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Original article
10 (
1_suppl
); S422-S430
doi:
10.1016/j.arabjc.2012.10.002

Thermodynamic properties of binary mixtures of 1,3,4-oxadiazole derivative with chloroform, N,N-dimethyl formamide at 303, 308 and 313 K and atmospheric pressure

Department of Chemistry, DST-FIST sponsored Mahatma Gandhi Campus, Maharaja Krishnakumarsinhji Bhavnagar University, Bhavnagar 364022, Gujarat, India

⁎Corresponding author. Tel.: +91 9687615488. drgodhani@yahoo.com (Dinesh R. Godhani)

Disclaimer:
This article was originally published by Elsevier and was migrated to Scientific Scholar after the change of Publisher.

Peer review under responsibility of King Saud University.

Abstract

The density (ρ), viscosity (η) and ultrasonic velocity (U) of pure solvents (chloroform (CF), N,N-dimethyl formamide (DMF)) and solutions of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI-C) (0.001, 0.002, 0.004, 0.006, 0.008, and 0.010 mol dm−3) in CF and DMF are investigated at 303, 308 and 313 K at atmospheric pressure. Various thermodynamic parameters such as acoustical impedance (Z), adiabatic compressibility (κa), inter molecular free path length (Lf), Rao's molar sound function (Rm), Van der Waals constant (b), internal pressure (π), relaxation time (τ), free volume (Vf) and solvation number (Sn) are calculated by using ρ, η and U data. The results obtained are interpreted in terms of solutesolvent and solutesolute interactions. The structure making or structure-breaking abilities of the solute in CF and DMF solvent are also studied.

Keywords

Molecular interaction
Thermodynamic parameter
Ultrasonic velocity
1,3,4-Oxadiazole

Nomenclature

C (mol dm−3)

concentration

T (K)

absolute temperature

M (kg mol−1)

molecular weight of solutions

M1

molecular weight of solvent

M2

molecular weight of solute

W1

weight fraction of solvent

W2

weight fraction of solute

R (J mol−1 K−1)

universal gas constant

b (m3)

Van der Waals constant

m

meter

Pa

pascle

s

second

κb

Boltzmann constant

h

Plank's constant

Greek symbol

ρ (kg m−3)

density

η (mPa s)

viscosity

U (m s−1)

ultrasonic velocity

Z (kg m−2 s−1)

specific acoustical impedance

κa (Pa–1)

adiabatic compressibility

Lf (m)

intermolecular free length

Rm (m10/3 s−1/3 mol−1)

Rao's molar sound function

π (Pa)

internal pressure

Vf (m3)

free volume

Superscripts

CF

chloroform

DMF

N,N-dimethyl formamide

A R

analytical reagent

1

1 Introduction

The five member 1,3,4-oxadiazole heterocycles are useful intermediates for the development of molecules of pharmaceutical interest where several promising antitumor compounds are found to contain the oxadiazole ring system (Rostom et al., 2003; Kumar et al., 2009). 1,3,4-Oxadiazole heterocycles are good bioisosteres of amides and esters, which can contribute substantially in increasing pharmacological activity by participating in hydrogen bonding interactions with the receptors (Guimaraes et al., 2005). The 2,5-disubstituted-1,3,4-oxadiazole derivatives are known for various pharmacological activities such as antibacterial (El-Emam et al., 2004), anti-inflammatory (Mullican et al., 1993), analgesic (Khan and Akhtar, 2003), antiviral and anticancer (Shah et al., 1998), antihypertensive (Upadhyay and Ram, 1999), anticonvulsant (Khan et al., 2001), antiproliferative (Liszkiewicz et al., 2003; Zahid et al., 2009), herbicidal (Kennedy and summers, 1981), hypoglycemic (O'Neal et al., 1962), hypnotic and sedative (Adelstein et al., 1976), MAO inhibitor (Mazouz et al., 1990) and insecticidal (Misra, 1983).

