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Measurement and Correlation for Acoustic, Transport, Refractive, and High-Temperature Volumetric Data of Substituted Benzylamines Somenath Panda, Dharmendra Singh, Gyanendra Sharma, Anusha Basaiahgari, and Ramesh L. Gardas* Indian Institute of Technology Madras, Chennai 600036, India S Supporting Information *

ABSTRACT: In this study, we have reported precise high-temperature volumetric data of industrially important benzylamines, namely, benzylamine, N-methylbenzylamine, N,N-dimethylbenzylamine, and dibenzylamine. The effect of temperature and methyl or benzyl substitution on benzylamines have been discussed. Other physicochemical properties such as speed of sound, viscosity, and refractive index have been measured in the temperature range from 293.15 to 343.15 K and used to calculate several derived properties. Temperature dependence of density and refractive index data were fitted with the second order polynomial equation whereas viscosity data have been fitted well according to Arrhenius equation. The correlation between density and refractive index has also been quantified through a set of empirical equations. The molar refraction parameter has been estimated by Lorenz−Lorentz equation. Finally, the critical properties have been estimated with the “modified Lydersen−Joback−Reid” method and used to correlate the density of studied benzylamines.

1. INTRODUCTION Organic liquids form an important part of any industrial process due to their various roles in solvation, extraction process, as reaction medium, and others. Primary selection of a liquid suitable for a specific process is based on the thermophysical properties of that liquid. The most relevant and easily determinable properties include density, viscosity, speed of sound, refractive index, and so forth. Many industrial processes operate at high temperature and the thermophysical properties at high temperature are of utmost importance for process design. On the other hand, the change in properties with temperature is also important in designing any reactor. Though some of the physical properties of common organic solvents are known and the properties at higher temperatures can be extrapolated from lower temperature data, it is important to know the accurate data in several ways. Further, these data can be used in the development or optimization of theoretical models and correlations, which could be used further to predict similar entities. In addition, an accurate and ready to use database will be handy for the process designer besides accurate characterization of any liquid.1 Additionally, the change in molecular interaction pattern also can be studied through these findings. Benzylamines and their derivatives constitute an important family of solvents due to their wide range of applicability and low-cost. They have diverse applications in the form of surface active compounds, cosmetics, preservatives, antiseptics, antimicrobial agents, corrosion inhibitors, and pharmaceuticals.2−4 Benzylamines have the potential to be used in higher temperature applications due to its higher boiling point and greater thermal stability. But the lack of high-temperature data © XXXX American Chemical Society

prevents the further extension of their applicability. In fact, the accurate high-temperature data are scarce for almost all of industrially important liquids hindering many potential possibilities. Recently, in a few reports experimentation has been done to this unexplored range of temperature, which has shown promising results useful for scientists as well as engineers.5,6 Keeping the current scenario in mind, we have measured the high-temperature data for a group of benzylamine-based organic liquids, namely, benzylamine (BA), N-methylbenzylamine (MBA), N,N-dimethylbenzylamine (DMBA), and dibenzylamine (DBA). To the best of our knowledge, there is no open literature reporting density of these or related compounds at higher temperature. Other important transport property such as speed of sound, viscosity, and refractive index has been measured at lower-temperature ranges. The results show the actual change in transport properties with temperature. Also, the change in properties with the substitutions in moiety has been thoroughly studied and correlated. In addition, the correlation between the density and refractive index has also been verified with the help of some empirical equations. The critical properties have been obtained experimentally and correlated with the available and well-established Joback’s method. This will enhance our current understanding about the molecular interactions and critical properties. Received: July 25, 2016 Accepted: March 27, 2017

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DOI: 10.1021/acs.jced.6b00667 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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2. EXPERIMENTAL DETAILS 2.1. Chemicals. All chemicals were supplied by SigmaAldrich with high purity. The purity and CAS number have been reported in Table 1. Before experiments, all amines were

Metrohm 870 KF coulometric Karl Fischer apparatus and found to be less than 100 ppm. 2.2. Speed of Sound, Density, and Viscosity Measurements. The speed of sound was measured with an Anton Paar density and sound velocity meter (DSA 5000 M). It uses 3 MHz steady vibration over a cell length of 1 cm. The temperature is controlled by a built-in precise Peltier thermostat with an accuracy of ±0.01 K. High-temperature density of liquids was measured by DMA HP density meter working on the oscillating U-tube principle. The measuring cell is made of Hastelloy C-276 and can be used to determine density up to 3 × 103 kg/m3 at temperatures up to 200 °C and pressures up to 70 MPa. The temperature of the measuring cell is precisely controlled by a Peltier device within 0.05 K. DSA 5000 M density meter is attached to DMA HP as an evaluation unit. Prior to use, the instrument was calibrated at each temperature point using water and dodecane as reference liquids The calibration was further confirmed by measuring the density of Millipore water and toluene. The details of

