INTRODUCTION. waves of very high frequencies. Hyper sound, sometimes called praeter sound or micro

1 INTRODUCTION 1.1 GENERAL INTRODUCTION Ultrasonics is the branch of physics concerned with ultrasonic waves; it is defined as the vibrations of frequencies greater than the upper limit of the audible range for humans that is, greater than about 20 KHz. The term sonic is applied to ultrasound waves of very high frequencies. Hyper sound, sometimes called praeter sound or micro sound is sound waves of frequencies greater than 10 13 hertz. An ultrasonic wave being transmitted through a substance is of two types. Each type causes a specific movement in the elements of medium and the paths that these elements follow as they move in response to the wave are called their orbits. If these orbits are parallel to the line of propagation, the waves are called longitudinal waves. If the path followed by the elements is normal to the direction of propagation, the waves are called transverse waves or shear waves. Since liquids do not possess shear elasticity, transverse waves cannot exist in liquids. Rectilinear propagation is a characteristic exhibited by ultrasonic waves because of their short wavelength 1, 2. The short wavelength of the ultrasonic waves is the factor that has been made possible by the application of these waves in many cases. Ultrasonic waves with low amplitude have been used by several workers 3-14 to investigate the structural and physico-chemical behaviour of pure liquids and their liquid mixtures. Speed of sound study provides a lot of information on molecular interactions. Ultrasonic wave propagation affects the physical properties of the medium and hence can furnish information on the liquid and liquid mixtures. The study of the propagation behaviour of ultrasonic waves in solids, liquids, liquid mixtures, electrolyte solutions,

2 suspensions, polymers, soaps etc. is now rather well established as an effective means for examining certain physical properties of materials or medium, molecular interactions etc. 15-18. The study of molecular interactions and the variations in these interactions due to structural changes have been carried out by various experimental techniques such as Infrared Spectroscopy technique 19, Nuclear Magnetic Resonance 20, 21, Raman spectra 22 and dielectric property measurements 23. But, the complete understanding of the nature of intermolecular and intramolecular interaction may not be possible by any single method. Ultrasonic methods have the added advantage of being less cost with efficiency comparable to other methods. Hence, a number of works have reported the study through ultrasonic method 24-27. Studies on speed of sound, density, viscosity, acoustic, thermodynamic, excess thermodynamic parameters and their deviations in binary systems have been the subject of many investigations in the recent years 28-34. These investigations on different systems reveal specific interactions between the molecules of the component liquids. It has been reported by several workers 3, 9 that occurrence of complex formation can be explained successfully by excess parameters such as excess speed of sound (U E ), excess isentropic compressibility (K s E ), excess free length (L f E ) etc. The positive values of U E and negative values of K E s show strong interactions occurring in liquid mixtures showing the possibility of complex formation 14. This occurs due to the formation of discrete groups of molecules arranged into specific geometric structures which are influenced not only by the shape of molecules but also by the mutual interactions occurring between them. A parallel measurement of sound velocity, density and viscosity of liquid

3 mixtures allows one to obtain information about their volume (V), compressibility (K s ), free length (L f ), internal pressure ( i ), acoustic impedance (Z), enthalpy (H) and changes in their properties. Complex formations, formation of hydrogen bond, dipole dipole, dipole- induced dipole interactions in solutions and their effect in physical properties of the mixture have received much attention. Density and viscosity of liquid mixtures are required in most engineering calculations where fluid flow of mixture is an important factor. Knowledge of the dependence of densities and viscosities of liquid mixtures on composition is of great interest from a theoretical stand point since it may lead to better understanding of the fundamental behaviour of liquid systems. Also it is essential in the design processes involving chemical separations, equipment design, solution theory, heat transfer, fluid flow and molecular dynamics. Viscosity data are useful for testing theories and empirical relations such as Grunberg and Nissan 35, Hind and Ubbelohde 36, Katti and Chaudhri 37, Heric 38, Frenkel 39, Tamura and Kurata 40 etc for liquid mixtures. In chemical industry 41, 42 there exists a continuous need for reliable thermodynamic data of binary systems. Mixed solvents, rather than pure liquids find practical applications in many chemical and industrial processes. Their excess thermodynamic parameters enable us to understand the physico-chemical properties in a continuous manner. An excess thermodynamic function denoted by superscript E is defined as the difference between the thermodynamic functions of mixing of a real mixture and the value corresponding to the ideal solution at the same conditions of temperature, pressure and composition. For an ideal solution all excess function are zero. Excess

