%, ur () =2.2%.

Table 5 Experimental flash points TFP at different DCPD mole fractions x1 and p = 0.1012 MPa of three binary mixtures.

DCPD + methylcyclohexane

x1

TFP (K)

DCPD + toluene

51.072

0.0000

0.0987

515072

0.1024

0.2012

51.072

0.3023

TFP (K)

DCPD + p-xylene

511072

0.0000

...072

55.022

0.1024

...022

0.2018

55.0.2

0.1971

...0.2

511072

0.3008

557022

0.3006

..20.2

0.4007

557072

0.4006

555072

0.3993

..70.2

0.5024

552022

0.4997

575022

0.4999

..10.2

0.6001

57.072

0.6060

577072

0.6007

..5072

0.6994

572012

0.7014

..7022

0.7014

.7.072

0.8017

...052

0.7987

..7022

0.8001

.75072

0.9021

..1052

0.8991

.750.2

0.8993

.72052

.5.0.2 1.0000 1.0000 Standard uncertainties u are u(x) =0.012, u(TFP) = ±1.1K, u (P) = 0.0005 MPa.

.5.0.2

Jo ur

e-

Pr

.5.0.2

na l

1.0000

pr

0.0000

x1

f

TFP (K)

oo

x1

A

Models

C

2307.909 10341.626 1270.763 1290.968 1374.800 1327.62 1453.430 1446.832

P = 3.97 mmHg at 30°C. P = 6.82 mmHg at 40°C. P = 11.33 mmHg at 50°C.

DCPD + methylcyclohexane

DCPD + Toluene

DCPD + p-xylene

ADD 2.02 9.10 2.93 9.67 4.78 10.80 5.96 11.56

0.81 6.69 0.68 6.60 1.88 7.52 3.04 8.23

0.66 3.86 0.99 4.05 2.29 4.79 2.81 5.07

na l

P = 2.23 mmHg at 20°C.

e-

278.52492 [47] UNIFAC [48] 445.040 methylcyclohexane [47] UNIFAC_ Dortmund 221.416 [49] 223.701 toluene [47] ASOG 220.750 [49] 217.625 p-xylene [47] Raoult's law 215.307 [49] 214.627 [48] : Antoine coefficients of DCPD were fitted by equation: log (P mmHg) = A-B/(T(°C)+C) 8.07932 13.6621 6.82300 3.98232 6.95464 4.05043 6.99052 4.10494

Pr

DCPD

B

Ref.

oo

Antoine coefficients

pr

Compounds

f

Table 6 Antoine coefficients of compounds and Average absolute deviations values (ADD) of flash point derived by Eq 7.

Jo ur

[49] : Antoine coefficients of DCPD were used Landolt-Börnstein database and fitted by equation: log (P bar) = A-B/(T(K)+C) [50] : Antoine coefficients of methylcyclohexane, toluene, and p-xylene were used Poling and Prausnitz database and fitted by equation: log (P bar) = A-B/(T(K)+C)

Table 7 Data of density ρ and dynamic viscosity  at different DCPD mole fractions x1 and p = 0.1012 MPa for the first, second and third mixtures.

293.15

298.15

303.15

308.15

313.15

318.15

oo

T/K 288.15

 (mPa.s)

f

ρ (g/cm3)

