Experimental and Computational Studies of Binary Mixtures of

Article pubs.acs.org/jced

Experimental and Computational Studies of Binary Mixtures of Isobutanol + Cyclohexylamine S. Ranjbar,* A. Soltanabadi, and Z. Fakhri Faculty of Chemistry, Razi University, Kermanshah, Iran S Supporting Information *

ABSTRACT: The densities and viscosities of binary mixtures of isobutanol + cyclohexylamine have been measured over the entire range of composition at the various temperatures (293.15−313.15 K) and at atmospheric pressure. From these measurements, the thermal expansion coefficients, isothermal coefficient of pressure excess molar enthalpy, excess molar volumes, and deviations in viscosities have been calculated too. The nonideality behavior of the mixture was evidenced in the excess molar volumes and deviations in viscosities. The results have been fitted to the Redlich−Kister polynomial equation. The Grunberg−Nissan equation was used to correlate the viscosity data. The most stable geometry of isobutanol−isobutanol, cyclohexylamine−isobutanol, and cyclohexylamine−cyclohexylamine were studied using the density functional theory (DFT) in gases phase. In liquid phase, the molecular dynamics simulations have been performed and used to calculate the densities, mean square displacement (MSD), self-diffusion coefficients, and radial distribution functions of the mixtures with different mole fractions at 298.15 K and 1 atm. For these mixtures, using molecular dynamics simulation and quantum calculations, the structural and dynamical hydrogen bonding (H-bonding) interactions are considered too. These techniques are used to determine the hydrogen-bonded networks formed by the isobutanol and cyclohexylamine mixture.

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INTRODUCTION Isobutanol is a feedstock for the different chemical syntheses and is a very suitable solvent for use in the petrochemical and refining industries and as an intermediate in the polymerization process. This solvent has numerous industrial applications. Some of these applications including; paint solvent, varnish remover, ink ingredient, paint additive (to decrease viscosity alkyd resin paints and thus improves their brush ability and flow), gasoline additive (to decrease carburetor freezing), and so forth. Low concentrations of isobutanol avert cobwebbing in varnishes formulated from spirit-soluble resins and apply a useful effect in water-based paints. Also, this solvent is a cellulosic biofuel. Isobutanol has high energy content in comparison to ethanol and does not cause stress corrosion cracking in pipelines.1 Cyclohexylamine is used in vulcanized rubber industry for the act of preparing of vulcanization accelerator CBS (N-cyclohexyl-2-benzothiazole sulfonamide). This amine is useful in the production of artificial sweeteners and in the water treatment industry. Also, cyclohexylamine is applied in the making of pharmacological, insecticides, plasticizers, gas absorbents, dyes stuffs, corrosion inhibitors, and so forth.2 Many engineering designs involving fluid flow, heat transfer, and mass transfer require quantitative data of densities and viscosities of multicomponent mixtures.3−5 The amines and alkanols are self-associated. Binary mixtures of amines with alcohols are considered as super solvents. Based on the important properties of these mixtures, several chemical reactions and industrial processes are considered in these solvents. The experimental density and viscosity of these liquids are often required for the thermodynamic and thermophysical © XXXX American Chemical Society

excess properties. These properties are useful in interpreting the nature and patterns of intermolecular interactions that are present in liquids and their mixtures.6 Molecular dynamic (MD) simulation is a method for considering the physical movements of interacting particles. In this method, the trajectories of particles are obtained by numerically integrates Newton’s equations of motion. Having interatomic potentials or molecular mechanics force fields, forces and potential energies between the particles can be calculated. To simulate a system, it is usually preferred that the modifications of Newton’s equations are carried out from in the canonical ensemble or isothermal−isobaric ensemble (in these ensembles temperature is conserved) to in the microcanonical ensemble (energy is conserved).7 In recent years, a lot of work on the determination of physical and chemical properties of solutions has been carried out by MD simulation. This theoretical method has potential for calculating transport properties of fluids, so a great deal of current research deals with the density, self-diffusion coefficient, and radial distribution function (RDF). In the solutions, hydrogen bonds can seriously influence the geometrical arrangements8 and molecular parameters.9 Hbonding can be determined using rather indirect techniques in experimental studies. However, experimental methods such as spectroscopic and relaxation measurements only can supply qualitative information on the dynamics of the H-bonds. Unlike the experimental methods, MD simulation can provide direct Received: February 21, 2016 Accepted: June 27, 2016

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DOI: 10.1021/acs.jced.6b00158 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

The apparatus used in this work is an Anton Paar digital vibrating u-tube densitometer thermostated (model DMA 4500). Two integrated Pt 100 platinum thermometers were provided for good precision in temperature control internally ±0.01 K. The apparatus is precise to within 5 × 10−5 gr·cm−3, and the standard uncertainty for density, u(ρ), was 1 × 10−5 gr· cm−3. The densitometer was calibrated with double-distilled water and dry air as per the manufacturer’s instructions. The following relation holds for the period of vibration, τ, and the density, ρ, at the temperature T