4 functions may be positive or negative, their sign and magnitude representing the deviation from ideality. Both thermodynamic functions of mixing and excess functions become identical in respect of quantities where entropy does not appear. Deviations from ideal behavior in terms of various properties like molar volume, adiabatic compressibility, viscosity etc. have been widely used for the structural variations and molecular interaction of liquid mixtures. Several theories were proposed to study the speed of sound in binary and ternary mixtures. They are Flory s theory 43, Jacobson s free length theory 44, Schaaffs collision factor theory 45, Junjie s empirical relation 46, Nomoto s equation 47, Narasimhan and Manikam s combined equation 48, Vandael ideal mixing relation 49, impedance relation 50, Rao s specific velocity 51, Patterson theory 52 and Flory-Patterson theory 43,52,53. Theoretical evaluation of speed of sound in binary liquid mixtures and its correlation to study the molecular interaction has been successfully done in recent years 54-64 using the above theoretical relations. The basic aims of ultrasonic, volumetric and viscometric study are, 1) Study molecular interactions in the light of variation of various acoustic and thermodynamic parameters 2) Comparing the speed of sound values computed using various theories with experimental values and to find out the suitability of these theories to the systems investigated. 3) Studying molecular interactions in the light of deviations of theoretical velocities from experimental data and,

5 4) Comparing the viscosities calculated using various empirical relations with experimental data and to check more suitable empirical relation to the systems investigated. Ultrasonics find extensive applications in several fields, they are shown in fig. 1.

6 APPLICATIONS OF ULTRASONICS ULTRASONICS Paint industry Sono chemistry Acoustic Microscopy Binary/Ternary liquids Polymers Surfactants Drug industry Electro chemistry Textile Computer technology Under water acoustics industry Fig. 1

7 1.2 THEORETICAL ASPECTS The theories employed in the calculation of various acoustical and thermodynamic parameters and several empirical equations used in the present study are given. The experimentally determined values of speed of sound (U), density ( ) and viscosity ( ) are used to deduce these following properties. SPEED OF SOUND (U) A thorough survey of literature reveals that there are lots of methods for computing speed of sound 65-67. The speed of sound determined by interferometer method is considered as more reliable and precise. In this instrument, we can determine the wavelength (λ) of the ultrasonic wave in liquid and liquid mixtures. The expression used to determine the ultrasonic velocity is U = f.λ ms -1 (1) Where, f is the frequency of the generator which is used to excite the crystal. In the present investigation, a constant frequency (2 MHz) interferometer was employed and hence f value is 2 x 10 6 hertz. 1.2.1 THERMO ACOUSTIC PARAMETERS Various acoustic and thermodynamic parameters like, acoustic impedance (Z), isentropic compressibility (K s ), molar volume (V), free length (L f ), free volume (V f ), internal pressure ( i ), enthalpy (H) and relaxation time ( ) are evaluated using the experimentally determined values of U, and.

8 ACOUSTIC IMPEDANCE (Z) Sound travels through materials under the influence of sound pressure. Since, molecules or atoms of a liquid are bound elastically to one another, the excess pressure results in a wave propagating through the liquid 68. The acoustic impedance is given by the product of ultrasonic velocity and density as shown below: kg m -2 s -1 (2) Acoustic impedance is important in the determination of acoustic transmission and reflection at the boundary of two materials having different acoustic impedance. It is also useful in the designing of ultrasonic transducers and for assessing absorption of sound in a medium. ISENTROPIC COMPRESSIBILITY (K S ) Isentropic compressibility is a measure of intermolecular association or dissociation or repulsion. Singh and Kalsh 69 showed that the isentropic compressibility should be independent of temperature and pressure for unassociated and weakly associated molecules. It also determines the orientation of the solvent molecules around the liquid molecules. The structural arrangement of the molecule affects the isentropic compressibility. The increase or decrease of isentropic compressibility with increase in concentration of solute is due to either structure making or breaking property of the solute. Non linear variation of isentropic compressibility as a function of composition of liquid mixture is sufficient evidence for existence of molecular interactions in solutions. It can be calculated using the Laplace equation 70 kg -1 ms -2 (3) Where, U is the ultrasonic velocity and is the density of the solution.

9 MOLAR VOLUME (V) The molar volume can be computed using the following formula 63 : m 3 mol -1 (4) where, M is the effective molecular weight and is the density of the solution. FREE LENGTH (L f ) In the liquid state of matter, molecules are loosely packed, leaving free spaces among them. Determination of free length in liquids and liquid mixtures has been a subject to a semi-empirical relation to achieve the concept of intermolecular free length in order to explain the speed of sound in liquids and their mixtures. The free length is the distance between the surfaces of the neighboring molecules. In general when the ultrasonic velocity increases, the value of the free length decreases. The decrease in intermolecular free length indicates the interaction between the solute and solvent molecules due to which the structural arrangement in the neighborhood of constituent ions or molecules gets affected considerably. The intermolecular free length has been 44, 71 calculated using the following formula given by Jacobson Å (5) Where, K T is Jacobson's constant. This constant is a temperature dependent parameter whose value at any temperature (T) is given by (91.368 + 0.3565T) x 10-8. FREE VOLUME (V f ) Free volume is one of the significant factors in explaining the variations in the physio-chemical properties of liquids and liquid mixtures. The free space and its dependent properties have close connection with molecular structure and it may show interesting features about interactions, which may occur when two or more liquids are