x1

288.15

293.15

298.15

303.15

308.15

313.15

318.15

0.7823

0.7298

0.6819

0.6389

0.5998

0.5641

0.5314

0.7632

0.8903

0.8197

0.7605

0.7145

0.6717

0.6316

0.5952

0.7749

1.0030

0.9187

0.8517

0.7910

0.7439

0.7051

0.6697

0.7938

0.7869

1.1262

1.0430

0.9677

0.8907

0.8387

0.7996

0.7496

0.8108

0.8049

1.2800

1.1982

1.1001

1.0110

0.9497

0.9101

0.8519

0.8388

0.8336

0.8269

1.5048

1.3980

1.2801

1.1780

1.1091

1.0502

0.9802

0.8621

0.8571

0.8511

1.8108

1.6463

1.5040

1.3866

1.3061

1.2259

1.1378

DCPD (1) + methylcyclohexane (2) 0.7741

0.7698

0.7655

0.7611

0.7568

0.7524

0.0987

0.7906

0.7861

0.7820

0.7778

0.7733

0.7685

0.2012

0.8084

0.8026

0.7982

0.7929

0.7877

0.7819

0.3023

0.8262

0.8202

0.8139

0.8081

0.8022

0.4007

0.8439

0.8376

0.8315

0.8242

0.8184

0.5024

0.8632

0.8569

0.8517

0.8448

0.6001

0.8840

0.8792

0.8741

0.8680

0.6994

0.9082

0.9033

0.8985

0.8931

0.8880

0.8831

0.8780

2.2374

2.0321

1.8545

1.6933

1.5858

1.4726

1.3587

0.8017

0.9352

0.9289

0.9246

0.9197

0.9148

0.9101

0.9054

2.9045

2.6071

2.3675

2.1557

1.9926

1.8194

1.6681

0.9021

0.9613

0.9550

0.9504

0.946

0.9415

0.9367

0.9321

3.8059

3.3861

3.0290

2.7233

2.4765

2.2588

2.0592

1.0000

0.9858

0.9815

0.9772

0.9729

0.9685

0.9641

0.9597

5.0683

4.4632

3.9180

3.4564

3.1260

2.8104

2.5390

e-

Pr

na l

Jo ur

0.7480

pr

0.0000

DCPD (1) + toluene (2)

