Permittivities, Refractive Indices, Densities, and Excess Properties for

Article Cite This: J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Permittivities, Refractive Indices, Densities, and Excess Properties for Binary Systems Containing 1‑Alkanols and Cyclopentanone Ali Ghanadzadeh Gilani* and Shahrbanoo Ramezani

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Department of Chemistry, Faculty of Science, University of Guilan, 41335 Rasht, Iran ABSTRACT: This study reports the experimental relative permittivity, refractive index, and density data for several polar binary systems containing a cyclic ketone (cyclopentanone) and a series of alkanols from C2 to C10 over the entire composition range at T = 298.15 and p = 101.3 kPa. Further study was performed on a polar−nonpolar system composed of cyclopentanone and cyclohexane at the mentioned temperature and pressure. The experimental data were analyzed with various approaches in a consistence framework and in terms of intermolecular interactions between the constituent molecules. The effective and corrective Kirkwood correlation factors were calculated, in order to investigate the H-bond structure formation in the mixtures. The intermolecular interactions were investigated through various excess parameters, namely, excess permittivity, excess refractive index, excess molar volumes, excess Helmholtz energies, and excess Kirkwood correlation factors.

1. INTRODUCTION

has a skew C2 configuration belonging to the dipolar aprotic solvent group that is a good hydrogen-bond acceptor. According to previous research by Jadzyn and Świergiel,22 the cyclic ketones with an odd number of carbon atoms display a high ability to antiparallel molecular self-association. They have also pointed out that the cyclopentanone molecule (with a ring of five carbon atoms) demonstrates a strong tendency for antiparallel dipole orientation. According to Gupta et al.,23 cyclopentanone exists as a blend of open and cyclic dimers in an antiparallel structure formed by carbonyl−carbonyl contacts. Using density functional theory (DFT), they have estimated an internuclear distance of 3.16 Å among interacting atoms in cyclopentanone molecules (between the carbon and oxygen atoms of cyclopentanone molecules). In contrast to this cyclic ketone, the correlation factors for aliphatic ketones such as acetone and its derivatives in nonpolar solvents are larger than one,2,3 suggesting parallel molecular dipole association. Alcohols are very important organic chemicals, and their bulk properties are mainly determined by polar hydroxyl groups. They are associated liquids due to the dipole−dipole and hydrogen bonding interaction. The molecular association process plays a significant and effective role in physical and thermophysical properties of these polar molecules.28−30 The self-association and structural rearrangements of alcohols through hydrogen bonding have been the subject of considerable interest in recent years.5−7 The physicochemical and dielectric properties of pure alkanols and their mixtures have been largely studied by numerous authors.31−42 The present study deals with the dielectric, optical, and thermophysical properties of the binary H-bonded systems

1−4

In our previous publications, the dielectric, optical, and related excess data were reported for several H-bond donor/Hbond acceptor systems. Mainly heavy alcohols and noncyclic ketones were selected in the dielectric and optical studies, as they show a range of different behaviors. In earlier reports, detailed investigations have been carried out on the dielectric and its related properties of various hydrogen bonded systems by several researchers.5−10 The reported dielectric and optical data are an important issue in the evaluation of the liquid mixture behavior. They have provided many important data and remarks in regard to intermolecular interactions, self-association, and structural rearrangement in H-bonded systems.11−13 Using such studies, the nature and strength of intermolecular interactions in liquid mixtures, over a range of compositions or temperatures, were determined and interpreted.14−17 However, further studies on this issue are always needed for various scientific and technical purposes. Cyclic ketones are important polar organic chemicals, which have many uses in various industries. The physicochemical and thermophysical properties of this group of compounds have received more attention.18−23 Among this group of compounds, five-membered cyclic ketone (cyclopentanone, CPO) has many applications in chemical, aroma, perfumes, rubber, pharmaceuticals, and food industries.22 This cyclic ketone is a colorless and flammable liquid with a peppermint odor. It has promising potential as a solvent, intermediate, and organic developer in a wide range of applications and in manufacture of a variety of chemicals.24−26 CPO has been used as a polar solvent for the electronics industry. It is one of the most important oxygenated compounds in the pyrolysis of biomass for fuel production and fuel precursors.27 Cyclopentanone with a large dipole moment © XXXX American Chemical Society

Received: March 19, 2018 Accepted: June 15, 2018

A

DOI: 10.1021/acs.jced.8b00217 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Table 1. Material Description chemical

abbreviation

molar mass (g·mol−1)

CAS number

source

mass fraction puritya

cyclopentanone cyclohexane ethanol 1-butanol 1-hexanol 1-octanol 1-decanol

CPO CHX EA 1-BA 1-HA 1-OA 1-DA

84.12 84.16 46.07 74.12 102.18 130.23 158.29

120-92-3 110-82-7 64-17-5 71-36-3 111-27-3 111-87-5 112-30-1

Sigma-Aldrich Merck Scharlau Merck Scharlau Merck Merck

>0.99 >0.999 >0.998 >0.995 >0.98 >0.99 >0.99

a

Stated by the supplier.

Table 2. Values of Relative Permittivity, ε, Refractive Indices, nD, and Density, d, of the Studied Pure Liquids at T = 298.15 K and p = 101.3 kPaa ε

d (g·cm−3)

nD

compounds

exp.

exp.

lit.

exp.

lit.

cyclopentanone

13.52

13.4922 13.5863

lit.

1.4347

1.434920 1.4347121 1.4347664

0.94431

ethanol

24.37

1.3594

17.49

1.359633 1.359436 1.359735 1.3594165 1.397829 1.397335 1.397233

0.78526

1-butanol

1-hexanol

13.09

9.85

1.416129 1.415733 1.416038 1.416168 1.427533 1.426038 1.428029 1.427566 1.427640

0.81599

1-octanol

24.3231 24.3332 24.3533 24.3734 17.5433 17.4337 17.5166 17.1035 13.0633 13.2837 13.2538 13.0339 9.82140 9.85838 10.0133

1-decanol

7.74

7.66038

1.4352

0.82671

cyclohexane

2.02

2.02144 1.98967 2.015170

1.4235

1.437266 1.4354941 1.435538 1.4354942 1.423544 1.423569

0.9443519 0.944523 0.9445224 0.94410764 0.9389650 0.9438352 0.785335 0.7851036 0.7849365 0.78510442 0.806035 0.8057565 0.8056436 0.8058429 0.8149128 0.8152829 0.816038 0.815966 0.8218030 0.821238 0.8215928 0.8217529 0.82172042 0.8217252 0.8261528 0.82642141 0.826538 0.82645042 0.7736244 0.7739052 0.773767 0.774069 0.77388070

1.3971

1.4161

1.4276

0.80592

0.82198

0.77389

Standard uncertainties u are u(x2) = 0.001, u(nD) = 0.0005, u(εr) = 0.02, u(T) = 0.02 K, u(d) = 0.00050 g·cm−3, and u(p) = 0.5 kPa.

a

containing 1-alkanols (C2−C10) and cyclopentanone at 298.15 K and p = 101.3 kPa. The dielectric properties were analyzed in terms of the various approaches to obtain important information about the molecular interactions and the mixture structure. In this study, various excess parameters (i.e., excess permittivity, excess refractive index, excess molar volume, excess free energy, and excess Kirkwood correlation factor) were calculated and analyzed. The interpretation of the excess properties presents information about intermolecular interactions and the consequence of liquid structure. Moreover, such interpretation can

provide a good framework for checking the consistency of the obtained data. The dielectric behavior explanation of these systems is useful for a number of practical applications in the various fields of science and technology. To the best of our knowledge, the permittivity, thermophysical, and their related excess quantities of these binary systems have not been reported in the available literature.