10 mixed together. This molecular interactions between like and unlike molecules are influenced by structural arrangements along with shape and size of the molecules. A liquid may be treated as if it were composed of individual molecules each moving in a volume V f in an average potential due to its neighbors. That is, the molecules of a liquid are not quite closely packed and there are some free spaces between the molecules for movement and the volume V f is called the free volume 72. According to Eyring and Kincaid 73 the free volume is defined as the effective volume in which particular molecule of the liquid can move and obey perfect gas laws. Free volume is also defined as the average volume in which the centre of the molecules can move inside the hypothetical cell due to the repulsion of surrounding molecules. Free volume can be calculated by different methods. Chellaiah et al 74, Eyring et al 75, Kinacid et al 76, Mc Leod 77 and Hildebrand 78 have made a few approaches in calculating the free volume. Suryanarayana and Kuppusamy 79 on the basis of dimensional analysis, obtained an expression for free volume in terms of experimentally measurable parameters like ultrasonic velocity and viscosity and is given by m 3.mol -1 (6) Where, M eff is the effective molecular weight, which is expressed as M eff = (X 1 M 1 + X 2 M 2 ). Where, X and M are the mole fraction and molecular weight of the individual component in the mixture respectively. K is the temperature independent constant and its value is 4.28 x 10 9.

11 INTERNAL PRESSURE ( i ) The measurement of internal pressure is important in the study of thermodynamic properties of liquids. Internal pressure is a fundamental property of a liquid, which provides an excellent basis for examining the solution phenomenon and studying various properties of the liquid state. The internal pressure is the cohesive force, which is a resultant of force of attraction and force of repulsion between the molecules 80, 81. Internal pressure is the single factor which varies due to all types of solvent-solute, solute-solute and solvent-solvent interactions. Cohesion creates a pressure within the liquid of value between 10 3 and 10 4 atmospheres. It also gives an idea of the solubility characteristics. It is a measure of the change in the internal energy of liquid or liquid mixtures, as it undergoes a very small isothermal change. It is a measure of cohesive or binding forces between the solute and solvent molecules. In the basis of statistical thermodynamics, Suryanarayana et al 82 derived an expression for determination of internal pressure by the use of free volume concept. Internal pressure of the liquid mixture is obtained from the experimental values of ultrasonic velocity, density and viscosity using Pa (7) Where b stands for the cubic packing factor which is assumed to be 2 for all liquids and solutions. K is the temperature independent constant, R is the gas constant, T is the absolute temperature, is the viscosity, U is the speed of sound, is the density and M eff is the effective molecular weight.

12 ENTHALPY (H) The concept of molar cohesive energy has been used by several researchers 83-86 for comparing the interaction in the liquid mixtures. It is usually given as a product of internal pressure ( i ) and molar volume (V) H = i. V J.mol -1 (8) A molecule containing strong polar groups exerts corresponding strong attractive forces on its neighbors. If the intermolecular forces are small, the cohesive energy is low and the molecules have relatively flexible chains. RELAXATION TIME ( ) Relaxation time is the time taken for the excitation energy to appear as translational energy and it depends on temperature and on impurities. The dispersion of speed of sound in binary mixtures reveals information about the characteristic time of the relaxation process that causes dispersion. Relaxation time and absorption coefficient are directly correlated. The absorption of a sound wave is the result of the time lag between the passing of the ultrasonic wave and the return of the molecules to their equilibrium position. It is calculated using the relation 87 sec (9) 1.2.2 EXCESS THERMODYNAMIC PARAMETERS The excess thermodynamic parameters which play a major role in understanding the nature of molecular interaction in liquid mixtures have been studied by several workers 88-91. The excess thermodynamic parameters are defined as the difference between the experimental and ideal mixture values. It gives a measure of the non-ideality of the system as a consequence of associative or of other interactions 92.

