. Chapter 1

Introduction

1. l General introduction

electromagnetic theory of Clerk Maxwell furnishes a great unifying

nciple; it indicates that the wireless waves which convey speech and

music from one corner of the earth to another, the infrared mdiations. which give

us warmth, the visible light rays which enable us to see the things around us, the

ultraviolet radiations which bring about photochemical reactions, the X-rays that

reveal the internal architecture of crystalline solids and the y-rays that shoot out

from radio active bodies are a1 fundamentally of the same physical nature. They

constitute a whole gamut of radiations having widely different frequencies and

wavelengths. According to Maxwell's theory, all these radiations travel through

the space with the same unique velocity of 3 x 1o8 rn/s and their essential

difference is one of frequency or the number of vibrations per second. Indeed,

considered from the phenomenological standpoint, it is difficult to conceive of an

upper limit to the frequency spectrum of the electromagnetic radiations.

If we now consider the vibrations of material media which constitute

'sound' in its broadest sense, we have a simibr, though not identical, state of

affairs. Sound is defined as a mechanical vibratory form of energy which is

propagated through a medium by means of the motion of the particles of the

medium. The phenomenon of propagation is a complex interpky between the

parameters of the sound wave and the characteristic of the medium. An upper

limit to the frequency spectrum of sound can, however, be fixed when it is

remembered that the idea of sound wave propagation in a medium ceases to

have any precise meaning when the wavelength is of the same order of

magnitude as the intermolecular distance.' Since sound velocity is of the order

of a thousand meter per second, and the intermolecular distance.of the order of

a few Angstrom units (10-' cm), the upper frequency limit of the acoustic

spectrum can be fwed at about a million million (1012) vibrations per second. ' The acoustic spectrum extending from the vey lowest frequencies up to

the highest conceivable, can thus be divided into three broad ranges. The

audible range of frequencies lies between 20 Hz and 20 idb. Ordinary methods

of producing sustained sounds do not enable us to excite vibrations of

frequencies far above this range. For generating vibrations of higher frequencies,

we have to resort to electro-acoustical methods which consw& in transforming

electrifal oscillations into mechanical oscillations of the same freq.quency by taking *

advantage of the piezo-electric projxrty exhibited by crystalline In this

manner, we can generate mechanical oscillations of a hundred million (10~)

vibrations per second, and such inaudible sounds are known as "uhtrasonicsn. It

is impossible to excite artificially sound waves of frequency higher than, a y 10'

vibrations per second. However, the d'kcovery that the thermal agitation always

present in fluids and solids can be identified with spontaneous sound waves of

very high frequency pervading such media is one of the triumphs of modem

physical theory. In the ever-present heat motion of the molecules of a medium,

nature has thus placed at our disposal sound waves of frequencies far beyond

the range of artificial excitation. These can be conveniently designated as

'hypenonicsn .' Any material that has eksticity can propagate u h n i c waves. The

propagation of ultrasonic waves is through the displacement of successive

elements of the medium. If the substance is elastic there is a restoring force that

tends to bring each element of material back to its original position. S i aU

such media possess inertia, the particle continues to move after it returns to the

position from which it started and finally reaches another different position, past

the original one. From the second pint , it returns to its starting position about

which it continues to oscillate with constantly diminishing amplitude. The

elements of materials will execute different movements as wave passes through

them. As the wave travels through the material successive elements in it

experience these dispbcernents, each such element in the wave path moving a

little later than its neighbour. In other words, the phase of wave of vibration

changes along the path of wave transmission.*'

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 cakd their

orbits. These orbits may be pamllel to the line of propagation in which case, 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

ulhsonic waves because of their short ~avelength.~'

The accurate measurement of the sound speed is very inconvenient for

sound of audible frequency due to its long wave length and the consequent large

size of the apparatus.4 However, measurements at frequencies above the

audible range (ultrasonic frequencies) can be readily made on samples of liquid

of about 100 cc or less. The short wavelength of the ultrasonic waves h the

factor that has been made possible the application of these waves in many cases.

