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Density, Sound Speed, and Viscosity of Dihydropyridine Derivatives in Dimethyl Sulfoxide at Different Temperatures Shipra Baluja* and Rahul M. Talaviya Physical Chemistry Laboratory, Department of Chemistry, Saurashtra University, Rajkot-360005, Gujarat, India S Supporting Information *

ABSTRACT: Some novel dihydropyridine derivatives, viz., 4-(4-hydroxy3-methoxyphenyl)-6-(2-hydroxyphenyl)-2-oxo-1,2-dihydropyridine-3carbonitrile, 4-(4-hydroxy-3-methoxyphenyl)-6-(4-hydroxyphenyl)-2-oxo1,2-dihydropyridine-3-carbonitrile, 6-(4-chlorophenyl)-4-(4-hydroxy-3methoxyphenyl)-2-oxo-1,2-dihydropyridine-3-carbonitrile, and 4-(4-hydroxy3-methoxyphenyl)-2-oxo-6-phenyl-1,2-dihydropyridine-3-carbonitrile have been synthesized, and characterization of these synthesized compounds has been done by IR, 1H NMR, 13C NMR, and mass analyses. The densities (ρ), viscosities (η), and ultrasonic velocities (U) of these dihydropyridine derivatives have been measured in dimethyl sulfoxide at different temperatures over a wide range of molalities. From these experimental data for ρ, η, and U, various acoustical parameters and some apparent molar parameters have been calculated. The obtained results are interpreted in terms of solute−solvent and solute−solute interactions, giving an idea of the structure-making or structure-breaking abilities of the studied compounds in dimethyl sulfoxide solution.

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pharmaceutical properties.25−29 In the present work, some new dihydropyridine derivatives were synthesized, and their structures were confirmed by IR, 1H NMR, 13C NMR, and mass analyses. The densities (ρ), viscosities (η), and ultrasonic velocities (U) of solutions of these compounds in DMSO with different molalities were measured at different temperatures. From these experimental data, some acoustical properties of the solutions, such as adiabatic compressibility (κS), intermolecular free length (Lf), specific acoustic impedance (Z), Rao’s molar sound function (Rm), molar compressibility (W), van der Waals constant (b), solvation number (Sn), etc., were evaluated in order to understand the molecular interactions. The apparent molar adiabatic compressibility (ϕκ) and apparent molar volume (ϕv) were also calculated and were fitted using the Gucker and Masson equations, respectively. The obtained data also provide valuable information regarding the nature and strength of the molecular interactions, the formation of hydrogen bonds, etc. that occur in the studied solutions.

INTRODUCTION Over the past few years, the ultrasonic technique has been employed in investigations of various complexes, polymers, binary liquid mixtures, etc., because of its nondestructive nature and accuracy.1−5 The most important features of the ultrasonic technique are robustness, precision, low cost, rapidity, and easy automation. Ultrasonic studies have found extensive applications in chemical engineering design, process simulation, solution theory, civil engineering, nuclear power generation, and molecular dynamics in chemical industries.6−8 In many chemical industries, knowledge of the acoustical properties of electrolyte and nonelectrolyte solutions is essential in the design of processes involving chemical separation, heat transfer, mass transfer, extraction, crystallization, etc.9−12 The ultrasonic technique is useful for the study of intermolecular interactions in liquid mixtures, which provides valuable information regarding internal molecular interactions, molecular association, complex formation,13−15 etc. A literature survey shows that many investigators have carried out studies on acoustical properties of organic compounds in various solvents using the ultrasonic technique.16−20 In the present work, as per our ongoing program of research,21−23 an acoustical study of some synthesized dihydropyridine derivatives has been carried out in dimethyl sulfoxide (DMSO) at various temperatures. Dihydropyridine derivatives are an important class of heterocyclic compounds that have showed significant applications in different fields.24 A literature survey shows that this class of compounds has a wide spectrum of biological and © XXXX American Chemical Society

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EXPERIMENTAL SECTION Materials. The solvent, DMSO, was of AR grade supplied by LOBA Chemie Pvt. Ltd. (Mumbai, India) and was purified by the standard method.30 The purity of DMSO was checked by GC−MS (Shimadzu model no. QP2010) and found to be 99.6%. The purified DMSO was stored over molecular sieves. The chemicals used in the synthesis of dihydropyridine derivatives, Received: July 21, 2015 Accepted: February 17, 2016

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DOI: 10.1021/acs.jced.5b00627 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

Figure 1. Reaction scheme for the formation of the dihydropyridine derivatives.

frequency for the measurements of ultrasonic velocity was 3 MHz. The density and ultrasonic velocity are extremely sensitive to temperature, and hence, the temperature inside the DSA 5000M instrument was controlled to within 0.01 K by a built-in Peltier device. Taking the purities of the samples into consideration, the standard uncertainty for density (u(ρ) was 0.5 kg·m−3. Before each series of measurements, the apparatus was calibrated with ultrapure water in the experimental temperature range. Measurement of Viscosity. The viscosities of water, pure DMSO, and different solutions of the synthesized compounds in DMSO were measured at different temperatures (298.15, 308.15, and 318.15 K) using a Ubbelohde viscometer with a standard relative uncertainty (ur(η)) of 0.09. The temperature was controlled by the digital temperature controller of the NOVA viscosity bath with an accuracy of 0.5 °C. The sample solutions were allowed to attain the desired temperature in the viscosity bath before the measurements. A digital stopwatch with an accuracy of 0.01 s (Hanhart, Gütenbach, Germany) was used to measure the flow time of water, pure DMSO, and solutions. Measurement of Melting Temperature by Differential Scanning Calorimetry. DSC measurements for all of the compounds were done using a Shimadzu DSC-60 calorimeter under a nitrogen atmosphere at a flow rate of 100 mL·min−1. The sample was enclosed in an aluminum crucible using a crimper and subjected to a temperature scan from room temperature to 400 °C with an empty aluminum crucible as the reference. The instrument was calibrated with standard indium metal (observed melting point = 157.19 °C) and tin metal (observed melting point = 233.02 °C) before the experiments.