Table 1. Chemicals Used, Source, CAS Number, and Purity chemicals

abbreviation

CAS no.

purity

benzylamine

BA

100-46-9

≥99.5%

N-methylbenzylamine

MBA

103-67-3

97%

N,Ndimethylbenzylamine dibenzylamine

DMBA

103-83-3

≥99%

DBA

103-49-1

97%

supplier SigmaAldrich SigmaAldrich SigmaAldrich SigmaAldrich

kept over barium oxide for 24 h in vacuum desiccator. Further, water content of the studied benzylamines was measured with a

Table 2. Experimental Density Data for the Studied Benzylamines Measured by DMA HP and DSA 5000M in Wide Temperature Range of 283.15−448.15 K and at Atmospheric Pressure (∼0.1 MPa) ρ/kg·m−3 BA T/K 283.15 288.15 293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15 348.15 353.15 358.15 363.15 368.15 373.15 378.15 383.15 388.15 393.15 398.15 403.15 408.15 413.15 418.15 423.15 428.15 433.15 438.15 443.15 448.15

DMA HP

983.4 978.9 974.4 973.2a 970.0 965.7 961.3 956.9 952.5 948.2 943.7 939.4 935.0 930.6 926.2 921.8 917.3 912.9 908.5 904.0 899.7 895.2 890.6 886.2 881.6 877.1 872.5 867.9 863.3 858.7 854.0 849.3

MBA DSA 5000M

983.66 979.35 975.01 970.67 966.33 961.98 957.63 953.27 948.90 944.53 940.14

DMA HP 952.8 948.4 944.0 939.6 939b 935.1 930.7 926.4 922.0 917.6 913.3 908.9 904.5 900.0 895.6 891.2 886.7 882.3 877.8 873.4 868.9 864.4 860.0 855.4 851.0 846.4 841.8 837.3 832.6

DMBA DSA 5000M

944.55 940.23 935.90 931.57 927.24 922.90 918.55 914.19 909.83 905.50 901.19

DMA HP 907.6 903.2 898.9 900c 894.6 890.2 885.9 881.7 877.4 873.2 868.9 864.6 860.4 856.0 851.8 847.5 843.2 838.9 834.6 830.2 825.9 821.5 817.1 812.7 808.2 803.7 799.2 794.7 790.1

DBA

DSA 5000M

899.32 895.10 890.88 886.65 882.42 878.18 873.94 869.68 865.43 861.16 856.89

DMA HP 1034.3 1030.3 1026.2 1026d 1022.2 1018.1 1014.2 1010.2 1006.3 1002.4 998.5 994.6 990.8 986.9 983.1 979.3 975.4 971.6 967.8 964.0 960.2 956.4 952.6 948.8 945.0 941.2 937.4 933.6 929.8 926.0 922.2 918.5 914.6 910.8 907.0

DSA 5000M

1026.48 1022.59 1018.70 1014.82 1010.94 1007.07 1003.20 999.34 995.48 991.63 987.79

a Reference 7. bReference 35. cReference 39. dReference 40. Standard uncertainties u are u(T) = 0.01 K, u(P) = 1 kPa. Combined uncertainties considering the effect of impurity uc(ρ)= 3 kg·m−3 for MBA and DBA, uc(ρ) = 1 kg·m−3 for BA and DMBA.

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boiling points, therefore a different temperature range at a higher region was selected for different liquids. The density data obtained from DSA 5000 M in the range of 293.15 to 343.15 K has also been reported in Table 2 and are almost identical with the measurements from DMA HP, considering the slightly higher uncertainty in DMA HP. The average relative deviation of the density values measured from DMA HP and DSA 5000 M were calculated to be 0.07%, 0.09%, 0.07%, and 0.07% for BA, MBA, DMBA, and DBA, respectively. Literature data for density are available at few temperatures and are found to be consistent with our measured values.7,8 The literature and experimental data for benzylamine and dibenzylamine have graphically been presented in Figures S2 and S3. This negligible difference may be attributed to difference in purity level and instrument configuration. From Figure 1, it is observed that the density values decreases with the increase in temperature following the usual trend.9 The reason behind it could be that with the increase in temperature, the increased kinetic energy leads to more vibration of molecules, which creates more free spaces between the molecules and thereby, the density decreases.10 With the addition of methyl group from primary (BA) through secondary (MBA) to tertiary (DMBA) structures, a linear decrease (about 4%) in density is observed, while the addition of one benzyl group to MBA leads to a huge increase (8.79%) in density value for DBA. The decrease in density with the addition of alkyl substituent may be caused by less arranged structures resultant of increased bulkiness. On the other hand, the symmetric structure of DBA molecules facilitates better arrangement and efficient packing, leading to higher density among the studied benzylamines. The density data has been correlated using the following second order polynomial equation11

