Effect of Alkyl Chain Length on Derived Thermodynamic Properties of

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Thermodynamics, Transport, and Fluid Mechanics

Effect of alkyl chain length on derived thermodynamic properties of 1-alkyl-3methylimidizolium chloride ionic liquids and their mixtures with ethanol Mary E McCorkill, James S. Dickmann, and Erdogan Kiran Ind. Eng. Chem. Res., Just Accepted Manuscript • DOI: 10.1021/acs.iecr.9b02574 • Publication Date (Web): 30 Jul 2019 Downloaded from pubs.acs.org on July 31, 2019

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Industrial & Engineering Chemistry Research

Effect of alkyl chain length on derived thermodynamic properties of 1-alkyl-3methylimidizolium chloride ionic liquids and their mixtures with ethanol Mary E. McCorkill, James S. Dickmann, Erdogan Kiran* Department of Chemical Engineering Virginia Tech Blacksburg, VA 24060 ( *Corresponding author; [email protected])

Abstract Densities of the ionic liquids [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl and their mixtures with ethanol were determined up to 40 MPa and 398K. Density was modeled as a function of temperature, pressure, and composition using the Sanchez-Lacombe equation of state. Using the model, derived thermodynamic properties, namely isothermal compressibility, isobaric expansivity, and internal pressure, were calculated. This allowed for the estimation of the Hildebrand solubility parameters of these ILs. Internal pressure was found to go through a maximum at low concentrations of ionic liquid in the case of [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl. These observations were interpreted in terms of a significant effect of the alkyl chain length on the interactions between the IL and the cosolvent, ethanol. It is speculated that this is in part due to possible clustering between the anion (Cl-) and ethanol.

Keywords: Ionic liquids, Density, High pressure, Compressibility, Internal pressure, Solubility parameter

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Industrial & Engineering Chemistry Research 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

I.

Introduction: Ionic liquids (ILs) are salts with melting points below 100oC [1-5]. They ae being considered for

various applications ranging from biomass processing [2-9] to polymerizations [3, 10-13]. They are viewed as tunable solvents due to the wide range of physical properties and solvent capabilities that can be achieved by changing the cation/anion combination or by adding functional groups [2, 4-7, 10-11, 1416]. Incorporating a cosolvent, such as ethanol, to these systems is being considered as a way to introduce additional tunability to their volumetric and thermodynamics properties such as density, compressibility and solvating power, and to their transport properties such as viscosity and diffusivity [3, 5, 18] which is important industrial process applications. The purpose of the present study is to assess the effect of alkyl chain length on the density and thermodynamic properties of 1-alkyl-3-methylimidazolium chloride ionic liquids. The specific ILs examined in this study are 1-ethyl-3-methylimidazolium chloride, [C2C1im]Cl, 1-propyl-3methylimidazolium chloride, [C3C1im]Cl, 1-butyl-3-methylimidazoium chloride, [C4C1im]Cl, and 1-hexyl-3methylimidazolium chloride, [C6C1im]Cl, the basic structure of which is shown in Figure 1. Additionally, mixtures of these ILs with an organic solvent, ethanol, have been studied. The mixtures of ionic liquids with ethanol is of particular interest in processing of lignocellulosic materials [1-2,4-6,9,13,16-19]. Due to the strong hydrogen bonding network of cellulose, lignocellulosic materials are insoluble in most solvents [1-5,9,16]. However, it has been shown that certain ILs, including, [C2C1im]Cl [3,5], [C3C1im]Cl [5], [C4C1im]Cl [1-3,8-10,13,18,20,22], and [C6C1im]Cl [6, 22] can dissolve cellulose and / or lignin. Mixtures of these ILs with ethanol would lower the viscosity and enhance diffusivity. In this first phase of the study we report in the thermodynamic properties of the mixtures and their modeling. Their transport properties, in particular viscosity, will be assessed and reported in the future.

Figure 1. Structure of the IL 1-alkyl-3-methylimidazolium (cation) chloride (anion), [CRC1im]Cl, where R is an alkyl group.


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II.

Materials and Methods a. Materials The ionic liquids [C2C1im]Cl and [C4C1im]Cl with ≥95%purity were purchased from Sigma-Aldrich.

The molecular weights and melting points are 146.64 g/mol and 360 K for [C2C1im]Cl, and 174.70 g/mol and 338 K for [C4C1im]Cl. These ionic liquids were dried in a vacuum oven at 343 K for 48 hours before use. The ionic liquids [C3C1im]Cl and [C6C1im]Cl were synthesized for this study. The molecular weight and melting point of [C3C1im]Cl is 160.67 g/mol and 333 K. The molecular weight of [C6C1im]Cl is 202.76 g/mol. The melting temperature of [C6C1im]Cl is not provided, but the glass transition temperature of [C6C1im]Cl is reported as 198 K. These melting and glass transition temperatures are the values reported in the literature by Ionic Liquid Technologies. Dried samples of the ILs were further analyzed by in our laboratory by differential scanning calorimetry to assess their crystallization / melting conditions. Using a Perkin Elmer Diamond DSC system, the samples were cooled down to 233 K and held there for two hours. They were then heated to 363 K at a rate of 10 K/min. Only [C2C1im]Cl and [C4C1im]Cl samples displayed melting transitions, which were at 348.7 K and 332.5 K, respectively, indicating that only these ionic liquids could be crystallized at 233 K. The synthesis of [C3C1im]Cl and [C6C1im]Cl utilized 1-methylimidazole, 1-chloropropane, 1chlorohexane, and ethyl acetate. 1-Methylimidazole with ≥ 99 % purity, 1-chloropropane with ≥ 98 % purity, and 1-chlorohexane with ≥ 99 % purity were all purchased from Sigma-Aldrich. Ethyl acetate with purity 99.9 % was purchased from Fisher Scientific. Ethanol with 100% purity was purchased from Decon Labs, Inc. These chemicals were used as received.

b. Synthesis of [C3C1im]Cl and [C6C1im]Cl To synthesize [C3C1im]Cl and [C6C1im]Cl, the corresponding primary alkyl halide was reacted with 1-methylimidazole. Figure 2 shows this reaction, where R represents the alkyl chain. Additionally, approximately 50 mL of ethyl acetate was added as the solvent. The reaction was run under reflux at the boiling point of ethyl acetate, 350 K, and proceeded for 48 hours. The duration of the reaction time was decided based on when visible phase separation occurred. The reaction was carried out at ambient pressure. A magnetic stir bar was utilized for mixing the reaction mixture.