such as vanillin, different substituted acetophenones, and ethyl cyanoacetate, were purchased from Spectrochem Pvt. Ltd. (Mumbai, India), and the purities of these chemicals were 97.0−99.5%. The synthesized dihydropyridine derivatives were recrystallized in methanol before use for acoustical studies. The purities of the synthesized compounds were also checked by GC−MS and found to be greater than 98.0%. Synthesis. An ethanolic solution of acetophenone or substituted acetophenone (0.01 mol), 4-hydroxy-3-methoxybenzaldehyde (0.01 mol), ethyl cyanoacetate (0.01 mol), and ammonium acetate (0.04 mol) was refluxed. Completion of the reaction was confirmed by analytical thin-layer chromatography (TLC) performed on aluminum plates coated with silica gel 60 F254 (E. Merck) using 0.6:0.4 hexane/ethyl acetate as the mobile phase. After completion of the reaction, the reaction mass was cooled, and the obtained solid was stirred with toluene for half an hour. The resultant solid was filtered, washed with methanol to remove unreacted reagents, and dried under vacuum to give the crude product. The reaction scheme is given in Figure 1. Overall, four compounds were synthesized, and the IUPAC names and acronyms used for these compounds are 4-(4-hydroxy-3methoxyphenyl)-6-(2-hydroxyphenyl)-2-oxo-1,2-dihydropyridine-3-carbonitrile (VMDP-1), 4-(4-hydroxy-3-methoxyphenyl)6-(4-hydroxyphenyl)-2-oxo-1,2-dihydropyridine-3-carbonitrile (VMDP-2), 6-(4-chlorophenyl)-4-(4-hydroxy-3-methoxyphenyl)-2-oxo-1,2-dihydropyridine-3-carbonitrile (VMDP-3), and 4-(4-hydroxy-3-methoxyphenyl)-2-oxo-6-phenyl-1,2-dihydropyridine-3-carbonitrile (VMDP-4). Spectroscopic Studies. For the structure confirmation, IR, 1H NMR, 13C NMR, and mass analyses were done. The IR spectra were taken on an IRaffinity-1S Fourier transform infrared spectrophotometer (Shimadzu). 1H NMR and 13C NMR spectra were taken on a Bruker AVANCE III (400 MHz) NMR spectrometer. In all cases, the 1H NMR and 13C NMR spectra were obtained in perdeuterated DMSO (DMSO-d6) using tetramethylsilane as an internal standard. The NMR chemical shifts (δ) are reported in parts per million. Mass spectra were determined using a direct inlet probe on a Shimadzu GC−MS instrument (model no. QP2010). Melting points of compounds were measured by differential scanning calorimetry (DSC) on a Shimadzu DSC-60 differential scanning calorimeter under a nitrogen atmosphere. Property Measurements. Measurements of Density and Ultrasonic Velocity. Ultrasonic velocity and density measurements on pure DMSO and different solutions of compounds were done at different temperatures (298.15, 308.15, and 318.15 K) using an Anton Paar sound velocity and density meter (DSA 5000M) with accuracies of 0.5 m·s−1 and 0.005 kg·m−3, respectively. The working

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RESULTS AND DISCUSSION The sources, purification methods, purities, and analysis methods for the various chemicals used in the present work are given in Table 1. Table 2 shows the physical properties of the synthesized compounds. Figures 2 to 5 show IR, 1H NMR, 13C NMR, and mass spectra, respectively, for the compound VMDP-3. Spectral Data. VMDP-1. IR (ν, cm−1): 3724.69, 3337.56 (−OH), 2215.14 (−CN), 1746.41 (−CO), 1579.70 (−NH−), 1450.11 (−CH−), 1393.53 (−CH−), 1256.58, 1019.90 (C−N), 1291.48 (C−O), 929.33 (−OH). 1H NMR (400 MHz, DMSO-d6): δ 3.8647 (s, 3H, OCH3), 6.7213 (s, 1H, CH), 6.8264−6.9255 (m, 4H, CH), 7.2179−7.2375 (d, 1H, J = 7.84 Hz, CH), 7.3254 (s, 1H, CH), 7.7661−7.7867 (d, 2H, J = 8.24 Hz, CH), 9.7281 (s, 1H, OH), 10.2429 (s, 1H, OH), 12.4460 (s, 1H, NH). 13C NMR (400 MHz, DMSO-d6): δ 55.79, 97.36, 105.88, 112.49, 115.53, 117.14, 121.84, 126.64, 127.67. 128.82, 130.96, 132.39, 147.54, 149.16, 150.67, 159.59, 162.30. MS: m/z 334. B



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Table 1. Sample Description chemical name

source

initial mole-fraction purity

purification method

final mole-fraction purity

analysis method

dimethyl sulfoxide 4-hydroxy-3-methoxybenzaldehyde ethyl cyanoacetate 4-hydroxyacetophenone 2-hydroxyacetophenone 4-chloroacetophenone acetophenone VMDP-1a VMDP-2b VMDP-3c VMDP-4d

LOBA Chemie Pvt. Ltd. Spectrochem Pvt. Ltd. Spectrochem Pvt. Ltd. Spectrochem Pvt. Ltd. Spectrochem Pvt. Ltd. Spectrochem Pvt. Ltd. Spectrochem Pvt. Ltd. synthesis synthesis synthesis synthesis

99.5% 99.0% 99.1% >97.0% >98.0% >98.0% >99.0% − − − −

fractional distillation − − − − − − recrystallization recrystallization recrystallization recrystallization