calibration method and values obtained for water and toluene have been given in Supporting Information. As shown in Figure S1, the low average relative deviations between the experimental and literature values of densities for water (0.003%) and toluene (0.008%) indicates a good precision of the instrument. Dynamic viscosities of amines were measured by an Anton Paar micro viscometer (Lovis 2000ME), which works on rolling ball technique and is attached to the same evaluation unit (DSA 5000M). The standard uncertainties over measurements were estimated to be less than 0.005 kg·m−3 for density measurements with DSA 5000M; 0.1 kg·m−3 for density measurements with DMA HP; 0.05 m·s−1 for speed of sound and 0.005 mPa·s for viscosity. Prior to measurement, the density meter was calibrated with dry air and Millipore quality freshly degassed water whereas the Lovis was calibrated with the reference liquid (S3, N26, and N100 liquid for 1.59, 1.8, and 2.5 mm capillaries, respectively) provided by Anton Paar. 2.3. Refractive Index Measurements. The refractive index measurements were done on Anton Paar Abbemat 500 refractometer at a wavelength of 589 nm. Measurements were done in the temperature range from 283.15 to 343.15 K and at atmospheric pressure. Prior to measurements, the sample holder was thoroughly cleaned and the instrument was calibrated with Millipore quality freshly degassed water. The sample was kept on the top of the measuring prism and irradiated at different angles by a light-emitting diode (LED). The refractometer uses reflected light to measure the refractive index. The maximum deviation in temperature is 0.01 K, and the maximum uncertainty is 2 × 10−5 for the refractive index.

3. RESULTS AND DISCUSSION 3.1. Density. The experimental density data in the range of 283.15 to 448.15K has been presented in Table 2 and plotted in Figure 1. As studied benzyl amines have different melting and

ρ = a + bT + cT 2

(1) −3

where ρ is the density of the liquid in kg·m , T is the temperature in K; a, b, and c are adjustable parameters. These fitting parameters along with their average absolute relative deviation (ARD) obtained by least-square analysis are listed in Table 3. The ARD were calculated by the following equation ⎛ 1 ARD = ⎜⎜ ⎝n

∑

|ρexp − ρcal | ⎞ ⎟100 ⎟ ρexp ⎠

(2)

where n is number of data points and ρexp and ρcal denote experimental and calculated densities, respectively. These experimental density data were further used to calculate the molecular volume (Vm) of each benzylamines by the following equation1,12 Vm =

Figure 1. High-temperature density plot of substituted benzylamine. Red triangle, BA; red square, MBA; green circle, DMBA; blue diamond, DBA. The symbol represents experimental values and the solid line symbolizes the values calculated from eq 1.

M Nρ

(3)

where M is the molar weight, N is Avogadro’s number, and ρ is the density of liquids. The calculated Vm values of the liquids are listed in Table 3. As the name implies, Vm quantifies the

Table 3. Experimental Molecular Volume (Vm) Data at 298.15 K, Fitting Parameters, and ARD from Equation 1

BA MBA DMBA DBA

Vm (Å3)

a/kg·m−3

b × 103/kg·m−3·K−1

c × 104/kg·m−3·K−2

ARD

109.5 129.0 151.1 193.0

1219.22 1186.74 1131.65 1268.94

−749.97 −785.06 −742.94 −868.71

−1.8994 −1.4693 −1.7488 1.3751

0.012 0.007 0.015 0.011

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The derived values of βs have been reported in Supporting Information (see Table S2). As the name implies, βs gives an account of the compressibility of the liquid. The liquid can be compressed when molecules occupy the available free spaces as a result of applied pressure. The increase in temperature increases the free space between two molecular collisions, thereby βs also increases. The molecular arrangements are obvious to play a role here, as can be seen from the trend in βs as DBA < BA < MBA < DMBA. Two benzyl moieties in DBA gives more compact packing, hence less compressibility value compared to the less efficiently packed alkyl chain substituted benzylamines.9,18 Speed of sound can also be used as a tool to study the molecular interaction in a liquid. The intermolecular free length (Lf) is an important measure of the free space available inside the molecular arrangementsand can be estimated using the empirical formula proposed by Jacobson19

average volume occupied by the molecules. With the addition of substituents, the molecular volumes tend to increase in the order BA < MBA < DMBA < DBA. The contribution of each methyl group toward the molecular volume was found to be around 20−22 Å3, which is in reasonable agreement with the literature report.13 Isobaric expansion coefficient is another thermodynamically and industrially important parameter and can be calculated from the available density data by the following equation11 α=−

1 1 ⎛ dρ ⎞ ⎜ ⎟ = − (b + 2cT ) ⎝ ⎠ ρ dT P ρ

(4)