Such sound waves are generated by applying an alternating electric fieid of

suitable frequency to a crystal of quartz which is thereby set into resonant

longitudinal oscillations (piezoelectric effect). Ultrasonic waves are generated

from the free surface of an oscillating crystal and their wavelengths can be

measured by setting up standing waves in the liquid between the crystal surface

and a parallel reflector. By this and similar methods using the oscillating quartz,

the uhrasonic speed can be measured4

The study of the propagation behaviour of uhsonic waves in solids,

liquids, liquid mixtures, eledrolyte solutions, suspensions, polymers, etc. is now

rather well established as an effective means for examining certain physical

properties of materials or This thesis deals with the uhrasonic study

of certain binary and temay liquid mixtures. Ultrasonic velocity in the samples

is measured using Matec 7700 ultrasonic velocity measufmg system. In addition,

the density and viscosity of the samples are measured. Various thermo-

acoustical parameters and excess functions are computed. The nature and type

of intermolecular interactions taking place in the liquid mixtures are explained on

the basis of the computed parameters.

1.2 Briefreview

Ultrasonics has long been accepted as a powerful tool in the investigation

of acoustical properties of ,liquids and several theories are amilable in the

literature to predict the ultrasonic velocity in liquids and liquid mixtures. These

include Flow Patterson theoy (m), Jacobson's free length theory (FLT),

Schaaffs' collision fador theoy (CFT), Nornoto's relation (M) and Van Dael's

ideal mixture relation (IMR). The experimental determination of ultrasonic

velocity and calculations there from the quantities like compressibility ,

intermolecular freelength, internal pressure, Rao' constant, Wada's constant,

acoustic nonlinearity palameter etc. paw way to study the nature, type and

strength of intermolecular interactions present in liquid mixtures. A brief review

of the theoretical and experimental uhsonic studies in pure liquids, binary and

ternary liquid mixtures, and of acoustic nonlinearity parameter @/A) are given

below.

Eying et al12put forward a theory of liquid state, where they deriwd a

relation between free volume and available volume of liquids. This theory of

liquid state has been used by many workers for the study of liquids and liquid

mixtures. schaaffsI3 iniroduced sound velocity in Van der Waak' equation of

state and obtained a formula for molecular radius from sound velocity and

density values. He compared the molecular radius calculated from sound velocity

and density with the value evaluated from molecular refraction. It was found that

the molecular radius obtained from sound velocity and density represents a very

useful measure for the she of molecules. In another paper, schaaffs14 derived an

improved formula for molecular radius by replacing the isothermal sound

velocity by adiabatic sound velocity. bo15 related the sound velocity (U) in and

molar volume (V) of liquids by the formula, U% = R', where R is a constant

called Rao's constant, which is independent of temperature. wada16 derived a

relation between adiabatic compressibility ( &) and molar volume (V) of liquids

which is given by the formula, B' = K'" where B' is a constant called Wada's

constant, which is independent of temperature and presswe.

~acobson" related 'the intermolecular free length in liquids to

cornpressibility , surface tension and viscosity of liquids. ~acobson'' made a

detailed study of the intermolecular free length in liquids and it was found that

the sound velocity and compressibility depend on the free length between

molecules. The d u e s of the Jacobson's constant at different temperatures were

presented in another paper by ~acobson.'~ The study of the relationship between

sound velocity and chemical constitution of the medium through which sound

traverses, was carried out by Parthasarathy et aLm They obtained some general

rules for the variation of sound velocity in different types of liquids. schaaffsZ1

derived the co l ion factor theory for the evaluation of sound velocity in pure

liquids by considering the sound velocity as a function of space filling and

collision factors. He found that the sound velocity is proportional to the produd

of the collision fador which dexribes the eksticity of the collisions of molecules

with one another and the space filling fador of the molecules. Nutsch-

~uhnkie? extended the Schaaffs' collision fador theory of pure liquids for the

evaluation of sound velocity in binary mixtures. b r k P measured the sound

velocity in almhols and related it to chemical constitution in akoholr. He found

that the molecular association tends to decrease the cohesive energy between

associated groups in alcohols. Pattenon et alZ4 derived a theoretical expression

for surface tension of plyatomic liquids from the principle of corresponding

states. E3artonZ5 studied the relation between internal pressure and liquid

structure and found that the internal pressure is a useful quantity to study the

properties of Liquids. Del Grosso et a~~~ measured the sound velocity in pure

water between O.OOl°C and 95.126"C with an accuray of 0.015 &c.

h c k Z 7 obtained internal pressure for the solwnts dimethy l sulphoxide,

propylene carbonate, formamide and methanol from thermal pressure coefficient

measurements. He observed divergence in internal pressure and cohesive

energy density, and explained it in terms of the nature of the solvent-solvent

interactions. Namsirnharn eta^*^ made use of the hole theory of the Liquid state

for the study of propagation behaviour of u h n i c waves in same oiganic

liquids. They derived expressibns for the ultrasonic absorption and dispersion,

and their variation with temperature and pressure using the concept of holes in

Liquids. schaaffs2' showed that the divergence between the free length theory

and collision fador theory comes from the fad that in CFT the molecules are

treated as reaCnoneMc substances, whereas in the the*$ of free lengths, they

are treated as rigid spheres. Pandey et a13' investigated the temperature and

pressure dependence of free volume and intermolecular free length in liquids.