The ionic liquids produced were liquids at room temperature and insoluble in ethyl acetate. A separation funnel was used to separate the ionic liquid (bottom layer) from the ethyl acetate and remaining reactants (top layer). The ionic liquid layer was then rinsed one to three times with 25 mL of ethyl acetate to remove any unreacted 1-methylimidizole or haloalkane contaminants. The ionic liquid was then dried in the vacuum oven at 343 K for 48 hours and stored in the desiccant chamber. The outcome of the synthesis process was verified with FTIR which are shown in Figure 3.

Figure 2. Reaction between 1-methylimidazole and chloroalkane to form ionic liquid.

Absorbance

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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[C3C1im]Cl

[C6C1im]Cl

3350

2850

2350

1850

Wavelength

1350

(cm-1)

Figure 3. IR spectra for [C3C1im]Cl and [C6C1im]Cl.


850

350

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c. Density Determinations A high-pressure view-cell was used to obtain density data across a range of pressures at isothermal conditions. The specifics of the view-cell and details of the operational procedures have been previously published [3,20-23]. The system incorporates a motorized pressure generator to change the position of a movable piston in the cell and thereby continually vary the volume of the cell. The volume of the view-cell is recorded in real-time using a linear variable differential transformer (LVDT) to track the position of the piston. From the initial mass loading by measuring the volume, density data are generated as function of the varying pressure in the cell at a given pressure. Pressure is typically scanned with the motorized pressure generator at a rate of about .5 MPa/s. This system measures density with an accuracy of ± 1%. For [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl and their mixtures with ethanol, density data were generated for pressures ranging from 10 to 40 MPa at 298, 323, 348, 373, and 398 K. Density measurements were performed on mixtures of ILs with ethanol at 25, 50, and 75 mass percent. Density data for [C2C1im]Cl and its mixtures with ethanol (including pure ethanol) have been previously determined in our laboratory and published [3]. To carry out these experiments, a measured amount of ionic liquid is first loaded to the view cell. The cell is then sealed, and a vacuum pump is utilized to remove any remaining air. Then, based on the mass of ionic liquid loaded, the correct amount of ethanol is pumped into the cell from a container (positioned on an analytical balance with 0.01 g accuracy), for a target mixture composition. The total sample (IL plus ethanol) masses ranged from 12 to 15 g. The ionic liquid-ethanol solution is allowed to mix using a magnetic stir bar positioned in the view cell.

d. Modeling with Sanchez-Lacombe Equation of State and Mixing Rules The Sanchez-Lacombe equation of state (S-L EOS) was used to model the density data and evaluate other derived thermodynamic properties. The S-L EOS is a fluid lattice model where each lattice site is occupied by either a molecule or a vacant site, which allows for the modelling of pressure effects and compressibility of the fluid [24-27]. S-L EOS is given by Equation 1 where 𝜌, 𝑃, and 𝑇 are the reduced density, pressure, and temperature respectively.

(

( 1𝑟)𝜌) = 0

𝜌2 + 𝑃 + 𝑇 𝑙𝑛(1 ― 𝜌) + 1 ―


(1)


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And 𝜌 ∗ , 𝑃 ∗ , and 𝑇 ∗ are the characteristic density, pressure, and temperature. 𝜌=

𝜌

𝑃=

∗

𝜌

𝑃 𝑃

𝑇=

∗

𝑇

(2)

𝑇∗

The relationship between the characteristic parameters and the molecular parameters, 𝑘, 𝜀 ∗ , and 𝑣 ∗ are given in Eq 3 where MW is the molecular weight of the mixture, 𝑘 is Boltzmann’s constant, 𝜀 ∗ is the interaction energy of a molecule segment inside a lattice site, 𝑣 ∗ is the volume of the lattice site, and r represents the number of lattice sites. 𝜀∗ 𝑇 = 𝑘 ∗

∗

𝑃 =

𝜀∗

𝑟=

𝑣∗

𝑀𝑊𝑃 ∗ 𝑘𝑇 ∗ 𝜌 ∗

(3)

Equations 4-6 give the mixing rule relations employed in the present study to determine the parameters, 𝜌 ∗ , 𝑃 ∗ , and 𝑇 ∗ , for the mixtures. Here, 𝑤𝑖 is the mass fraction and 𝜌𝑖∗ is the characteristic density , 𝜙𝑖 is the close pack volume fraction, and 𝜙0𝑖 is the the average close packed mer volume fraction of component i in the mixture.

1 ∗ 𝜌𝑚𝑖𝑥

=

𝑤𝑖

∑𝜌 𝑖

∗ 𝑖

∗

𝑃

=

𝑚𝑖𝑥

∑∑ 𝑖

𝜙𝑖𝜙𝑗𝑃𝑖𝑗∗

∗ 𝑇𝑚𝑖𝑥

=

𝑗

∑ 𝑖

𝑤𝑖 𝜌𝑖∗

𝜙𝑖 = ∑

𝜙0𝑖 =

∗ 𝑃𝑚𝑖𝑥

( ) 𝑤𝑗

𝑗

𝜌𝑗∗

𝑃𝑖∗ 𝜙𝑖 ∗ 𝑇𝑖 ∑ 𝜙𝑗 𝑗

(5)

𝑃𝑗∗

(6)

𝑇𝑗∗


𝜙0𝑖

𝑇𝑖∗

𝑃𝑖∗

(4)

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Equation 7 shows the characteristic pressure cross parameter, 𝑃𝑖𝑗∗ , in terms of an empirical interaction parameter, 𝑘𝑖𝑗, and the characteristic pressures of components i and j. Equation 8 shows the interaction parameter as a function of close packed volume fraction where kA and kB are constants. 𝑃𝑖𝑗∗ = (1 ― 𝑘𝑖𝑗) ∗ 𝑃𝑖∗ 𝑃𝑗∗ 𝑘𝑖𝑗 = 𝑘𝐴𝜙𝑖 ― 𝑘𝐵

(7) (8)

The number of lattice sites, r, and the molecular weight, MW, of the mixture are evaluated using Equations 9 and 10. 1 𝑟𝑚𝑖𝑥

=

𝜙𝑗

∑𝑟 𝑗

1 = 𝑀𝑊𝑚𝑖𝑥

(9)

𝑗

𝑤𝑖

∑𝑀𝑊

(10)

𝑖

𝑖

Modeling the density with the S-L EOS with these mixing rules then allows for the determination of the thermodynamic parameters such as the isothermal compressibility, isobaric expansivity and the internal pressure for the pure components or the mixtures using the defining equations given by Equations 11-13 [20, 25, 28]. 𝜅𝑇 =

( )

1 ∂𝜌 𝜌 ∂𝑃

(11)

𝑇

Equation 12 shows the isobaric expansivity, 𝛽𝑃, which is a measure of the volume change of the fluid as a function of temperature. 𝛽𝑃 = ―