99.6% 99.0% 99.1% >97.0% >98.0% >98.0% >99.0% 98.3% 98.1% 98.6% 98.2%

GC−MSe − − − − − − GC−MSe GC−MSe GC−MSe GC−MSe

a VMDP-1 = 4-(4-hydroxy-3-methoxyphenyl)-6-(2-hydroxyphenyl)-2-oxo-1,2-dihydropyridine-3-carbonitrile. bVMDP-2 = 4-(4-hydroxy-3methoxyphenyl)-6-(4-hydroxyphenyl)-2-oxo-1,2-dihydropyridine-3-carbonitrile. cVMDP-3 = 6-(4-chlorophenyl)-4-(4-hydroxy-3-methoxyphenyl)2-oxo-1,2-dihydropyridine-3-carbonitrile. dVMDP-4 = 4-(4-hydroxy-3-methoxyphenyl)-2-oxo-6-phenyl-1,2-dihydropyridine-3-carbonitrile. eGC−MS = gas chromatography−mass spectrometry.

Table 2. Physical Properties of the Synthesized Dihydropyridine Derivatives at the Experimental Pressure (p = 0.1 MPa)a compound

R

molecular formula

molecular weight/ g·mol−1

Tfus/K

VMDP-1 VMDP-2 VMDP-3 VMDP-4

2-hydroxy 4-hydroxy 4-chloro H

C19H14O4N2 C19H14O4N2 C19H13O3N2Cl C19H13O3N2

334 334 352 318

507.64 599.48 601.49 616.27

a The standard uncertainties u are u(Tfus) = 0.9 K and u(p) = 0.01 MPa.

Figure 4. 13C NMR spectrum of VMDP-3.

Figure 2. IR spectrum of VMDP-3.

Figure 5. Mass spectrum of VMDP-3.

VMDP-2. IR (ν, cm−1): 3734.12, 3317.56 (−OH), 2218.14 (−CN), 1747.55 (−CO), 1579.70 (−NH−), 1460.11 (−CH−), 1394.53 (−CH−), 1276.88, 1029.99 (C−N), 1230.58 (C−O), 939.33 (−OH). 1H NMR (400 MHz, DMSO-d6): δ 3.8709 (s, 3H, OCH3), 6.7219 (s, 1H, CH), 6.8429−6.8869 (m, 2H, CH), 7.0233 (s, 1H, CH), 7.2222− 7.2412 (d, 1H, J = 7.60 Hz, CH), 7.3317 (s, 1H, CH), 7.7689− 7.7894 (d, 2H, J = 8.20 Hz, CH), 9.7170 (s, 1H, OH), 10.2284 (s, 1H, OH), 12.4254 (s, 1H, NH). 13C NMR (400 MHz, DMSO-d6): δ 55.78, 97.12, 106.05, 112.51, 115.56, 115.76, 115.97, 117.06, 121.85, 126.58, 129.04, 130.34, 147.54, 149.15, 149.77, 159.51, 162.30, 164.94. MS: m/z 334.

Figure 3. 1H NMR spectrum of VMDP-3. C



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Table 3. Comparisons of Measured Densities (ρ), Viscosities (η), and Ultrasonic Velocities (U) of Pure DMSO with Literature Values at Different Temperatures at the Experimental Pressure (p = 0.1 MPa)a ρ/kg·m−3

η·103/N·s·m−2

U/m·s−1

T/K

exptl

lit.

exptl

lit.

exptl

lit.

298.15

1095.276

1.814

1.83040 1.84841

1484.8

308.15

1085.226

1.472

1.53437 1.49841

1450.9

1485.133 1484.038 1483.039 1451.333 1451.638

318.15

1075.189

1095.2931 1095.3232 1095.3933 1085.2531 1085.3332 1085.3034 1075.1035 1075.2131 1075.3034

1.176

1.31042

1417.4

1417.733 1416.337

The standard uncertainties u are u(T) = 0.01 K, u(p) = 0.01 MPa, u(ρ) = 0.5 kg·m−3, and u(U) = 0.5 m·s−1, and the standard relative uncertainty ur is ur(η) = 0.09. a

VMDP-3. IR (ν, cm−1): 3479.58, 3441.01 (−OH), 2924.09 (O−H), 2222.00 (−CN), 1651.07, 1597.06, 1570.06 (−NH−), 1465.90, 1427.32 (−CH−), 1350.17 (−CH−), 1280.73, 1257.59 (C−N), 1203.58 (C−O), 1172.72, 1118.71 (C−H), 910.40 (N−H), 864.41, 786.96 (C−Cl). 1H NMR (400 MHz, DMSO-d6): δ 3.8622 (s, 3H, OCH3), 6.8806 (s, 1H, CH), 6.9308−6.9514 (d, 1H, J = 7.84 Hz, CH), 7.2436−7.2684 (d, 1H, J = 9.92 Hz, CH), 7.3446 (s, 1H, CH), 7.6047−7.6259 (d, 2H, J = 8.48 Hz, CH), 7.9186−7.9389 (d, 2H, J = 8.12 Hz, CH), 9.7776 (s, 1H, OH), 12.7288 (s, 1H, NH). 13C NMR (400 MHz, DMSO-d6): δ 55.75, 112.48, 115.47, 116.99, 121.85, 126.48, 128.86, 129.60, 135.85, 141.14, 147.50, 149.14, 159.85, 162.25, 164.46. MS: m/z 352. VMDP-4. IR (ν, cm−1): 3724.54, 3523.95 (−OH), 2222.00 (−CN), 1737.86 (−CO), 1649.14, 1591.27 (−NH−), 1473.62 (−CH−), 1377.17 (−CH−), 1249.52, 1022.27 (C−N), 1228.66 (C−O), 910.48 (N−H). 1H NMR (400 MHz, DMSO-d6): δ 3.8515 (s, 3H, OCH3), 6.5668 (s, 1H, CH), 6.9478−7.3144 (m, 6H, CH), 7.5257 (s, 2H, CH), 9.7431 (s, 1H, OH), 12.4439 (s, 1H, NH). 13C NMR (400 MHz, DMSO-d6): δ 55.66, 95.89, 104.41, 109.43, 111.84, 115.69, 117.36, 120.34, 122.66, 126.88, 128.45, 129.46, 146.72, 148.98, 150.71, 158.89, 159.59, 162.31, 168.43. MS: m/z 318. Density, Viscosity, and Ultrasonic Velocity Studies. The experimental values of density (ρ), viscosity (η), and ultrasonic velocity (U) of the pure solvent are given in Table 3 along with literature values.31−43 Table 4 shows the experimental density, ultrasonic velocity, and viscosity data for the studied compounds at different temperatures along with their standard uncertainties (in the table footnote). It is evident from Table 4 that all three experimentally measured properties increase with increasing molality of the compound at all three studied temperatures. Furthermore, for all of the studied compounds, as the temperature increases, the ultrasonic velocity decreases. The variations of the ultrasonic velocity (U) with molality for the synthesized compounds at 298.15 K are shown in Figure 6. The increase in ultrasonic velocity indicates that the solute molecules strongly attract solvent molecules, causing molecular association in solution. The type and magnitude of the interactions depend upon the structures of the compound and the solvent. In the present study, the solvent is the same for all of the compounds, so the various substitutions in the different compounds are responsible for the different magnitudes of the intermolecular interactions. From Figure 6 it can be observed that the ultrasonic velocity is higher in VMDP-2 and lower in VMDP-4. The compound VMDP-2