They found that the intermolecular free length increases with increase in

temperature and decreases with increase in pressure. The free volurne is found

to show an increase with increase in temperature. Suryanarayana et d3' derived

free vohme and intemal pressure formulae for liquids from the dimensional

analys'i. The resuits obtained for free volume and internal pressure by these

formulae are found to be comparable with other previous results. % ~ k w i a ~ ~

studied the propagation of u b n i c waws in a large number of liquids based

on hole theory of liquids. ~ a n d e y ~ evaluated sound vebcity in liquid argon,

krypton, xenon and nitrogen over a wide range of temperature and pressure

using b y ' s theory and found that the theoretid sound velocities are in good

agreement with measured values. G U ~ ~ Z ? compared the values of Rao's

constant and Wada's constant in some liquids. Emst et determined the

molecular radii of liquids using various formulae available in the Literature. They

found that the malecuhr radius is almost independent of tempemture and

specific heat ratio. ~ u r ~ a n a r a ~ a n a ~ ~ derived an alternate equation for internal

pressure of liquids based on an already existing relationship between free volume

and internal pressure of a liquid system. Tong et =l3' studied the properties of

the ultrasonic speed in organic liquids using Schaaffs' theory and derived

formube for the coefficients of the speed in organic liquids. Ultrasonic velocities

were measured in hydrocarbons of n-alkanes, l-alkenes and naphthenes as a

function of temperature by Wang et Velocities of all the hydrocarbons

measured are found to decrease approximatety linearly with increasing

temperature, aithough the rate of decrease is different for different hydrocarbons.

~ornoto~' derived an empirical formula for the sound velocity in binary

liquid mixtures consalsting of two component liquids, on the assumption of the

Linear dependence of the molecular sound velocity or Rao's constant on

concentration and the additivity of molar volume. He found that this formula

holds true for such mixtures for which the Linearity of the molecular sound

veloc0@ and the additivity of the molar volume is comparativeiy Qood. The empirical formula derived by Jambson for free length of pure liquids was

extended to binary mixtures by K a ~ l g u d . ~ He calculated the free length of ten

binary systems using the extended formula and found that the deviation from

additivity of ultrasonic veloc'i depends upon whether L,, is greater than

L,. Reddy et a f l studied the ultrasonic behaviour of a hrge number of

binary liquid mixtures containing tiethybmine as common component. Thqr

found that the molecular sound velocity varies linearly with concentration in all

binary mixtures except in mixtures of nitrobemme, o-nihotoluene and

ochloroaniline. KaulgudQ2 studied the ultrasonic velocity and compressibility in

binary liquid mixtures containing acetone, acetonitrile and nitmmethane. The

excess compressibility d u e s were explained in terms of the decrement or

increment in intermolecular free length in solution after mixing. Reddy et

studied the thermodynamics of binary liquid mixtures of benzene, carbon

tetrachloride, carbondisulphide, pxylene, m-xylene, o-xylene. toluene, dioxan

and tetralin with cyclohexane as common component. The agreement between

the calculated and experimental excess functions is found to be good in all cases

except in the system of cyclohexane-toluene. A study of Liquid m'udures based on

statistical thermodynamics was carried out by F I O ~ ~ ~ ~ . Theoretical expressions for

the equation of state, contributions to the free energy, enthalpy, entropy,

chemical potential and excess volume were derived. Abe et a145 studied the

thermodynamic properties of mixtures of small, nonpolar molecules based on the

statistical theory developed by Floy.,

Fort et alU investigated the adiabatic compressibillties of fourteen binary

liquid systems representing different types and degree of interaction between the

components. They showed that the sign and magnitude of excess compressibility

can be used to find the nature, type and strength of intermolecular interactions

present in the binary mixtures. Charge transfer, dipole-induced dipole and

dipole-dipole interadions and hydrogen bonding between unlike components

contribute negative values to excess compressibility where as dispersion forces

contribute positive values to excess c~rn~ressibility.~~ Van Dael et a14' derived