( )

1 ∂𝜌 𝜌 ∂𝑇

(12)

𝑃

Equation 13 shows the internal pressure, 𝜋, which is a measure of how the internal energy of a substance changes with volume, which can be expressed in terms compressibility and expansivity. 𝜋=

( ) = 𝑇( 𝜅 ) ― 𝑃 ∂𝑈 ∂𝑉

𝛽𝑃

𝑇

(13)

𝑇



Internal pressure provides an estimate of the Hildebrand solubility parameter, σ, which is the square root of the cohesive energy density, CED, representing internal energy (U) per unit volume, which can be further expressed in terms of the heat of vaporization Δ𝐻𝑣 and the gas constant R as shown in Equation 14[14, 24, 29-31]. 𝜎 = 𝐶𝐸𝐷 =

∆𝐻𝑣 ― 𝑅𝑇 𝑈 = 𝑉 𝑉𝑚

(14)

Typically, the CED is determined using the heat of vaporization. However, this technique cannot be used with substances that do not volatilize or have negligible vapor pressures as is the case with ILs. For such systems internal pressure provides an estimate [29-31] through Equation 15. 𝜎≈ 𝜋

(15)

This is only an estimate as internal pressure represents how attractive and repulsive forces change with volume with changes in temperature and pressure and not the internal energy per unit volume [26, 30] and further it as it is also the case with the Hildebrand solubility parameter, does not account for intermolecular forces that may be present in the fluid, such as hydrogen bonding or polar molecular interactions [30-31].

III.

Results and Discussion a. Density Isotherms and Modeling with Sanchez-Lacombe Equation of State Figure 4 shows the density data for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 298, 323,

348, 373, and 398 K over the pressure range of 10 to 40 MPa. [C2C1im]Cl has a relatively high melting point of 360 K. For this reason, density data for this IL and the mixture containing 75 % IL are reported only for 373 and 398 K. [C3C1im] Cl and [C4C1im] Cl have melting points at 333 and 338 K, respectively, but they exist at room temperature as subcooled liquid. Therefore, density data could be collected for these ILs at 298 and 323 K. However, for [C4C1im]Cl, density determinations could not be done above 28 MPa due to solidification. Figure 5 shows the density for the mixtures of these ionic liquids with ethanol. All four ILs were found to be miscible with ethanol across the range of concentrations, temperatures, and pressures examined in this study. The data shows the expected trends in that densities increase with pressure along an isotherm, decrease with temperature at a constant pressure, and increase with the ionic liquid


Page 8 of 41

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content in the mixtures. Figure 6 shows the comparison of the density data for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 348K. The densities for [C2C1im]Cl and [C3C1im]Cl were found to be similar at 348 K. Density was found to decrease as alkyl chain length increased in the case of [C4C1im]Cl and [C6C1im]Cl, indicating the poorer packing efficiency when the alky chain length increases. The density data were then modeled with the S-L EOS. The black dots in the figures represent the Sanchez-Lacombe model fit. Tables 1-4 show the Sanchez-Lacombe characteristic parameters, P*, T*, ρ*, for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl and their mixtures with ethanol. The root mean squared deviation (RSME), the percent average deviation (% AAD), and the percent bias (% 𝛽) are also included in the tables. It should be noted that the [C2C1im]Cl data had been previously published [3]. However, updated mixing rules have been utilized to model the density. Table 5 shows values for binary interaction parameter kij, assuming kij is constant. RSME was found to increase with increasing alkyl chain length on the cation, indicating that this form of the model begins to break down with cation modifications. Due to this limitation, kij was assumed to vary as a function of close packed volume fraction (equation 8). RSME values were found to decrease by up to 64% using this concentration dependent form of kij. Table 6 shows parameters ka and kb used to model the kij and the mixtures of IL with ethanol throughout the present work. The effectiveness of the model was tested also using the limited density data available in the literature [32-34] for pure ionic liquids [C4C1im]Cl and [C6C1im]Cl. The predictions of the density using the present S-L model parameters at the pressure/temperature conditions at which the data are reported in the literatures were comparable, differences being small. Specifically, data for [C4C1im]Cl have been reported over a temperature range from 352.1 to 452.0 K and at pressures ranging from 10200 MPa [32]. This data by Machida et al., was compared with the values that would have been predicted with the present S-L EOS fits for this IL. The % AAD and % 𝛽 were found to be numerically same at 1.61 % and 1.61 %, respectively, with an RSME of 0.0179 g/cm3, indicating density values that are slightly underpredicted by the model. Data for [C6C1im]Cl have been reported from 293.15 to 353.15 K up to 20 MPa in one study [33], and from 311.5 to 451.2 K over a pressure range from 10-200 MPa in another study [34]. For the first set of data [33], the % AAD, % 𝛽 and RSME were found to be 0.505 %, 0.505 % and 0.00542 g/cm3, respectively. For the second set of data [34] corresponding values were 0.889 %, -0.806 %, and 0.0101 g/cm3, respectively. These show density values for this IL that are slightly overpredicted by the model, while differences remining still small.



The effect of the alkyl chain length on the fitted S-L parameters was also studied. The parameter P* was found to decrease with increasing alkyl chain length. As can be assessed from the S-L model Equations 1 and 2, decreasing value of P* will increase 𝑃 , and thereby increase the effect of pressure on density, and lead to a possible increase in compressibility with increasing alkyl chain length. As will be discussed in the next section, this is indeed mostly observed, with the exception of [C4C1im]Cl. The S-L parameter ρ* was also observed to decrease with increasing alkyl chain length. This is basically consistent with the overall trend of decreasing density of the ILs with the alkyl chain length as discussed earlier in the manuscript. The parameter T* is observed to display a large increase in going from [C2C1im]Cl to [C3C1im]Cl, then leveling off. This may partly be due to the narrower T-range (348 K to 398 K) in which density data were collected for [C2C1im]Cl compared to the wider range (from 298 to 398 K) for the other ionic liquids, which may have impacted the final T* value during the fitting process. Table 7 provides the linear correlation equations for P* and ρ* as a function of the alkyl chain length. For T*, only an average value based on ILs [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl is given in the table. Using the correlation equations and this average value for T*, while the model fits were found display an absolute average deviation of 2.5 % for [C2C1im]Cl, the deviations were than 0.6% for the other ionic liquids.