The sound velocity is a purely thermodynamic property. Many thermodynamic properties can be elucidated from sound velocity, viscosity and density data. Thermodynamic data are very important tool for understanding molecular interaction; solute–solvent and solute–solute, occurring in the solution. In recent years, the measurements of ultrasonic velocity have been adequately employed in understanding the nature of molecular interaction in pure liquids, binary and ternary mixtures (Srinivasalu and Ramachandra Naidu, 1991; Varadarajalu and Lakshminarayanan Reddy, 1998; Aswar, 1998). A literature survey reveals that ultrasonic velocity of various organic, inorganic and biological compounds in various solvents has been studied (Zhang et al., 2011; Baluja and Oza, 2002; Baluja and Shah, 2004). Our research group has also studied acoustical properties of synthesized compounds in various solvents (Godhani and Parsania, 2002; Godhani et al., 2001).

The choice of 1,3,4-oxadiazole is due to its multi-applicability in the field of medicine. The applications of these compounds attract us to study their behavior in various solvents and also investigate their thermodynamic properties. In the present paper, we have used this technique for the better understanding of the molecular interactions in some solutions. The present work deals with thermodynamic properties of the newly synthesized 1,3,4-oxadiazole derivative of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C) in chloroform (CF) and N,N-dimethyl formamide (DMF) solutions at 303, 308 and 313 K and at atmospheric pressure. The results are interpreted in terms of molecular interaction occurring in the solutions.

2

2 Experimental

2.1

2.1 Materials

The 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C) used in this study was synthesized in our laboratory. The molecular weight of PDI–C is 500.15. The structure of PDI–C was confirmed by IR, 1H NMR and CHN analyses. The structure of the present synthesized new PDI–C is shown in Fig. 1. The solvents: chloroform (CF) and N,N-dimethyl formamide (DMF) used in the present study were of A R grade and were purified according to literature methods (Riddick et al., 1986). The estimated purity of solvents was more than 99.8% and was confirmed by HPLC with PDA detector. The schiff-base of (Z)-N′-(2-hydroxybenzylidene)-2-(4-oxo-3-o-tolyl-3,4-dihydroquinazolin-2-ylthio)acetohydrazide was synthesized in our laboratory (Sanghani et al., 2008). The 1,3,4-oxadiazole derivative of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C) was synthesized by reacting schiff-base with acetic anhydride and was purified three times from chloroform – n-hexane prior to its use.

Structure of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C).
Figure 1
Structure of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C).

2.2

2.2 Synthesis of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C)

A mixture of Schiff-base 0.005 mol (2.50 g) and acetic anhydride (10 mL) was taken into a 100 mL round bottomed flask and was refluxed for 3.5 h in an oil bath. The progress of the reaction was monitored with the aid of TLC. The excess of acetic anhydride was then distilled off and the remaining mixture was poured in the ice cold water to form a yellowish solid compound PDI–C. The product was separated by filtration and crystallized from chloroform – n-hexane to afford the title compound PDI–C. The purity of the compound was checked by aluminum coated TLC plates 60 F245 (E. Merck) and the compound is purified by column chromatography using silica gel (60–120 mesh) and chloroform: n-hexane as an eluent. Yield – 63%, m.p. 248 °C.

Anal. calc. for C27H24N4O3S: C–64.78; H–4.83; N–11.19%. Found: C–64.75; H–4.85; N–11.22%.

FT–IR: 3070 cm−1 (Ar–H), 2933 cm−1 (C–H asym. str.), 2851 cm−1 (C–H sym. str.), 1708 cm−1 (CdbndN str.), 1520 cm−1 (CdbndC str.), 1475 cm−1 (–CH2 ben.), 1386 cm−1 (–CH3 ben.), 1273 cm−1 (C–N str.), 1012 cm−1 (C–O abs.), 755 cm−1 (1,2–disubstituted ring).