As it can be observed from values listed in Supporting Information (see Table S1), α-values are in the range of (7.65 to 11.25) × 10−4 K−1 over the studied temperature region, which reflects the volumetric changes with temperature. The overall trend obtained is DMBA > MBA > BA > DBA at all studied temperatures. The isobaric expansion coefficient values for all liquids show increasing trend with increase in temperature. The values obtained are similar to already reported ones for glycols1 and hydrocarbons.14 However, αvalues for ILs are somewhat lower than these organic liquids and does not change much with temperature at atmospheric pressure.15 3.2. Speed of Sound. The speed of ultrasonic sound through the studied liquids has been plotted in Figure 2. The

Lf = K

1 ρu 2

(6)

where K is Jacobson’s constant, a temperature-dependent variable, and ρ and u are density and speed of sound, respectively. The variation in Lf values with temperature is listed in Supporting Information (see Table S3). The importance of the parameter lies in the fact that when a sound wave passes through one molecule to another, it experiences a time lag due to the empty space between the two. Obviously, this space is the intermolecular free length contributing to the decrease in speed of sound. Because of this reason, the Lf values increase with the increase in branching of the benzylamines and increase in temperature. The decrease in the Lf value for DBA indicates more close-packed arrangement, which is also supported by the density data.9,17 3.3. Viscosity. The dynamic viscosity data are reported in Table 4 and plotted in Figure 3 as a function of temperature from 293.15 to 343.15 K at atmospheric pressure. From the plot, it is found that the trend followed by the viscosity follows the same order as density, that is, BA > MBA > DMBA, and as expected, DBA shows the highest viscosity owing to its different molecular structure and efficient packing. One of the main factors governing the viscosity is the van dar Waals interaction between the molecules of the liquids.20,21 The decrease in van dar Waals attraction force as well as the increased bulkiness with methyl substitution may be contributing to the decrease in viscosity. On the other hand, for the more bulky and closepacked DBA molecules it is comparatively more difficult to slide over other molecules, which reflects in higher viscosity values. However, with the increase in temperature the molecules attain more and more vibrational energy, making it easier to overcome the aforesaid difficulty, leading to a sharp decrease in viscosity with temperature. For common Newtonian liquids, the Arrhenius type equation can be used to study the variation in transport properties with temperature change.22,23 In this equation, the viscosity and temperature can be correlated as24

Figure 2. Temperature-dependent speed of sound curve of substituted benzylamine over the studied range of 298.15− 343.15 K. Red triangle, BA; red square, MBA; green circle, DMBA; blue diamond, DBA.

experimental data in the temperature range of 293.15 to 343.15 K are reported in Table 4. As a normal trend, a linear decrease in speed of sound is observed with temperature, which is in accordance with the previous reports.16 Similar to the trend observed in density, a gradual decrease in speed of sound with the substitution of methyl group is observed as BA > MBA > DMBA, and a sudden increase is noticed for benzyl group substitution for DBA. The speed of sound data could be a useful tool for looking into the molecular regime. Isentropic compressibility (βs), an important thermodynamic parameter used in primary screening for a process specific liquid, can be derived from these data by applying the Newton−Laplace equation17 1 βs = ρu 2 (5)

ln η = ln η∞ +

Eη RT

(7)

where η is the dynamic viscosity, η∞ is the viscosity at infinite temperature, Eη is the activation energy, T is the temperature in K, and R is the universal gas constant. The η∞ and Eη are estimated from intercept and slope of the viscosity data fitting

where ρ is the density of the liquid and u is the speed of sound. D



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Table 4. Experimental Speed of Sound and Viscosity (η) Data for the Studied Benzylamines in the Temperature Range of 293.15−343.15 K and at Atmospheric Pressure (∼0.1 MPa)a u/m·s−1

a

η/mPa·s

T/K

BA

MBA

DMBA

DBA

BA

MBA

DMBA

DBA

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

1580.59 1561.06 1541.20 1521.44 1501.89 1482.42 1462.90 1443.46 1424.09 1404.80 1385.58

1472.73 1452.86 1433.10 1413.47 1393.98 1374.57 1355.29 1336.13 1317.13 1298.40 1280.20

1348.15 1329.00 1309.58 1290.30 1271.18 1252.23 1233.46 1214.83 1196.38 1178.08 1159.94

1575.43 1557.24 1538.83 1520.57 1502.43 1484.47 1466.36 1448.75 1431.32 1414.03 1397.25