contains 4-hydroxy substitution, and hence, there may be the possibility of intermolecular interactions in solution, which causes a higher ultrasonic velocity. However, in case of VMDP-4, there is no substitution present on the aryl ring, and hence, the lower ultrasonic velocity may be due to weak or negligible hydrogen bonding with DMSO. To study the molecular interactions of the compounds in solution, some acoustical parameters such as adiabatic compressibility (κS), intermolecular free length (Lf), acoustical impedance (Z), Rao’s molar sound function (Rm), van der Waals constant (b), molar compressibility (W), and solvation number (Sn) were calculated using the experimental data on ultrasonic velocity (U), density (ρ), and viscosity (η) using standard equations. The adiabatic compressibility (κS) is given by43

κS =

1 U 2ρ

(1)

The intermolecular free length (Lf) is expressed as44 Lf = KJκS1/2

(2)

where KJ = (93.875 + 0.375T) × 10−8 is the temperaturedependent Jacobson’s constant. The acoustical impedance (Z) is given by Z = Uρ

(3)

Rao’s molar sound function (Rm) is expressed as ⎛M⎞ R m = ⎜ ⎟U1/3 ⎝ρ⎠

(4)

where M is the apparent molecular weight of the solution. The van der Waals constant b is given by b=

⎧ ⎫ ⎤⎪ ⎛ RT ⎞⎡ M⎪ MU 2 ⎥⎬ ⎟⎢ 1 + ⎨1 − ⎜ − 1 ⎪ ⎝ MU 2 ⎠⎢⎣ ρ⎪ 3RT ⎦⎥⎭ ⎩

(5)

where R = 8.3143 J·K−1·mol−1 is the gas constant and T is the absolute temperature. The molar compressibility (W) is expressed as ⎛M⎞ W = ⎜ ⎟κS−1/7 ⎝ρ⎠ D

(6) DOI: 10.1021/acs.jced.5b00627 J. Chem. Eng. Data XXXX, XXX, XXX−XXX


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Table 4. Densities (ρ), Viscosities (η), and Ultrasonic Velocities (U) of DMSO Solutions of Dihydropyridine Derivatives with Various Molalities (m) at Different Temperatures at the Experimental Pressure (p = 0.1 MPa)a m/mol·kg−1 0.00000 0.00915 0.01834 0.03687 0.05558 0.07449 0.09360 0.00000 0.00923 0.01851 0.03721 0.05609 0.07519 0.09447 0.00000 0.00932 0.01868 0.03755 0.05663 0.07590 0.09537 0.00000 0.00915 0.01834 0.03687 0.05558 0.07449 0.09359 0.00000 0.00923 0.01851 0.03721 0.05609 0.07519 0.09447 0.00000 0.00932 0.01868 0.03755 0.05663 0.07590 0.09537

ρ/kg·m−3 VMDP-1 1095.276 1096.094 1097.163 1098.321 1099.498 1100.684 1101.827 VMDP-1 1085.226 1086.409 1087.158 1088.467 1089.657 1090.647 1091.964 VMDP-1 1075.189 1076.399 1077.178 1078.468 1079.563 1080.708 1081.898 VMDP-2 1095.276 1096.117 1097.171 1098.339 1099.521 1100.693 1101.858 VMDP-2 1085.226 1086.437 1087.192 1088.482 1089.693 1090.673 1091.981 VMDP-2 1075.189 1076.452 1077.219 1078.491 1079.592 1080.741 1081.944

U/m·s−1 at 298.15 K 1484.8 1486.0 1487.0 1488.6 1490.2 1491.7 1493.5 at 308.15 K 1450.9 1452.1 1453.1 1454.2 1455.2 1456.3 1457.0 at 318.15 K 1417.4 1418.6 1419.5 1420.8 1422.0 1423.0 1424.3 at 298.15 K 1484.8 1486.3 1487.3 1488.9 1490.6 1492.0 1493.7 at 308.15 K 1450.9 1452.4 1453.2 1454.5 1455.6 1456.5 1457.4 at 318.15 K 1417.4 1419.0 1420.1 1421.5 1422.7 1424.0 1425.1