Page 10 of 41

Page 11 of 41

1.14

[C3C1im]Cl

1.12

Density (g/cm3)

Density (g/cm3)

1.14

[C2C1im]Cl

1.12 1.1

348 K

1.08

373 K

1.06

398 K

1.04

298 K

1.1

323 K

1.08

373 K

1.06

398 K

348 K

1.04

1.02

1.02

1

1 0.98

0.98 0

10

20

30

40

50

0

10

Pressure (MPa)

20

30

40

50

Pressure (MPa)

1.14

1.14

[C4C1im]Cl

1.12

[C6C1im]Cl

1.12

1.1

1.1

1.08

Density (g/cm3)

Density (g/cm3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.08

298 K 323 K

1.06

1.06

348K 373K

1.04

298 K 323 K

1.04

398K

1.02

348 K 373 K

1.02

1

1

0.98

0.98 0

10

20

30

40

50

398 K

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 4. Experimental data for the variation of density with pressure at 298, 323, 348, 373, and 398K for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl. Sanchez-Lacombe EOS model fits are represented by black dots.



1.2 1.1

[C3C1im]Cl 348 K

1.15

Density (g/cm3)

Density (g/cm3)

1.2

[C2C1im]Cl 348 K

1.15

IL

1.05 1

75% IL

0.95

50% IL

0.9

1.1

IL

1.05

75% IL

1 0.95

50% IL

0.9

0.85

25% IL

0.85

0.8

ethanol

0.8

0.75

25% IL

ethanol

0.75

0.7

0.7 0

10

20

30

40

50

0

10

Pressure (MPa)

1.2

1.2

IL

1.05 1

75% IL

0.95 0.9

50% IL

0.85

25% IL

0.8

1.1

40

1.05

50

IL

1

75% IL

0.95 50% IL

0.9 0.85

25% IL

0.8

ethanol

0.75

30

[C6C1im]Cl 348 K

1.15

Density (g/cm3)

1.1

20

Pressure (MPa)

[C4C1im]Cl 348 K

1.15

Density (g/cm3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 12 of 41

ethanol

0.75 0.7

0.7 0

10

20

30

40

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 5. Experimental data for the variation of density with pressure for 0, 25, 50, 75 and 100 mass % IL content in ethanol at 348 K for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl. Sanchez-Lacombe EOS model fits are represented by black dots.


Page 13 of 41

1.1

348 K

1.09

[C3C1im] Cl

1.08

Density (g/cm3)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


1.07 1.06

[C2C1im] Cl

1.05

[C4C1im] Cl

1.04 1.03

[C6C1im] Cl

1.02 1.01 1 0

10

20

30

40

50

Pressure (MPa) Figure 6. Experimental data for the variation of density with pressure for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 348 K. Sanchez-Lacombe EOS model fits are represented by black dots.

Table 1. S-L EOS parameters for mixtures of [C2C1im]Cl and ethanol. Mass %

Ethanol

25

50

75

[C2C1im]Cl

P* (MPa)

464.54

489.47

516.26

552.24

612.51

T* (K)

549.03

560.42

570.72

587.12

623.35

ρ* (g/cm3)

.88699

0.94624

1.0140

1.0922

1.1834

RSME (g/cm3)

.00138

0.00400

0.00324

0.00251

0.00173

% AAD

.151

0.406

0.269

0.216

0.130

%𝛽

-.00774

-0.102

0.180

-0.0262

-0.00173



Page 14 of 41


Ethanol

25

50

75

[C3C1im]Cl

P* (MPa)

464.54

498.10

505.62

479.43

410.51

T* (K)

549.03

623.21

692.21

726.91

709.66

ρ* (g/cm3)

.88699

0.94189

1.0040

1.0749

1.1566

RSME (g/cm3)

.00138

0.00663

0.00602

0.00485

0.00231

% AAD

.151

0.673

0.594

0.380

0.170

%𝛽

-.00774

0.673

-0.507

0.378

0.00198


Ethanol

25

50

75

[C4C1im]Cl

P* (MPa)

464.54

482.45

474.28

451.65

440.25

T* (K)

549.03

604.59

637.23

660.29

714.79

ρ* (g/cm3)

.88699

0.93532

0.98923

1.0497

1.1181

RSME (g/cm3)

.00138

0.00309

0.00422

0.00506

0.00186

% AAD

.151

0.318

0.374

0.443

0.145

%𝛽

-.00774

-0.204

0.0720

-0.102

0.000429


Ethanol

25

50

75

[C6C1im]Cl

P* (MPa)

464.54

486.18

446.19

383.91

377.06

T* (K)

549.03

622.53

629.45

610.71

699.82

ρ* (g/cm3)

.88699

0.93194

0.98169

1.0371

1.0990

RSME (g/cm3)

.00138

0.00329

0.00345

0.0619

0.00212

% AAD

.151

0.322

0.344

6.21

0.165

%𝛽

-.00774

-0.0808

-0.215

6.21

0.00202


Page 15 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 5. Mixing rule fits using constant binary interaction parameters and the root mean squared deviations (RSME). IL

[C2C1im]Cl

[C3C1im]Cl

[C4C1im]Cl

[C6C1im]Cl

kij

0.03383

-0.030331

-0.09405

-0.17651

RSME (g/cm3)

0.00370

0.00538

0.00628

0.00906

Table 6. Mixing rule fits using volume fraction dependent binary interaction parameters and the root mean squared deviations (RSME). IL

[C2C1im]Cl

[C3C1im]Cl

[C4C1im]Cl

[C6C1im]Cl

kA

0.07612

0.06019

0.26520

0.79783

kB

0.00248

-0.64970

-0.20947

-0.46194

RSME (g/cm3)

0.00310

0.00479

0.00397

0.00322

Table 7. Equations for determining the S-L parameters based on alkyl chain length R for IL [CRC1im]Cl along with the quality of fits for the four ILs studied. P* = -48.152*R + 640.65 T* = 708.09 ρ* = -0.0213*R + 1.219 [CRC1im]Cl

% AAD

%𝛽

RSME

[C2C1im]Cl

2.53

-2.53

0.027

[C3C1im]Cl

0.248

0.209

0.00333

[C4C1im]Cl

0.597

-0.597

0.00668

[C6C1im]Cl

0.472

0.472

0.00535

b. Derived Thermodynamic Properties of Mixtures of IL and Ethanol: Isothermal Compressibility. Figure 7 shows a comparison of the isothermal compressibility for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 298, 323, 348, 373, and 398K. As expected, the isothermal compressibilities decrease with increasing pressure or decreasing temperature. Figure 8 shows a comparison of the isothermal compressibilities for the pure ILs at 348K. With the exception of [C4C1im]Cl, compressibility is observed to increase with alkyl chain length.