an empirical relation called ideal mixture relation, for evaluating sound velocity

in binary liquid mixtures which has been found successful in predicting u b n i c

velocity in binary mixtures. Lam et d" obtained a theoretical formub for the

surface tension of binary liquid mixtures based on the principle of corresponding

states which along with Flory's theory44 has been used for the prediction of

u b n i c velocity in liquid mires . Deshpande et a14' studied the swnd

velocities and related properties in binary mixtures of aniline. They used free

volume and its excess value to explain the behaviour of liquid mixtures.

Ultmsonic velocity, excess molar volume and exfess cornpressibity were

determined for the systems+qdopentanoI + cycbhexanol, cyclopentanol

+ cycloheptanol and cyclohexanol + cycloheptanol by Kiyohara et al" The

molecubr interactions were explained on the basis of excess functions.

Prakash et a15' studied the ultrasonic velocity in, compressibility and

intermolecular free length of the six binay mixtures-n-butanol + chloroform,

n-butanol + yclohexanol, acetone + methanol, acetone + ethanol,

cyclohexanone + n-butanol and cyclohexanone + n-hbutanol. The variation

of these parameters were explained in terms of the association property of the

mixtures. Ubsonic study of molecular association in binay liquid mixtures of

o- and m-toluidine in CC& was carried out by Adgaonkar et al.52 Velocity,

compressibility, Rao's constant , Wada's constant and Van der Waals' constant

were determined for these systems. Mishra et a!" compared the velocity values

evaluated using FLT and Cm in binary Liquid mixtures of aromatic compounds

with cyclic saturated rings and carbon tetrachloride with experimental velocity

values. It was found that, the velocity values evaluated using both theories are

approximate in nature. Ravindra Prasad et al" evaluated sound velocities in

binary mivtures of triethylamine with alcohol or phenol based on FLT and CFT.

It appeals that Cm has an edge over FLT in these mixtures.

Mishra et dS5 evaluated the interaction parameters from viscosity data of

binary liquid mixtures. Pandey et alS6 studied the intermolecular interaction in

the binary liquid mixtures--benzene + ethylene dichloride, benzene + carbon

tetrachloride, acetone + chloroform, acetone + methyl iodide, acetone + carbondkulphide and benzene + pxyiene--based on excess internal pressure

values. They found that the excess internal pressure is a powerful tool for

predicting inte rmolecuhr interactions in binary liquid rnixtu res . pandey5'

computed Van der Waak' constant, excess internal pressure and sound velocity

in the binary liquid mixtureAnzene + pcylene, benzene + pdioxan and

acetone + methyl iodide--using FIory's statistical theory. The agreement

between experimental and theoretical values is found to be good. Molecular

interaction studies in binay Liquid mixtures from viscosity measurements were

camed out by Chaturvedi ef alSB Pandey et a ~ " evaluated excess internal

pressure in binary liquid mixtures of benzene + n-hewne and benzene + ndodecane, and correlated it with intermolecular interactions. Sabesan et a/."

studied bina y liquid mixtures based on excess enthalpy values and found that

the strength of interadion follows the order aldehyde < ester < ketone.

Ultrasonic investigation of molecular interadion in binary liquid mixtures of

cyclohexanol was carried out by Sivanamyana et al6' Molecular interactions

were explained on the basis of excess cornpressibility values. Choudary et a1.62

compared the experimental ultrasonic velocity with the velocity values evaluated

using FLT and CFT in 1,1,2,2-tetmchloroethane with alcohols and showed that

FLT gives a better estimate of sound speed in binary mixtures. Ultrasonic study

of molecular interaction in binay Liquid mixtures of benzene, phenol, toluene

and aniline in CC& was carried out by Tabhane et Srivastam et a/.

studied the ultrasonic velocity and adiabatic compressibility of tripheny bn

chloride in acetone at various temperatures. The results were interpreted in the

light of solute-sobent interactions.

Choudary et studied binary liquid mixtures with 1,1,2,2-

tetrachlorwthane as common component at 303.15 K and 313.15 K They used

the sign of excess compressibility to predict the existence of weak dipolar

interactions between unlike molecules. Prakash et al." studied the acoustic and

p hysicochemical properties of the binary mixtures of electron donating

hydrocarbons with tetrachloroethane. It was found that the binary mixtures are

characterised by the dipole-induced dipole intemction of the electron donor-

acceptor type, in which aromatic hydrocarbons behave as electron donors.