2. EXPERIMENTAL SECTION 2.1. Chemicals. Material description, the name, source, stated purity of the chemicals, and measured properties along B



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with the literature data are listed in Tables 1 and 2. The chemical structures of the liquids are shown in Figure 1.

well-known dielectric permittivities (HPLC grade cyclohexane, 1,4-dioxane, and methanol). Uncertainty in the capacitance measurement was 1 pF. (v) Relative permittivities of the liquid solutions (ε12) were determined by substitution of the measured capacitance values of the empty dielectric cell (Cair), the standard liquid (C1), the liquid solution (C12), and the permittivity of the standard liquid (ε1) in the following equation:44 ε12 = 1 +

(C12 − Cair) ·(ε1 − 1) (C1 − Cair)

(1)

The standard uncertainty in the relative permittivity measurement was 0.02. The temperature of the instruments was measured with an uncertainty of 0.02 K. The uncertainties of the measurements were analyzed experimentally and computed via the method of standard uncertainties.45

3. RESULTS AND DISCUSSION 3.1. Dipole Moment Data. The Guggenheim equation,46 as expressed below, was used to calculate the molecular dipole moments (μ) of the liquids in cyclohexane at infinite dilution. Figure 1. Chemical used in this study.

μ2 =

All of the materials were used without further purification. The stated purities of the chemicals were confirmed by their density and refractive index measurements at 298.15 K. Concerning the combined uncertainty of the measured and reported data, the experimental values are relatively in good agreement with the literature data. 2.2. Apparatus and Procedure. (i) Sample preparations were performed by accurately weighing of appropriate amounts of the solute into 10 cm3 volumetric flasks using an electronic analytical balance (AND, model HR-200) with an accuracy of ±0.1 mg. The standard uncertainty of the mole fraction was 0.0010. The studied chemicals were stored with 4 Å molecular sieves (Merck) before measurements. (ii) Refractive indices of the liquid samples were determined at T = 298.15 K for the wavelength of yellow sodium light using a thermostated Abbe Refractometer (Model CETI). The standard uncertainty in refractive index measurements was estimated to be 0.0005. The refractometer was calibrated before use with HPLC water (Merck). The standard uncertainty in temperature for the instrument measurements was 0.02 K. (iii) Densities of the samples were measured using a DA-645 Kyoto density meter which is automatically thermostated within 0.01 K. The manufacturer’s stated uncertainty is 0.00005 g·cm−3, but the standard uncertainty in density measurement was estimated to be 0.0005 g·cm−3. The instruments were calibrated with dry air and HPLC water before use. (iv) Electric capacitance measurements of the liquid samples were performed at an alternating current field frequency of 10 kHz using a Wayne Kerr 6425 precision component analyzer. A three-terminal stainless-steel cylindrical capacitor was used in this experiment.43 The dielectric cell was completely filled with the samples. The capacitance of the empty cell was about 27 pF. The dielectric cell was calibrated using reference liquids with

27kT (Δ/C)o 4πNA(ε1 + 2)(nD12 + 2)

(2)

Here, Δ = (ε12 − − The subscripts 1 and 12 represent the solvent and the solution, respectively. nD1 is the refractive index of the nonpolar solvent. k is the Boltzmann constant, NA is the Avogadro constant, and T is the absolute temperature. C (mol·cm−1) is the concentration of the solute. For the calculation of μ, a series of six to eight dilute solutions of each compound in cyclohexane were studied. The measured molecular dipole moments of the studied compounds at infinite dilution together are listed in Table 3. The standard uncertainty in the dipole moments was estimated to be 0.04 D. nD122)(ε1

nD12).

Table 3. Dipole Moments, μ, of Cyclopentanone and the 1Alkanols in Cyclohexane at T = 298.15 K and p = 101.3 kPaa μ/Db compound

abbreviation

exp.

lit.

cyclopentanone ethanol 1-butanol 1-hexanol 1-octanol 1-decanol

CPO EA 1BA 1HA 1OA 1DA

3.27 1.70 1.72 1.71 1.68 1.66

3.3022 1.69147 1.66147 1.64947 1.64947 1.61947

a

Standard uncertainties u are u(T) = 0.02 K and u(μ) = 0.04 D. bD = 3.3356 × 10−30Cm.

The literature data are also listed in the same table.47 The obtained dipole moment values for cyclopentanone show good agreement with the literature data within the combined uncertainties of both experimental and literature data sets. For the primary alcohols, however, our results reported here show noticeable discrepancies compared to the literature data. These differences could have various origins, such as the use of different nonpolar media (solvent effect), different approaches in dipole calculation, and so on. 3.2. Effective Dipole Moment for the Pure Liquids. The effective dipole moments (μeff = g1/2μ) and the self-association C



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should be due to the existence of strong molecular selfassociation through dipole−dipole interaction in this cyclic ketone (in both the solution and pure state). The permittivity increments (Δε) for the (CHX + CPO) binary system were determined using the following equation:

capability of the pure cyclic ketone and alkanols with an even number of carbon atoms (C2−C10) at 298.15 K were obtained using the Kirkwood correlation factor (g). The values of effective dipole moment were calculated from the Kirkwood−Frohlich relation48 gμ 2 =

Δε = ε12 − (x1ε1 + x 2ε2)

9kT (ε − ε∞)(2ε + ε∞) V̅ 4πNA ε(ε∞ + 2)2

Here, x1 and x2 are the mole fractions of the pure components, ε1 and ε2 are the permittivity values of the pure liquids, and ε12 is the relative permittivity of the mixtures. The calculated Δε values are given in Table 4 as well. The effective dipole moments (μeff) for the solutions containing CPO and a nonpolar solvent (CHX) were calculated using the following expression49

(3)