13 Using the experimentally determined values of density, viscosity and speed of sound, various thermodynamic parameters like excess isentropic compressibility (K E s ), excess molar volume (V E ), excess free length (L E f ), excess Gibbs free energy of activation ( G *E ) and excess Enthalpy (H E ), were calculated. The excess values of the parameters have been computed from the following expressions: Excess isentropic compressibility An excess/deviation function corresponding to a thermodynamic or acoustic property is defined as the difference between the experimental value of the parameter describing the property of the mixture and the ideal value of that parameter. Benson and Kiyohara 93 stated that the thermodynamic properties of an ideal mixture must be mutually related in the same way as for those of pure substances and real mixtures. Also Douheret et al 94 suggested that the interpretation of the nature of molecular interactions in mixtures require a correct calculation of a thermodynamic property of the ideal liquid mixtures by the application of correct ideal mixing rules. In the present work the authors have calculated the excess values of isentropic compressibility and excess free length values to check the applicability of thermo dynamical ideality (the ideal mixing rules) to the components under study. The excess values of isentropic compressibility K E s were calculated as follows, K s E = K s K s id (10) Where K s E is its excess value, K s id is the ideal isentropic compressibility value and K s represent the calculated value of isentropic compressibility for the mixture, is the

14 density and U represents the speed of sound. K s id for an ideal mixture was calculated from the relation recommended by Benson and Kiyohara 93 and Douheret et al 94. o o 2 o2 id o TV i (α i ) o i i s i s,i o i i o Cp,i xicp,i K = K -T x V α (11) in which K, V, o s,i i o o α i, o C p,i are the isentropic compressibility, molar volume, isobaric thermal expansion coefficient and molar isobaric heat capacity of pure component i, T represents temperature, i is the volume fraction and x i represents the mole fraction of i in the mixture. Excess molar volume: The density values have been used to calculate the excess volumes, V E, using the following equation, 1 1 2 2 1 1 2 2 V (12) E X M X M X M X M 1 2 where is the density of the mixture and X 1, M 1, and 1 and X 2, M 2, and 2 are the mole fraction, molar mass, and density of pure components 1 and 2, respectively. Excess free length: The excess values of free length L E f were calculated by using the expression, L E f = L f K T (K id s ) 1/2 (13) Where L f represents the calculated value for the mixture and K T represent a temperature dependent constant whose value is K T =(91.368+0.3565T)x10-8.

15 Excess Gibbs free energy of activation ( G *E ): Excess Gibbs free energy of activation G *E was calculated as follows, ηv ΔG =RT ln -x ln ηv *E 1 1 1 η2v2 η2v2 (14) Where R represents gas constant, T is absolute temperature, is the viscosity of the mixture and 1, 2 are the viscosities of the pure compounds, V is the molar volume of mixture and V 1, V 2 are the molar volumes of the pure compounds. Excess Enthalpy: Excess enthalpy H E was calculated from usual relation, E H H ( X H X H ) (15) 1 1 2 2 Where H represents the calculated value of enthalpy for the mixture and H 1, H 2 represent enthalpy of pure components 1 and 2, respectively The excess values for the above parameters were fitted by the method of nonlinear least-squares to a Redlich-Kister type polynomial 95. n i-1 E Y =x1 1-x 1 Ai 2x1-1 (16) i=1 Where Y E = Ks E, V E, G *E, H E. The values of coefficient A i were determined by a regression analysis based on the least-squares method and are reported along with the corresponding standard deviations between the experimental and the calculated values of the respective functions in Table 4. The standard deviation (σ) was calculated using the relation

16 E E E obs cal 2 σ(y )= Y -Y /n-m (17) 1/2 Where n represents the number of experimental points and m is the number of adjustable parameters. 1.2.3 THEORETICAL EVALUATION OF SPEED OF SOUND Nomoto s relation: Nomoto 47 established an empirical formula for ultrasonic velocity in binary liquid mixtures based on two assumptions. They are, (i) there is a linear dependence of the molar sound velocity (R) on the concentration and (ii) The molar volume (V) is additive. The mole fraction of the component liquids are taken to be X 1 and X 2. The linear dependence of the molecular sound velocity on concentration can be expressed as, R = X 1 R 1 + X 2 R 2 where R 1 and R 2 are the molar sound velocities of the component liquids. Similarly the additivity of the molar volume is expressed as, V = X 1 V 1 + X 2 V 2 where V 1 and V 2 are the molar volumes of the component liquids. In the case of binary mixtures the formula for the sound velocity (U N ) is given as, U NOM = (18) Where, Molar sound velocity, ;

17 Molar volume ; Impedance dependent relation: Impedance dependent relation 50 is, (19) where Xi is the mole fraction, i the density of the mixture and Z i is the acoustic impedance. Van Dael and Van Geel s ideal mixture relation: The acoustical behavior of binary liquid mixtures was studied in detail by Van Dael et al 49. The expression for sound velocity (U IMR ) of binary mixtures is, U IMR = (20) where U IMR is the ideal mixing speed of sound in liquid mixture. U 1 and U 2 are ultrasonic velocities of individual compounds. Jungie equation: Jungie equation 46 for calculating speed of sound is, U JM = (21) where X i, V i, M i and U i are the mole fraction, molar volume, molecular weight and speed of sound of the constituent components respectively. Free length theory (FLT): Free length theory 44 relation is given as, U FLT = (22) Where, = 2