2.03 1.83 1.65 1.50 1.37 1.26 1.17 1.08 1.00 0.94 0.87

1.76 1.58 1.40 1.27 1.16 1.07 0.99 0.91 0.85 0.79 0.74

1.31 1.19 1.09 1.01 0.93 0.87 0.81 0.76 0.71 0.67 0.63

9.20 7.60 6.46 5.65 4.82 4.17 3.66 3.21 2.87 2.59 2.39

Standard uncertainties u are u(u) = 0.5 m·s−1, u(η) = 0.07 mPa·s, u(T) = 0.01 K, u(P) = 1 kPa

becomes more difficult for molecules to move over each other leading to higher viscosity. This fact could be attributed to physical constraints or molecular entanglement25 or to other stronger interaction among the molecules. 3.4. Refractive Index. The refractive index (RI) for all four liquids has been measured from 293.15 to 343.15 K at atmospheric condition and reported in Table 6. Measurement of RI at higher temperature was not possible due to instrument limitations. Comparison between the only available literature and experimental data for RI of benzylamine has been presented in Figure S4. The trend observed is DMBA < MBA < BA < DBA. As in density, the RI of DBA is the highest among four. The overall change in refractive index with temperature has been plotted in Figure 4. In order to analyze the effect of temperature, the data was fitted to second order polynomial as reported earlier26

Figure 3. Temperature-dependent viscosity curve of substituted benzylamine over studied range of 298.15−343.15 K. Red triangle, BA; red square, MBA; green circle, DMBA; blue diamond, DBA.

nD = d1 + d 2T + d3T 2

in eq 7. These parameters along with their standard deviation are given in Table 5.

where nD is the refractive index of liquids, T is the absolute temperature in K, and di are the fitting parameters. The fitting parameters of the polynomial equation along with their % ARD have been reported in Table 7. The relation between refractive index and other thermophysical properties are important in understanding the nature of a liquid. The refractive index is a measure of dielectric response to an external electric field induced by electromagnetic waves (light). By considering refractive index as the first order approximation response to electronic polarization within an instantaneous time scale, the Lorenz−Lorentz equation provides the relation between density and refractive index as well as the molar refractivity (Rm)27,28

Table 5. Fitting Parameters and Deviation for Arrhenius Equation (Equation 7) liquid BA MBA DMBA DBA a

En ± σa/J·mol−1 14.06 14.45 12.11 22.71

± ± ± ±

1.05 1.09 1.04 1.16

104 × η∞ ± σa/mPa·s

ARD

± ± ± ±

0.64 1.16 0.45 1.79

62.52 45.84 89.71 7.96

0.13 0.23 0.10 0.40

(8)

Standard uncertainty.

From the Arrhenius equation, two important parameters (η∞ and Eη) for understanding the physical properties could be obtained. The first one gives an extrapolation of the viscosity to the infinite temperature. At this point, contribution of the intermolecular interaction to the total viscosity becomes practically negligible, and the structural geometry becomes the main factor determining the viscosity. Thus, η∞ quantifies the total structural contribution of the molecules to the dynamic viscosity.9,16,17 The decrease in η∞ with increase in methyl groups substitution indicates to the less structural contribution of more branched molecules. The importance of the second parameter, Eη (activation energy) is in describing the physical energy barrier that must be overcome by a molecule to flow over the other. So, as the Eη value increases it

Rm =

2 M ⎛ nD − 1 ⎞ ⎟ ⎜ 2 ρ ⎝ nD + 1 ⎠

(9)

where M is the molar mass, ρ is the density, and nD is the refractive index. The molar refractivity (Rm) is an important property to characterize a liquid. The Rm values are given in Table 6. Several empirical equations have also been used by different authors which correlates the density with the refractive indices. These equations were proposed by different scientists to understand the inherent relation between the two properties. They can be expressed in a common form as29 E



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Table 6. Experimental Refractive Index (nD) and Molar Refraction (Rm) Data for the Studied Benzylamines in the Temperature Range of 293.15−343.15 K and at Atmospheric Pressure (∼0.1 MPa)a Rm

nD

a

T/K

BA

MBA

DMBA

DBA

BA

MBA

DMBA

DBA

293.15 298.15 303.15 308.15 313.15 318.15 323.15 328.15 333.15 338.15 343.15

1.5427 1.5387 1.5352 1.5323 1.5295 1.5271 1.5250 1.5230 1.5207 1.5191 1.5173

1.5224 1.5195 1.5168 1.5143 1.5121 1.5100 1.5078 1.5056 1.5034 1.5010 1.4986

1.5024 1.4999 1.4973 1.4952 1.4927 1.4904 1.4880 1.4856 1.4832 1.4809 1.4785

1.5740 1.5717 1.5695 1.5672 1.5650 1.5629 1.5608 1.5587 1.5566 1.5545 1.5523

33.20 32.85 32.52 32.22 31.94 31.67 31.42 31.18 30.92 30.70 30.46

34.91 34.58 34.27 33.97 33.69 33.42 33.14 32.86 32.58 32.29 32.00

35.89 35.57 35.24 34.95 34.63 34.32 34.01 33.71 33.40 33.10 32.79

66.81 66.33 65.85 65.38 64.92 64.46 64.01 63.57 63.13 62.69 62.24

Standard uncertainties, u(nD) = 0.001, u(T) = 0.01K, u(P) = 1 kPa.