Here, ε and V̅ are the relative permittivity and molar volume of the pure liquid, respectively. ε∞ is the permittivity at optical frequency, which often is taken as the refractive index squared (ε∞ ≈ nD2). μ is the dipole moment of the isolated molecule (determined in diluted solutions in nonpolar solvent or the gas phase). The Kirkwood correlation factor (g) is a measure of the short-range molecular association between the like molecules. The deviation of g from unity is a measure of molecular association. The relative permittivity, ε, density, d, and refractive index, nD, of the pure compounds were measured at T = 298.15 K, and are listed in Table 2. The effective dipole moments of the pure liquids were calculated using the experimental data. The dielectric data presented here (for the pure liquids) suggest that the correlation factor for the cyclic ketone is less than unity (g < 1). This indicates a strong tendency of antiparallel dipole association leading to the reduction of the effective dipole moment of the ketone molecule. This type of molecular association is due to the overlapped dimers formed by carbonyl−carbonyl contacts.23 3.3. Effective Dipole Moment for the Polar−Nonpolar System. Relative permittivities (ε12) and refractive indices (nD12) were experimentally determined for cyclopentanone (CPO) in cyclohexane (CHX) over the entire mole fraction range at T = 298.15 K and p = 101.3 kPa. The selected experimental data are listed in Table 4. The concentration dependence of the permittivity and refractive index of solutions of CPO in CHX is shown in Figure 2a. As can be seen, a nonlinear change in both of the curves can be observed upon moving from the dilute to the concentrated side. This effect

μeff 2 = gμ2 =

ε12

nD12

Δε

μeff/D

g = (μeff/μ)2

0.000 0.030 0.050 0.100 0.150 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

2.02 2.25 2.39 2.78 3.19 3.61 4.51 5.51 6.60 7.78 9.06 10.45 11.94 13.52

1.4235 1.4235 1.4235 1.4236 1.4237 1.4239 1.4244 1.4252 1.4262 1.4274 1.4289 1.4306 1.4325 1.4347

0.000 −0.054 −0.105 −0.199 −0.283 −0.365 −0.498 −0.572 −0.598 −0.580 −0.510 −0.381 −0.206 0.000

2.683 2.619 2.573 2.547 2.522 2.493 2.487 2.490 2.497 2.508 2.523 2.539 2.554

1.000 0.673 0.641 0.619 0.607 0.595 0.581 0.579 0.580 0.583 0.588 0.595 0.603 0.610

(2ε12 + nD2)2 9kT 4πNAx 2 (nD2 + 2)2 (2ε12 + 1)

ÅÄÅ ÅÅ (ε12 − 1) ij x1M1 + x 2M 2 yz jj zz − 3x1M1(ε12 − 1) ÅÅ jj zz ÅÅ ε d d1(2ε12 + ε1) ÅÅÇ 12 12 k { É Ñ 3x M (n 2 − 1) ÑÑÑÑ − 2 2 D Ñ d 2(2ε12 + nD2) ÑÑÑÑÖ

(5)

where the subscripts 1 and 2 represent the solvent and the solute. xi, di, and Mi are the mole fraction, density, and molar mass of the ketone and the pure solvent molecules. The effective solution dipole moment (μeff) values are given in Table 4. The Kirkwood correlation factors (g) of CPO in CHX solutions as a function of the solute mole fraction are shown in Figure 2b. It can be seen that the g factor decreases with increasing solute concentration, indicating a high degree of antiparallel association (Figure 3a). On the other hand, the Kirkwood correlation factor is larger than 1 for the 1-alkanols, suggesting a strong tendency for parallel molecular orientation through the hydrogen bonding and dipole−dipole interactions. Typically, Figure 3b demonstrates the formation of a multimer structure in ethanol molecules. This phenomenon leads to the increase of the effective dipole moment. 3.4. The Polar−Polar Binary System (1-Alkanols + Cyclopentanone). Table 5 presents the experimental relative permittivities (ε12), refractive indices (nD12), and densities (d12), over the complete composition range, at 298.15 K. The corresponding excess quantities for the binary systems containing linear primary alcohols (C2−C10) and cyclopentanone are listed in the same table. Parts a−c of Figure 4 demonstrate the concentration dependence of permittivity, refractive index, and density of the studied binary systems at 298.15 K, respectively. As can be observed, the measured properties of the mixture increase nonlinearly toward the corresponding quantity of cyclopentanone, suggesting the presence of intermolecular interaction, particularly hydrogen bond formation (OH···OC), between the constituent molecules (Figure 3c). However, the occurrence of various structural forms of the system constituents and different types of intermolecular interactions should be considered in the mixture behavior. As far as the authors are aware, there are no or little literature data concerning these systems that are available at T = 298.15 K. Therefore, the experimental density values for the systems containing cyclopentanone and 1-alkanols were only compared graphically with the available literature density data50−52

Table 4. Relative Permittivity, ε12, Refractive Index, nD12, Effective Dipole Moment, μeff, Dielectric Increment, Δε, and Dipole Correlation Factor, g, with the Mole Fraction (x2) of the Binary Mixtures [Cyclohexane (1) + Cyclopentanone (2)] at T = 298.15 K and p = 101.3 kPaa x2

(4)

Standard uncertainties u are u(x2) = 0.001, u(nD) = 0.0005 g·cm−3, u(εr) = 0.02, u(T) = 0.02 K, u(d) = 0.00050, and u(p) = 0.5 kPa. a

D



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Figure 2. Plot of (a) the relative permittivity (□) and the refractive index (○) of solutions of cyclopentanone in cyclohexane. (b) Dipole correlation factor (△), g, as a function of cyclopentanone mole fraction at T = 298.15 K and p = 101.3 kPa.

Figure 3. Different types of intermolecular interactions for cyclopentanone, 1-alkanols (ethanol): (a) dimer structure of cyclopentanone, (b) multimer structure of ethanol, (c) possible H-bonding of cyclopentanone molecules with the alcohol. 2 2 2 ij μ 2 d1 y jj 1 x + μ2 d 2 x zzzg = 9kT (ε − n )(2ε + n ) jj 1 2z 2 2 j M1 M 2 zz{ eff 4πNA ε(n + 2) k

reported at T = 303.1550 and 308.1551 K. Parts a and b of Figure 5 compare our density data obtained for the (1-butanol or 1hexanol + cyclopentanone) and (1-octanol + cyclopentanone) systems with the literature data, which have been reported at the higher temperatures (at T = 303.15 and 308.15 K). As shown in the figure, there are large discrepancies between our density values (obtained in T = 298.15 K) and those reported in the literature at T = 303.15 and 308.15 K, respectively. The discrepancies in density values might have several reasons such as precision of the instrument and calibration, accuracy in mole fraction, and measurements. However, the differences due to the different working temperatures should also be considered. As the literature data50 for systems containing 1-butanol and 1-hexanol have been reported in terms of volume fraction, our density data were also plotted in terms of volume fraction (for comparison purposes). The modified forms of the Kirkwood equation (eq 3) were used to investigate the dipole orientation in the polar binary liquid mixtures (liquids 1 and 2). The modified equations were established by Kumbharkhane et al.53 as follows

(6)

2 2 2 ij μ 2 d1g y jj 1 1 x + μ2 d 2g2 x zzzg = 9kT · (ε − n ) ·(2ε + n ) jj 1 2z zz f j M1 M2 4πNA ε(n2 + 2)2 k {

(7)

Here, geff and gf are the effective and corrective Kirkwood correlation factors, respectively. These parameters are measures of hetero intermolecular interaction in the mixtures. The obtained geff and gf for the binary mixtures (1-alkanols + CPO) were calculated and are given in Table 6. The effective Kirkwood correlation factors for the pure 1-alkanols are larger than unity, indicating the homo interaction between the like molecules with the parallel dipole orientation. In contrast, this parameter is acutely less than 1 for the CPO, suggesting the strong self-association between the cyclic ketone molecules with the antiparallel dipole orientation. As shown in Figure 6a, for all E