18 Molar volume at absolute zero, ; Surface area per mole, ; Where, 1, 2, represents the first and second component of the liquid mixture. Rao s specific velocity: Rao s specific velocity 51 is calculated using the following equation, where X i is the mole fraction, U i is the ultrasonic velocity, i the density of the mixture (23) and r i is the Rao s specific sound velocity = and Z i is the acoustic impedance. Chi-square test for goodness of fit: formula, According to Karl Pearson 96, the Chi-square value is calculated using the (24) For (n-1) degrees of freedom, where, n is the number of data used. Average percentage error (APE): The average percentage Error 97 is calculated using the relation, (25) Where, n- number of data used. Umix(obs) = experimental values of ultrasonic velocities. Umix(cal) = computed values of ultrasonic velocities.

19 1.2.4 THEORETICAL EVALUATION OF The dynamic viscosities of the binary liquid mixtures have been calculated using the following empirical relations. 1. Grunberg and Nissan relation: Grunberg and Nissan 35 model is based on Arrhenius equation for the measurement of viscosity of liquid mixtures (26) where G 12 is an interaction parameter which is function of the components 1 and 2 as well as temperature. 2. Hind and Ubbelohde relation: Hind and Ubbelohde 36 suggested an equation for the viscosity of binary liquid mixtures (27) where H 12 is an interaction parameter and is attributed to unlike pair interactions. 3. Katti and Chaudari relation: Katti and Chaudari 37 proposed the equation (28) where W vis is an interaction term and R is universal gas constant. 4. Heric and Brewer relation: Heric and Brewer 38 derived the relation (2.5.4) where 12 is the interaction term. 5. Frenkel Frenkel s 39 one parameter relation,

20 (29) where 12 is the interaction term. 6. Tamura and Kurata Tamura and kurata 40 derived the relation, (30) where T 12 is the interaction term. In all the above relations for viscosity, η is the viscosity of the mixture, X 1 and X 2 are the mole fractions, M 1 and M 2 are the molar masses, 1 and 2 are the mole fractions of the liquid mixture, η 1 and η 2 are the viscosity of the 1st and 2nd compound of the liquid mixture. 1.3 LITERATURE SURVEY Gonzalez et al 98 measured the densities and speeds of sound over the whole composition range, at T = (298.15, 303.15 and 308.15) K and p = 0.1 MPa, for the binary systems of ethanol, or 1-propanol, or 2-propanol and 1-butyl-3- methylpyridinium bis(trifluoromethylsulfonyl)imide, or 1-butyl-1-methylpyrrolidinium bis(trifluoromethylsulfonyl)imide. The density and speed of sound data were used to calculate the corresponding excess molar volumes and excess molar isentropic compressions, which were fitted with the Redlich-Kister equation. From the obtained results, a discussion was carried out in terms of interactions and structure factors in these binary mixtures. The density, viscosity and speed of sound at temperatures (303.15, 308.15 and 313.15) K were measured by Rathnam et al 99 for the binary mixtures of ethyl benzoate with tetrahydrofuran, 1,4-dioxane, anisole, and butyl vinyl ether over the entire range of

21 mixture composition. From these data excess volume, V E, isentropic compressibility, K s, intermolecular free length, L f, internal pressure, π i and free volume, V f, have been calculated. The computed excess quantities were fitted to the Redlich Kister equation. This work also provides a test of Katti-Chaudhri and McAllister's (3-body and 4-body) equations for correlating the viscosities of the binary mixtures. Almasi 100 measured the densities and viscosities for binary mixtures of dimethyl carbonate with 2-propanol up to 2-heptanol at various temperatures and ambient pressure. From experimental data, excess molar volumes, V E m. were calculated and correlated by the Redlich Kister equation to obtain the binary coefficients and the standard deviations. Excess molar volumes, V E m, are positive for all studied mixtures over the entire range of the mole fraction. The ERAS-model has been applied for describing the binary excess molar volumes and also Peng-Robinson-Stryjek-Vera (PRSV) equation of state (EOS) has been used to predict the binary excess molar volumes and viscosities. Also several semi-empirical models were used to correlate the viscosity of binary mixtures. The viscosity (η), density (ρ) and ultrasonic velocity (u) of pure diethyl ether (DEE) and three alkanols, namely methanol, n-propanol and n-butanol, and their binary mixture with DEE as a common component have been experimentally measured at 303.16 K under atmospheric pressure by Dash et al 101. The experimentally measured parameters were employed to compute the values of isentropic compressibility (β s ), intermolecular free length (L f ), molar volume (V m ), acoustic impedance (Z), available volume (V a ), free volume (V f ), internal pressure (π i ) and the viscous relaxation time (τ). Furthermore, the deviation functions such as were estimated in the entire range of DEE