microscopic information about intermolecular interactions of H-bonding.10 Present theoretical and experimental studies have probed H-bonding in solvents.11−16 It may be said that, in the interactions between solutions and cosolvents, hydrogen bonds have an important role. On the basis of H-bonding, various research has taken place to understand solvent properties and also its structural changes after mixing with other fluids.17−20 Since both selected molecules in this study have functional groups that form hydrogen bonds, this class of molecules is a good choice for the study of hydrogen bond network of systems. In this work, at atmospheric pressure and T = 293.15−313.15 K, the density and viscosity of pure isobutanol and cyclohexylamine and some of their mixtures are determined. Using these results, the excess molar volume, VEm, thermal coefficient, α, isothermal coefficient of excess molar enthalpies, (∂HEm/∂P)T,xi, and viscosity deviations, Δη, are also derived. In the gas phase, using quantum mechanics, the equilibrium geometry and stability of isobutanol−isobutanol, isobutanol− cyclohexylamine, and cyclohexylamine−cyclohexylamine were calculated. Also, in the liquid phase, using MD simulation, the microscopic structure, H-bonding, and diffusivities of the pure isobutanol, pure cyclohexylamine, and their mixtures are simulated. All nonbonded and bonded parameters needed for the simulations of these components have been taken from literature.21,22 The simulation processes is performed as follows: First, after a brief description of molecular modeling, the simulation technique is clarified. At 298.15 K and 1 atm, using the simulation results, the density, MSD, and self-diffusion coefficient of the mixtures with different mole fractions were determined, and then the calculated densities compared with experimental results. Finally, simulated RDFs of the solutions are also explained.

ρ(T ) = a + bτ 2

where a and b are the instrument constants determined by adjustment with bidistilled and degassed water and dry air. The viscosities of pure organic liquids and binary mixture were determined using Anton Paar AMVn Automated microviscometer at an angle of 70° with a certified precision of 1 × 10−4 mPa·s. AMVn is a falling ball viscometer which measures the rolling time of a ball through transparent and opaque liquids according to Höppler’s falling ball principle. Various combinations of ball/capillary of different diameters d were selected allowing to measure viscosities. In this work, measurements were made using a capillary with a diameter of 1.6 mm and with 150 μL sample volume. Results are given as relative, kinematic, or dynamic viscosity. The standard uncertainty in the viscosity measurements was within 3 × 10−2 mPa·s. All measurements described above were performed at least four times, and the results reported are the averages of these measurements. Furthermore, the accuracies of the densities and viscosities measurements were ascertained by comparing the experimental values for pure solvents with the corresponding literature values (Table 2).

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RESULTS AND DISCUSSION Densities. The densities, ρ*i , for pure liquids and their binary mixture, ρ, at different concentrations were determined over the temperature range 293.15−313.15 K at intervals of 5 K. The results have been compared with the literature values and presented in Table 3. It is seen that the experimental values compare fairly well with the literature values. The excess molar volumes, VEm, of the binary mixture of isobutanol + cyclohexylamine were computed by applying the following equation

EXPERIMENTAL SECTION Materials. Two products were high purity Merck reagents and were used without further purification. The compound name, CAS number, molar mass, supplier, and purity were reported in Table 1. Two products were high purity Merck Table 1. Compound Name, CAS Number, Molar Mass, Supplier, and Purity of Isobutanol and Cyclohexylamine compound

CAS number

molar mass (g·mol−1)

supplier

purity

isobutanol cyclohexylamine

78-831-1 108-91-8

74.12 99.18

Merck Merck

≥0.99 ≥0.99

(1)

2

VmE =

∑ xiMi(1/ρ − 1/ρi*)

(2)

i=1

where Mi and xi are the molar mass and the mole fraction the ith component in the mixture, respectively. The results of such calculations are given in Table 3. The standard uncertainty in the excess molar volumes measurements is about 3 × 10−3 m3· mol−1. The computed excess molar volumes of the binary mixture were correlated with the following Redlich−Kister expression23

reagents and were used without further purification. The stated purities of the solvents by the manufacturer were further ascertained by comparing their density with the corresponding literature values, and they are in good agreement (Table 2). Airtight stopper brown bottles were used for the preparation of the binary mixtures. Apparatus and Procedure. The densities and viscosities of the investigated binary mixture and corresponding pure substances were measured immediately after their preparation, and all of the properties were measured simultaneously. The mass measurements were made using an electronic balance (model: Mettler AE 163, Switzerland) accurate to 0.01 mg. The standard uncertainty for mole fractions, u(x), was 1 × 10−4.

VmE = x1(1 − x1) ∑ Ai (1 − 2x1)i i=0

(3)

where x1 is the mole fraction of the isobutanol and Ai’s are the obtained fitting parameter by the least-squares method. The comparisons of the experimental excess molar volumes, VEm, with those obtained from the Redlich−Kister equation for the binary mixture are represented in Figure 1. B



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Table 2. Densities, ρ, and Viscosities, η, of the Pure Liquids with the Available Corresponding Literature Values at the Various Temperatures and Pressure of 0.1 MPa ρ (g·cm−3) component isobutanol

cyclohexylamine

T (K)

exptl

lit.

exptl

lit.

293.15 298.15 303.15 308.15 313.15 293.15 298.15 303.15 308.15 313.15

0.8020 0.7981 0.7942 0.7903 0.7863 0.8669 0.8623 0.8578 0.8532 0.8487

0.8016848 0.797449 0.7940650 0.7901251 0.7861250 0.86674753 0.86220753 0.85767153 0.85313853 0.84860753

4.023 3.404 2.882 2.476 2.097 2.134 1.944 1.786 1.573 1.417

4.08552 3.429849 2.87752 2.49751 2.09152 2.13254 1.90054 1.79755

of the excess molar enthalpy of mixing with pressure at fixed composition and temperature. Viscosity. The viscosity deviations, Δη, were calculated by using the relation