η·103/N·s·m−2

m/mol·kg−1

1.814 1.880 1.958 2.037 2.124 2.201 2.301

0.00000 0.00915 0.01834 0.03687 0.05558 0.07447 0.09354

1.472 1.535 1.570 1.608 1.645 1.685 1.716

0.00000 0.00923 0.01850 0.03717 0.05603 0.07507 0.09429

1.176 1.247 1.287 1.327 1.359 1.399 1.458

0.00000 0.00932 0.01868 0.03753 0.05656 0.07579 0.09519

1.814 1.885 1.963 2.060 2.144 2.243 2.323

0.00000 0.00915 0.01834 0.03688 0.05562 0.07457 0.09371

1.472 1.544 1.576 1.623 1.663 1.704 1.729

0.00000 0.00924 0.01852 0.03725 0.05620 0.07537 0.09475

1.176 1.265 1.312 1.364 1.392 1.421 1.462

0.00000 0.00932 0.01870 0.03760 0.05673 0.07608 0.09564

ρ/kg·m−3 VMDP-3 1095.276 1096.416 1097.301 1098.533 1099.792 1100.991 1102.291 VMDP-3 1085.226 1086.431 1087.473 1088.831 1089.981 1091.084 1092.317 VMDP-3 1075.189 1076.426 1077.194 1078.516 1079.891 1080.994 1082.353 VMDP-4 1095.276 1096.018 1096.688 1097.594 1098.593 1099.695 1100.841 VMDP-4 1085.226 1086.019 1086.782 1087.931 1088.738 1089.593 1090.639 VMDP-4 1075.189 1076.083 1076.695 1077.846 1078.839 1079.747 1080.752

U/m·s−1 at 298.15 K 1484.8 1486.1 1487.2 1488.4 1489.6 1490.5 1491.1 at 308.15 K 1450.9 1452.4 1453.4 1454.7 1455.9 1456.7 1457.6 at 318.15 K 1417.4 1418.9 1419.9 1421.0 1422.2 1423.2 1424.5 at 298.15 K 1484.8 1485.9 1486.8 1488.0 1489.1 1490.3 1491.0 at 308.15 K 1450.9 1451.9 1452.8 1453.9 1455.0 1456.0 1456.8 at 318.15 K 1417.4 1418.1 1419.1 1420.5 1421.6 1422.6 1423.7

η·103/N·s·m−2 1.814 1.954 1.993 2.037 2.081 2.129 2.172 1.472 1.545 1.571 1.614 1.655 1.699 1.730 1.176 1.264 1.294 1.324 1.355 1.391 1.427 1.814 1.876 1.916 1.976 2.020 2.063 2.107 1.472 1.525 1.562 1.603 1.638 1.668 1.697 1.176 1.242 1.276 1.319 1.345 1.370 1.410

The standard uncertainties u are u(T) = 0.01 K, u(p) = 0.01 MPa, u(m) = 0.0001 mol·kg−1, u(ρ) = 0.5 kg·m−3, and u(U) = 0.5 m·s−1, and the standard relative uncertainty ur is ur(η) = 0.09.

a

where M is the apparent molecular weight of the solution. Finally, the solvation number (Sn) is given by Sn =

M 2 ⎛ 1 − κS ⎞⎛ 100 − X ⎞ ⎟ ⎟⎜ ⎜ ⎠ M1 ⎝ κS0 ⎠⎝ X

the adiabatic compressibilities of the pure solvent and solute, respectively. The dissociation constants and conductances of these synthesized compounds were also studied in DMSO. It was observed that these compounds behave as weak electrolytes. Thus, for the present study a low concentration range was selected, where these compounds dissociate. So, in the present study the above equations were used for the synthesized dihydropyridine derivatives.

(7)

where X is the number of grams of solute in 100 g of the solution and M1 and M2 are the molecular weights and κ0S and κS E



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and the newly formed aggregates may be more compact, causing κS to decrease. Thus, the ultrasonic velocity (U), which is inversely related to κS (eq 1), increases with increasing molality, as shown in Figure 6. Furthermore, the acoustic impedance (Z) was also observed to increase with increasing molality, which again confirms association between compound and solvent molecules. The various acoustical parameters were also correlated with the molality (m) at different temperatures, and their least-squares equations along with regression coefficients (R2) are summarized in Tables 5 to 8 for the studied compounds. It is evident from these tables that the regression coefficients for almost all of the parameters are in the range 0.919−1.000. For Rao’s molar sound function (Rm), the van der Waals constant (b), and the molar compressibility (W), the value of the regression coefficient is 1, i.e., the changes in these parameters with molality are linear. This suggests the absence of complex formation in the solutions. The interactions between solute and solvent molecules can also be studied by the parameter called the solvation number (Sn), which is the number of solvent molecules attached to the central ion (solute) by their translation degree of freedom. Figure 9 shows the variations of Sn with molality for the studied compounds at 298.15 K. The solvation number was found to be positive for all of the compounds and to increase with molality. The positive solvation number indicates appreciable solvation of the studied compounds, i.e., the structure-forming nature

Figure 6. Variations of the ultrasonic velosity (U) with molality for the dihydropyridine derivatives in DMSO at 298.15 K: blue ◆, VMDP-1; red ■, VMDP-2; green ▲, VMDP-3; purple ■, VMDP-4.