Figures 9-12 show the calculated isothermal compressibility at 298, 323, 348, 373 and 398 K for mixtures with 50 % IL; and at 348 K for mixtures with 0, 25, 50, 75 and 100 % IL. Figure 13 shows a comparison of the isothermal compressibility of the ILs as a function of mass % IL at 348 K and 10 MPa. For [C2C1im]Cl, the isothermal compressibility decreases linearly with increasing IL content. The [C3C1im]Cl follows a similar trend up to 75 mass% IL, where the compressibility goes through a minimum before increasing to the pure IL value. The [C4C1im]Cl and [C6C1im]Cl appear to undergo both a decrease and an increase with IL content in the mixture. This trend is especially distinct for the [C6C1im]Cl for which compressibility appears to go through a minimum between 25 and 50 mass % IL and a maximum at 75 mass % IL.


Page 16 of 41

Page 17 of 41

0.001

0.001

[C3C1im]Cl

0.0008

0.0008

0.0006

κT (1/MPa)

κT (1/MPa)

[C2C1im]Cl

398 K 373 K 348 K

0.0004

0.0006

398 K 373 K 348 K

0.0004

323 K 298 K

0.0002 0

10

20

30

40

0.0002

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

0.001

0.001

[C4C1im]Cl

[C6C1im]Cl 0.0008

κT (1/MPa)

0.0008

κT (1/MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


0.0006 398K 373K

0.0004

398 K

0.0006

373 K 348 K

0.0004

348K

323 K

323K

298 K

298K

0.0002 0

10

20

30

40

0.0002 50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 7. Variation of isothermal compressibility with pressure for the ILs [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 298, 323, 348, 373, and 398K.



0.00065 [C6C1im]Cl

κT (1/MPa)

0.0006

348 K

[C3C1im]Cl

0.00055

[C2C1im]Cl

0.0005 [C4C1im]Cl

0.00045 0.0004 0.00035 0

10

20

30

Pressure (MPa)

40

50

Figure 8. Comparison of variation of isothermal compressibility with pressure for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 348 K.

0.0018

0.0018

50% [C2C 1]Cl

0.0016 0.0014 0.0012 0.001

398 K

0.0008

373 K 348 K

0.0006

323 K 298 K

0.0004

[C2C 1]Cl 348 K

0.0016

κT (1/MPa)

κT (1/MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 18 of 41

0.0014 0.0012 ethanol

0.001

25% IL

0.0008

50% IL

0.0006

75% IL

0.0004

IL

0.0002

0.0002 0

10

20

30

40

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 9. Variation of isothermal compressibility with pressure for the 50 mass % mixture of [C2C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C2C1im]Cl in ethanol at 348 K (right).


Page 19 of 41

0.0018

0.0018

50% [C3C1im]Cl

0.0014 0.0012 0.001 0.0008 398 K 373 K 348 K 323 K 298 K

0.0006 0.0004 0.0002 0

10

20

30

40

[C3C1im]Cl 348 K

0.0016

κT (1/MPa)

κT (1/MPa)

0.0016

0.0014 0.0012 0.001

ethanol

0.0008 0.0006

25% IL

0.0004

IL 75% IL

50% IL

0.0002 50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 10. Variation of isothermal compressibility with pressure for the 50 mass % mixture of [C3C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C3C1im]Cl in ethanol at 348 K (right). 0.0018

0.0018

50% [C4C1im]Cl

0.0016 0.0014 0.0012 0.001 0.0008

373K

0.0012 ethanol

0.001

25% IL

0.0006

348K 323K 298K

0.0004

0.0014

0.0008

398K

0.0006

[C4C1im]Cl 348K

0.0016

κT (1/MPa)

κT (1/MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50% IL 75% IL

0.0004

0.0002

IL

0.0002 0

10

20

30

40

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 11. Variation of isothermal compressibility with pressure for the 50 mass % mixture of [C4C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C4C1im]Cl in ethanol at 348 K (right).



0.0018

0.0018

50% [C6C1im]Cl

0.0016 0.0014 0.0012 0.001

398 K

0.0008

373 K 348 K 323 K 298 K

0.0006 0.0004

[C6C1im]Cl 348 K

0.0016

κT (1/MPa)

κT (1/MPa)

0.0014 0.0012 ethanol

0.001 0.0008

75% IL 25% IL 50% IL IL

0.0006 0.0004

0.0002

0.0002 0

10

20

30

40

50

0

10

Pressure (MPa)

20

30

40

50

Pressure (MPa)

Figure 12. Variation of isothermal compressibility with pressure for the 50 mass % mixture of [C6C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C6C1im]Cl in ethanol at 348 K (right). 0.0016 0.0014

κT (1/MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 20 of 41

348 K 10 MPa

[C2C1im]Cl

0.0012 [C6C1im]Cl

0.001 0.0008

[C4C1im]Cl

0.0006 0.0004

[C3C1im]Cl

0.0002 0 0

20

40

60

Mass % IL

80

100

Figure 13. Comparison of variation of isothermal compressibility with mass % IL for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 348 K and 10 MPa.


Page 21 of 41 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Isobaric Thermal Expansion. Figure 14 shows a comparison of the isobaric expansivity for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 10, 20, 30, and 40 MPa as a function of temperature. The isobaric expansivity increases with increasing temperature or decreasing pressure. Figure 15 shows a comparison of the isobaric expansivity of the ionic liquids at 10 MPa. As shown expansivity decreases significantly in going from ethyl to loner alkyl chains. Interesting, there is not much difference between propyl, butyl and hexyl alkyl chains. Figures 16-19 show the calculated isobaric expansivity at 10, 20, 30, and 40 MPa for the mixtures with 50 mass % IL; and at MPa for the mixtures with 0, 25, 50, 75 and 100 mass % IL. Figure 20 shows a comparison of the isobaric expansivity of the ILs as a function of mass % IL at 348 K and 10 MPa. For [C2C1im]Cl, the isobaric expansivity was found to be higher than the other ILs and to decrease with increasing mass % IL linearly. Similar to the isothermal compressibility, the expansivity of [C3C1im]Cl decreases with increasing mass % IL, passing through a minimum at 75 mass % before increasing to the value of the pure IL. The [C4C1im]Cl and [C6C1im]Cl displayed cubic trends. Again, the [C6C1im]Cl showed more distinct cubic trend with a minimum at 50 mass% and a maximum at 75 mass %.