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Table 5. Permittivity, ε12, Refractive Index, nD12, Density, d12, Refractive Index Deviation, ΔnD, Dielectric-Dispersion Increment, Δ(ε − n2), Excess Refractive Index, nED, and Excess Permittivity, εE(ϕ), Excess Molar Volume, V̅ E, with Mole Fraction, x2, or Volume Fraction, ϕ2, of (Alcohols + Cyclopentanone) Mixtures at T = 298.15 K and p = 101.3 kPaa x2

ϕ2

ε12

nD12

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.000 0.118 0.231 0.340 0.445 0.546 0.643 0.737 0.828 0.915 1.000

24.37 22.42 20.69 19.16 17.78 16.60 15.59 14.77 14.16 13.75 13.52

1.3594 1.3696 1.3793 1.3884 1.3968 1.4046 1.4117 1.4182 1.4242 1.4296 1.4347

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.000 0.115 0.227 0.334 0.439 0.540 0.637 0.732 0.824 0.913 1.000

17.49 16.31 15.37 14.58 13.97 13.5 13.18 13.03 13.04 13.19 13.52

1.3971 1.4015 1.4057 1.4098 1.4137 1.4175 1.4212 1.4248 1.4282 1.4315 1.4347

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.000 0.114 0.224 0.332 0.435 0.536 0.634 0.730 0.822 0.913 1.000

13.09 12.44 12.00 11.68 11.51 11.48 11.59 11.87 12.27 12.83 13.52

1.4161 1.4175 1.4189 1.4204 1.4221 1.4239 1.4258 1.4279 1.4301 1.4324 1.4347

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.000 0.113 0.223 0.330 0.433 0.535 0.633 0.729 0.821 0.912 1.000

9.85 9.63 9.51 9.50 9.65 9.94 10.37 10.97 11.69 12.55 13.52

1.4276 1.4276 1.4278 1.4282 1.4287 1.4294 1.4302 1.4311 1.4321 1.4333 1.4347

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900

0.000 0.113 0.222 0.329 0.432 0.533 0.631 0.728 0.820 0.912

7.74 7.75 7.84 8.07 8.43 8.93 9.56 10.34 11.27 12.31

1.4352 1.4345 1.4339 1.4335 1.4333 1.4332 1.4332 1.4333 1.4336 1.4341

d12 (g·cm−3)

Δ(ε − n2)

Ethanol (1) + CPO (2) 0.78526 0.000 0.81102 −0.872 0.83348 −1.522 0.85369 −1.972 0.87179 −2.269 0.88817 −2.365 0.90291 −2.289 0.91599 −2.021 0.92718 −1.542 0.93658 −0.861 0.94431 0.000 1-Butanol (1) + CPO (2) 0.80592 0.000 0.82075 −0.784 0.83531 −1.329 0.84988 −1.723 0.86447 −1.936 0.87888 −2.009 0.89305 −1.932 0.90681 −1.684 0.92001 −1.277 0.93267 −0.729 0.94431 0.000 1-Hexanol (1) + CPO (2) 0.81599 0.000 0.82387 −0.652 0.83261 −1.153 0.84244 −1.535 0.85365 −1.748 0.86602 −1.821 0.87948 −1.754 0.89417 −1.517 0.90992 −1.161 0.92664 −0.646 0.94431 0.000 1-Octanol (1) + CPO (2) 0.82198 0.000 0.82728 −0.585 0.83341 −1.071 0.84125 −1.447 0.85089 −1.663 0.86220 −1.740 0.87488 −1.677 0.88918 −1.445 0.90527 −1.093 0.92362 −0.601 0.94431 0.000 1-Butanol (1) + CPO (2) 0.82671 0.000 0.82938 −0.566 0.83322 −1.053 0.83924 −1.400 0.84747 −1.617 0.85791 −1.695 0.87034 −1.643 0.88481 −1.442 0.90152 −1.091 0.92101 −0.630 F

V̅ E (cm3 mol−1)

εE(ϕ)

ΔnD

0.000 −0.671 −1.172 −1.520 −1.762 −1.846 −1.800 −1.601 −1.227 −0.688 0.000

0.0000 0.0033 0.0054 0.0070 0.0079 0.0081 0.0077 0.0067 0.0052 0.0030 0.0000

0.0000 0.0019 0.0031 0.0040 0.0045 0.0047 0.0045 0.0039 0.0031 0.0019 0.0000

0.0000 −0.2131 −0.3463 −0.4551 −0.5298 −0.5835 −0.6071 −0.5840 −0.4794 −0.2862 0.0000

0.000 −0.723 −1.221 −1.583 −1.779 −1.848 −1.780 −1.553 −1.178 −0.674 0.000

0.0000 0.0006 0.0011 0.0014 0.0016 0.0016 0.0015 0.0014 0.0010 0.0006 0.0000

0.0000 0.0000 0.0000 −0.0001 −0.0001 −0.0001 −0.0001 0.0000 0.0000 0.0000 0.0000

0.0000 −0.1545 −0.2639 −0.3607 −0.4465 −0.5015 −0.5213 −0.4910 −0.3987 −0.2493 0.0000

0.000 −0.659 −1.166 −1.553 −1.767 −1.841 −1.773 −1.534 −1.174 −0.652 0.000

0.0000 −0.0007 −0.0011 −0.0015 −0.0016 −0.0017 −0.0017 −0.0014 −0.0011 −0.0006 0.0000

0.0000 −0.0009 −0.0016 −0.0021 −0.0023 −0.0024 −0.0023 −0.0020 −0.0015 −0.0009 0.0000

0.0000 0.2243 0.3905 0.4795 0.4696 0.4095 0.3240 0.2120 0.1081 0.0335 0.0000

0.000 −0.636 −1.157 −1.563 −1.789 −1.872 −1.802 −1.556 −1.173 −0.647 0.000

0.0000 −0.0007 −0.0012 −0.0015 −0.0017 −0.0018 −0.0017 −0.0015 −0.0012 −0.0007 0.0000

0.0000 −0.0008 −0.0014 −0.0017 −0.0020 −0.0020 −0.0019 −0.0017 −0.0013 −0.0008 0.0000

0.0000 0.3536 0.6386 0.7389 0.6869 0.5502 0.4128 0.2764 0.1595 0.0532 0.0000

0.000 −0.642 −1.181 −1.573 −1.805 −1.892 −1.829 −1.607 −1.211 −0.699

0.0000 −0.0007 −0.0012 −0.0016 −0.0017 −0.0018 −0.0017 −0.0015 −0.0012 −0.0007

0.0000 −0.0006 −0.0012 −0.0015 −0.0017 −0.0017 −0.0017 −0.0015 −0.0012 −0.0006

0.0000 0.6797 1.1786 1.3447 1.2575 1.0040 0.7032 0.4214 0.2048 0.0678

nED



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Table 5. continued x2

ϕ2

ε12

nD12

1.000

1.000

13.52

1.4347

d12 (g·cm−3)

