Density, Viscosity, Refractive Index, and Related Thermophysical Properties of Dibutyl Ether +2-Butanol + Cyclohexane Ternary Systems

: New measured data for density, ( ρ ), dynamic and kinematic viscosities, ( μ D and μ c ), and refractive index, ( n D ), are presented at T = 298.15 K and p = 0.1 MPa for binary and ternary mixtures containing dibutyl ether, 2-butanol, and cyclohexane. As a result, the derived properties are estimated based on the measured data. Excess molar volume, ( V E ), dynamic viscosity deviation ( Δ μ D ), and deviation in refractive index, ( Δ n D ), as derived properties, are fitted using the Redlich − Kister equation. In addition, perturbed-chain statistical associating fluid theory equation of state is employed to correlate the measured data of density.


INTRODUCTION
For the industrial and transportation sectors, fossil fuels such as coal, oil, and natural gas are the primary sources of energy.Fossil fuels, which are considered non-renewable energy sources, account for more than 80% of the world's primary energy supply. 1 The global demand for energy is steadily increasing owing primarily to population increase and economic development.If the current consumption rates continue, oil and gas reserves will be consumed completely by the end of the century. 2,3Additionally, transportation is a significant consumer of fossil fuels.Petroleum-based liquid fuels, such as gasoline, diesel, liquefied petroleum gas, and natural gas, are commonly used in automobiles. 4These nonrenewable materials contribute to environmental damage and climate change.In this context, a transition to alternate energy sources is urgently required in order to lessen the toxicity of pollutants released by automobiles.Previous research has shown that biofuels, which are generated directly from plants, are the best renewable alternative to fossil fuels.In Brazil, Australia, India, United States of America, and European Union, the majority of gasoline is blended with biofuels like ethanol and bio-ethers.In the same lines, the use of ethers and alcohols as oxygenated gasoline additives yields positive results due to their capacity to reduce pollutants and enhance the octane number. 5Some oxygenated components were added to the gasoline reformulation, such as alcohols, ethers, and glycol ethers, in order to increase the octane rating and lower the toxicity of the contaminants. 6Our research into the thermophysical characteristics of binary and ternary mixtures containing oxygenated components with alcohols and hydrocarbon components 7−17 led to this paper.At 0.1 MPa and 298.15 K, a study of density, dynamic and kinematic viscosities, and refractive index for binary mixtures composed of (i) dibutyl ether (1) + 2-butanol (2), (ii) dibutyl ether (1) + cyclohexane (2), (iii) 2-butanol (1) + cyclohexane (2), and the ternary mixture constituted by dibutyl ether (1) + 2-butanol (2) + cyclohexane (3) is presented in this work.The following derived properties are calculated using reported measured data: V E , Δμ D , and Δn D .The Redlich−Kister equation is employed to fit the derived properties.Furthermore, the varied observed densities for studied binary and ternary mixtures are modeled using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EoS).The influence of intermolecular interactions is examined in this paper for all binary and ternary mixtures studied.

EXPERIMENTAL SECTION
2.1.Apparatus and Procedure.At 0.1 MPa and 298.15 K, a Stabinger SVM 3000 viscosimeter is used to measure densities (ρ), and dynamic and kinematic viscosities (μ D and μ c ), for pure components (dibutyl ether, 2-butanol, and cyclohexane) as well as for binary and ternary mixtures.Two rotating concentric tubes make up this apparatus.Its working mode is based on the Couette principle, which asserts that viscosity is proportional to torque difference between rotating cylinders.The relative uncertainty of μ D is 2% (k = 2), μ c is 3% (k = 2), and the expanded uncertainties of ρ, T, p, and x i are 0.0005 g.cm −3 (k = 2, level of confidence: 95.45%), 0.04 K, 0.01 MPa, and 0.0008, respectively.The refractive index (n D ) of the pure components, as well as their binary and ternary mixtures, is measured using an Abbe digital refractometer.The refractive index has an expanded uncertainty of 0.00005 (k = 2, 0.95 degree of confidence).Air and decane are used to calibrate the Stabinger SVM 3000 viscosimeter, while air and water are used to calibrate the Abbe digital refractometer.
2.2.Chemicals.Dibutyl ether (DBE), 2-butanol, and cyclohexane are the chemicals used in this work, and they are given with a high mole fraction purity (>99%).Table 1 lists the chemical characteristics of the investigated components.Using an OHAUS analytical balance with a precision of 0.0001 g, different mixtures composed of dibutyl ether, 2-butanol, and cyclohexane are created by mass.The mole fraction standard uncertainty is predicted to be 0.0008.−59