The standard deviations were computed by applying the following equation σ=

1 n−p

n

∑ (Yi ,expt − Yi ,calc)2 (4)

i=1

2

Δη = η −

where n is the number of experimental data points, p is the number of parameters of the fitting polynomial, and YEexpt and Ycal are experimental and calculated properties values, respectively. The values of the parameters Ai and the standard deviations, σ, are presented in Table 4. Figure 1 shows that the computed values of excess molar volumes are negative over the whole mole fractions. In this figure we see that the increasing temperature causes VEm values become more negative. Such behavior may be accounted to the penetration of dissimilar molecules in each other (because of increasing kinetics energy of the molecules) or strong H−bond formation between the −OH group of isobutanol and the −NH group of cyclohexylamine in comparison to pure components (ideal mixture). Thermal Expansion Coefficient. Having the measured densities at investigated temperatures, and also fitting of ln ρ versus of temperature, the thermal expansion coefficients of pure components, α*i , and thermal expansion coefficients of various binary mixtures, α,

αi* = −(∂ ln ρi* /∂T )P

(5)

α = −(∂ ln ρ /∂T )P , x1

(6)

ρ° = 103 kg·m 3

=

VmE

− T (αVm −

∑ xiMiαi/ρi*)

(9)

where η is the dynamic viscosity of the mixture and η*i is the dynamic viscosity of the pure component i. Measured dynamic viscosities and the viscosity deviations at various temperatures are given in Table 3. The standard uncertainty in the viscosity deviations measurements was within 5 × 10−2 mPa·s. The comparisons of the experimental viscosity deviations, Δη, with those obtained from the Redlich−Kister equation for the binary mixture are represented in Figure 2. According to Kauzman and Eyring,24 the viscosity of a mixture strongly depends on the entropy of mixture, which is related to liquid structure and enthalpy (and consequently to the molecular interactions between the components of the mixture). Vogel and Weiss25 affirm that mixtures with strong interactions between different molecules (HE < 0 and negative deviations from Raoult’s law) present positive viscosity deviations (Δη > 0), whereas for mixtures with positive deviations of Raoult’s law and without strong specific interactions, the viscosity deviations are negative (Δη < 0). Also, the negative deviation in viscosity may be attributed to the difference between size and shape of the component molecules or when one of the components is strongly self-associated. The results of Δη are fitted in the Redlich−Kister equation (YE ≡ Δη). The calculated values of Ai, along with standard deviations σ, are given in Table 4. The viscosities of the binary mixtures were fitted by different semiempirical equations. One of them, which we examined, is the Grunberg and Nissan equation. This equation suggests logarithmic relation between the viscosity of binary liquid mixtures and of pure components26

(7)

where a and α (thermal expansion coefficient) are fitting parameters. The results of such calculations are given in Table 5. The standard uncertainty in the thermal expansion coefficient measurements was within 5 × 10−6 K−1. Isothermal Coefficient of Excess Molar Enthalpy. Using (∂H/∂P)T,ni = V(1 − αT) and HEm = Hm − Hm *, we can show (∂HmE/∂P)T , xi

∑ ηi*xi i=1

can be determined. From fitting results, the linear variation of ln ρ with T is summarized as −ln ρ /ρ° = a + αT

η (mPa·s)

2

ln η =

∑ xi ln ηi + x1x2G12 i=1

(10)

where G12 is a constant, proportional to interchange energy. It may be regarded as an approximate measure of the strength of molecular interactions between the mixing components. The adjustable Grunberg−Nissan parameters and their standard deviations at different temperatures are given in Table 6. The positive values of G12 may be attributed to the presence of

(8)

where (∂HEm/∂P)T,xi is defined as the isothermal coefficient of excess molar enthalpy. The obtained values of this coefficient, for the binary mixtures at various temperatures, have been presented in Table 3. This quantity represents the dependence C



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Table 3. Experimental Values of Densities, ρ, Excess Molar Volumes, VEm, Thermal Expansion Coefficients, α, Isothermal Coefficient of Excess Molar Enthalpies, H′ ≡ (∂HEm/∂P)T,x1, Viscosities, η, and Viscosities Deviations, Δη, for the Binary Mixtures of Isobutanol (1) + Cyclohexylamine at Various Temperatures and a Pressure of 0.1 MPaa T (K)

293.15

298.15

303.15

308.15

313.15

x1

10−3 ρ (kg·m−3)

106 VEm (m3·mol−1)

103 α (K−1)

106 H′ (m3·mol−1)

η (mPa·s)

Δη (mPa·s)

0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148 0.91737 1.00000 0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148 0.91737 1.00000 0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148 0.91737 1.00000 0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148 0.91737 1.00000 0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148

0.8669 0.8657 0.8650 0.8618 0.8570 0.8509 0.8470 0.8394 0.8308 0.8208 0.8141 0.8020 0.8623 0.8612 0.8606 0.8574 0.8526 0.8466 0.8428 0.8351 0.8267 0.8168 0.8102 0.7981 0.8578 0.8567 0.8561 0.8529 0.8482 0.8422 0.8385 0.8309 0.8226 0.8127 0.8062 0.7942 0.8532 0.8522 0.8516 0.8485 0.8438 0.8378 0.8341 0.8266 0.8184 0.8086 0.8021 0.7903 0.8487 0.8477 0.8472 0.8441 0.8394 0.8335 0.8298 0.8224 0.8142 0.8045