f (nD) = f (nD) =

f (nD) =

(nD2 − 1) (nD2 + 2)

(14)

(nD2 − 1) (nD2 + 0.4)

(15)

(nD2 − 1)(2nD2 + 1) nD2

(16)

The average value of constant k for each liquid for each equation along with their deviations has been given in Table 8. Table 8. k-Values According to Different Empirical Equations

Figure 4. Temperature-dependent refractive index plot of substituted benzylamine over studied range of 298.15−343.15 K. Red triangle, BA; red square, MBA; green circle, DMBA; blue diamond, DBA. The symbol represents experimental values and the solid line symbolizes the values calculated from eq 8.

system BA MBA DMBA DBA overall AAD (%)

Table 7. Fitting Parameters for Polynomial Equation of Refractive Index (Equation 8) liquid

d1

BA MBA DMBA DBA

2.1450 1.7484 1.6545 1.7426

f (nD) = kρ

d2 −3.39 −1.04 −5.56 −6.98

× × × ×

d3 10−03 10−03 10−04 10−04

4.55 9.00 1.26 4.20

× × × ×

ARD % 10−06 10−07 10−07 10−07

0.013 0.013 0.004 0.003

where f(nD) is a function of refractive index (nD), k is an empirical constant which depends on liquid type and wavelength at which the refractive index is measured, and ρ is the density of the liquid. In this work, the most common equations have been used as proposed by Arago-Biot (eq 11), Dale−Gladstone (eq 12), Newton (eq 13), Lorentz−Lorenz (eq 14), Eykman (eq 15), and Oster (eq 16). (11)

f (nD) = (nD − 1)

(12)

f (nD) = (nD2 − 1)

(13)

D−G

Eykman

Oster

A−B

Newton

0.5495 0.5533 0.5589 0.5594 0.0004

0.7205 0.7271 0.7362 0.7304 0.0010

2.1836 2.1686 2.1570 2.2807 0.0123

1.5900 1.6381 1.6988 1.5532 0.0154

1.3892 1.3888 1.3918 1.4338 0.0041

One important thing to note that the above empirical equations do not take into account the effect of temperature in density and refractive index correlation. From our measurement and an earlier report, ILs29 show some change in k values with temperature. The pattern of change in k is different for different equations. Considering that the dependence of k on temperature is almost negligible (as observed for eq 11 as an example and shown in Figure 5), these set of equations give the best fit for our experimental data. The beauty of the equations lies in the fact that if one can get precise density or RI data, other one can be derived very precisely with the help of these simple equations. 3.5. Estimation of Critical Properties. The knowledge of critical properties and other thermophysical parameters are essential to develop an efficient thermodynamic model for pure component as well as their mixtures. Several group contribution methods have been proposed by different scientists to estimate the critical parameters for different group of liquids. Among them, the methods developed by Lyndersen30 and Joback and Reid31 are relatively simple and most widely used. In these

(10)

f (nD) = nD

L−L 0.3204 0.3245 0.3297 0.3227 0.0008

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intermolecular interaction between the respective molecules. The critical properties reported here could not be compared due to the nonavailability of literature data. To correlate predicted density values with the experimental results, Valderrama proposed a modified correlation36 based on the method already given by Spencer and Danner.37 The modified equation was given as follows MPc ⎡ APcVcB ⎤ ⎢ ⎥ ρ= RTc ⎣ RTc ⎦

Ω

(21)

and ⎡ 1 + (1 − T )2/7 ⎤ R ⎥ Ω = −⎢ ⎢⎣ 1 + (1 − TbR )2/7 ⎥⎦

Figure 5. Plot of k-values correlating the density and refractive index versus temperature using eq 11. Red triangle, BA; red square, MBA; green circle, DMBA; blue diamond, DBA.

where, ρ is the density of the liquid in g/cm3, R is the universal gas constant, A and B are constants, TR is the reduced temperature (TR = T/Tc), and TbR is the reduced temperature at the normal boiling point (TbR = Tb/Tc). Spencer and Danner35 obtained the values for A and B parameters in eq 21 as 0.3445 and 1.0135, respectively. In this work, we have proposed new values for A and B parameters to predict the densities of studied benzyl amines with the least deviation and presented in Table 10. The estimated density values along with

methods, a property of a compound is calculated by summing up the contribution of each constituting group multiplied by the number of occurrence. By combining the best results of above-mentioned methods, Alvarez and Valderrama32 proposed a “modified Lydersen−Joback−Reid” method that has shown good correlation for liquids of higher molecular weight and has been successfully extended also to ionic liquids and deep eutectic solvents.33,34 In this study, we have used this modified group contributors to estimate the properties like boiling point (Tb), density (ρ), critical pressure (Pc), critical temperature (Tc), and critical volume (Vc). The modified Lydersen− Joback−Reid method used in this study can be summarized in the following four equations Tb = 198.2 + Tc =