1H NMR: 8.39–8.41 δppm (1H, d), 7.70–7.78 δppm (4H, m), 7.73–7.75 δppm (1H, d), 6.90–7.20 δppm (6H, m), 4.93 (1H, s), 2.52 δppm (2H, s), 2.66 δppm (6H, s), 1.85 δppm (3H, s).

2.3

2.3 Measurements of density, viscosity and ultrasonic velocity

2.3.1

2.3.1 Apparatus and procedure

All the samples were prepared freshly and retained at the desired temperature for 24 h to ensure their solubility at the temperature. Samples were kept in bottles with PTFE septum under vacuum until further use.

2.3.2

2.3.2 Density, viscosity and ultrasonic velocity

Ultrasonic velocity, density and viscosity measurements in pure solvents (CF and DMF) and solutions of compound PDI–C (0.001, 0.002, 0.004, 0.006, 0.008, and 0.010 mol dm−3) in CF and DMF were made at 303, 308, and 313 K, by using M–81 multi frequency ultrasonic interferometer (2 MHz) (Mittal Enterprise, New Delhi), a Single Capillary Pycnometer made of borosil glass having a bulb capacity of 10 mL and an Ubbelohde viscometer. The Ubbelohde viscometer with 25 mL capacity was used for the viscosity measurement. Ubbelohde viscometer was calibrated with fresh conductivity water immersed in a water bath that was maintained at the experimental temperature. The flow time of water (tw) and the flow time of solution (ts) were measured with a digital stop clock with an accuracy of ±0.01 s (Model: RACER HS–10 W). Ultrasonic velocity (U), density (ρ) and viscosity (η) measurements were accurate to ±0.1 m s−1, ±0.1 kg m−3 and ±0.003 mPa s, respectively. The uncertainty of temperature is ±0.01 K and that of solution concentrations is ±0.0001 mol dm−3. The values of Ultrasonic velocity (U), density (ρ) and viscosity (η) were average of at least three measurements and the reproducibility of measurement values for sample.

2.3.2.1
2.3.2.1 Theoretical equations

From the experimental data of density, viscosity and ultrasonic velocity, various acoustical parameters are evaluated using standard equations:

Adiabatic compressibility:

(1)
κ a = 1 / U 2 ρ

Rao's molar sound function (Bagchi et al., 1986):

(2)
R m = ( M / ρ ) U 1 / 3 where M is the apparent molecular weight of solution and can be calculated according to the following equation: M = M1W1 + M2W2where W1 and W2 are weight fractions of solvent and solute respectively. M1 and M2 are molecular weights of the solvent and solute respectively.

Van der Waals constant (Vigoureux, 1952):

(3)
b = M / ρ { 1 - [ RT / ( MU 2 ) ] [ ( 1 + ( MU 2 ) / 3 RT ) - 1 ] } where R {8.3143 (J K−1 mol−1)} is the gas constant and {T (K)} is absolute temperature.

Internal pressure (Suryanarayana, 1979):

(4)
π = b RT ( K η / U ) 1 / 2 ( ρ 2 / 3 / M 7 / 6 ) where R {8.3143 (J K−1 mol−1)} is the gas constant and b′ (2) is the packing factor and K (4.28 × 109) is a constant.

Solvation number:

(5)
S n = M 2 / M 1 [ ( 1 - k a ) / k a 1 ] [ ( 100 - X ) / X ] where X is the number of grams of solute in 100 g of the solution. M1 and M2 are the molecular weights and κa1 and κa are adiabatic compressibility of solvent and solute respectively.

Free volume (Surayanarayana and Kuppusami, 1976):

(6)
V f = [ MU / K η ] 3 / 2

Intermolecular free path length (Jacobson et al., 1954):

(7)
L f = κ j κ a 1 / 2 where κj {(93.875 + 0.375T) × 10−8} is a temperature-dependent Jacobson's constant.