0.0000 −0.2721 −0.5993 −0.9989 −1.1901 −1.2207 −1.5150 −1.3587 −1.0998 −0.6834 −0.6541 0.0000 0.0000 −0.2729 −0.6104 −1.0062 −1.1978 −1.2225 −1.5221 −1.3584 −1.1053 −0.6837 −0.6578 0.0000 0.0000 −0.2741 −0.6137 −1.0105 −1.2026 −1.2247 −1.5260 −1.3604 −1.1082 −0.6870 −0.6596 0.0000 0.0000 −0.2796 −0.6226 −1.0195 −1.2057 −1.2294 −1.5313 −1.3641 −1.1118 −0.6900 −0.6554 0.0000 0.0000 −0.2871 −0.6273 −1.0331 −1.2143 −1.2352 −1.5363 −1.3731 −1.1167 −0.6988

1.0574 1.0501 1.0441 1.0383 1.0378 1.0350 1.0279 1.0228 1.0121 1.0014 1.0009 0.9880 1.0574 1.0501 1.0441 1.0383 1.0378 1.0350 1.0279 1.0228 1.0121 1.0014 1.0009 0.9880 1.0574 1.0501 1.0441 1.0383 1.0378 1.0350 1.0279 1.0228 1.0121 1.0014 1.0009 0.9880 1.0574 1.0501 1.0441 1.0383 1.0378 1.0350 1.0279 1.0228 1.0121 1.0014 1.0009 0.9880 1.0574 1.0501 1.0441 1.0383 1.0378 1.0350 1.0279 1.0228 1.0121 1.0014

0.0000 −0.0610 −0.2067 −0.5264 −0.8646 −1.0127 −1.2125 −1.1562 −0.8663 −0.4681 −0.6262 0.0000 0.0000 −0.0572 −0.2065 −0.5223 −0.8644 −1.0110 −1.2129 −1.1534 −0.8664 −0.4644 −0.6291 0.0000 0.0000 −0.0537 −0.2008 −0.5162 −0.8620 −1.0096 −1.2110 −1.1522 −0.8648 −0.4629 −0.6306 0.0000 0.0000 −0.0530 −0.1988 −0.5130 −0.8586 −1.0100 −1.2101 −1.1522 −0.8636 −0.4611 −0.6281 0.0000 0.0000 −0.0536 −0.1938 −0.5130 −0.8589 −1.0111 −1.2089 −1.1560 −0.8633 −0.4632

2.134 2.408 2.575 2.838 3.048 3.246 3.403 3.522 3.534 3.606 3.668 4.023 1.944 2.146 2.279 2.474 2.644 2.805 2.937 3.037 3.047 3.088 3.130 3.404 1.786 1.948 2.055 2.204 2.334 2.454 2.558 2.626 2.629 2.646 2.677 2.882 1.573 1.697 1.791 1.917 2.022 2.123 2.212 2.275 2.303 2.309 2.345 2.475 1.417 1.516 1.578 1.678 1.761 1.840 1.902 1.960 1.998 1.999

0.000 0.159 0.213 0.259 0.261 0.260 0.225 0.161 0.002 −0.099 −0.199 0.000 0.000 0.113 0.160 0.186 0.195 0.203 0.187 0.145 0.019 −0.070 −0.153 0.000 0.000 0.095 0.137 0.159 0.168 0.173 0.167 0.128 0.029 −0.052 −0.115 0.000 0.000 0.069 0.110 0.131 0.137 0.143 0.141 0.116 0.060 −0.015 −0.056 0.000 0.000 0.057 0.079 0.100 0.108 0.115 0.109 0.101 0.076 0.016

D



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Table 3. continued T (K)

x1

10−3 ρ (kg·m−3)

106 VEm (m3·mol−1)

103 α (K−1)

106 H′ (m3·mol−1)

η (mPa·s)

Δη (mPa·s)

0.91737 1.00000

0.7980 0.7863

−0.6575 0.0000

1.0009 0.9880

−0.6299 0.0000

2.015 2.097

−0.026 0.000

Standard uncertainties, u, are u(T) = 0.01 K, u(P) = 1 kPa, u(x) = 1 × 10−4, u(ρ) = 1 kg·m−3, u(VEm) = 2 × 10−9 m3·mol−1, u(α) = 5 × 10−6 K−1, u(η) = 3 × 10−2 mPa·s, u(Δη) = 5 × 10−2 mPa·s.

a

Figure 1. Excess molar volumes, VEm, of binary mixture of isobutanol + cyclohexylamine versus mole fraction of isobutanol, x1, at the various temperatures and at atmospheric pressure. The symbols represent experimental values, and the lines represent the corresponding correlations by the Redlich−Kister equation. Error bars are smaller than the symbol size.

Table 4. Reduced Parameters of eq 3, Ak, and Standard Deviations of eq 4, σ, from Fitting of VEm(cm3·mol−1) and Δη (mPa·s) for the Binary Solutions of Isobutanol + Cyclohexylamine at the Various Temperatures T (K) 293.15 298.15 303.15 308.15 313.15

VEm Δη VEm Δη VEm Δη VEm Δη VEm Δη

A0

A1

A2

A3

A4

A5

σ

−5.6230 0.9960 −5.6379 0.8007 −5.6494 0.6984 −5.6639 0.5759 −5.6862 0.4537

3.6486 0.6627 3.6586 0.2559 3.6472 0.1462 3.6548 −0.0097 3.6296 0.0107

1.8275 −0.9582 1.7618 −0.7616 1.7180 −0.6322 1.6219 −0.1949 1.4707 0.1460

−21.9582 2.1466 −22.2462 2.1286 −22.2387 2.0679 −22.3248 1.8116 −22.2656 0.4411

−4.7192 −0.7506 −4.7092 −0.7208 −4.6784 −0.4976 −4.5685 −0.4929 −4.4256 −0.6227

27.8629 1.6713 28.2318 1.0278 28.2444 0.4068 28.1818 −0.2428 28.0905 0.8923

0.065 0.015 0.066 0.010 0.067 0.006 0.066 0.001 0.065 0.003

strong molecular interactions27,28 between the mixing components in the mixture. As presented in Table 6, values of G12 decrease with increasing temperature in the mixture. These values at the high temperatures may be showing weak molecular interactions.