22 mole fraction. The compositional variation of deviation functions were correlated to the Redlich Kister-type polynomial equation. The sign and magnitude of deviation parameters have been interpreted in terms of H-bonding, proper interstitial accommodation in the structural process and the dipole dipole type of molecular interactions between DEE and alkanol molecules. Theoretical values of ultrasonic velocity in all three binary mixtures have been estimated using five different empirical relations, such as Nomoto's relation, Junjie's relation, Rao's relation, Van Deal-Vageel's ideal mixing relation and impedance dependence relation. The relative merit of these relations with the measured values of ultrasonic velocity is discussed in this article. Densities, viscosities and speeds of sound of binary mixtures of ethyl benzoate with cyclohexane, n-hexane, heptane and octane have been measured over the entire range of composition at (303.15, 308.15 and 313.15) K and at atmospheric pressure by Rathnam et al 102. From these experimental values, excess molar volume (V E ), deviation in viscosity (Δη) and deviation in isentropic compressibility (ΔK s ) have been calculated. The viscosities of binary mixtures were calculated theoretically from the pure component data by using various empirical and semi-empirical relations and the results compared with the experimental findings. Rathnam et al 103 measured the densities (ρ), viscosities (η) and ultrasonic speeds (u) of binary mixtures of methyl benzoate with benzene, isopropyl benzene, isobutyl benzene, acetophenone, cyclopentanone, cyclohexanone or 3-pentanone including those of pure liquids over the entire composition range at temperatures 303.15 and 313.15 K respectively. The excess molar volumes (V E ) and the other excess thermodynamic properties such as deviations in isentropic compressibilities (Δk s ), ultrasonic speed ( u),

23 viscosity ( η) and excess free energy of activation ( G* E ) were calculated using the experimentally measured ρ, η and U respectively. The experimental mixture viscosities were analyzed on the basis of Tamura Kurata, Heric (2-Parameter), Eyring Margules and Jouyban Acree models. A good agreement among experimental data and the values estimated by theoretical procedure was obtained. Limiting partial molar volumes for six tertiary amines in methanol were obtained from accurate experimental density data at 298.15 K by Sousa et al 104. Volumetric contributions for the specific interaction between the lone pair of electrons of the amine group and the methanol have been obtained. Aliphatic hydrocarbons were used as reference compounds to account for the destruction of the methanol structure and non-polar solute-solvent interaction. Three types of differently shaped aliphatic hydrocarbons were considered aiming at analyzing the effect of the solute structure. Specific interactions between tertiary amines and methanol could then be derived. Hydrocarbons which are homomorphic forms of the amines were chosen as reference. Densities (ρ) and viscosities (η) for water (W) + triethylene glycol (TrEG),W +tetraethylene glycol (TeEG), and W+ tetraethylene glycol dimethyl ether (TeEGDME) were measured for the whole range of composition at five different temperatures ranging from 303.15 K to 323.15 K by Begum et al 105. Surface tensions for these systems were measured at 303.15 K for different mole fractions. The excess molar volumes, V E m, and excess viscosities, (η E ), were calculated from measured parameters. Derived volumetric and viscosimetric properties were fitted to Redlich Kister type equation. The properties were found to change significantly with increasing the number of glycol units and to be greatly affected by methyl substitution within the glycol unit.

24 For un substituted glycols a gradual increase in density and viscosity was observed on increasing the concentration, whereas for the methyl-substituted glycol TeEGDME sharp maxima were apparent in the density composition and viscosity composition curves. The surface tensions of aqueous solutions of methyl-substituted glycol TeEGDME were found to be significantly lower than other aqueous glycols. Viscosity and surface tension were measured for binary mixtures of N,Ndimethylformamide DMF with pentan-1-ol, hexan-1-ol, and heptan-1-ol at T = (298.15, 303.15, 308.15, and 313.15) K and atmospheric pressure over the entire mole fraction range by Mohammad et al 106. Deviations in viscosity and surface tension were calculated using experimental results. Moreover, the values of the excess Gibbs free energy of activation G *E, surface enthalpy H and surface entropy S of these mixtures were determined. Viscosity measurements of the binary systems were correlated with Grunberg and Nissan, the three-body and four-body McAllister expressions. Viscosity deviation, surface tension deviation and excess Gibbs energy of activation functions were fitted to the method of Redlich Kister (R K) polynomial to estimate the coefficients and standard deviations. The effects of chain length of alkan-1-ols and temperature on the thermodynamic properties of binary systems were studied. The vapour pressures of liquid (2-diethylaminoethylamine (2-DEEA) + cyclohexane) mixtures were measured by a static method between (T = 273.15 and T = 363.15) K at 10 K intervals by Khimeche et al 107. The excess molar enthalpies H E at 303.15 K were also measured. The molar excess Gibbs energies G E were obtained with Barker s method and fitted to the Redlich Kister equation. The Wilson equation was also used. Deviations between experimental and predicted G E and H E, by using