3

3 Results and discussion

The density (ρ), viscosity (η) and ultrasonic velocity (U) of pure solvents chloroform (CF) and N,N-dimethylformamide (DMF) used in the present work are reported in Table 1 and compared with the available literature data and a satisfactory agreement was found. The ρ, η and U of pure solvents and solutions of 2-((4-acetyl-5-(2-hydroxyphenyl)-5-methyl-4,5-dihydro-1,3,4-oxadiazol-2-yl)methylthio)-3-o-tolylquinazolin-4(3H)-one (PDI–C) in CF and DMF were measured at 303, 308 and 313 K and are reported in Table 2. It is clear from Figs. 2–4 that ρ, η and U increased with concentration (C) and decreased with temperature (T). The concentration and temperature dependence of these data were tested by least square analysis. Least square means that the overall solution minimizes the sum of the squares of the errors made in solving every single equation. The degree of linearity was judged on the basis of correlation coefficient. A fairly good to excellent correlation between the given parameters and concentration was observed at three temperatures in different solvent systems. The observed correlation between ρ and C, η and C, and U and C is R2 = 0.900–0.996, 0.972–0.996 and 0.945–0.991 respectively. The obtained R2 values supported a fairly good to excellent linear dependence of ρ, η and U with C and T. The observed trends for different C and T in ρ, η and U were CF > DMF, DMF > CF and DMF > CF respectively (Figs. 2–4). The increased ρ, η and U with C suggest that the increase of cohesive forces is due to powerful molecular interactions, while the decrease of these parameters with T indicates that cohesive forces decreased. The increasing temperature has two opposite effects namely increase of molecular interaction (structure formation) and destruction of structure formed previously. When the thermal energy is greater than the interaction energy, it causes the destruction of previously formed structure. Thus, the increase of T favors the increase of kinetic energy and volume expansion and hence, results in the decrease of ρ and η.

Table 1 Comparison of measured density (ρ), viscosity (η) and ultrasonic velocity (U) data for pure CF and DMF with literature values at 303, 308 and 313 K.
Organic liquids Present work Literature
T = 303 K T = 308 K T = 313 K T = 303 K T = 308 K T = 313 K
ρ (kg m−3) ρ (kg m−3)
CF 1475.3 1470.8 1465.8 1475.4a 1472.7a 1467.6a
DMF 941.7 937.2 933.6 939.7b 936.8e 929.8h
η (mPa s) η (mPa s)
CF 0.6628 0.6279 0.5781 0.6080d 0.6393f 0.5460d
DMF 0.7588 0.7056 0.6353 0.7520c 0.7070c 0.6641c
U (m s−1) U (m s−1)
CF 960.0 950.8 932.4 959.0d 949.6a 933.6a
DMF 1442.0 1432.0 1402.0 1446g 1426g 1404g
Table 2 The density (ρ), viscosity (η) and ultrasonic velocity (U) of PDI–C in CF and DMF solutions at 303, 308 and 313 K.
Concentration of PDI–C solutions (mol dm−3) Chloroform + PDI–C system DMF + PDI–C system
ρ (kg m−3) η (mPa s) U (m s−1) ρ (kg m−3) η (mPa s) U (m s−1)
T = 303 K T = 303 K
0.000 1475.3 0.6628 960.0 941.7 0.7588 1442.0
0.001 1476.7 0.6642 968.0 943.2 0.7608 1447.2
0.002 1476.8 0.6650 971.2 943.3 0.7623 1448.4
0.004 1476.9 0.6665 972.8 943.4 0.7641 1450.4
0.006 1477.2 0.6678 974.4 943.6 0.7672 1452.4
0.008 1477.8 0.6696 976.0 943.8 0.7695 1453.6
0.010 1478.1 0.6705 980.8 944.4 0.7724 1456.8
T = 308 K T = 308 K
0.000 1470.8 0.6279 950.8 937.2 0.7056 1432.0
0.001 1471.1 0.6295 958.0 939.3 0.7086 1434.8
0.002 1471.3 0.6303 960.0 939.6 0.7102 1435.6
0.004 1471.6 0.6315 964.0 940.3 0.7128 1436.8
0.006 1471.9 0.6328 965.2 940.8 0.7137 1438.4
0.008 1472.4 0.6341 967.2 941.4 0.7176 1440.4
0.010 1472.9 0.6358 970.0 942.2 0.7213 1443.2
T = 313 K T = 313 K
0.000 1465.8 0.5781 932.4 933.6 0.6353 1402.0
0.001 1465.9 0.5798 941.2 936.1 0.6383 1407.6
0.002 1466.2 0.5806 942.4 936.5 0.6401 1410.4
0.004 1466.6 0.5818 943.2 937.0 0.6415 1414.4
0.006 1467.2 0.5834 944.8 937.3 0.6439 1416.0
0.008 1468.1 0.5848 946.4 938.0 0.6463 1420.4
0.010 1468.8 0.5868 948.0 938.7 0.6501 1426.0
The plots of density (ρ) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
Figure 2
The plots of density (ρ) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
The plots of viscosity (η) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
Figure 3
The plots of viscosity (η) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
The plots of velocity (U) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
Figure 4
The plots of velocity (U) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).