Pc =

∑ nΔTbM

Table 10. Modified Parameters of Equation 21

Tb (18)

M [CM + ∑ nΔPM]2

(19)

Vc = EM +

∑ nΔVM

parameters

BA

MBA

DMBA

DBA

A B

0.0452 1.3380

0.0440 1.3140

0.0401 1.3414

0.0401 1.3572

their deviations are reported in Table 9. It is observed from the comparison that the predicted value varies about 3% for the liquids from the experimental values. Though these prediction methods are not totally perfect and have been criticized,38 it is quite appreciable to get a quick and rough idea about an unknown compound’s density and critical properties by a simple method without much calculation. To the best of our knowledge, there is no literature available for the critical properties of the studied amines. So, the current investigation will provide a good amount of predictions for future use. The deviation indicates that further modification of the current method may lead to more accurate results, which is beyond the scope of our current discussion.

(17)

AM + BM ∑ nΔTM − (∑ nΔTM)2

(22)

(20)

where values of constants are given as AM = 0.5703; BM = 1.0121; CM = 0.2573; and EM = 6.75 The estimated critical properties of studied benzylamines have been reported in Table 9, while the groups considered and their respective values from modified Lynderson−Joback−Reid method33 are summarized in Table S4. It is observed that the predicted boiling point values are in good agreement with the literature value35 for BA and MBA, while the value predicted for DMBA and DBA differs more (11 and 50 K, respectively). These major deviations may be attributed to different

4. CONCLUSIONS In this work, a thorough investigation on high-temperature density (ρ) values was performed for four organic compounds based on benzyl amine and substituted benzyl amines. Other vital thermophysical properties such as speed of sound (u), viscosity (η), and refractive index (nD) also have been measured

Table 9. Predicted Density (at 298.15 K) from Modified Lynderson−Joback−Reid Method, Standard Deviation (SD), and Critical Properties

a

liquid

ρcal (g/cm3)

SD in ρ (%)

Tb (calc.)