0.0000

0.8713

0.8667

0.8620

0.8574

0.8527

0.8482

0.8434

0.6373

0.6003

0.5666

0.5357

0.5069

0.4807

0.4571

0.1024

0.8855

0.8808

0.8761

0.8714

0.8667

0.8622

0.8574

0.7269

0.6849

0.6448

0.6068

0.5742

0.5451

0.5187

0.2018

0.8985

0.8938

0.8891

0.8844

0.8797

0.8752

0.8704

0.8440

0.7905

0.7387

0.6900

0.6559

0.6205

0.5889

0.3008

0.9108

0.9062

0.9015

0.8968

0.8921

0.8876

0.8828

0.9818

0.9144

0.8543

0.7952

0.7533

0.7071

0.6667

0.4006

0.9227

0.9181

0.9135

0.9088

0.9041

0.8996

0.8948

1.1652

1.0795

1.0005

0.9255

0.8681

0.8118

0.76001

0.9341

0.9295

0.9249

0.9203

0.9156

0.9111

0.9064

1.3901

1.2794

1.1744

1.0829

1.0190

0.9488

0.8866

0.6060

0.9458

0.9413

0.9367

0.9322

0.9275

0.9230

0.9184

1.7188

1.5700

1.4401

1.3131

1.2225

1.1354

1.0621

0.7014

0.956

0.9515

0.947

0.9425

0.9379

0.9334

0.9288

0.7987

0.9661

0.9616

0.9572

0.9527

0.9482

0.9437

0.9392

0.8991

0.9762

0.9718

0.9674

0.9629

0.9585

0.9541

0.9496

1.0000

0.9858

0.9815

0.9772

0.9729

0.9685

0.9641

oo

f

0.4997

1.9479

1.7583

1.6020

1.4864

1.3745

1.2828

2.7722

2.4949

2.2397

2.0240

1.8747

1.7184

1.5800

3.7116

3.3055

2.9603

2.6654

2.4299

2.2077

2.0118

5.0683

4.4632

3.9180

3.4564

3.1260

2.8104

2.5390

pr

2.1436

0.9597

0.8652

0.8607

0.8565

0.8521

0.8478

0.8431

0.8396

0.7025

0.6517

0.6083

0.5753

0.5364

0.5094

0.5049

0.1024

0.8791

0.8746

0.8705

0.8664

0.8622

0.8576

0.8539

0.8183

0.7661

0.7144

0.6724

0.6225

0.59974

0.5879

0.1971

0.8916

0.8873

0.8833

0.8793

0.8751

0.8707

0.8669

0.9105

0.8509

0.7986

0.7508

0.7021

0.66534

0.6586

0.3006

0.9050

0.9008

0.8969

0.8929

0.8887

0.8844

0.8808

1.0534

0.9724

0.9075

0.8496

0.7934

0.74929

0.7357

0.3993

0.9175

0.9133

0.9095

0.9054

0.9012

0.897

0.8933

1.2214

1.1268

1.0404

0.9666

0.9051

0.85537

0.8296

0.4999

0.9299

0.9258

0.9219

0.9177

0.9135

0.9092

0.9054

1.4702

1.3467

1.2291

1.1406

1.0659

1.0007

0.9662

0.6007

0.9418

0.9378

0.9339

0.9296

0.9253

0.9208

0.9168

1.7913

1.6263

1.4829

1.3672

1.2792

1.1898

1.1378

0.7014

0.9533

0.9491

0.9453

0.941

0.9366

0.9320

0.9278

2.2190

2.014

1.8504

1.6934

1.5803

1.4567

1.3711

0.8001

0.9642

0.9599

0.9560

0.9516

0.9472

0.9427

0.9385

2.9051

2.6247

2.4017

2.174

1.9947

1.8264

1.6891

0.8993

0.9750

0.9707

0.9665

0.9622

0.9577

0.9533

0.9491

3.9002

3.5003

3.1263

2.8104

2.5289

2.2706

2.1038

1.0000

0.9858

0.9815

0.9772

0.9729

0.9685

0.9641

0.9597

5.0683

4.4632

3.9180

3.4564

3.1260

2.8104

2.5390

Jo ur

na l

Pr

0.0000

e-

DCPD (1) + p-xylene (2)

Standard and relative standard uncertainties u, ur are u(x) =0.012, u(T)= ± 0.02 K, u (P) = 0.0005 MPa, ur (ρ) = 0.25%, ur () =2.2%.

Table 8 Coefficients Ai of the Redlich-Kister equation and standard deviations  for excess molar volumes, 𝑉𝑚𝐸 (cm3/mol) and excess Gibbs energy, G*E (J/mol) for binary mixtures at temperatures T from 288.15 K to 318.15 K. A1

A2

A3



A0

A1

A2



f

A0

A3

A0

oo

T/K

DCPD (1) + methylcyclohexane (2)

DCPD (1) + toluene (2)

A1

A2

A3



DCPD (1) + p-xylene (2)

0.1003

-0.3067

-

0.41

-0.922

0.031

0.459

-

6.67

0.0903

-0.1719

-

0.48

-1.122

0.058

0.725

-

6.13

e-

12.036

-0.073

-6.134

-

7.43

0.6374

293.15

12.989

-0.177

-4.724

-

3.92

0.6944

298.15

13.956

-0.714

-6.211

-

6.65

0.7518

0.0855

-0.1756

-

0.43

-1.399

0.0007

0.749

-

5.84

303.15

15.650

-3.645

-9.041

7.617

4.49

0.8237

0.0598

-0.0007

-

0.13

-1.495

0.314

0.504

-

4.76

308.15

16.854

-4.408

-10.259

8.571

3.90

0.9132

0.0601

-0.1364

-

0.24

-1.586

0.276

0.611

0.554

1.40

313.15

18.297

-8.980

-10.497

16.466

3.88

0.9474

0.0879

-0.1383

-

0.40

-1.733

0.784

0.726

-0.193

1.08

318.15

19.755

-10.798

-10.415

17.010

1.61

1.0085

0.0545

-0.1432

-

0.30

-1.818

1.058

0.969

-1.036

3.86

na l

Pr

288.15

pr

𝑉𝑚𝐸 (cm3/mol)

G*E (J/mol)

-2720.8

-778.3

959.4

-

1.32

-2398.4

-629.6

101.7

-

4.67

-2519.5

-433.9

1033.4

-

13.72

293.15

-2562.8

-702.6

482.9

-

2.60

-2338.8

-639.1

175.4

-

4.19

-2457

-452.7

1426

-

19.20

298.15

-2474.6

-523.5

682.8

-

4.17

-2282.9

-615.9

255.4

-

6.62

-2341.2

-341.2

1929.8

-

12.34

303.15

-2417.4

-321.6

905.5

-

2.71

-2220.7

-507.2

400.3

-

9.80

-2199.3

-519.8

1983.9

824

15.68

308.15

-2220

-241.4

785.9

-

4.23

-2147.1

-530.1

521.4

-

9.37

-2032.5

-208

1686.6

-

6.60

313.15

-1933.7

-345.1

511

-

2.93

-2088.7

-502.1

651.8

-

8.61

-1920.3

-236.7

1680.5

-335.8

21.00

318.15

-1851.5

-400.4

633.3

-

3.62

-2011.1

-452.6

756.5

-

6.53

-1752.8

-358.4

1682.8

-

11.85

Jo ur

288.15

Table 9 Thermal expansion coefficients (α1,α2), thermal compressibility coefficients (κ1,κ2),interaction parameter χ12 of the PFP equation and standard deviation  for binary mixtures at temperatures T from 288.15 K to 318.15 K. T(K)

104 α1

104 α2

(K-1)

(K-1)

104κ1 (MPa-1)

104 κ2 (MPa-1)

χ21 (J/cm3)

equimolar calculated values contibutions (cm3/mol)



Interaction

Free vol.