MODELING
Gross and Sadowski developed the PC-SAFT EoS, 60,61 which can be written, in terms of the residual Helmholtz energy (ăr es ), as the sum of a hard-chain energy contribution (ăh c ), a dispersive energy contribution( ăd isp ), and an association interaction energy (ăa ssoc ) a a a a res hc disp assoc The non-associative parameters of the PC-SAFT EoS are segment number (m), segment energy parameter (ε/k), and segment diameter (σ).However, for complex fluids like associative fluids, it is advisable to include two additional parameters: the association volume (k A i Bi ) and the association energy (ε A i Bi ).
The Berthelot−Lorentz conventional mixing rule describes the parameters σ ij and ε ij for the mixture: where k ij is the binary interaction parameter for correcting the interaction between unequal chains segments.The binary interaction parameters are assumed to be zero for the mixtures analyzed in this study.
The PC-SAFT equation of state parameters are optimized using the following objective function: nwhere N is the number of measured data.
PC-SAFT EoS parameters were generated by fitting the measured density of studied pure components in this work.Due to the good representation of density of all studied mixtures, two associating sites (2B association scheme) were used.
−64 Furthermore, the association is explicitly taken into account in the PC-SAFT EoS, which is crucial for modeling the mixtures discussed in this paper.

Binary and Ternary Mixtures.
A mathematical polynomial equation is used to fit the density, ρ, for binary mixtures: where the P function presented ρ, x 1 is the mole fraction of component 1, and A i coefficients are calculated using the unweighted least-squares approach, and the optimal number of A i is established using the F-test. 65he calculation of dynamic viscosity is done according to ref 66 written as . (1 5 ) with x 1 : the mole fraction of component 1; C i : the adjustment coefficients; μ D1 and μ D2 : dynamic viscosity of pure components of each binary mixture.The excess molar volumes for all mixtures over a wide range of mole fractions are calculated using the equation: where n is the number of pure components in the mixture, x i denotes the mole fraction of component i, and M i is the molar mass, while the measured densities of the pure component i and the mixture are ρ i and ρ, respectively.
From the experimental values of viscosity for binary and ternary mixtures and corresponding mole fractions, dynamic viscosity deviation (Δμ D ), are calculated using the following equation:

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where μ Di is the absolute viscosity of pure component i and μ D : is the absolute viscosity of the mixture.The refractive index deviation, Δn D , are calculated using the following equation: where n D and n Di represent the refractive index of the mixture and pure component i, respectively.
The following Redlich−Kister equation 66 is used to link derived properties such as V E , Δμ D , and Δn D : ΔQ functions could be excess molar volume, (V E ), dynamic viscosity deviation, (Δμ D ), or deviations in the refractive index, (Δn D ), x is the mole fraction, and D i coefficients are generated using the unweighted least-squares method.The root-meansquare deviations σ are expressed as follows: where X could be the density, (ρ), dynamic and kinematic viscosities, (μ D and μ c ), or refractive index, (n D ); n: is the number of measured data, andp is the parameter number used in the Redlich−Kister equation.

Ternary Mixtures.
A mathematical polynomial equation is used to fit ρ for ternary mixtures: where the H function presented ρ, B ij coefficients are found using the unweighted least-squares approach, x i is the mole fraction of the i coefficient, n is the component number, and M is the polynomial degree.
Coefficients F i and the corresponding standard deviations (σ) are generated using the least-squares method.