25 DISQUAC model, were evaluated. The proximity effect of N atoms produces a decrease of the interactional parameters. New experimental excess molar enthalpy data (420 points) of the ternary systems dibutyl ether (DBE) and 1-butanol and 1-hexene at 298.15 K and 313.15 K, and DBE and 1-butanol and cyclohexane or 2,2,4-trimethylpentane (TMP) at 313.15 K at atmospheric pressure are reported by Aguilar et al 108. A quasi-isothermal flow calorimeter has been used to make the measurements. All the ternary systems show endothermic character. The experimental data for the ternary systems have been fitted using the Redlich Kister rational equation. Considerations with respect the intermolecular interactions amongst ether, alcohol and hydrocarbon compounds are presented. Excess molar enthalpies, H E, for the binary mixtures of 1,2-dichloroethane (1,2- DCE) with diethyl ether (DEE), methyl 1,1-dimethylethyl ether (MTBE), diisopropyl ether (DIPE), 1,3-dioxolane (1,3-DIOXO), 1,4-dioxane (1,4-DIOXA), tetrahydropyran (THP), ethylene glycol dimethyl ether (EGDME), diethylene glycol dimethyl ether (DEGDME), and diethylene glycol diethyl ether (DEGDEE), have been measured at 298.15 K and atmospheric pressure, using a Setaram Tian-Calvet C80 microcalorimeter by Amireche-Ziar 109. All the binary systems investigated are characterized by exothermic mixing over the entire composition range, except for 1,2- DCE + DIPE which presents a S-shape H E behavior. The experimental H E data have been fitted to the Redlich Kister polynomial equation. Molar volumes of zinc (II) chlorocomplexes in N,N-dimethylacetamide (DMA) and dimethylsulfoxide (DMSO) at 298.15 K have been evaluated from the density data

26 obtained for mixtures of Zn (ClO4)2 and ZnCl2 of the same molarities by Warminska et al 110. The results indicate that all zinc (II) chlorocomplexes in N,N-dimethylacetamide are four-coordinated while in dimethylsulfoxide a change in geometry during complexation of the second chloride anion is observed. Measurements of densities ρ, viscosities η, and refractive indices n D have been carried out for binary mixtures of diethyl carbonate (DEC) with acetophenone, cyclopentanone, cyclohexanone, and 3-pentanone over the entire composition range at the temperatures (303.15, 308.15 and 313.15) K and at atmospheric pressure by Rathnam et al 111. From these experimental data, the excess volumes V E, deviation in viscosity Δη and deviation in molar refraction ΔR have been calculated. The Redlich Kister polynomial equation has been used to estimate the binary fitting parameters and the standard errors. The Prigogine Flory Patterson (PFP) theory and its applicability in predicting V E at (303.15, 308.15 and 313.15) K has been tested. The experimental viscosities were analyzed on the basis of Lobe and Auslaender models. Further different mixing rules have been applied to predict the n D values of the studied mixtures. Densities, viscosities of binary liquid mixtures of pyridine andm-xylene, o- xylene and p-xylene were determined at 293.15, 303.15, 313.15 and 323.15 K. From the experimental results obtained, deviation in viscosity (Δη), excess molar volume (V E ), and excess Gibbs free energy of activation of viscous flow (ΔG *E ), were determined by Dikio et al 112. The deviations in viscosity, excess molar volume and excess Gibbs free energy of activation of viscous flow were correlated with Redlich Kister polynomial equation. Other parameters like Grunberg Nissan interaction constant (d ) and a

27 modified Kendall Monroe equation (Eη m ), were used to quantitatively analyze the interactions in the system. Linear alkanone or cyclohexanone + aromatic hydrocarbon mixtures have been studied using DISQUAC and the Kirkwood Buff formalism. The aromatic compounds considered are: benzene, toluene, 1,4-dimethylbenzene, 1,2,4-trimethylbenzene and ethylbenzene. Vapour-liquid equilibria (VLE), molar excess Gibbs energies, G E m, molar excess enthalpies, H E m, and isobaric molar excess heat capacities, C E pm, of the binary systems studied are well represented by DISQUAC by Gonzalez et al 113. There is a good agreement between experimental H m E values of related ternary mixtures, and DISQUAC predictions obtained by means of binary interaction parameters only DISQUAC improves very meaningfully UNIFAC results on H E m, C E pm, properties which are closely related to the molecular structure of the mixture components. The enthalpy (H CO-S int ) of the ketone aromatic hydrocarbon interactions has been evaluated. These interactions become weaker when the alkanone size increases in mixtures with a given aromatic hydrocarbon, or when the aliphatic surface of the alkylbenzene is increased in systems with a given ketone. Steric effects are more relevant in 1,4- dimethylbenzene mixtures than in those with ethylbenzene. The application of the Kirkwood Buff formalism to mixtures including toluene or ethylbenzene shows that orientational effects, related to ketone ketone interactions, exist in solutions with the shorter 2-alkanones. Such effects are weakened when the chain length of the 2-alkanone increases. The opposite behaviour is observed when increasing the aliphatic surface of the alkylbenzene in systems with a given 2-alkanone. The cyclohexanone + benzene mixture shows a structure close to random mixing.