0.001

0.001

[C2C1im]Cl

0.0009

10 MPa 20 MPa

0.0009

30 MPa 40 MPa

0.0008

βP (1/K)

βP (1/K)

0.0008 0.0007 0.0006

[C3C1im]Cl

10 MPa

0.0007

20 MPa 30 MPa

0.0006

0.0005

0.0005

0.0004

0.0004

0.0003

40 MPa

0.0003 250

300

350

400

450

250

Temperature (K)

300

350

400

450

Temperature (K) 0.001

0.001

[C4C1im]Cl

0.0009

[C6C1im]Cl

0.0009 0.0008

0.0008 0.0007

βP (1/K)

βP (1/K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 22 of 41

10 MPa 20 MPa 30 MPa 40 MPa

0.0006 0.0005

10 MPa

0.0007

20 MPa

0.0006

30 MPa 40 MPa

0.0005

0.0004

0.0004

0.0003 250

300

350

Temperature (K)

400

450

0.0003 250

350

Temperature (K)

450

Figure 14. Variation of isobaric expansivity with temperature for the ILs [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 10, 20, 30, and 40 MPa.


Page 23 of 41

0.001

10 MPa

[C2C1im]Cl

0.0009

βP (1/K)

0.0008 [C3C1im]Cl [C6C1im]Cl [C4C1im]Cl

0.0007 0.0006 0.0005 0.0004 250

300

350

400

450

Temperature (K) Figure 15. Comparison of variation of isobaric expansivity with temperature for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl and 10 MPa.

0.002

0.002

50% [C2C 1]Cl

0.0018

10 MPa

0.0012

20 MPa 30 MPa 40 MPa

βP (1/K)

0.0014

0.001

25% IL

0.0014

50% IL

0.0012

75% IL

0.001 0.0008

0.0006

0.0006

0.0004

0.0004 300

350

400

ethanol

0.0016

0.0008

250

[C2C 1]Cl 10 MPa

0.0018

0.0016

βP (1/K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


450

IL

250

Temperature (K)

300

350

400

450

Temperature (K)

Figure 16. Variation of isobaric expansivity with temperature for the 50 mass % mixture of [C2C1im]Cl in ethanol at 10, 20, 30, and 40 MPa (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C2C1im]Cl in ethanol at 10 MPa (right).



0.002

0.002

50% [C3C1im]Cl

0.0016

0.0016

0.0014

0.0014

0.0012 0.001 10 MPa 20 MPa 30 MPa 40 MPa

0.0008

0.001

0.0004

0.0004 350

400

50% IL

0.0008 0.0006

300

ethanol

25% IL

0.0012

0.0006 250

[C3C1im]Cl 10 MPa

0.0018

βP (1/K)

βP (1/K)

0.0018

450

75% IL

IL

250

Temperature (K)

300

350

400

450

Temperature (K)

Figure 17. Variation of isobaric expansivity with temperature for the 50 mass % mixture of [C3C1im]Cl in ethanol at 10, 20, 30, and 40 MPa (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C3C1im]Cl in ethanol at 10 MPa (right). 0.002

0.002

50% [C4C1im]Cl

0.0018

[C4C1im]Cl 348K

0.0018 0.0016

βP (1/K)

0.0016

βP (1/K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 24 of 41

0.0014 0.0012 10 MPa 20 MPa 30 MPa 40 MPa

0.001 0.0008

0.0014

ethanol

25% IL

0.0012 50% IL

0.001

75% IL

0.0008

0.0006

IL

0.0006

0.0004

0.0004 250

300

350

400

450

250

Pressure (MPa)

300

350

400

450

Temperature (K)

Figure 18. Variation of isobaric expansivity with temperature for the 50 mass % mixture of [C4C1im]Cl in ethanol at 10, 20, 30, and 40 MPa (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C4C1im]Cl in ethanol at 10 MPa (right).


Page 25 of 41

Isobaric Expansivity (1/K)

0.002

50% [C6C1im]Cl

0.0018 0.0016

βP (1/K)

0.0014 0.0012 10 MPa 20 MPa 30 MPa 40 MPa

0.001 0.0008 0.0006

0.002

[C6C1im]Cl 10 MPa

0.0018

ethanol

0.0016 0.0014 25% IL 50% IL 75% IL

0.0012 0.001 0.0008

IL

0.0006

0.0004

0.0004 250

300

350

400

450

250

Temperature (K)

300

350

400

450

Temperature (K)

Figure 19. Variation of isobaric expansivity with temperature for the 50 mass % mixture of [C6C1im]Cl in ethanol at 10, 20, 30, and 40 MPa (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C6C1im]Cl in ethanol at 10 MPa (right). 0.0016 0.0014

βP (1/K)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


348 K 10 MPa

[C2C1im]Cl

0.0012 [C4C1im]Cl

0.001

[C6C1im]Cl

0.0008 0.0006

[C3C1im]Cl

0.0004 0

20

40

60

80

100

Mass % IL Figure 20. Comparison of variation of isobaric expansivity with mass % IL for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 348 K and 10 MPa.



Internal Pressure. Figure 21 shows a comparison of the internal pressure for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 298, 323, 348, 373, and 398K as a function of pressure. As shown, internal pressure increases with increasing pressure and decreasing temperature. Figure 22 shows a comparison of the internal pressure of the ionic liquids at 348 K. As shown, this parameter which combines the effect of compressibility and expansivity (π = βP/κT) decreases with alkyl chain length. However, [C4C1im]Cl does not precisely follow the trend and shows slightly higher values than [C3C1im]Cl. Figures 23-26 shows the calculated internal pressure at 298, 323, 348, 373, and 398K for the mixture of 50 mass % IL, and at 348 K for mixtures of 0, 25, 50, 75, and 100 mass % IL. Figure 27 shows a comparison of the internal pressure of the ILs as a function of both mass % IL and mole % IL at 348 K and 10 MPa. For [C2C1im]Cl, the internal pressure is observed to increase with increasing mass % IL. Internal pressure in [C3C1im]Cl mixtures increased to a maximum at 50 mass % IL before decreasing to the value for pure [C3C1im]Cl. Both the [C4C1im]Cl and the [C6C1im]Cl showed a cubic trend. Again, this trend was more distinct for [C6C1im]Cl. The [C4C1im]Cl goes through a maximum at 50 mass % IL and a minimum at 75 mass % IL before increasing to the value of pure [C4C1im]Cl. The [C6C1im]Cl goes through a maximum at 25 mass % IL and a minimum at 75 mass % IL. The plots based on mole % in the figure provides a better represents of the concentration ranges associated with molecular interaction. The present interpretation of the trends, perhaps somewhat speculative, is that, as the length of the alkyl group on the cation increases, its association with the chloride anion decreases. The increase in the size (along with the bulkiness and asymmetry) of the nonpolar alkyl chains is assumed to lead to the disruption of the cation – anion interactions. Among the ionic liquids studied, [C2C1im]Cl would be the least affected due to especially its relatively symmetrical cation. In the other ILs, as a result of the disruption of cation-anion interaction in the ILs, Cl- ion is viewed as being available for clustering with ethanol. Such clustering would lead to an increase in the internal pressure. However, as the molar concentration of the IL in the mixtures increases, the contribution of the clustering effect to the internal pressure becomes less compared to that of the ionic liquid itself, leading to the observed maximum at the low IL contents. This maximum shifts to lower concentrations of IL as the propyl group is changed to a butyl, then hexyl group. This further suggest that as the cation – anion interactions in the ILs weaken with increasing alkyl chain length, the aggregate formations of Cl- with ethanol occurs more readily. The reason for the minimum in internal pressure seen at higher IL concentrations in [C4C1im]Cl and [C6C1im]Cl is not clear, however one may speculate that it is due to an increase in