Thermophysical Properties of Binary Mixtures.
To compare the measured values of density with those derived with the assumed correlation, the absolute average deviation (AAD) is used in this work: with N as the number of measured data.Table 3 shows the density (ρ), dynamic and kinematic viscosities (μ D and μ c ), and refractive index (n D ) experimental data for the studied binary mixtures.It is noted that the refractive index of the binary mixture DBE (1) + 2-butanol (2) present the same experimental value of the refractive index for several molar fractions because the difference between the refractive index of DBE and that of 2-butanol is less than the measurement uncertainty of this quantity.
Table 4 also lists the sets of coefficients A i and C i used to fit the measured values of ρ and μ D using polynomial equations eqs 5 and 6.
Table 5 lists the sets of adjustable coefficients D i required to correlate V E , ΔμD , or Δn D using the Redlich−Kister (eq 10).
The AADs between experimental densities and modeled by using the PC-SAFT EoS are provided in Table 6.The AADs for dibutyl ether (DBE), 2-butanol, and cyclohexane, respectively, are 0.004, 0.04, and 0.01%.
Figure 3 represents the changes in excess molar volumes as a function of the mole fraction x i for the three binary mixtures.It demonstrates that V E values are positive over a wide range of composition.Binary mixtures such as DBE (1) + 2-butanol (2) 2-butanol (1) + cyclohexane (2) have one strong self-

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associating component (alcohol) and two non-self-associating components (DBE and cyclohexane) that can form hydrogen bonding associations with the alcohol.The breakdown of hydrogen bonds in causes a volume expansion in the mixtures, which yields the positive term.The abovementioned sequence is reversed as maximum values shift toward larger concentrations of DBE and cyclohexane.
The excess volume values V E for the DBE (1) + cyclohexane (2) binary mixture are positive.Due to the absence of association effects, it is hypothesized that the cohesiveness between DBE and cyclohexane is insignificant (hydrogen bonds, double bonds, etc.).The positive contribution to V E for these mixtures could be due to disturbance in the hydrocarbon orientation order or breakdown of cohesive forces, as well as the steric effect, which prevents pure components from being in close proximity.Excess molar volume tendency curves for binary mixtures of DBE (1) + 2-butanol (2) and 2-butanol (1) + cyclohexane (2) were compared to those produced by Morrone and Francesconi, 67 Gonzaĺez et al., 58 Bernazzani et al., 69 and Kammerer and Lichtenthaler. 71At all compositions, this comparison reveals a high level of agreement.Furthermore, the comparison of experimental excess molar volume values with those reported by Berti et al. 70 and Teng and Acree 72 for DBE (1) + cyclohexane (2) indicates good agreement between both sets of data at all compositions.
Figure 4 shows plots of Δμ D derived from experimental data for three binary mixtures; additionally, the literature values 73,63 and our results are in good agreement.Over the entire range of composition, the variations in dynamic viscosity of these mixtures are negative.For the binary mixture of DBE (1) + cyclohexane (2), the lowest Δμ D value comes at mole fraction x 1 = 0.47.The internal friction force of this combination lowers as a result of the lower interaction between dissimilar molecules, resulting in negative viscosity deviations.
The Δμ D vs x 1 curves for alkanol-containing systems indicate the minimal value at mole fraction x 1 = 0.3 for the binary mixture DBE (1) + 2-butanol (2) and the minimum value at mole fraction x 1 = 0.6 for the binary mixture 2-butanol (1) + cyclohexane (2).The alteration of hydrogen bonding is the key factor affecting the fluctuations in Δμ D values of these binary mixtures.
The presence of non-polar molecules breaks the hydrogen bonds between 2-butanol molecules, causing the selfassociation of 2-butanol molecules to dissociate.As a result, the mixture's fluidity is superior to that of 2-butanol in its pure state on a macroscopic level.