Some of these evaluated parameters are given in Tables 5 to 8 for VMDP-1, VMDP-2, VMDP-3, and VMDP-4, respectively. Figures 7 and 8 show the variations of the adiabatic compressibility (κS) and intermolecular free length (Lf), respectively, with molality at 298.15 K for all of the compounds. Both of these acoustical parameters were found to decrease with increasing molality of the solution. The decrease in the intermolecular free length suggests a decrease in the distance between solute and solvent molecules, thus indicating an increase in solute−solvent interactions. This leads to a decrease in compressibility. As the solution molality increases, molecular association is enhanced

Table 5. Least-Squares Fit Equations and (In Parentheses) Regression Coefficients (R2) for the Density (ρ), Viscosity (η), Ultrasonic Velocity (U), Adiabatic Compressibility (κS), Intermolecular Free Length (Lf), Acoustic Impedance (Z), Rao’s Molar Sound Function (Rm), Molar Compressibility (W), van der Waals Constant (b), and Solvation Number (Sn) for VMDP-1 Solutions in DMSO at Different Temperatures least-squares fit equation (R2) parameter −3

ρ/kg·m η·103/N·s·m−2 U/m·s−1 κS·1010/m2·N−1 Lf·1011/m Z·10−6/N·m−2 Rm·104/m10/3·s−1/3·mol−1 W·103/m3·mol−1·(N·m−2)1/7 b·105/m3·mol−1 Sn

298.15 K

308.15 K

318.15 K

61.755m + 1095.7 (0.995) 4.4671m + 1.8527 (0.995) 81.356m + 1485.3 (0.999) −0.6783m + 4.1366 (0.998) −0.3445m + 4.1833 (0.998) 0.1814m + 1.6275 (0.998) 6.8682m + 8.1346 (1.000) 1.3276m + 1.5615 (1.000) 5.7046m + 6.7386 (1.000) 24.263m + 4.7684 (0.919)

60.478m + 1085.9 (0.998) 1.9737m + 1.5245 (0.992) 53.866m + 1451.9 (0.988) −0.5623m + 4.3685 (0.994) −0.2776m + 4.2990 (0.994) 0.1466m + 1.5766 (0.996) 6.8966m + 8.1462 (1.000) 1.3341m + 1.5634 (1.000) 5.8033m + 6.7880 (1.000) 45.435m + 4.195 (0.959)

60.071m + 1075.9 (0.998) 2.172m + 1.234 (0.987) 61.553m + 1418.2 (0.995) −0.6525m + 4.6210 (0.997) −0.3133m + 4.4215 (0.997) 0.1518m + 1.5259 (0.997) 6.9912m + 8.1577 (1.000) 1.3516m + 1.5653 (1.000) 5.9075m + 6.8393 (1.000) 39.607m + 4.2444 (0.942)

Table 6. Least-Squares Fit Equations and (In Parentheses) Regression Coefficients (R2) for the Density (ρ), Viscosity (η), Ultrasonic Velocity (U), Adiabatic Compressibility (κS), Intermolecular Free Length (Lf), Acoustic Impedance (Z), Rao’s Molar Sound Function (Rm), Molar Compressibility (W), van der Waals Constant (b), and Solvation Number (Sn) for VMDP-2 Solutions in DMSO at Different Temperatures least-squares fit equation (R2) parameter

298.15 K

308.15 K

318.15 K

ρ/kg·m−3 η·103/N·s·m−2 U/m·s−1 κS·1010/m2·N−1 Lf·1011/m Z·10−6/N·m−2 Rm·104/m10/3·s−1/3·mol−1 W·103/m3·mol−1·(N·m−2)1/7 b·105/m3·mol−1 Sn

61.841m + 1095.8 (0.995) 4.7594m + 1.8571 (0.994) 81.526m + 1485.6 (0.999) −0.6792 + 4.1351 (0.998) −0.3450m + 4.1825 (0.998) 0.1817m + 1.6278 (0.998) 6.868m + 8.135 (1.000) 1.3276m + 1.5615 (1.000) 5.7039m + 6.7385 (1.000) 28.874m + 4.2194 (0.921)

60.386m + 1086.0 (0.998) 2.0607m + 1.5335 (0.987) 55.079m + 1452.1 (0.990) −0.5689m + 4.3671 (0.994) −0.2809m + 4.2983 (0.994) 0.1478m + 1.5769 (0.996) 6.8998m + 8.1463 (1.000) 1.3346m + 1.5634 (1.000) 5.8039m + 6.7878 (1.000) 47.391m + 3.7614 (0.955)

60.010m + 1076.0 (0.999) 2.0343m + 1.2644 (0.966) 66.729m + 1418.6 (0.994) −0.6525m + 4.6210 (0.997) −0.3290m + 4.4201 (0.996) 0.1574m + 1.5264 (0.997) 7.0026m + 8.1582 (1.000) 1.3534m + 1.5654 (1.000) 5.9087m + 6.8391 (1.000) 41.327m + 3.4819 (0.946)

F



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298.15 K

308.15 K

318.15 K


63.944m + 1095.9 (0.999) 2.3584m + 1.9392 (0.996) 55.112m + 1486 (0.976) −0.5426m + 4.1322 (0.999) −0.2754m + 4.1811 (0.990) 0.1558m + 1.6285 (0.994) 8.7152m + 8.1351 (1.000) 1.6844m + 1.5616 (1.000) 7.3066m + 6.7380 (1.000) 55.43m + 4.7929 (0.975)

63.273m + 1086.1 (0.993) 2.069m + 1.5287 (0.996) 56.564m + 1452.2 (0.979) −0.5889m + 4.3659 (0.986) −0.2909m + 4.2977 (0.986) 0.1537m + 1.5772 (0.989) 8.8169m + 8.146 (1.000) 1.7034m + 1.5634 (1.000) 7.4351m + 6.7874 (1.000) 56.696m + 4.3005 (0.981)

65.107m + 1075.9 (0.999) 1.7419m + 1.2522 (0.995) 59.655m + 1418.5 (0.994) −0.6612m + 4.6191 (0.996) −0.3176m + 4.4205 (0.996) 0.1570m + 1.5261 (0.997) 8.9046m + 8.1594 (1.000) 1.7202m + 1.5656 (1.000) 7.5511m + 6.8402 (1.000) 52.278m + 4.5674 (0.932)