28 1.4 STATEMENT OF THE PROBLEM Alcohols are strongly associated in solution because of dipole-dipole interaction and hydrogen bonding. They are of great importance for their vital role in chemistry, biology and studies on hydrogen bonding in liquid mixtures. Alcohols are widely used as solvents. On the other hand alkyl benzoates are non-associated in solution, good hydrogen bonding acceptors. They are widely used in perfumery and pesticides. Volumetric, viscometric and Speed of sound investigations of liquids and liquid mixtures are of considerable importance and they play a vital role in understanding the intermolecular interactions occurring among the component molecules besides finding extensive applications in several industrial and technological processes. The deviations observed in the excess parameters indicate the strength of interactions present between the component molecules of the mixtures. The variations in the excess parameter values reflect the interactions between the mixing species, depending upon the composition, molecular sizes and shapes of the components and temperature. The effects which influence the values of excess thermodynamic functions may be the result of physical, chemical and structural contributions. In order to understand the nature of interactions between the components of liquid mixtures, it is of interest to discuss the same in terms of excess parameter rather than actual values. Non-ideal liquid mixtures show considerable deviation from linearity in their physical behavior with respect to concentration and these have been interpreted as arising from the presence of strong or weak interactions. The effect of deviation depends upon the nature of constituents and composition of mixtures. The deviations observed in the excess parameters indicate the strength of interactions

29 present between the component molecules of the binary mixtures under study. In general the values of excess thermodynamic functions are influenced by, The Specific forces that exist between the molecules, like the charge transfer complexes and existence of hydrogen bonds result in the negative excess values. Physical contributions comprised of non specific physical interactions like dispersion forces or weak dipole-dipole interactions. Structural characteristics, like the differences in the size and shape of the component molecules and their free volumes causes the geometrical fitting of one component into the other. Considering the above aspects the author has taken the present study on some binary and ternary mixtures at different temperatures. The binary systems in the present study are: 1) Methyl benzoate with 1-alkanols at T= (303.15, 308.15, 313.15, 318.15, 323.15) K a) 1-propanol + Methyl benzoate b) 1-butanol + Methyl benzoate c) 1-pentanol + Methyl benzoate 2) Ethyl benzoate with 1-alkanols at T= (303.15, 308.15, 313.15, 318.15, 323.15) K a) 1-propanol + Ethyl benzoate b) 1-butanol + Ethyl benzoate c) 1-pentanol + Ethyl benzoate 3) 2-propanol with alkyl benzoates at T= (303.15, 308.15, 313.15, 318.15, 323.15) K a) 2-propanol + Methyl benzoate b) 2-propanol + Ethyl benzoate

30 The ternary systems (equimolar) in the present study are: 1) Equimolar mixture of Methyl benzoate + 1-propanol with other 1-alkanols a) (Methyl benzoate + 1-propanol) + 1-butanol b) (Methyl benzoate + 1-propanol) + 1-pentanol 2) Equimolar mixture of Ethyl benzoate + 1-propanol with other 1-alkanols a) (Ethyl benzoate + 1-propanol) + 1-butanol b) (Ethyl benzoate + 1-propanol) + 1-pentanol at T= (303.15, 308.15, 313.15, 318.15, 323.15) K for both the systems. The present work deals with measurement of speed of sound (U), density ( ) and viscosity ( ) over the entire composition range at different temperatures in pure liquids and their mixtures. From these measured values different acoustical and transport parameters like acoustic impedance(z), isentropic compressibility (k s ), molar volume (V), free length (L f ) as well as thermodynamic parameters such as free volume (V f ) and internal pressure( i ), enthalpy(h) and relaxation time( ) are evaluated. Further deviation/ excess parameters of acoustic, thermodynamic and transport properties are evaluated from the above parameters. The excess functions have been fitted to the Redlich-Kister 96 type polynomial equation and their corresponding standard deviations are also evaluated. The experimental data of speed of sound and viscosity has been used to check the applicability of different theoretical velocity evaluated models and different viscosity models for all the systems investigated at various temperatures. The results obtained are presented and analyzed to study the molecular interactions between unlike molecules of different components of various binary and ternary (equimolar) liquid mixtures.