The density and viscosity of medium, pressure, temperature etc. affect the velocity. With a view to understand the effect of concentration, temperature, nature of solvents and the structure of PDI–C on structure forming or structure-breaking tendency various acoustical parameters like acoustical impendence (Z), adiabatic compressibility (κa), intermolecular free path length (Lf), Rao's molar sound function (Rm), Van der Waals constant (b), internal pressure (π), free volume (Vf) and solvation number (Sn) were determined by using the experimental data of ρ, η and U of PDI–C solutions in CF and DMF at three different temperatures according to standard equations. The concentration and temperature dependence of acoustical parameters furnish a wealth of information regarding the strength of molecular interaction occurring in the solutions. Various acoustical parameters were fitted with concentration by least square analysis to certain concentration and temperature dependence molecular interactions in PDI–C solutions and hence the structure forming or structure-breaking nature of compound PDI–C is under investigation.

Ultrasonic velocity (U) depends on intermolecular free path length (Lf) inversely. It can seen from Tables 3 and 4 that, in CF and DMF systems both velocity and acoustical impendence (Z) increase with C and decrease with T of solute. The intermolecular free path length (Lf) is observed to decrease with C and increase with T suggesting the presence of solvent–solute interactions (Fig. 6).

Table 3 The least-square equations and regression coefficients for PDI–C solutions in CF at 303, 308 and 313 K.
Parameter Least square equations (regression coefficients, R2) [CF + PDI–C system]
T = 303 K T = 308 K T = 313 K
ρ (kg m−3) 160.2C + 1476 (0.944) 194.5C + 1470 (0.986) 321.6C + 1465 (0.984)
η (mPa s) 0.717C + 0.663 (0.994) 0.672C + 0.628 (0.996) 0.752C + 0.579 (0.994)
U (m s−1) 1218.0C + 967.5 (0.945) 1261.0C + 957.5 (0.971) 730.9C + 940.5 (0.991)
Z × 106 (kg m−2 s−1) 1.956C + 1.428 (0.953) 2.044C + 1.408 (0.977) 1.376C + 1.378 (0.991)
κa × 10−10 (Pa−1) −18.60C + 7.234 (0.950) −20.09C + 7.414 (0.973) −13.49C + 7.713 (0.992)
Lf × 10−11 (m) −7.295C + 5.631 (0.950) −7.781C + 5.701 (0.973) −5.112C + 5.814 (0.991)
Rm × 10−4(m10/3 s−1/3 mol−1) 14267C3 − 2353.0C2 + 13.22C + 7.992 (0.993) 69352C3 − 1345.0C2 + 9.938C + 7.996 (0.993) −41.61C2 + 0.933C + 7.986 (0.933)
b × 10−5 (m3) −65.28C2 + 0.102C + 7.960 (0.955) −0.794C + 7.991 (0.974) −1.534C + 8.018 (0.980)
π × 108 (Pa) −3E + 06C4 − 52826C3 + 1399.C2 − 6.869C + 4.224 (0.896) −6E+06C4 + 96790C3 − 173.3C2 − 2.303C + 4.121 (0.901) 1.561C + 4.107 (0.987)
Vf × 10−7 (m3) 20935C3 − 3275C2 + 14.37C + 2.585 (0.918) −1.468C + 2.308 (0.954) −2.260C + 3.054 (0.979)