298.15 K

308.15 K

318.15 K


52.463m + 1095.5 (0.997) 2.5045m + 1.8637 (0.970) 57.173m + 1485.6 (0.999) −0.5119m + 4.136 (0.996) −0.2597m + 4.1830 (0.996) 0.1409m + 1.6275 (0.998) 6.0865m + 8.1365 (1.000) 1.1767m + 1.5618 (1.000) 5.0771m + 6.7397 (1.000) 35.962m + 4.8051 (0.943)

49.439m + 1085.7 (0.983) 1.848m + 1.5199 (0.982) 54.126m + 1451.6 (0.991) −0.5206m + 4.3709 (0.992) −0.2569m + 4.3001 (0.993) 0.1308m + 1.5760 (0.993) 6.1716m + 8.1467 (1.000) 1.1912m + 1.5636 (1.000) 5.1841m + 6.7888 (1.000) 38.98m + 4.7746 (0.976)

51.37m + 1075.7 (0.998) 1.7512m + 1.2137 (0.981) 60.756m + 1417.8 (0.991) −0.6115m + 4.6246 (0.994) −0.2934m + 4.4232 (0.994) 0.1385m + 1.5251 (0.995) 6.236m + 8.1586 (1.000) 1.2031m + 1.5655 (1.000) 5.2607m + 6.8406 (1.000) 27.046m + 5.3504 (0.982)

Figure 7. Variations of the adiabatic compressibility (κS) with molality for the dihydropyridine derivatives in DMSO at 298.15 K: blue ◆, VMDP-1; red ■, VMDP-2; green ▲, VMDP-3; purple ■, VMDP-4.

Figure 8. Variations of the intermolecular free length (Lf) with molality for the dihydropyridine derivatives in DMSO at 298.15 K: blue ◆, VMDP-1; red ■, VMDP-2; green ▲, VMDP-3; purple ■, VMDP-4.

of the compounds. This further proves association between the compounds and solvent molecules. As is evident from Figure 9, the degree of solvation is different for different compounds and is highest for VMDP-3 and lowest for VMDP-2. This may be due to the different substituents present in these compounds, which interact differently with the solvent. Thus, a chloro group at the para position (as in VMDP-3) causes maximum solvation, whereas with a hydroxyl group at the para position (as in VMDP-2) the solvation number is much decreased. However, when the hydroxyl group is at the ortho position (as in VMDP-1), the solvation number is slightly

higher. This suggests that not only the substituent but also its position affects solvation. The apparent molar compressibility and apparent molar compressibility were also evaluated. The apparent molar compressibility (ϕκ) is defined as ϕκ =

(ρ0 κS − ρκS0) ·1000 mρ0

+

κS0M ρ0

(8)

κ0S

where κS and are the adiabatic compressibilities and ρ and ρ0 the densities of the solution and solvent, respectively, m is the G



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molality of the solution, and M is the molecular weight of the solute. The apparent molar volume (ϕv) is given by ϕv =

1000·(ρ − ρ0 ) M − ρ mρ

(9)

Table 9 shows the values of the apparent molar compressibility and apparent molar volume for the solutions of all the compounds at all of the temperatures. It can be seen that the values for both parameters are negative in all cases. The apparent molar compressibilities of the solutions were fitted to Gucker’s relation,45 given by ϕκ = ϕκ° + Sκm1/2

Figure 9. Variations of the solvation number (Sn) with molality for the dihydropyridine derivatives in DMSO at 298.15 K: blue ◆, VMDP-1; red ■, VMDP-2; green ▲, VMDP-3; purple ■, VMDP-4.

where ϕ°κ is the limiting apparent molar compressibility at infinite dilution and Sκ is the interaction parameter. The values of ϕ°κ and Sκ were calculated from the intercepts and slopes, respectively, of the plots of ϕκ versus m1/2. These values are listed in Table 10.

Table 9. Apparent Molar Compressibilities (ϕκ) and Apparent Molar Volumes (ϕv) of Dihydropyridine Derivatives in DMSO at Different Temperatures m/mol· kg−1

ϕκ ·108/m5· N−1·mol−1

ϕv/m3· mol−1

VMDP-1 at 298.15 K 0.00915 −13.09 −74.629 0.01834 −13.41 −85.994 0.03687 −11.04 −69.310 0.05558 −10.34 −63.999 0.07449 −9.90 −61.416 0.09360 −9.72 −59.456 VMDP-3 at 298.15 K 0.00915 −16.24 −103.975 0.01834 −14.34 −92.272 0.03687 −11.21 −74.122 0.05558 −10.12 −68.437 0.07447 −9.36 −64.885 0.09354 −8.80 −63.640 VMDP-1 at 308.15 K 0.00923 −16.82 −108.891 0.01851 −14.49 −88.855 0.03721 −11.46 −74.439 0.05609 −10.26 −67.774 0.07519 −9.49 −62.130 0.09447 −9.09 −61.705 VMDP-3 at 308.15 K 0.00923 −18.74 −110.914 0.01850 −16.71 −103.313 0.03717 −13.01 −82.772 0.05603 −11.41 −72.708 0.07507 −10.25 −67.112 0.09429 −9.70 −64.917 VMDP-1 at 318.15 K 0.00932 −18.30 −112.412 0.01868 −15.55 −92.325 0.03755 −12.56 −76.011 0.05663 −11.28 −67.527 0.07590 −10.50 −63.835 0.09537 −10.21 −62.011 VMDP-3 at 318.15 K 0.00932 −20.35 −114.917 0.01868 −16.88 −93.066 0.03753 −13.07 −77.120 0.05656 −11.95 −72.569 0.07579 −10.95 −67.126 0.09519 −10.71 −66.189

m/mol· kg−1

ϕκ ·108/m5· N−1·mol−1

(10)