Δ(ε − n2)

1-Butanol (1) + CPO (2) 0.94431 0.000

εE(ϕ) 0.000

ΔnD

nED

0.0000

0.0000

V̅ E (cm3 mol−1) 0.0000

Standard uncertainties u are u(x2) = 0.001, u(nD) = 0.0005, u(d) = 0.00050 g·cm−3, u(εr) = 0.02, u(T) = 0.02 K, and u(p) = 0.5 kPa.

a

Figure 4. Plot of (a) relative permittivity, (b) refractive index, and (c) density of the [1-alkanols (1) + cyclopentanone (2)] binary systems as a function of mole fraction at T = 298.15 K and p = 101.3 kPa: (◇) ethanol, (+) 1-butanol, (□) 1-hexanol, (△) 1-octanol, and (○) 1-decanol.

of the studied systems, the geff values decrease with increasing CPO mole fraction, suggesting the tendency of dipoles toward antiparallel orientation. Figure 6b shows the variations of gf with the concentration of CPO for the studied systems. The gfvalues are lower than 1, suggesting that the 1-alkanol and CPO molecules can form a Hbonded hetero structure, which in turn reduces the effective dipoles.8 3.5. Excess Parameters. Excess properties such as excess permittivity (εE), excess refractive index (nED), and excess molar volume (VE) are defined as the difference between the actual value (experimentally measured) and the ideal value at the same thermodynamic state, i.e., YE = Yreal − Yideal. The excess properties depend on the molecular geometry and the intermolecular interactions between the mixture constituent components. 3.5.1. Excess Relative Permittivity. Excess permittivity (εE = εreal − εideal) is a measure of the strength of the hetero intermolecular interactions and is expressed by10 ε E(ϕ) = ε12 − (ϕ1ε1 + ϕ2ε2)

against the mole fraction of the cyclic ketone are plotted in Figure 7a. The dielectric-dispersion increment and excess permittivity data are negative for all of the studied binary systems across the full composition range, which suggests the decrease of the total number of effective dipoles in the mixtures and multimer structure formation. The excess values are large for the studied mixtures, particularly for the system containing ethanol, indicating the relatively strong hetero interaction between the alkanols and the ketone molecules. Generally, the hetero interactions in the binary systems containing cyclic ketone and 1-alkanols become weaker with increasing alkyl chain length or in the order of C10 ≥ C8 > C6 > C4 > C2. This can be due to the fact that the interactions between the alcohol and the cyclic ketone molecules become weaker when the chain length of the alcohols increases. 3.5.2. Excess Refractive Index. For the refractive index (a nonthermodynamic quantity), deviation from an ideal mixture can be expressed as follows55,56

(8)

In this work, the empirical dielectric-dispersion increment, Δ(ε − n2), which often is considered as the excess permittivity (the induced polarization effect is ignored), was also considered for comparison purposes. This equation is in terms of mole fraction and can be given by8,54

(10)

nDE = nD(1,2) − (ϕ1nD1 + ϕ2nD2)

(11)

where ϕ1 = x1V̅ 1/(x1V̅ 1 + x2V̅ 2) and ϕ2 = x2V̅ 2/(x1V̅ 1 + x2V̅ 2) are the volume fractions of liquids 1 and 2, respectively. V̅ 1 and V̅ 2 specify the molar volumes of the constituent components. x1 and x2 are the mole fractions and nD1 and nD2 are the refractive indices of liquids 1 and 2, respectively. As can be seen from the equations, ΔnD and nED are formulated in terms of mole fraction and volume fraction, respectively. However, from the experimental and theoretical points of view, the refractive index deviation should be calculated on the basis of volume fraction.55 Although no physical importance is described for ΔnD, comparison of its behavior with nED might be supportive. In this work, both ΔnD and nED for the studied binary systems were evaluated and compared using the above equations. The

Δ(ε − n2) = (ε12 − nD12 2) − [(ε1 − nD12)x1 + (ε2 − nD2 2)x 2]

ΔnD = nD(1,2) − (x1nD1 + x 2nD2)

(9)

However, from the physical point of view, the excess permittivity should be calculated on the basis of volume fraction. The εE(ϕ) values together with Δ(ε − n2) data for the polar−polar binary systems over the entire mole fraction range are given in Table 5. The dielectric-dispersion increment values G



Article

magnitude. As can be seen from the table, nED values for the mixture containing 1-butanol are close to zero. The positive values of nED indicate that packing in the (ethanol + CPO) binary mixture is higher than that in the pure liquid states.55,56 The negative values of nED in the (heavy alcohols or cyclohexane + CPO) binary systems indicate the weak interaction between the constituent components. 3.5.3. Excess Molar Volume. The excess molar volumes (a thermodynamic quantity) of the binary systems were calculated from the density measurements of the pure components and their mixtures using the following equation57−60 V̅ E = (M1x1 + M 2x 2)/d12 − [(M1x1/d1) + (M 2x 2/d 2)] (12)

M1 and M2 are the molar masses and d1 and d2 are the densities of liquids 1 and 2, respectively. In general, different types of interactions between constituent molecules can contribute in some extent to the V̅ E values in the mixture.58 The first is physical or nonspecific interactions mainly dipole−dipole and dispersion forces. The second is chemical or specific interactions mainly hydrogen bond and complex formation, and the third is structural or geometrical change due to differences in size and shape of the hetero molecules in the mixtures.59 The values of V̅ E cm3·mol−1 for the binary mixtures of (CPO + primary alcohols) are plotted against the mole fraction of the ketone at T = 298.15 K in Figure 7c. The excess molar volumes are negative for the (ethanol or butanol + CPO) systems and positive for the mixtures of [heavy alcohols (C6−C10) + CPO] across the full mole fraction range. The negative V̅ E values can be mainly attributed to the specific intermolecular interactions including hetero hydrogen bonding and other complex-forming interactions between the ketone and the light alcohols. Furthermore, the contributions of nonspecific interactions and geometrical effects in the negative values of the excess molar volumes are also important. The negative value suggests that the solution structure is more compact than the structure of the pure solvents. The values of the excess molar volume of (heavy alcohols + CPO) are positive throughout the entire composition range (Figure 7c) due to several effects. These effects are caused by the addition of the dipolar aprotic molecules (cyclic ketone), which break the molecular self-association of the constituent molecules, the declustering, and steric hindrance.35,60 The positive value of V̅ E suggests the formation of a less compact packing of the solution structure compared to the constituent liquids. The curves for the binary mixture of the cyclic ketone and the heavy alcohols are asymmetrical and appear to change toward zero at higher mole fractions of the cyclic ketone, which indicate that the interaction maximum is not matched to the equimolar composition. The values of V̅ E are large positive in the heavy alcohol-rich region (0.2 ≤ xketone ≤ 0.5) due to the breaking up of homo interactions of the ketone and the H-bonded network of the alcohols, which is not compensated by the hetero interactions between the dissimilar molecules. The maxima on the curves of V̅ E for the binary systems containing heavy alcohols and cyclopentanone are at x2 = 0.3. The excess molar volume of the three binary systems containing heavy alcohols and ketone increases in the sequence C10H21OH > C8H17OH > C6H13OH. The increase in V̅ E in going from 1-hexanol to 1-decanol can be due to the structural characteristics of the heavy alcohols (increasing alkyl chain