Page 26 of 41

Page 27 of 41

nonpolar interactions between the alkyl chain groups on cations that have been shielded from the corresponding anion by interaction with ethanol. 550

[C2C1im]Cl

Internal Pressure (MPa)


550

348 K 373 K

500

398 K

450 400 350

[C3C1im]Cl

500 450 400

298 K 323 K 348 K 373 K 398 K

350 300

300 0

10

20

30

40

50

0

10

Pressure (MPa)

20

30


500 450 298K 323K 348K 373K 398K

400 350

[C6C1im]Cl 500 450 400 298 K 323 K 348 K 373 K 398 K

350 300

300 10

20

50

550

[C4C1im]Cl

0

40

Pressure (MPa)

550


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


30

40

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 21. Variation of internal pressure with pressure for the ILs [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 298, 323, 348, 373, and 398K.




550

348 K

500

[C2C1im]Cl

450 [C4C1im]Cl

400

[C3C1im]Cl

350 [C6C1im]Cl

300 250 0

10

20

30

40

50

Pressure (MPa) Figure 22. Comparison of variation of internal pressure with pressure for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 348 K. 540

540

50% [C2C1im]Cl

520



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 28 of 41

500 480 460 440

298 K

420

323 K 348 K

400

373 K

380

398 K

360

500 460 420 400

50% IL

380

25% IL

360

320

320 20

30

40

50

75% IL

440

340 10

IL

480

340 0

[C2C1im]Cl 348 K

520

ethanol

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 23. Variation of internal pressure with pressure for the 50 mass % mixture of [C2C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C2C1im]Cl in ethanol at 348K (right).


540 520 500 480 460 440 420 400 380 360 340 320 300


50% [C3C1im]Cl 298 K 323 K 348 K 373 K 398 K

0

10

20

30

40

540 520 500 480 460 440 420 400 380 360 340 320 300

50

[C3C1im]Cl 348 K

50% IL 75% IL 25% IL

IL ethanol

0

10

Pressure (MPa)

20

30

40

50

Pressure (MPa)

Figure 24. Variation of internal pressure with pressure for the 50 mass % mixture of [C3C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C3C1im]Cl in ethanol at 348K (right). 540 520 500 480 460 440 420 400 380 360 340 320 300

50% [C4C1im]Cl



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 29 of 41

298K 323K 348K 373K 398K

0

10

20

30

40

50

540 520 500 480 460 440 420 400 380 360 340 320 300

[C4C1im]Cl 348K

50% IL IL 75% IL 25% IL ethanol

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 25. Variation of internal pressure with pressure for the 50 mass % mixture of [C4C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C4C1im]Cl in ethanol at 348K (right).


540 520 500 480 460 440 420 400 380 360 340 320 300


50% [C6C1im]Cl

298 K 323 K 348 K 373 K 398 K

0

10

20

30

40

540 520 500 480 460 440 420 400 380 360 340 320 300

50

Page 30 of 41

[C6C1im]Cl 348 K

25% IL 50% IL IL ethanol 75% IL

0

10

Pressure (MPa)

20

30

40

50

Pressure (MPa)

Figure 26. Variation of internal pressure with pressure for the 50 mass % mixture of [C6C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C6C1im]Cl in ethanol at 348K (right). 550

348 K 10 MPa

500 450


550


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



[C2C1im]Cl

[C3C1im]Cl

400 [C4C1im]Cl

350 300

348 K 10 MPa

500 450

[C2C1im]Cl

[C3C1im]Cl

400 [C4C1im]Cl

350 300

[C6C1im]Cl

[C6C1im]Cl

250

250 0

20

40

60

80

100

0

Mass % IL

20

40

60

80

100

Mole % IL

Figure 27. Comparison of variation of internal pressure with mass % IL (left) and mole % IL (right) for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 348 K and 10 MPa.


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Hildebrand Solubility Parameter. The Hildebrand solubility parameter was estimated as the square root of the internal pressure. Figure 28 shows a comparison of the solubility parameter for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl at 298, 323, 348, 373, and 398K as a function of pressure. The solubility parameter increases with increasing pressure and decreasing temperature. Figure 29 shows a comparison of the solubility parameter for the ionic liquids at 348 K. The trends are the same as with the internal pressure. The effect of the alkyl chai n length on the solubility parameter in these mixtures are interpreted in terms of the clustering notion discussed above with internal pressure. Figures 30-33 shows the calculated solubility parameter at 298, 323, 348, 373, and 398K for the mixtures with 50 mass % IL, and at 348 K for the mixtures of 0, 25, 50, 75, and 100 mass % IL. Figure 34 shows a comparison of the internal pressure of the ILs as a function of mass % IL at 348 K and 10 MPa. The trends are the same as with internal pressure. For [C2C1im]Cl, the solubility parameter increases with increasing mass % IL. The [C3C1im]Cl increases to a maximum at 50 mass % IL before decreasing to the value for pure [C3C1im]Cl. The [C4C1im]Cl goes through a maximum at 50 mass % IL and a minimum at 75 mass % IL before increasing to the value of pure [C4C1im]Cl. The [C6C1im]Cl goes through a maximum at 25 mass % and a minimum at 75 mass % IL.


[C2C1im]Cl

23

348 K 373 K 398 K

22

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[C4C1im]Cl

Solubility Parameter (MPa0.5)

23

22

21

21

20

298K 323K 348K 373K 398K

20

19

19

18

18

17

17 0

10

20

30

40

50

0

10

Pressure (MPa)


22 21 20

298K 323K 348K 373K 398K

19 18 17 10

20

30

40

50

23

[C3C1im]Cl

0

20

Pressure (MPa)

23

Solubility Parameer (MPa0.5)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Solubility Paramert (MPa0.5)


30

40

50

[C6C1im]Cl 22 21 20 19

298K 323K 348K 373K 398K

18 17 0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 28. Variation of solubility parameter with pressure for the ILs [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 298, 323, 348, 373, and 398K.