Sn −1E+07C3 + 15520C2 − 382.1C + 0.33 (0.999) −3E+09C4 + 5E+07C3 − 26904C2 + 666.4C − 0.376 (0.988) −4E+12C5 + 1E+11C4 − 9E + 08C3 + 3E + 06C2 − 4500.0C + 1.911 (1)
Table 4 The least-square equations and regression coefficients for PDI–C solutions in DMF at 303, 308 and 313 K.
Parameter Least square equations (regression coefficients, R2) [DMF + PDI–C system]
T = 303 K T = 308 K T = 313 K
ρ (kg m−3) 119.7C + 943.0 (0.900) 313.9C + 938.9 (0.996) −13836C2 + 320.8C + 934.5 (0.934)
η (mPa s) 1.274C + 0.759 (0.996) 1.335C + 0.707 (0.972) 1.234C + 0.637 (0.982)
U (m s−1) 1008.0C + 1446.0 (0.987) 897.5C + 1433.0 (0.977) 1897.0C + 1406.0 (0.979)
Z × 106 (kg m−2 s−1) 1.125C + 1.363 (0.981) 1.296C + 1.346 (0.987) 2.165C + 1.315 (0.980)
κa × 10−10 (Pa−1) −7.62C + 5.069 (0.985) −8.121C + 5.182 (0.984) −15.78C + 5.404 (0.980)
Lf × 10−11 (m) −3.557C + 4.714 (0.985) −3.751C + 4.766 (0.984) −7.168C + 4.867 (0.980)
Rm × 10−4 (m10/3 s−1/3 mol−1) 1.460C + 8.763 (0.967) 74.27C2 − 1.364C + 8.776 (0.955) −54526C3 + 945.7C2 − 2.663C + 8.754 (0.990)
b × 10−5 (m3) −113.4C2 + 0.793C + 7.633 (0.931) −2.026C + 7.667 (0.994) −61608C3 + 1134.0C2 − 6.684C + 7.705 (0.978)
π × 108 (Pa) 7E + 09C5 − 2E + 08C4 + 2E + 06C3 − 9084.0C2 + 18.49C + 4.849 (1) 3.640C + 4.695 (0.969) 1.909C + 4.637 (0.947)
Vf × 10−7 (m3) −2.503C + 1.854 (0.987) −1.468C + 2.308 (0.954) −154.2C2 − 0.111C + 2.311 (0.923)
Sn −2E + 07C3 + 20679C2 + 54.92C + 0.111 (0.962) −89578C2 + 1444.0C − 1.015 (0.963) 2E + 13C5 − 4E + 11C4 + 4E + 09C3 − 2E + 07C2 + 25724C − 13.55 (1)
The plots of adiabatic compressibility (κa) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
Figure 5
The plots of adiabatic compressibility (κa) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).

When ultrasonic waves are incident on the solution, the molecules get perturbed. Since the medium has some elasticity and hence perturbed molecules regain their equilibrium positions. When a solute is added to a solvent, its molecules attract certain solvent molecules toward them, this phenomenon is known as compression. Every solvent has a limit for compression and is known as limiting compressibility. The decrease of adiabatic compressibility (κa) might be due to aggregation of solvent molecules around solute molecules supporting strong solvent–solute interactions. The adiabatic compressibility (κa) of the solutions of PDI–C was also found to decrease with C and increase with T in both systems (Fig. 5). This phenomenon can be attributed to the solvated molecules that were fully compressed by the electrical forces of the ions. The compressibility of the solution was mainly due to the free solvent molecules. The presence of compressibility of the solution decreases with the increase in solute concentration, due to solute–solvent interactions in the system. This was further confirmed by the increase in viscosity of PDI–C solutions in CF and DMF systems.