Figure 5. Plot showing the variation of the density of solutions of (a) 1butanol or (b) 1-hexanol and (c) 1-octanol in cyclopentanone as a function of the ketone mole fraction at different temperatures: (●) T = 298.15 K, (■) T = 303.15 K, and (◆) T = 308.15 K. The literature values are taken from refs 50 and 51.

corresponding values for the refractive indices deviation and excess refractive index are given in Table 5. The values of ΔnD for the binary mixtures of (1-alkanols + CPO) are plotted against the mole fraction of the cyclic ketone at T = 298.15 K in Figure 7b. Both the values of ΔnD and nED for the binary system containing ethanol and CPO are positive in the entire mole fraction range, but the three systems containing heavy alcohols (C6, C8, C10) and the cyclic ketone are negative with comparable H



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Table 6. Effective Kirkwood Correlation Factor, geff, and Corrective Kirkwood Correlation Factor, gf, with Mole Fraction (x2) for the Binary Systems of [1-Alkanols (1) + Cyclopentanone (2)] at T = 298.15 K and p = 101.3 kPaa binary polar system ethanol + CPO

1-butanol + CPO

1-hexanol + CPO

1-octanol + CPO

1-decanol + CPO

x2

geff

gf

geff

gf

geff

gf

geff

gf

geff

gf

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

3.139 2.477 1.993 1.630 1.351 1.136 0.969 0.840 0.741 0.667 0.611

1.000 0.953 0.913 0.882 0.858 0.844 0.840 0.849 0.876 0.925 1.000

3.162 2.296 1.765 1.410 1.164 0.986 0.857 0.763 0.694 0.645 0.611

1.000 0.949 0.911 0.881 0.863 0.854 0.855 0.870 0.898 0.940 1.000

3.121 2.080 1.542 1.217 1.007 0.867 0.770 0.704 0.659 0.629 0.611

1.000 0.942 0.902 0.873 0.855 0.850 0.856 0.876 0.905 0.947 1.000

2.907 1.799 1.298 1.025 0.860 0.757 0.692 0.653 0.628 0.616 0.611

1.000 0.935 0.885 0.853 0.835 0.834 0.846 0.872 0.907 0.950 1.000

2.658 1.537 1.097 0.876 0.752 0.680 0.637 0.614 0.606 0.604 0.611

1.000 0.919 0.860 0.828 0.815 0.819 0.835 0.864 0.903 0.947 1.000

a

Standard uncertainties u are u(x2) = 0.001, u(T) = 0.02 K, and u(p) = 0.5 kPa.

length) and their different abilities to interact with the cyclic ketone molecules. For the binary systems, a correlation (generally negative correlation) exists between the excess molar volume (V̅ E) and the excess refractive index (nED). This correlation can be more described with associated changes of V̅ E and nED. As shown in Figure 8, the nED values are plotted versus V̅ E for the studied binary systems, at T = 298.15 K. As can be observed, positive nED values are in connection with negative values of V̅ E.56 The (ethanol + CPO) binary system confirms the negative V̅ E values connected with large positive nDE values, which represented specific interaction between the constituent components. The (1-butanol + CPO) system shows a section of relatively large negative V̅ E values associated by the almost unchanged nDE values close to zero. Finally, the systems containing heavy alcohols and the cyclic ketone show variation of negative nED values with positive values of V̅ E (negative correlation). As a result, by increasing the carbon chain length of the heavy alcohols (from C6 to C10), the V̅ E shifted to values that are more positive.

Figure 6. Plot of (a) the effective correlation factor (geff) and (b) the corrective correlation factor (gf) of [1-alkanols (1) + cyclopentanone (2)] binary systems as a function of mole fraction at T = 298.15 K and p = 101.3 kPa: (◇) ethanol, (+) 1-butanol, (□) 1-hexanol, (△) 1octanol, and (○) 1-decanol.

Figure 7. Plot of (a) dielectric-dispersion increment, Δ(ε − n2), (b) refractive index deviation (ΔnD), and (c) excess molar volume (V̅ E) of the [1alkanols (1) + cyclopentanone (2)] systems as a function of mole fraction at T = 298.15 K and p = 101.3 kPa: (◇) ethanol, (+) 1-butanol, (□) 1hexanol, (△) octanol, (○) decanol, and (×) cyclohexane. I



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exhibit both positive and negative behavior in the alcohol-rich and ketone-rich regions, respectively. It is evident from the figure that the system including 1-butanol exhibits small negative values for ΔAEii in the CPO-rich region, indicating the weak homo interaction. In contrast, a reverse trend can be observed for the system including 1-octanol. As shown in Figure 9c, ΔAE12 varies with mole fraction and is negative in the wide range of mole fraction, which specifies the parallel orientation of the dipoles. From the magnitudes of ΔAE12, the systems containing 1-decanol show the largest strength of the short-range interaction within the tested alcohols in the alcohol-rich side. In contrast, the (ethanol + CPO) binary system presents a larger negative variation in the ketone-rich side. For all of the systems, the variations of ΔAE were found to be positive in both the alcohol-rich and ketone-rich sides, as is shown in Figure 9d. The positive values of ΔAE indicate the interaction between 1-alkanol and cyclopentanone molecules through the dipole−dipole and H-bonding interactions and formation of antiparallel molecular alignment.62 3.5.5. Excess Kirkwood Correlation Factor. The Reis and Iglesias approach11 was employed to acquire excess Kirkwood correlation factors for the pure components and their resulting mixture (gE1 , gE2 , and gE12) to obtain additional information on the molecular interactions and the consequence of molecular reorganization. The excess Kirkwood correlation factors have been given as ÄÅ ÅÅ V (ε − n 2)(2ε + n 2) g1ε1 E 1 12 1 g1 = × ÅÅÅÅ 1 12 2 2 Å V ε (ε1 − n1 )(2ε1 + n1 ) ÅÅÇ 1̅ 12 É ideal 2 ideal 2 Ñ (ε − n1 )(2ε + n1 ) ÑÑÑÑ − ÑÑ ideal ε ÑÑÑÖ (14)

Figure 8. Correlation between excess refractive indices nED and excess molar volumes V̅ E for the (1-alkanols + cyclopentanone) systems at T = 298.15 K and p = 101.3 kPa: (◇) ethanol, (+) 1-butanol, (□) 1hexanol, (△) octanol, and (○) decanol.