Thermophysical Properties of Ternary Mixtures.
Table 7 shows the experimental densities, dynamic and kinematic viscosities, and refractive indices of DBE (1) + 2butanol (2) + cyclohexane (3) as a function of mole fraction x i .Table 8 contains also the sets of coefficients used to fit the measured data of ρ using a polynomial equation (eq 12).Table 9 shows the sets of adjustable coefficients required to correlate V E , Δμ D , or Δn D using eqs 13 and 14. Figure 5 shows the experimental density values as a function of mole fraction of x 3 for the ternary mixture DBE (1) + 2-butanol + cyclohexane (3).This graphic includes also densities predicted using the PC-SAFT equation of state, which demonstrates a good agreement with experimental data for the examined ternary mixture.
Overall, the V E values for the examined ternary mixture are positive at T = 298.15K, as presented in Figure 6.Positive V E values can be explained by the breaking effect mechanism between the mixtures of 2-butanol (1) + cyclohexane (2) or DBE (1) + 2-butanol (2).However, due to the breaking of hydrogen bonds in alcohol, a volume expansion in the mixture occurs, which generates the positive term.The V E of the mixture DBE (1) + cyclohexane (2) are positive over the      whole range of mole fraction, and it is proposed that the cohesion between cyclohexane and DBE is negligible because of the absence of the association effects.The positive values of V E for these studied mixtures are justified by the breaking of cohesion forces or the disruption in the orientation order of the hydrocarbon, and can be justified also by the steric effect, that prevent the proximity of pure components.Figure 7 shows the dynamic viscosity deviations against the molar fraction for the ternary mixture at 298.15 K.The values of Δμ D are clearly negative over the entire range composition, which can be explained by the destruction of hydrogen bonds and dispersion force.Observations at 298.15 K were expected to exhibit negative values of deviations in the refractive index, (Δn D ) due to the ternary mixture interactions, as shown in Figure 8.A negative value of Δn D demonstrates that the refractive index deviations of liquid mixture are impacted not only by the strength of the specific interaction but also by the molecular size and shape of the components that composed the mixture.In the experimental measurement of the mixtures, the behavior of V E has an opposite tendency compared to the Δn D , considering that the decline of V E values derives from the increase in the number of dipoles per unit volume. 75

CONCLUSIONS
Density, (ρ), dynamic and kinematic viscosities, (μ D and μ c ), and refractive index, (n D ), measurements of the ternary mixtures dibutyl ether (1) + 2-butanol (2) + cyclohexane (3) and their corresponding binary mixtures over the whole range of composition was carried out.Based on the collected data, the excess molar volumes, (V E ), dynamic viscosity deviations, (Δμ D ), and refractive index deviations, (Δn D ) of these mixtures were also computed.The Redlich−Kister equation was used to fit the V E , Δμ D , and Δn D for binary mixture compositions, while the Cibulka semi-empirical equation was used to fit the ternary mixtures.The structural effects and intermolecular forces presented in the studied mixtures can be analyzed using the values of V E , Δμ D , and Δn D .In order to determine the values of V E in alkanol-containing systems, the process of breaking hydrogen bonds between 2butanol molecules and geometrical interstitial accommodation are fundamental aspects.The PC-SAFT EoS agrees well with the measured density data for the studied binary and ternary mixtures.These results are crucial for further research into gasoline additives.

Table 1 .
Purity and Related Data of Chemicals a Determined by gas chromatography by the supplier Sigma Aldrich.

Table 4 .
Coefficients Needed for Eqs 5 and 6 with Standard Deviations Obtained for the Studied Binary Mixtures in this Work at T = 298.15K and at p = 0.1 MPa

Table 5 .
Coefficients D i Needed for the Redlich−Kister Eq 10 with Standard Deviations Obtained for the Studied Binary Mixtures in This Work at T = 298.15K and at p = 0.1 MPa 3

Table 8 .
Coefficients B ij Needed for the Polynomial Eq 12 with Standard Deviations Obtained for the Studied Ternary Mixtures in This Work at T = 298.15K and at p = 0.1 MPa