The plots of intermolecular free path length (Lf) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).
Figure 6
The plots of intermolecular free path length (Lf) against concentration (C) for PDI–C in (a) CF at 303 K (♦), 308 K (■) and 313 K (▴); (b) DMF at 303 K (♦), 308 K (■) and 313 K (▴).

According to Jacobson's intermolecular free length theory for liquids, the molecules of the liquid are assumed to be spherical and the average value of the distance that the ultrasonic waves travel between the two molecules is called the intermolecular free path length. Decrease of Lf with C further supported solvent–solute interactions. Due to solvent–solute interactions, structural arrangement is considerably changed.

The linear changes in Rao's molar sound function (Rm) and Van der Waals constant (b) shown in Tables 3 and 4 (correlation coefficient γ = 0.931–0.994) suggest that the absence of any complex or aggregate formation takes place in both CF and DMF systems (except at 308 K in DMF system).

The internal pressure (π) is the resultant of forces of attraction and repulsion between the molecules in a solution. The results of adiabatic compressibility and intermolecular free path length, which were found decreased with C and increased with T, while velocity and viscosity were found increased with C and decreased with T in CF and DMF systems, suggest that solute–solvent interaction is more predominant. This was confirmed from the results of internal pressure which was found to be increased. The internal pressure (π) increased with C and decreased with T in both solvent systems (except at 303 and 313 K in CF system). Internal pressure of a solution is single factor, which plays an important role in transport properties of solutions. The increase of internal pressure (π) and decrease of free volume (Vf) indicate the increase of cohesive forces and vice versa in the solutions of PDI–C in both solvent systems. The increase in internal pressure and decrease in free volume with concentration in both systems indicate ordered structural arrangement due to decreasing entropy of the system. The free volume (Vf) of a solute molecule at a particular temperature and pressure depends on the internal pressure of a liquid in which it is dissolved. The decrease in free volume causes internal pressure to increase or vice versa. However, Tables 3 and 4 show that the internal pressure increased and free volume decreased in both solvent systems. This again confirmed the existence of solute–solute and solute–solvent interactions in the system studied so far.

The degree of interaction was also measured in terms of solvation number (Sn). The negative solvation number indicates the structure-breaking tendency of solute (Woland, 1988). The decrease in the Sn with C suggested the presence of solute–solute interaction. The resultant value of the Sn depends upon solvent–solute and solute–solute interactions. It is clear from Tables 3 and 4 that solvation is powerful in DMF and minimum in the CF system. The lone pairs and –Cl are electronegative groups whereas –CH3, –OH and phenyl rings are electro positive groups. Halogen group forms weak H–bond with electropositive groups and hence solvation number was minimum in CF as compared to DMF system. It is clear from our results that Sn values are positive which shows the structure-forming tendency in CF and DMF systems. The variation in Sn with C and T values suggested the presence of strong dipole–dipole interaction. This is further suggestive that solute–solute and solute–solvent interactions are present in solution and the structure-forming tendency of PDI–C in CF and DMF.

4

4 Conclusions

On the basis of the experimental findings, it is concluded that ρ, η and U increased with concentration and decreased with temperature in both systems. Powerful molecular interactions resulted in the structure forming as judged on the basis of positive values of the solvation number. Thus, electronegative (–Cl and lone pairs) and electropositive (–CH3, –OH and phenyl rings) groups have played an important role on molecular interactions. The various thermodynamic parameters have been studied in this work; support each other and also the existence of weak and strong dispersive forces in the binary mixtures. The parameters obtained from the correlating equations have also provided us with valuable information.

Acknowledgements

The authors are thankful to Prof. P.H. Parsania, Head, Department of Chemistry, Saurashtra University, Rajkot for providing valuable guideline for the entire research of work.

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