3.5.4. Excess Helmholtz Energy. The total excess free energy (ΔAE) related to the long-range and short-range interactions between the components in a mixture can be expressed by the Winkelmann and Quitzsch approach.61 The equation for excess free energy has been introduced as ΔAE = ΔAoE + ΔAiiE + ΔA12E

(13)

Here ΔAoE = −(NA /2)∑i = 1,2 xiμi 2 (R fi − R ofi) represents the excess energy due to long-range electrostatic interaction, ΔAiiE = −(NA /2)∑i = 1,2 xi 2μi 2 (gii − 1)(R fi − R ofi) indicates the excess energy due to the short-range interaction between like molecules, and ΔAE12 = −(NA/2)[x1x2μ1μ2(g12 − 1)(Rf1 + Rf 2 − Rof1 − Rof 2)] stands for the excess energy due to the short-range interaction between dissimilar molecules. Rof i = (8πNA/9V̅ i)(εi − 1)(nDi2 + 2)/(2εi + nDi2) is the reaction field factor for the pure components, and Rf i = (8πNA/9V̅ i)(ε12 − 1)(nDi2 + 2)/(2ε12 + nDi2) is the reaction field factor for the mixture. gii and μi are the Kirkwood factor and the dipole moment of pure components. g12 is the correlation factor between liquids 1 and 2. In this work, it is assumed that g12 = gf.62 Recently, a more formal approach for the calculation of gf was established by Reis and Iglesias;11 however, the assumption that g12 = gf fulfills the analysis requirements for the excess data within the combined uncertainties. Table 7 lists the calculated excess energies for the binary mixture at T = 298.15 K. As shown in Figure 9a, values of the excess energy related to long-range interaction (ΔAEo ) for the binary systems (heavy alcohols + CPO) are positive over the whole composition range and vary with the cyclic ketone concentration. The system containing ethanol exhibits negative behavior of ΔAEo . The change in the sign of ΔAEo suggests the presence of different forces corresponding to the repulsive and attractive forces between the dipoles in the mixtures. Figure 9b shows the sigmoidal-shaped curves for excess energies related to the short-range homo interaction (ΔAEii ). The values of ΔAEii for the systems containing ethanol and 1-butanol are mainly positive, indicating the strong homo interaction between the similar alcoholic molecules through hydrogen bonding (this trend is larger positive for ethanol). The figure displays a similar but reverse trend of variations for ΔAEii , which was observed for the (1-octanol or 1-decanol + CPO) binary systems. The values of ΔAEii for the system containing 1-hexanol

g2E =

g2ε2

(ε2 − n2 )(2ε2 + n2 2) ÄÅ ÅÅ V (ε − n 2)(2ε + n 2) 2 12 2 × ÅÅÅÅ 2 12 ÅÅ V ε ̅ 2 12 ÅÇ 2

ÑÉ (ε ideal − n2 2)(2ε ideal + n2 2) ÑÑÑÑ − ÑÑ ÑÑ ε ideal ÑÖ g12E = x1B1g1E g1ideal

μ12 μ12 2

μ12 μ12 2

+ x 2B2 g2E

μ2 2 μ12 2

(15)

+ x1(B1 − B1ideal )

+ x 2(B2 − B2ideal )g2ideal

μ2 2 μ12 2

(16)

where the subscripts 1 and 2 represent liquids 1 and 2. μ122 = x1μ12 + x2μ22. Bi =

(ni 2 + 2)2 /(2ε12 + ni 2) (n12 2 + 2)2 /(2ε12 + n12 2)

Biideal =

[( n

(ni 2 ideal 2

and

+ 2)2 /(2ε ideal + ni 2)

) + 2)]2 /[2ε ideal + (n ideal)2 ]

(17)

where the subscript i stands for liquid 1 or 2, (nideal)2 = ϕ1n12 + ϕ2n22, and gideal is defined as J



Article

Table 7. Values of the Total Excess Energy ΔAE (J·mol−1), Excess Energy for Long-Range Interactions, ΔAEo , Short-Range Interactions between the Like Molecules, ΔAEii , and Interaction between the Unlike Molecules ΔAE12 with the Mole Fraction (x2) of 1-Alkanols and Cyclopentanone at T = 298.15 K and p = 101.3 kPa system ethanol (1) + cyclopentanone (2)

1-butanol (1) + cyclopentanone (2)

1-hexanol + cyclopentanone (2)

1-octanol + cyclopentanone (2)

1-decanol + cyclopentanone (2)

xketone

ΔAEo

ΔAEii

ΔAE12

ΔAE

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

0.00 −37.90 −63.94 −77.99 −78.78 −69.44 −50.99 −28.32 −8.58 2.33 0.00 0.00 −6.29 −2.67 10.59 28.63 49.27 67.23 75.37 69.18 46.58 0.00 0.00 28.48 62.79 101.04 135.98 162.19 174.13 163.82 133.69 77.82 0.00 0.00 69.16 139.84 205.20 253.51 279.71 279.42 246.76 188.47 104.00 0.00 0.00 112.86 217.55 300.83 355.77 376.48 362.95 313.75 232.42 128.89 0.00

0.00 55.46 94.06 116.25 123.47 115.95 96.56 69.02 39.24 14.10 0.00 0.00 42.79 65.63 73.23 67.17 51.75 30.97 10.17 −5.05 −10.31 0.00 0.00 27.45 35.21 30.20 15.30 −4.27 −23.27 −35.89 −38.53 −26.88 0.00 0.00 8.37 3.15 −12.49 −34.49 −56.00 −71.38 −75.21 −65.44 −40.06 0.00 0.00 −4.93 −21.26 −46.21 −72.60 −94.17 −105.82 −103.51 −84.96 −51.17 0.00

0.00 1.20 2.44 1.67 −1.54 −6.07 −10.10 −11.32 −8.76 −3.49 0.00 0.00 0.47 0.25 −1.53 −4.21 −6.69 −7.73 −6.61 −3.92 −1.20 0.00 0.00 −0.54 −2.49 −5.41 −7.85 −8.64 −7.42 −4.61 −1.89 −0.27 0.00 0.00 −1.97 −6.56 −11.25 −13.17 −11.78 −7.94 −3.40 −0.48 0.30 0.00 0.00 −4.21 −12.34 −18.03 −18.71 −14.61 −8.35 −2.58 0.53 0.73 0.00

0.00 18.76 32.56 39.93 43.15 40.44 35.47 29.39 21.90 12.94 0.00 0.00 36.97 63.21 82.29 91.58 94.32 90.47 78.93 60.21 35.08 0.00 0.00 55.39 95.51 125.83 143.44 149.28 143.44 123.32 93.27 50.67 0.00 0.00 75.56 136.43 181.45 205.84 211.93 200.10 168.15 122.54 64.25 0.00 0.00 103.73 183.94 236.58 264.46 267.70 248.78 207.66 147.99 78.44 0.00

K



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Figure 9. Plot of (a) the excess Helmholtz energy for long-range interactions, ΔAEo (J mol−1), (b) the excess energy for short-range homo interactions, ΔAEii (J mol−1), (c) the excess energy for short-range interactions between unlike molecules, ΔAE12 (J mol−1), and (d) the total excess energy, ΔAE (J mol−1), of the [1-alkanols (1) + cyclopentanone (2)] binary systems as a function of mole fraction at T = 298.15 K and p = 101.3 kPa: (◇) ethanol, (+) 1-butanol, (□) 1-hexanol, (△) 1-octanol, and (○) 1-decanol.

giideal = gi ×

εi(ε ideal − ni 2)(2ε ideal + ni 2) ε ideal(εi − ni 2)(2εi + ni 2)

molecular order. This trend highlights the important role of alkyl chain length on the intermolecular interactions.