were used as input for full optimization with the density functional theory (DFT). The geometry optimization were performed at the Becke’s three parameter hybrid method with LYP correlation (B3LYP) level of DFT with 6-31++G** basis set for all atoms. The calculated vibrational frequencies of all optimized structures revealed a lack of imaginary frequencies, ensuring the presence of a minimum. All calculations are carried out using the Gaussian 03 suites of program. Quantum Optimization. The most stable structures of isobutanol and cyclohexylamine are shown in Figure 3. Also, the most stable structures of isobutanol−isobutanol, cyclohexylamine−cyclohexylamine, and cyclohexylamine−isobutanol are shown in Figure 4. To obtain the most stable geometry form of these three pairs, at first, one of the optimized molecules was initially put at all possible sites of another optimized molecule, and then, to find most stable conformer

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COMPUTATIONAL SECTION Quantum Calculations. The quantum chemical calculations were used to predict the equilibrium geometry and stability of isobutanol and cyclohexylamine (based on energy minimization). In this way, first the initial structures of isobutanol and cyclohexylamine were established by molecular mechanical method. Then, the obtained structures by the molecular mechanic were used (as first estimate) as input for the restricted Hartree−Fock (HF) with the 3-21G* basis set. Thereafter, the optimized structures at the level of HF method E



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Table 5. Fitting’s Parameters of eq 7 and R Squared, R2, at the Various Mole Fractions for Binary Mixtures of Isobutanol (1) + Cyclohexylamine x1

a

103 α (K−1)

R2

0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148 0.91737 1.00000

−0.167 −0.163 −0.161 −0.155 −0.149 −0.142 −0.135 −0.124 −0.111 −0.096 −0.087 −0.069

1.0574 1.0501 1.0441 1.0383 1.0378 1.0350 1.0279 1.0228 1.0121 1.0014 1.0009 0.9880

1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 1.0000 0.9999 1.0000 0.9999 0.9999

Table 6. Parameters, G12, and Standard Deviation, σ, for the Binary Mixture of Isobutanol + Cyclohexylamine T (K)

G12

σ

293.15 298.15 303.15 308.15 313.15

0.4701 0.4022 0.3617 0.3580 0.3254

0.047 0.039 0.035 0.026 0.018

between every intermolecular pair of atoms or group of atoms and that these interactions depend only on the separation of the atoms (groups). All of these models have an implicit orientation dependence, which recognizes that the relative positions of the atoms (groups) within the molecule are the major factor in defining the molecular shape.29 Several force fields, including AMBER,30 CHARMM,31 and OPLS,32 have been developed and applied successfully in a variety of systems. However, the results33−37 showed reasonable agreement with the experimental results for more alcohols and amines when they have been used OPLS force field to predict the transport properties and H-bonding structures. For the binary mixture of isobutanol + cyclohexylamine, we adopted the OPLS (optimized potentials for liquid simulations) force field molecular model from Jorgensen and its modifications proposed by Haughney, van Leeuwen, and Smit38−42 to predict the transport properties. The potential energy of the systems was modeled using the following standard functional form

structure of each pair, the optimization calculation was carried out. Some of the significant optimized values of the geometrical parameters (bond lengths, bond angles, and dihedral angles) of the all studied components are reported in Table 7 (in fact, a few important parameters are reported). The optimized bond lengths for all components in this table show that the change of all N−C and O−C bond lengths in all components are smaller than 0.01 Å. The largest change was observed in O−H bond in isobutanol, which increased from 0.965 in isobutanol to 0.982 Å in isobutanol−cyclohexylamine. The values of the optimized C−C−C bond angle of isobutanol in Table 7 show that the bond angle does not change significantly (1 ⎪ ⎭ ⎩ ⎣⎝ ij ⎠

N−1 N

+

∑ i=1

(11)

Figure 2. Viscosity deviations, Δη, of binary mixture of isobutanol + cyclohexylamine versus mole fraction of isobutanol, x1, at the various temperatures and at atmospheric pressure. The symbols represent experimental values, and the lines represent the corresponding correlations by the Redlich−Kister equation. Error bars are smaller than the symbol size. F



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Figure 3. Optimized structures of isobutanol and cyclohexylamine using the Gaussian program at the B3LYP level of DFT with the 6-31++G** basis set.