P*-effect

DCPD (1) + methylcyclohexane (2) 8.72

11.10

13.0

10.61a

79.48

25.80

2.4800

0.0854

0.6012

293.15

8.76

11.17

14.0

10.97a

74.83

22.41

2.4602

0.1270

0.8855

298.15

8.80

11.36

14.7

11.49a

81.50

29.25

2.8140

0.1008

0.7392

303.15

8.92

11.43

15.6

11.96a

86.62

41.18

3.2119

0.0981

0.7453

308.15

9.08

11.49

16.8

12.42a

91.05

48.17

313.15

9.12

11.69

18.1

12.94a

90.69

63.28

318.15

9.17

11.76

19.2

13.44a

92.56

73.70

ro of

288.15

8.72

10.55

13.0

10.60a

-5.88

293.15

8.76

10.73

14.0

10.70a

-8.48

298.15

8.80

10.78

14.7

10.74a

303.15

8.92

10.84

15.6

10.80a

308.15

9.08

10.79

16.8

313.15

9.12

10.96

18.1

318.15

9.17

11.38

19.2

0.7450

3.6667

0.1025

0.8635

3.9265

0.1057

0.9118

1.39

-0.1743

0.0495

0.3830

0.99

-0.2621

0.0576

0.4928

re

288.15

0.0905

-p

DCPD (1) + toluene (2)

3.4799

1.09

-0.2995

0.0589

0.5452

-9.66

0.96

-0.3162

0.0558

0.5757

lP

-9.44

-8.26

1.24

-0.2811

0.0446

0.5508

11.00a

-10.89

1.56

-0.3850

0.0514

0.6683

11.09a

2.54

-0.5836

0.0724

0.8980

na

10.90a

-16.03

10.04

13.0

8.24b

-23.36

1.83

-0.6291

0.0265

0.4291

10.10

14.0

8.56b

-25.04

2.98

-0.7116

0.0275

0.4659

10.13

14.7

8.89b

-26.57

3.16

-0.7884

0.0276

0.4740

8.92

10.21

15.6

9.18b

-25.98

4.29

-0.8084

0.0262

0.4771

308.15

9.08

10.31

16.8

9.61b

-24.87

5.62

-0.8134

0.0239

0.4683

313.15

9.12

10.38

18.1

9.88b

-25.73

7.80

-0.8819

0.0251

0.5161

318.15

9.17

10.43

19.2

10.19b

-25.77

8.35

-0.9214

0.0253

0.5385

8.72

293.15

8.76

298.15

8.80

303.15

Jo

288.15

ur

DCPD (1) + p-xylene (2)

1

𝜕𝜌𝑖

𝜌𝑖

𝜕𝑇 𝑃

α1 and α2 (isobaric expansivity) were calculated by Eq 𝛼𝑖 (K −1 ) = (− ) ( κ1 (isothermal compressibility) estimed, κ2 extrapolated.

) .

ur

na

lP

re

-p

ro of

From Ref[51], b From Ref[52, 53].

Jo

a

Table 10 Interaction parameters gij, uij, λij, αij, γij, Zij and standard deviations  for the different viscosity models studied at temperatures from 288.15 K to 318.15 K. 1st binary