(18)

4. CONCLUSIONS Relative permittivities, refractive indices, densities, and their related excess data for the binary mixtures containing 1-alkanols and a dipolar aprotic liquid (cyclopentanone) were determined over the full composition range at T = 298.2 K and p = 101.3 kPa. The experimental data were analyzed using various approaches and coherently interpreted in terms of homo and hetero interactions. For all of the studied systems, the gf values are lower than 1, which indicates that the alcohol and ketone molecules align in the opposite direction form multimers (antiparallel alignment). The geff values for the constituent mixtures explain the strong associative character of these liquids but with opposite dipole direction. The geff values show a decreasing trend as the mole fraction of cyclopentanone increases. The negative values of excess permittivity, εE(ϕ), for the studied binary systems indicate the formation of hydrogen bonded multimer structures. The hetero interactions in the

Table 8 summarizes the calculated excess Kirkwood correlation factors for the entire composition range of the (1alkanol + CPO) binary mixtures at T = 298.15 K. Variations of excess Kirkwood correlation factors of the (heavy alcohols + CPO) are displayed in Figure 10. As can be seen, the gE1 , gE2 , and gE12 are generally negative for the studied mixtures. The negative values indicate the opposed correlation of dipoles in the liquid mixtures, which leads to a decrease in order of the liquid mixture. This process causes the number of neighbor molecules in a mixture to decrease, and thus, the dislocation of interrupted molecules increases. This interruption can be clarified in terms of the different factors such as molecular interaction, molecular shape, and steric hindrance. Typically, the variations of gE12 for the liquid mixtures are in the following magnitude order: gE12(C10OH + CP) < gE12(C8OH + CP) < gE12(C6OH + CP) ≈ gE12(C4OH + CP). The presence of the alcohol molecules in the neighboring region of cyclopentanone molecules disturbs the mixture L



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Table 8. Calculated Values of gE1 , gE2 , and gE12 of the 1-Alkanols (C2−C10) in Cyclopentanone at T = 298.15 K and p = 101.3 kPa system ethanol (1) + cyclopentanone (2)

1-butanol (1) + cyclopentanone (2)

1-hexanol + cyclopentanone (2)

1-octanol + cyclopentanone (2)

1-decanol + cyclopentanone (2)

xketone

gE1

gE2

gE12

0.000 0.100 0.200 0.300 0.400 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.600 0.700 0.800 0.900 1.000 0.000 0.100 0.200 0.300 0.400 0.600 0.700 0.800 0.900 1.000

0.000 −0.053 −0.098 −0.132 −0.160 −0.185 −0.184 −0.168 −0.138 −0.095 0.000 −0.163 −0.275 −0.358 −0.405 −0.415 −0.373 −0.300 −0.203 −0.072 0.000 −0.176 −0.309 −0.408 −0.461 −0.455 −0.391 −0.295 −0.160 −0.001 0.000 −0.150 −0.268 −0.355 −0.395 −0.370 −0.304 −0.219 −0.110 0.024 0.000 −0.116 −0.207 −0.250 −0.257 −0.190 −0.129 −0.061 −0.018 0.015

−0.035 −0.039 −0.048 −0.057 −0.065 −0.067 −0.060 −0.046 −0.026 0.000 −0.012 −0.051 −0.077 −0.095 −0.104 −0.101 −0.088 −0.066 −0.037 0.000 0.015 −0.019 −0.049 −0.072 −0.085 −0.088 −0.076 −0.058 −0.032 0.000 0.019 −0.007 −0.031 −0.049 −0.060 −0.060 −0.049 −0.035 −0.018 0.000 0.023 0.009 −0.012 −0.027 −0.034 −0.030 −0.022 −0.012 −0.005 0.000

0.000 −0.047 −0.071 −0.084 −0.091 −0.084 −0.072 −0.053 −0.029 0.000 0.000 −0.132 −0.182 −0.199 −0.193 −0.150 −0.118 −0.081 −0.043 0.000 0.000 −0.134 −0.191 −0.211 −0.202 −0.149 −0.113 −0.075 −0.036 0.000 0.000 −0.106 −0.151 −0.165 −0.154 −0.106 −0.075 −0.046 −0.021 0.000 0.000 −0.078 −0.110 −0.109 −0.095 −0.052 −0.032 −0.014 −0.005 0.000

binary systems become weaker with increasing alkyl chain length. The strength of the hetero interaction reaches a maximum when the composition is approximately 0.5. For the (ethanol + cyclopentanone) system, the excess refractive index (nDE ) values are positive over the full composition range, which suggests that packing in this mixture is higher than in the pure liquids. For the systems containing heavy alcohols and cyclopentanone, the nED values are negative, indicating the weak interaction between the pure liquids. The nED

values for the system (1-butanol + cyclopentanone) are close to zero. For the (ethanol or butanol + cyclopentanone) systems, the values of excess molar volume (V̅ E) are negative across the full composition range, which indicates the specific interactions are mainly responsible for this behavior. The V̅ E values are positive for the (heavy alcohols + cyclopentanone) systems, which suggests the formation of a less compact packing structure compared to the pure liquids. M



Article

Figure 10. Plot of the excess Kirkwood correlation factor (gEi ) versus the ketone mole fraction for (a) 1-hexanol + cyclopentanone, (b) 1-octanol + cyclopentanone, and (c) 1-decanol + cyclopentanone: (△) gE1 , (□) gE2 ; (○) gE12.

Positive values of the total excess free energy (ΔAE) are observed for the studied systems, indicating the formation of multimer structures with an antiparallel orientation. Sigmoidalshaped curves can be observed for excess energies related to the homo interaction (ΔAEii ). The values of ΔAEii for (ethanol or 1butanol + cyclopentanone) are mainly positive, indicating the strong homo interaction through hydrogen bonding. For the systems containing 1-octanol and 1-decanol, the variation of ΔAEii is also sigmoidal-shaped. For the studied systems, the excess Kirkwood correlation factors (gEi ) are shown to be negative. This indicates that the dipoles tend to align in opposite directions in the mixtures (antiparallel alignment). The extent of this disruption might be interpreted in terms of the hetero H-bond formation, steric hindrance, and molecular shape. From the experimental data analysis, coherent results were observed for the studied dielectric and thermodynamic parameters, which leads to a similar conclusion on the values of geff, gf, gEi , εE, and ΔAE. Finally, it is worth mentioning that, generally, a negative correlation exists between the excess molar volume (V̅ E) and the excess refractive index (nED).

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AUTHOR INFORMATION

Corresponding Author

*Phone: 0098 131 3233262. Fax: 0098 131 3233262. E-mail: [email protected]. ORCID

Ali Ghanadzadeh Gilani: 0000-0002-3394-1064 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors thank the university authorities for providing the necessary facilities to carry out the work. REFERENCES

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