Tb (lit.)a

Tc

Pc

Vc

BA MBA DMBA DBA

0.920455 0.892120 0.888822 0.967624

3.561 3.410 3.113 2.955

458.97 459.49 444.64 623.45

458 457−462 456 573

681.98 680.39 648.99 875.58

42.68 39.52 32.10 29.04

356.79 453.66 468.21 546.47

Reference 35. G



Article

(3) Pirisino, R.; Ciottoli, G. B.; Buffoni, F.; Anselmi, B.; Curradi, C. N-Methyl-Benzylamine, A Metabolite of Pargyline in Man. Br. J. clin. Pharmac. 1979, 7, 595−598. (4) Gupta, A. K.; Gardas, R. L. The Constitutive Behavior of Ammonium Ionic Liquids: A Physiochemical Approach. RSC Adv. 2015, 5, 46881−46889. (5) Barrue, R.; Perron, J. C. Density and Electrical Conductivity Measurements of Conducting Liquids at High Temperatures and Pressures- Application to Tellurium. Rev. Sci. Instrum. 1981, 52, 1536− 1541. (6) Kell, G. S. Density, Thermal Expansivity, and Compressibility of Liquid Water from 0° to 150°C: Correlations and Tables for Atmospheric Pressure and Saturation Reviewed and Expressed on 1968 Temperature Scale. J. Chem. Eng. Data 1975, 20, 97−105. (7) Weng, W. L.; Chang, L. T.; Shiah, I. M. Viscosities and Densities for Binary Mixtures of Benzylamine with 1-Pentanol, 2-Pentanol, 2Methyl-1-butanol, 2-Methyl-2-butanol, 3-Methyl-1-butanol, and 3Methyl-2-butanol. J. Chem. Eng. Data 1999, 44, 994−997. (8) Lee, M. J.; Hwang, S. M.; Kuo, Y. C. Densities and Viscosities of Binary Solutions Containing Butylamine, Benzylamine, and Water. J. Chem. Eng. Data 1993, 38, 577−579. (9) Chhotaray, P. K.; Gardas, R. L. Thermophysical Properties of Ammonium and Hydroxylammonium Protic Ionic Liquids. J. Chem. Thermodyn. 2014, 72, 117−124. (10) Singh, D.; Gardas, R. L. Influence of Cation Size on the Ionicity, Fluidity, and Physiochemical Properties of 1,2,4-Triazolium Based Ionic Liquids. J. Phys. Chem. B 2016, 120, 4834−4842. (11) Rocha, M. A. A.; van den Bruinhorst, A.; Schroer, W.; Rathke, B.; Kroon, M. C. Physicochemical Properties of Fatty Acid Based Ionic Liquids. J. Chem. Thermodyn. 2016, 100, 156−164. (12) Oswal, S. L.; Oswal, P.; Modi, P. S.; Dave, J. P.; Gardas, R. L. Acoustic, Volumetric, Compressibility and Refractivity Properties and Flory’s Reduction Parameters of Some Homologous Series of Alkyl Alkanoates from 298.15 to 333.15K. Thermochim. Acta 2004, 410, 1− 14. (13) Ye, C.; Shreeve, J. M. Rapid and Accurate Estimation of Densities of Room-Temperature Ionic Liquids and Salts. J. Phys. Chem. A 2007, 111, 1456−1461. (14) Navia, P.; Troncoso, J.; Romaní, L. New Calibration Methodology for Calorimetric Determination of Isobaric Thermal Expansivity of Liquids as a Function of Temperature and Pressure. J. Chem. Thermodyn. 2008, 40, 1607−1611. (15) Antón, V.; García-Mardones, M.; Lafuente, C.; Guerrero, H. Volumetric Behavior of Two Pyridinium Based Ionic Liquids. Fluid Phase Equilib. 2014, 382, 59−64. (16) Panda, S.; Gardas, R. L. Measurement and Correlation for the Thermophysical Properties of Novel Pyrrolidonium Ionic Liquids: Effect of Temperature and Alkyl Chain Length on Anion. Fluid Phase Equilib. 2015, 386, 65−74. (17) Sharma, G.; Gardas, R. L.; Coronas, A.; Venkatarathnam, G. Effect of Anion Chain Length on Physicochemical Properties of N,Ndimethylethanolammonium Based Protic Ionic Liquids. Fluid Phase Equilib. 2016, 415, 1−7. (18) Kavitha, T.; Attri, P.; Venkatesu, P.; Devi, R. S. R.; Hofman, T. Influence of Alkyl Chain Length and Temperature on Thermophysical Properties of Ammonium Based Ionic Liquids with Molecular Solvents. J. Phys. Chem. B 2012, 116, 4561−4574. (19) Jacobson, B. Ultrasonic Velocities in Liquids and Liquid Mixtures. J. Chem. Phys. 1952, 20, 927−928. (20) Tokuda, H.; Hayamizu, K.; Ishii, K.; Susan, M. A. B. H.; Watanabe, M. Physiochemical Properties and Structures of Room Temperature Ionic Liquids. 2. Variation of Alkyl Chain Length in Imidazolium Cation. J. Phys. Chem. B 2005, 109, 6103−6110. (21) Tokuda, H.; Tsuzuki, S.; Susan, M. A. B. H.; Hayamizu, K.; Watanabe, M. How Ionic Are Room-Temperature Ionic Liquids? An Indicator of the Physicochemical Properties. J. Phys. Chem. B 2006, 110, 19593−19600.

with great accuracy in the temperature range of 293.15−343.15 K. Effect of temperature has been evaluated and it was observed that values of all experimentally determined properties such as ρ, u, η, and nD decreased with increase in temperature. On the other hand, corresponding derived properties, isobaric expansion coefficient (α) and isentropic compressibility (βs), showed opposite behavior, that is, their values increased with increase in temperature. In addition to the effect of temperature, the influence of structural modification has also been examined. Substitution of methyl groups on benzyl amines acted as a driving force for gradual decrease in ρ, u, η, and nD values, leading to the trend BA > MBA > DMBA while substitution by two benzyl groups lead to sudden elevation in values resulting in DBA > BA > MBA > DMBA. The trend observed was similar for density, viscosity, and refractive index, whereas for speed of sound it was slightly different, that is, DBA ≈ BA > MBA > DMBA. As observed in the case of effect of temperature, derived properties α and β showed exactly the opposite trend DMBA > MBA > BA > DBA to that of experimentally measured properties. By scrutinizing the effect of temperature and structural modification, some useful insights to the molecular organization have been gained. Moreover, an attempt to predict the critical properties through a simple method has been made. This study on these industrially important liquids will not only help the chemical engineers to design process and product but also provide a deeper understanding in the realm of molecular liquids.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00667. Tables of temperature-dependent isobaric expansion coefficient (α); isentropic compressibility (βs); intermolecular free length (Lf); group contribution values from modified Lynderson−Joback−Reid Method; plot of comparison of experimental and literature density of water, toluene, benzylamine, and dibenzylamine; plot of comparison of experimental and literature refractive index of benzylamine and details of calibration method of DMA HP (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*Tel.: +91 44 2257 4248. Fax: +91 44 2257 4202. E-mail: [email protected] ORCID

Ramesh L. Gardas: 0000-0002-6185-5825 Funding

The authors are grateful to IIT Madras for financial support, through Institute Research and Development Award (IRDA), CHY/15-16/833/RFIR/RAME. Notes

The authors declare no competing financial interest.

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REFERENCES

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