molecular interactions are described by the last term of eq 11, including the pairwise additive atom−atom 12−6 Lennard− Jones potential for the van der Waals interactions and the Coloumbic term for the electrostatic interactions between point charges centered on the atoms. The σij are the energy minima for the Lennard−Jones interactions for atoms i and j on different molecules, and the ij are the equilibrium interatomic separations at zero potential. The parameters for like atom interactions, εii and σii, are taken from the force field of OPLS.21,22 The cross term parameters for i ≠ j interactions are obtained from the conventional combination rules, εij = (εiiεjj)1/2 and σij = (σij + σij)/2. The qi and qj are charges on atoms i and j and ε° the dielectric permittivity constant for vacuum. Based on atomic labels of Figure 3, for each molecule, the values of the effective charges of atoms and intermolecular Lennard−Jones (nonbonded parameters) are given in the Supporting Information. Simulation Details. MD simulations of pure isobutanol, pure cyclohexylamine, and mixture of isobutanol + cyclohexylamine composed of a cubic box containing 200 molecules which were performed using the DL_POLY 2.20 package.43 The structures of isobutanol and cyclohexylamine were optimized at the B3LYP/6-31++G** level using Gaussian 03. For all systems, initial configurations were generated by randomly placing the appropriate number of isobutanol and cyclohexylamine in a cubic simulation box. The Nose−Hoover thermostat and barostat44 with 0.1 and 0.5 ps relaxation times were used to control the temperature and pressure. Periodic boundary conditions were employed, and the equations of motion were integrated using the Verlet leapfrog scheme.45 The initial extensive MD simulations were performed in the NPT ensemble for 1 atm and 298.15 K until the total energy of the system converged. All intermolecular interactions between the atoms in the simulation box and the nearest image sites were calculated within a cutoff distance of Rcutoff = 14.0 Å for all simulated systems. The electrostatic long-range interactions were calculated using the Ewald summation method45 with a precision of 1 × 10−6. The time step for all of the simulations was set as 1.0 fs, and all of the simulations were done at P = 1 atm and T = 298.15 K for over the whole mole fractions of the mixture. The simulations were started in NPT ensemble at low density. The system was equilibrated for 500 ps. For calculation of the equilibrium densities, the simulation has been continued for another 1.0 ns, and the results of the last step were gathered for analysis. The mean square displacement MSDs were averaged over a set of three NVT simulations each with a total 0.5 ns equilibration followed by a 1.0 ns production in

Figure 4. Optimized structures of (a) isobutanol−isobutanol, (b) cyclohexylamine−cyclohexylamine, and (c) isobutanol−cyclohexylamine using the Gaussian program at the B3LYP level of DFT with the 6-31++G** basis set.

where the first three terms represent the intramolecular bond, angle, and torsional interactions. Harmonic functions with force constants kb and kθ describe the intramolecular bond stretching and angle bending motions, respectively. The bond lengths and bond angles are represented by harmonic potentials with the equilibrium values of req and θeq, respectively, and also the cosine series describes the torsional motions. All intramolecular parameters (bonded parameters) are taken from the force field of OPLS.21,22 The sums are taken over all bonds, angles, and dihedrals in each of the cyclohexylamine and isobutanol. For each molecule, the harmonic bond, angular, and dihedral potentials are given in the Supporting Information. InterG



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Table 7. Some Important Bond Lengths, R (Å), Bond Angles, ∠ABC (degree), and Dihedral Angles, ∠ABCD (degree), of Cyclohexylamine and Isobutanol (B3LYP/6-31++G**)a cyclohexylamine

a

isobutanol

A−B

RA−B (Å)

A−B−C

∠ABC

A−B−C−D

∠ABCD

A−B

RA−B (Å)

A−B−C

∠ABC

A−B−C−D

∠ABCD

C1−C2 C1−N C1−H1 C2−C3 C2−H2a C2−H2e C3−C4 C3−H3e C3−H3a C4−H4a C4−H4e N−HN

1.535 1.470 1.107 1.537 1.099 1.099 1.537 1.097 1.0997 1.0995 1.097 1.0175

C2−C1−C2 C2−C1−N N−C1−H1 C1−C2−C3 C2−C3−C4 C2−C3−H3e C2−C3−H3a C3−C4−C5 C3−C4−H4a C3−C4−H4e C4−C5−C6 C1−C6−C5 C1−N−HN C2−C1−C6

110.5 109.6 112.0 111.8 111.5 109.9 109.4 111.3 109.1 110.2 111.5 111.8 110.9 110.5

C6−C1−C2−C3 N−C1−C2−C3 N−C1−C2−C9 N−C1−C2−C10 C2−C1−C6−C5 N−C1−C6−C5 C1−C2−C3−C4 C1−C2−C3−H3e C1−C2−C3−H3a C2−C3−C4−C5 C2−C3−C4−H4a C2−C3−C4−H4e C3−C4−C5−C6

−55.5 −176.4 −55.1 61.0 55.5 176.4 55.2 177.8 −65.6 −54.2 66.4 −176.8 54.2

C1−C2 C3−O C2−C3 C1−H1 O−HO C2−H2

1.535 1.431 1.529 1.096 0.965 1.099

C1−C2−C3 C2−C3−O C2−C1−H1 C3−C2−C1 C1−C2−C3 C1−C2−H2 C3−O−HO

111.5 108.9 110.8 110.0 111.5 108.3 109.1

O−C3−C2−C1 O−C3−C2−C1 C2−C3−O−HO C3−C2−C1−H1 C3−C2−C1−H1

−174.0 61.5 −178.5 63.5 −177.0

a: axial C−H bonds, e: equatorial C−H bonds.

which the positions of particles were recorded every 0.1 ps. The starting point of each NVT simulation was an equilibrated final configuration of a relevant NPT simulation. By the end of the equilibration, the total energies and volumes were monitored until the corresponding time series were stationary. Simulated Densities. The simulated densities of the pure components and mixture typically agree with the experimental results to within maximum 3.72%. The computed densities of isobutanol + cyclohexylamine and their binary mixture using NPT simulations at 298.15 K and 1 atm are shown in Table 8.