Page 33 of 41


24

348 K

23

[C2C1im]Cl

22 21 [C4C1im]Cl

20

[C3C1im]Cl

19 18

[C6C1im]Cl

17 0

10

20

30

40

50

Pressure (MPa) Figure 29. Comparison of variation of solubility parameter with pressure for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 348 K.

24



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


50% [C2C1im]Cl

23 22 21 20

348 K 373 K

19

398 K

18

24

[C2C1im]Cl 348 K

23

IL

22 21

75% IL

20

50% IL 25% IL

19

ethanol

18 17

17 0

10

20

30

40

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 30. Variation of solubility parameter with pressure for the 50 mass % mixture of [C2C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C2C1im]Cl in ethanol at 348K (right).



24

50% [C3C1im]Cl

23 22



24

298 K 323 K 348 K 373 K 398 K

21 20 19 18

[C3C1im]Cl 348 K

23 22 21

50% IL 75% IL 25% IL

20

IL

19

ethanol

18 17

17 0

10

20

30

40

0

50

10

20

30

40

50

Pressure (MPa)

Pressure (MPa)

Figure 31. Variation of solubility parameter with pressure for the 50 mass % mixture of [C3C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass %


[C3C1im]Cl in ethanol at 348K (right).


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 34 of 41

24

50% [C4C1im]Cl

23 22 21

298K 323K 348K 373K 398K

20 19 18

24

[C4C1im]Cl 348 K

23 22 21

50% IL IL 75% IL

20 25% IL

19

ethanol

18 17

17 0

10

20

30

40

50

0

10

Pressure (MPa)

20

30

40

50

Pressure (MPa)

Figure 32. Variation of solubility parameter with pressure for the 50 mass % mixture of [C4C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C4C1im]Cl in ethanol at 348K (right).


24

24

23


50% [C6C1im]Cl

22 21 20

298 K 323 K 348 K 373 K 398 K

19 18 17 0

10

20

30

40

[C6C1im]Cl 348 K

23 22 21 20

25% IL 50% IL

19

ethanol

18

IL 75% IL

17

50

0

Pressure (MPa)

10

20

30

40

50

Pressure (MPa)

Figure 33. Variation of solubility parameter with pressure for the 50 mass % mixture of [C6C1im]Cl in ethanol at 298, 323, 348, 373, and 398K (left) and for the mixtures of 0, 25, 50, 75, and 100 mass % [C6C1im]Cl in ethanol at 348K (right). 23

348 K 10 MPa

22 21


23

Solubility Parameter (MPa)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60



Page 35 of 41

[C2C1im]Cl [C3C1im]Cl

20 19

[C4C1im]Cl [C6C1im]Cl

18

348 K 10 MPa

22 21

[C2C1im]Cl

[C3C1im]Cl

20 19

[C4C1im]Cl

18

[C6C1im]Cl

17

17 0

20

40

60

80

100

0

Mass % IL

20

40

60

80

100

Mole % IL

Figure 34. Comparison of variation of solubility parameter with mass % IL for [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl and [C6C1im]Cl at 348 K and 10 MPa.



IV.

Conclusions

The Sanchez-Lacombe equation of state has been shown to effectively model the density data and evaluate the derived thermodynamic properties, namely compressibility, expansivity, internal pressure and the solubility parameter of imidazolium based ionic liquids ( [C2C1im]Cl, [C3C1im]Cl, [C4C1im]Cl, and [C6C1im]Cl) with differing alkyl chain lengths and their mixtures with ethanol as a function of pressure, temperature and compositions. The data show that with the exception of [C4C1im]Cl, compressibility is observed to increase with alkyl chain length. Expansivity decreases significantly in going from ethyl to longer alkyl chains. Interestingly, there is not much difference between propyl, butyl and hexyl alkyl chains. Internal pressure, which is a combination of effects of compressibility and expansivity, decreases with alkyl chain length. However, [C4C1im]Cl does not precisely follow the trend and shows slightly higher values than [C3C1im]Cl. The trends observed with the solubility parameters are the same as with the internal pressure. The effect of the alkyl chain length on the internal pressure and thus the solubility parameter in these mixtures are interpreted in terms of clustering notion discussed above with internal pressure. In general, the isothermal compressibility was observed to increase with increasing temperature, decreasing pressure, and decreasing IL content. While mixtures of [C2C1im]Cl and [C4C1im]Cl with ethanol closely followed this general trend, mixtures of [C3C1im]Cl were observed to go through a minimum at 75 % IL, and mixtures of [C6C1im]Cl with ethanol were observed to go through a minimum between 25 and 50 % IL, and a maximum at 75 mass % IL. The isobaric expansivity was found to generally increase with increasing temperature, decreasing pressure, and decreasing IL content. Again, [C2C1im]Cl and [C4C1im]Cl did not deviate from this trend. However, expansivity in mixture of [C3C1im]Cl with ethanol was observed to go through a minimum at 75 % IL, and mixtures of [C6C1im]Cl went through a minimum at 50 % IL, followed by a maximum at 75 % IL. The internal pressure and solubility parameters generally increased with increasing pressure, decreasing temperature, and increasing mass % IL. [C2C1im]Cl did not deviate from this trend. The values in mixtures of [C3C1im]Cl with ethanol displayed a maximum at 50 % IL. Mixtures of [C4C1im]Cl went through a maximum at 50 mass % and a minimum at 75 mass %, while mixtures of [C6C1im]Cl went through a maximum at 25 mass % and a minimum at 75 mass %.


Page 36 of 41

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The differences in the derived thermodynamic properties are linked to the differences in the alkyl chain length of these ionic liquids. The present findings suggest that as the length of the alkyl group on the cation increases, its association with the chloride anion decreases, which is assumed to lead to the disruption of the cation – anion interactions. Among the ionic liquids studied, [C2C1im]Cl is least affected. In the other ILs, as a result of the disruption of cation-anion interaction in the ILs, Cl- ion is viewed as being available for clustering with ethanol, thereby leading to an increase in the internal pressure. However, as the molar concentration of the IL in the mixtures increases, the contribution of the clustering effect to the internal pressure becomes less compared to that of the ionic liquid itself, leading to the observed maximum at the low IL contents. That the location of the maximum shifts to lower concentrations as the propyl group is changed to a butyl, then hexyl group suggest that as the cation – anion interactions in the ILs weaken with increasing alkyl chain length, the aggregate formations of Cl- with ethanol occurs more readily.

Acknowledgements This research has in part been supported by the National Science Foundation through Award No: CBET 1509390. We would also like the thank Michael Williams for performing the DSC analysis on the ionic liquids used in this study.

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Effect of Alkyl Chain Length on Derived Thermodynamic Properties of

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