2nd binary

3rd binary

1st binary

2nd binary

3rd binary

g12

-285.1

347.3

-1923.9

α12

1.9019

2.0862

1.5266

g21

-2180.3

-2437.5

-465.2

α21

-0.9693

-1.0148

-0.7766

2.35

1.12

3.62



0.84

1.49

2.49

u12

-996.5

790.1

-1542.3

γ12

1.0503

1.0141

1.1082

u21

-47.92

-1448.8

679.2

γ 21

0.2022

0.2057

-0.0932



4.57

2.06

8.87



1.77

0.83

3.57

λ12

988.7

131

1950.4

Z12

1.9504

1.7627

1.9711

λ21

2456.1

2983

1255.6

Z21

1.2969

1.0542

1.0009



2.59

1.36

3.66



1.77

0.82

3.57

g12

73.1

437.8

-2318.1

α12

1.9286

2.1027

1.4652

g21

-2351.7

-2458.7

72.2

α21

-1.0087

-1.0251

-0.7271

1.63

1.16

4.37



0.47

0.77

3.38

u12

-835.7

822.5

-2518.8

γ12

0.9658

0.9762

1.0725

u21

-180.7

-1459.7

2518.8

γ 21

0.2123

0.2077

-0.1531

2.17

12.18



1.16

1.19

4.40

46.1

2229.5

Z12

1.8034

1.6140

1.8318

2973

973.2

Z21

1.2313

0.9889

0.9096

1.37

4.34



1.16

1.19

4.40

α12

1.8244

2.0372

1.3508

Models

Models

Eyring_NRTL

 Eyring_UNIQUAC

Eyring _Wilson

Lobe

Heric

McAllister

T=293.15 K

Eyring _Wilson



3.19

λ12

738.6

λ21

2532.7



Eyring _Wilson

-p

McAllister

-624.7

62.4

-3017.9

g21

-1704.2

-2152.5

1226.4

α21

-0.9625

-1.0120

-0.6318

1.83

1.56

4.76



0.72

0.98

4.02

u12

-1114.9

433.7

-2437.2

γ12

0.9099

0.9083

1.0093

u21

169.9

-1210.6

2437.2

γ 21

0.1277

0.1355

-0.2475



3.62

3.08

10.95



1.43

1.06

4.93

λ12

1040.2

176.2

2754.7

Z12

1.7021

1.5282

1.7377

λ21

1953.8

2696.9

489.7

Z21

1.1218

0.9143

0.8272

1.96

1.74

4.70



1.43

1.06

4.93



Eyring_UNIQUAC

Heric

g12

Jo

Eyring_NRTL

ur

T=298.15 K

1.85

Lobe

re

Eyring_UNIQUAC

lP



na

Eyring_NRTL

ro of

T=288.15 K



Lobe

Heric

McAllister

T=303.15 K g12

-1394.6

-611.8

-3419.1

g21

-898.3

-1576.6

2.09

u12

α12

1.7281

1.9665

1.2890

2048.4

α21

-0.9168

-0.9914

-0.5732

1.96

4.72



1.28

0.81

4.20

-1494.5

-101.3

-2405.6

γ12

0.8488

0.8485

0.9538

u21

693.2

-814

2405.6

γ 21

0.0613

0.0672

-0.2875



4.42

4.15

10.48



2.02

1.22

5.02

λ12

1512.9

504.7

3021.8

Z12

1.6063

1.4466

1.6272

λ21

1346.2

2239.3

236.9

Z21

1.0338

0.8466

0.7721

2.15

2.07

4.75



2.02

1.22

5.02

g12

-1220.5

-948

-2940.8

g21

-878.9

-1192

1490.6

1.57

2.38

3.66

u12

-1360.2

-425.4

-2268.8

u21

586.5

-524.9

2268.8



3.09

5.23

λ12

1289.5

662.9

λ21

1256.1

 Eyring_UNIQUAC

Eyring _Wilson



Lobe

Heric

McAllister

T=308.15 K

Eyring _Wilson



1.62

Eyring_NRTL

g12

1.3032

α21

-0.5223

-0.9718

-0.6500



1.79

1.10

3.13

γ12

0.6297

0.8735

0.8385

γ 21

-0.1813

0.0349

-0.2043

1.84

2.21

3.78

McAllister

Z12

1.7241

1.3380

1.5097

0.9561

0.7782

0.7651



278.1

Z21

2.45

3.64



1.84

2.21

3.78

α12

2.2742

2.0453

1.3783

Lobe

-620.6

-2684.9

-1368.9

-1413.4

1138

α21

-1.3374

-1.0560

-0.7493

1.27

2.01

2.55



0.50

0.42

2.93

u12

-1088.1

-165.3

-2250

γ12

0.5114

0.7470

0.7674

u21

290.4

-711.1

2250

γ 21

0.3526

0.1331

-0.1156



2.61

4.28

6.34



0.59

0.91

3.46

λ12

709.1

402.7

2220.5

Z12

1.3768

1.2420

1.3810

λ21

1506.6

2069.6

352.4