Table 9. Optimized Bond Lengths, Angles, and Dihedral Angles for Cyclohexylamine−Cyclohexylamine, Isobutanol− Isobutanol, and Isobutanol−Cyclohexylamine (B3LYP/631++G**) molecules bond length bond angle

Table 8. Calculated Densities, ρcal, Experimental Densities, ρexp, and Percent Error in Densities, Eρ [= 100(ρcal/ρexp − 1)], of Binary Mixtures of Isobutanol (1) + Cyclohexylamine at 298.15 K and at Pressure of 0.1 MPa from Molecular Dynamic Simulationa x1

10−3 ρcal (kg·m−3)

10−3 ρexp (kg·m−3)

Eρ (%)

0.00000 0.06096 0.12054 0.23570 0.34583 0.45126 0.55228 0.64916 0.74215 0.83148 0.91737 1.00000

0.873 0.895 0.887 0.873 0.872 0.865 0.862 0.847 0.841 0.844 0.826 0.820

0.8623 0.8612 0.8606 0.8574 0.8526 0.8466 0.8428 0.8351 0.8267 0.8168 0.8102 0.7981

1.24 3.92 3.07 1.82 2.28 2.17 2.28 1.42 1.73 3.33 1.95 2.74

dihedral angle

cyclohexylamine− cyclohexylamine

isobutanol− isobutanol

isobutanol− cyclohexylamine

HN···N 2.278 Å

HO···O 1.910 Å

HO···N 1.934 Å

164.7°

172.4°

165.5°

N−H···N−C1 60.1°

O−H···O−C1 −154.6°

O−H···N−C1 144.1°

dihedral angles of the HO···O, HO···N, and HN···N hydrogen bond. Based on this table, we see that, the hydrogen bond length follows: HO···O < HO···N < HN···N, and the bond angle follows HO···O (172.4°) > HO···N (165.5°) > HN···N (164.7°). Thus, the H-bond interaction strength as follows: HO···O > HO···N > HN···N. H-Bonding Interaction in the Liquid Phase. MD simulations can provide information about the H-bonding structures and dynamics on a microscopic level. The structural and dynamical properties of the amines and alcohols species are strongly influenced by the hydrogen bonds, particularly by the formation of H-bond between the both species. The aim of almost all modern theories of liquids is to calculate the radial distribution function by the statistical thermodynamics. The radial distribution function (RDF) can be calculated by MD simulations.47 RDF HO···O of pure isobutanol, HN···N of pure cyclohexylamine, and HO···N of their mixtures (versus x1 for isobutanol) are calculated and shown in Figures 5 to 7. For the pure isobutanol, computed HO···O RDFs are shown in the Figure 5. In this figure, the peaks of O with whole atoms of hydrogen in this molecule can be seen. For the HO···O pair, there are two peaks; the first one that is sharp is located at ∼1.82 Å, and the other one that is wide and weak is located at a distance of ∼3.3 Å. The first distance is slightly less than the sum of the van der Waals radii of H and O atoms [RO···HO ≤ 2.48 Å (threshold distance)]46 which is an H-bond and

a

Estimated uncertainties in the simulated values of calculated density is u(ρcal) = 10 kg·m−3.

H-Bonding Interactions in the Gas Phase. The H-bond is a specific intermolecular interaction which plays an important role in many physical properties of a large variety of molecular systems. When the H-bond is formed, the bond distance is smaller than the sum of the van der Waals radius of X (X ≡ F, O, N) and H atoms, X···HX, and also, the angle between them is greater than 90°.46 In this study, the distance of H-bonding interaction between HO···O, HO···N, and HN···N is investigated (Figure 4). Table 9 shows the bond length, bond angle, and H



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Figure 5. Simulated radial distribution functions O···HO, O···H1, O···H2, and O···H3 of pure isobutanol using the DL_POLY 2.20 program and OPLS force field at 298.15 K and at 1.0 atm. The O, HO, H1, H2, and H3 labels are defined according to Figure 3.

Figure 6. Simulated radial distribution functions N···HN, N···H1, N···H2, N···H3, and N···H4 of pure cyclohexylamine using the DL_POLY 2.20 program and OPLS force field at 298.15 K and at 1.0 atm. The N, HN, H1, H2, H3, and H4 labels are defined according to Figure 3.

represents intermolecular interaction between H and O. This H-bond is formed between O of a molecule (central molecule) and HO atoms of other molecules which are located in the nearest shell. The second distance (3.3 Å) which is greater than 2.48 Å is not an H-bond and can be related to HO of the central molecule with O atoms of other molecules which are located in the closest layer. This reasoning is consistent with quantum computing (Figure 3). The peaks for H1 and H2 are weak. These peaks are attributed to the intermolecular interaction of O atom of the central molecule with H1 and H2 atoms of other molecules which are located in different shells. The O···H3 peaks (wide and weak) are located at ∼3.2 Å and ∼4.5 Å. Two peaks show interactions of intermolecular between O of the central molecule with H3 atoms of other molecules which are located in the nearest shell.

The RDFs of pure cyclohexylamine are shown in Figure 6 for the HN···N pair. There are two peaks; both of them reveal intermolecular interactions. Regarding Figure 4b and the HN··· N threshold distance (RN···HN ≤ 2.52 Å),46 it may be concluded that the first peak which appears at 2.07 Å is an H-bond. This H-bond is due to the interaction between N of central molecule with the closest HN of other molecules which are located in the nearest shell (black dashed line in Figure 4b). The second wide peak (that is greater than 2.52 Å) is located at 3.53 Å. This peak may be combined from three intermolecular interactions. The first is related to the interaction of the central N with the second HN of other molecules which are located in the closest layer, whereas the second and third interactions are related to the interaction of two HN of the central molecule with N of I



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Figure 7. Simulated radial distribution functions of N···HO for the various mole fractions of the binary mixtures of isobutanol + cyclohexylamine using the DL_POLY 2.20 program and OPLS force field at 298.15 K and at 1.0 atm. The N and HO labels are defined according to Figure 4c.