Table 10. Coefficients in eqs 10, 11, and 12 for Dihydropyridine Derivatives in DMSO at Different Temperatures

ϕv/m3· mol−1

coefficient

VMDP-2 at 298.15 K 0.00915 −14.82 −76.725 0.01834 −14.08 −86.358 0.03687 −11.46 −69.719 0.05558 −10.69 −64.346 0.07449 −10.07 −61.518 0.09359 −9.89 −59.735 VMDP-4 at 298.15 K 0.00915 −11.85 −67.700 0.01834 −10.95 −64.376 0.03688 −8.87 −52.797 0.05562 −8.21 −50.322 0.07457 −8.00 −50.230 0.09371 −7.65 −50.552 VMDP-2 at 308.15 K 0.00923 −18.79 −111.465 0.01851 −14.98 −90.416 0.03721 −11.95 −74.783 0.05609 −10.69 −68.322 0.07519 −9.69 −62.427 0.09447 −9.31 −61.860 VMDP-4 at 308.15 K 0.00924 −12.48 −73.019 0.01852 −11.98 −71.587 0.03725 −10.01 −62.159 0.05620 −8.84 −53.762 0.07537 −8.21 −50.099 0.09475 −7.91 −49.631 VMDP-2 at 318.15 K 0.00932 −21.42 −117.330 0.01868 −17.48 −94.224 0.03755 −13.73 −76.542 0.05663 −12.10 −67.973 0.07590 −11.29 −64.215 0.09537 −10.79 −62.434 VMDP-4 at 318.15 K 0.00932 −12.65 −83.079 0.01870 −12.08 −69.936 0.03760 −10.76 −61.627 0.05673 −9.84 −56.388 0.07608 −9.15 −52.767 0.09564 −8.88 −51.473

A·1010/m2·N−1·kg· mol−1 B·1010/m2·N−1·kg3/2·mol−3/2 ϕ°κ ·107/m5·N−1·mol−1 Sk·107/m5·N−1·kg1/2·mol−3/2 ϕv°/m3·mol−1 Sv/m3·kg1/2·mol−3/2 A·1010/m2·N−1·kg· mol−1 B·1010/m2·N−1·kg3/2·mol−3/2 ϕκ°·107/m5·N−1·mol−1 Sk·107/m5·N−1·kg1/2·mol−3/2 ϕv°/m3·mol−1 Sv/m3·kg1/2·mol−3/2 A·1010/m2·N−1·kg· mol−1 B·1010/m2·N−1·kg3/2·mol−3/2 ϕ°κ ·107/m5·N−1·mol−1 Sk·107/m5·N−1·kg1/2·mol−3/2 ϕv°/m3·mol−1 Sv/m3·kg1/2·mol−3/2

VMDP-1

VMDP-2

298.15 K −1.17 −1.37 1.62 2.31 −1.45 −1.76 1.60 2.78 −79.58 −85.08 63.84 81.62 308.15 K −1.48 −1.41 2.99 2.51 −1.56 −1.89 2.39 3.21 −104.05 −110.72 117.54 165.62 318.15 K −2.00 −1.63 2.45 2.94 −2.04 −2.17 4.06 3.70 −126.95 −117.04 146.58 184.47

VMDP-3

VMDP-4

−1.42 2.71 −1.78 3.07 −111.32 162.53

−1.05 1.65 −1.36 2.01 −77.63 106.85

−1.73 3.67 −2.56 4.39 −113.24 224.98

−1.11 1.77 −1.48 2.31 −88.86 133.43

−1.84 3.96 −1.94 2.38 −133.19 248.81

−1.17 1.82 −1.67 2.47 −104.85 184.63

The apparent molar volume (ϕv) is also related to the molality by Masson’s equation:46

ϕv = ϕv° + Svm1/2

(11)

where ϕ°v is the limiting apparent molar volume at infinite dilution and Sv is the solute−solvent interaction parameter. The values of ϕv° and Sv were evaluated from the intercepts and slopes, respectively, of the plots of ϕv versus m1/2 and are reported in Table 10. The type of intermolecular interaction in solution can also be confirmed by evaluating the constants in Bachem’s relation:47 κS = κS0 + Am + Bm3/2

(12)

where A and B are constants and m is molality of the solution. The values of A and B were determined from the intercepts and slopes, respectively, of the plots of (κS − κ0S)/m versus m1/2 and are also given in Table 10. H



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As shown in Table 10, the values of A, ϕ°κ , and ϕ°v are negative whereas the B, Sκ, and Sv values are positive for all of the studied compounds at different temperatures. The negative values of A, ϕκ°, and ϕv° suggest the existence of solute−solvent interactions in the studied solutions. When the solute causes electrostriction in the solution, it results in a decrease in compressibility, which is reflected by a negative ϕκ° value. Furthermore, the positive Sκ, Sv, and B values indicate a structure-forming tendency of the studied compounds in DMSO.

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CONCLUSIONS The acoustical parameters evaluated for DMSO solutions of the studied compounds suggest the predominance of solute−solvent interactions, which are found to increase with molality. However, these interactions are found to decrease with increasing temperature. The type and magnitude of the interactions depend on the substitution present in the compound. The compound containing a p-hydroxy group causes strong solute−solvent interactions in comparison with other groups. The apparent molar properties also confirm the existence of solute−solvent interactions in solution.

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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.5b00627. 1 H and 13C NMR spectra for all of the compounds along with their peak integrations (Figures S1 to S8), DSC thermograms for the standard metals indium (literature melting point = 156.60 °C48) and tin (literature melting point = 231.90 °C49) (Figures S9 and S10, respectively), and DSC thermograms for all of the studied compounds (Figures S11 to S14) (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: shipra_baluja@rediffmail.com. Notes

The authors declare no competing financial interest.

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REFERENCES

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