Z21

1.1069

0.7854

0.7564

1.32

2.08

2.55



0.59

0.92

3.46

-325.5

-649.1

-2200.8

α12

2.2204

2.0146

1.3605

Jo

ur



Eyring _Wilson

1.9664

-477.7

g21

Eyring_UNIQUAC

1.1531

1938.4

na

T=313.15 K

Heric

8.22

2454.5

α12

-p

Eyring_UNIQUAC

re



Lobe

lP

Eyring_NRTL

ro of

Eyring_NRTL



Heric

McAllister

T=318.15 K Eyring_NRTL

g12

Lobe

Eyring_UNIQUAC

Eyring _Wilson

g21

-1441

-1302.4

696.8

α21

-1.2960

-1.0270

-0.7452



1.44

1.87

3.50



0.54

0.28

3.09

u12

-1085.3

-181.1

-2234.1

γ12

0.5574

0.7589

0.7021

u21

290.6

-662.7

2234.1

γ 21

0.2993

0.0865

-0.1157



2.99

4.02

8.63

0.52

1.36

3.55

λ12

594.6

366.5

1718.7

Z12

1.2707

1.1604

1.3211

λ21

1529.4

1966.7

427.2

Z21

1.0003

0.7238

0.7462

1.49

1.92

3.46



0.52

1.36

3.55



Heric

 McAllister

NRTL, Calculated with the third non randomness parameter 𝛼 = 0.3.

Jo

ur

na

lP

re

-p

ro of

[gij]= J/mol, [uij]= J/mol, [λij]= J/mol.

Table 11 Interaction parameters gij, uij, λij, and standard deviations  for the different Gibbs energy models studied at temperatures from 288.15 K to 318.15 K. 1st binary

Models

2nd binary

3rd binary

T=288.15K

Heil

g12

1333.2

1484.4

189.2

-151.4

1447.2

-187.7

g21

-3283.3

-3137.7

-2360.4

-1865

-2964.1

-1677.6

21.3

5.21

35.71

17.76

15.38

61.72

u12

1312.2

2119.1

195.6

301.2

2140

-71.0522

u21

-1833.9

-2119.1

-1107.9

-1030.1

-2140

-797.1894



36.26

9.55

56.80

29.43

26.59

102.68

λ12

-65.1

-375

-640.3

-652.1

-359.1

-735.4

λ21

-2139.5

-1562.1

-1539.8

-1334.8

-1402.2

-1099.9

22.41

5.76

36.58

18.23

15.93

62.21



1457.7

1743.1

302.8

730.6

1392.7

561.7

g21

-3251.8

-3254.3

-2402.2

-2325.3

-2893.2

-2190.1



11.32

5.91

u12

1526.7

2128.4

u21

-1878.5

λ12

Heil

λ21

13.69

18.05

147.89

203.2

860.3

-2147

253.1

-2128.4

-1139.7

-1340.7

2147

-1045.5

12.47

94.09

23.86

32.03

217.36

-276.3

-578.9

-147.6

-373.3

-332.5

-2091.4

-1589.1

-1545.7

-1528.2

-1351.1

-1351.9

12.21

6.55

61.26

14.18

18.62

149.55

20.67 18

ur



60.20

lP



re

g12

na

UNIQUAC

T=313.15 K

-p

T=293.15K NRTL

T=298.15K

g12

1735.4

-11.2

1243

1241.1

871.7

-2711.2

-3219.4

-2071.2

-2622.6

-2742.4

-2288.4



12.28

9.67

77.89

17.10

19.71

123.20

u12

884.5

2140.6

16.0364

1206.4

2134.1

360

u21

-1500.2

-2140.6

-989.2847

-1553.1

-2134.1

-1089



22.42

17.65

125.27

30.53

35.46

193.42

λ12

-279.7

-272.4

-699.7

99.4

-422.3

-157.8

λ21

-1819.6

-1554.9

-1365.4

-1654.1

-1260.3

-1360.8

g21

UNIQUAC

Heil

T=318.15 K

705.4

Jo

NRTL

3rd binary

T=308.15 K

 UNIQUAC

2nd binary

ro of

NRTL

1st binary



13.00

10.29

78.78

g12

-47.9

1141.7

-212.6

g21

-2107.4

-2817.5

-1792.5



19.19

14.74

100.47

u12

368.6

2138.1

-95.9799

u21

-1150.3

-2138.1

-861.6429



32.78

23.87

158.14

λ12

-637.9

-492

-779.8

λ21

-1495.8

-1359.8

-1189.8

19.79

15.30

101.14

17.63

20.27

124.42

NRTL

UNIQUAC

Heil



NRTL, Calculated with the third non randomness parameter α= 0.3.

Jo

ur

na

lP

re

-p

[gij]= J/mol, [uij]= J/mol, [λij]= J/mol.

ro of

T=303.15 K