Figure 8. Simulated mean square displacement, MSD, versus time, t, for pure isobutanol (1) and cyclohexylamine in three solutions (x1 = 0, 0.45, 0.55), using the DL_POLY 2.20 program and OPLS force field at 298.15 K and at 1.0 atm. The self-diffusion coefficients, Dself/(cm2/s), for cyclohexylamine in solutions with x1 = 0, 0.45, 0.55, and also for pure isobutanol are 8.3 × 10−7, 4.7 × 10−7, 4.1 × 10−7, and 3.3 × 10−7, respectively. The coefficients have been calculated in the time ranges of 300−1000 ps.

For the N···H4 pair, there are three peaks that appear at 4.48 (sharp), 5.33 (sharp), and 6.88 Å (weak and wide). Based on Figure 3, the sharp peaks are due to intramolecular interactions of N with H4a and H4e atoms, respectively, and the third peak is due to intermolecular interactions. Figure 7 shows the intermolecular interaction of N of cyclohexylamine and HO of isobutanol at the various mole fractions and 298.15 K. For the HO···N pair, there are two set peaks. The first set (is focused at 1.85 Å) represents the interaction of N with HO, which is located in the nearest shell, and it can be attributed to H-bonding. Also, due to H-bonding strength, each peak in this set has a specific intensity. Based on MD simulations, it may be concluded that a mixture with x1 = 0.55, the maximum molecular association, occurs. This

other molecules which are located in the closest shell (blue dotted lines in Figure 4b). For the N···H1 pair, there is a low intensity peak which is located at 4.83 Å. This peak shows the average distance of H1 from N. This distance is due to intermolecular interactions. For N···H2 pair, the peak appears at 5.58 Å. This peak is also related to intermolecular interaction. For N and H3, there are three peaks that are appeared at 2.83 (weak), 4.13 (sharp), and 4.63 Å (sharp). The first peak is attributed to intermolecular interactions, whereas the second and third peaks are attributed to intramolecular interactions. Based on Figure 3, we may conclude that the peaks at 4.13 and 4.63 Å are associated with intramolecular interactions of N with H3a and H3e, respectively. J



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conclusion can be confirmed by Figure 1. The second set can be attributed to the interaction between N with HO atoms of isobutanol molecules which are located in the next nearest shell. Diffusion Coefficient. The self-diffusion coefficient of a fluid can be calculated using the Einstein equation Dself =

1 d lim < [ri(t ) − ri(0)]2 > 6 t →∞ dt

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00158. Comparison of the experimental properties of the mixtures between this work and ref 49, the harmonic bond, angular bond, dihedral potentials, and the optimized structures output files of isobutanol and cyclohexylamine (PDF)

(12)

where the quantity in braces is the ensemble-averaged MSD of the molecules and ri is the vector coordinate of the center of mass of molecule i. The trajectories were dumped at 1.0 ns every 100 fs at 298.15 K after 500 ps of equilibration, and the self-diffusion coefficients obtained from the slopes of the line were fitted to the MSDs in the range 300−1000 ps. The MSDs regarding NVT simulations of pure and one binary mixture of isobutanol + cyclohexylamine for center of mass up to a time of 1.0 ns are shown in Figure 8. According to this figure, all MSD curves are linear after initial 300 ps. Based on this behavior, the self-diffusions, Dself (slope of curve/6), are calculated in the time ranges of 300−1000 ps. The values of these coefficients are reported in Figure 8. Also, in this figure, we see that, with the increase of isobutanol, diffusion is decreased. This behavior is logical because, after increasing isobutanol concentration, the molecular mobility of the molecules decreases which results in viscosity increment (Hbonding of HO···O is stronger than HO···N and HN···N).

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AUTHOR INFORMATION

Corresponding Author

*E-mail address: [email protected]. Fax: +98 83 34274562. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors would like to thank the Research Council of Razi University for providing the necessary facilities for performing the research.

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REFERENCES

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CONCLUSIONS In this work, at the different temperatures and at atmospheric pressure, the densities and viscosities of the pure and binary mixtures of isobutanol and cyclohexylamine are experimentally measured. The excess molar volumes, viscosity deviations, thermal expansion coefficients, and isothermal coefficient of pressure excess molar enthalpies have been derived from experimental results. The excess molar volumes are negative throughout the composition range. The positive values of Δη in these mixtures can be interpreted in terms of strong interactions between unlike molecules. The negative Δη, may indicates the weakening of the self-association of the molecules due to unequal size by the addition of the second component. Analysis of viscosity data based on the Grunberg−Nissan treatment shows that specific interaction exists among the molecules of components. In the gas phase, quantum mechanics shows that the H-bond strength as follows: HO···O > HO···N > HN···N. In the liquid phase, using the molecular dynamics simulations, density, microscopic structures, and self-diffusion of the pure isobutanol, cyclohexylamine, and their mixtures at 298.15 K and 1 atm are calculated. The simulated densities of the pure components and mixture typically agree with the experimental results to within maximum 3.92%. By the RDF the structures of molecules have been investigated. Also, based on Figures 4 to 7, it can be concluded that the quantum mechanics and simulations are in agreement with each other. Because the H-bonding of HO···O is stronger than HO···N and HN···N, the increase of isobutanol to cyclohexylamine caused a decrease in diffusion or mobility of molecules. Finally, the OPLS force field gives reasonable results for the densities of the liquids, but to improve these results, we can use the polarized force field. K



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