Excess volumes for the binary mixtures of methyl ethyl ketone with benzene,

toluene, chlorobenzene , bromobenzene and nitrobenzene at 303.15 and

313.15 K were determined by Jayakkshrni et The values were

terms of b y ' s theory. bentropic compressibilities for the binary

methyl ethyl ketone with benzene, toluene, chlotobenzene, bromo

nitrobenzene at 303.15 and 313.15 K were determined by Subramanya

The resub were explained in terms of dipoleinduced dipole and

interactions between dissimilar components. Nikarn et a16' studied the

temperature and concentration dependence of ultrasonic velocity and allied

parameters of monochluroacetic acid in aqueous ethanol. The evaluated

parameters were discussed in the light of solute+olvent interactions. Ultrasonic

investigation of binary liquid mixtures of o-cresol with acetop henone, ethyl

acetate and methyl ethyl ketone was carried out by Ganapathy et a1." Rao's

constant, Wada's constant and Van der Waals' constant were computed and an

analysis of these values suggests molecular association in these mixtures.

Kannan et a/.'' evaluated ultrasonic velocity using Nornoto's relation and Ideal

mixture relation in binary liquid mixtures of n-propanol with CCh, toluene,

hexane and carbondisulphide. It was found that both the theories are satisfactory

to different extents in different mixtures. Khasare et aP2 studied the molecular

interaction in binary liquid mixtures of 1,kiioxane in benzene and cyclohexane.

Molecular interactions due to donor-acceptor type or hydrogen bonding are

found to be present in these mixtures. Prakash et aln reported the acoustic and

physicochemical behaviour of dimethyl formamide with benzene and toluene at

30, 35 and 40°C. They made use of isentropic compressibility, intermolecular

free length, available volume and mokt volume for the study of these binay

mixtures.

Ratha et calculated ultrasonic velocity using FLT and CFT in binary

mixtures of dichloromethane, a polar liquid, with aromatic hydrocarbon and a

comparison of theoretical velocity with the experimental value showed a g o d

agreement between the two. ~hanwalkar'~ evaluated u h s o n i c velocity in ten

binary liquid mixtures using FLT and Cm. It was found that the FLT leads to a

better prediction of sound velocity in the binary mixtures. Rarnbabu et

studied the binay mixtures of y-butyrobctone with aliphatic and .isomeric

alcohok. The negative values of excess isentropic compressibihty and

intermolecular free length in these mixtures suggest that, there exists strong

hydrogen bonded interactions between unlike molecules. Govindappa et dn

measured ultrasonic velocity in binaly liquid mixtures of lc hlorobutane with

hydrocarbons at 303.15 K The results were analysed in terms of FLT and CFT

and showed that theoretical velocity values are in good agreement with the

experimental values . Ultrasonic studies of binary mixtures of 1 2d ic hlorobenzene

with l-alkanols at 303.15 K were carried out by Vijayalakshrni et al" The

deviation in isentropic compressibility from ideal behaviour was interpreted in

terms of structure making effect of molecules. Vijayabhaskar Reddy et a~~~

investigated the volumetric and ultrasonic behaviour of ethylacetate with some

c hloroethanes and ch loroethenes. The experimental data were used to explain

the effect of successive chlorination and unsaturation of ethane molecule.

Molecular interaction study in the binay mixtures of benzyl alcohol with dioxan

and acetone at 30, 35 and W C was carried out by Prakash et alBO by making

use of the behaviour of excess functions like compressibiliiy, intermolecular free

length, molar volume and viscosity. Ewari et al. studied the thermoacoustical

parameters in ethyl and propyl benzoates at 228-293 K The trends of variation

of these parameters were used to describe the molecular order and interaction,

anhamnicity , microheterogeneity and structural information. The study of

thermodynamics of molecular interactions of 1,2-dibrornoethane + aromatic hydrocarbon mixtures at 308.15 K was carried out by Spah et alB2 The results

were interpreted on the basis of electron donor-acceptor type interactions and

also in terms of the loss of favourable orientational order of the pure

components.

Rajaguru et alB3 studied the excess thermodynamic functions of binary

mixtures of ally1 alcohol with 1-4-dioxane and CC&. The results were interpreted

in terms of heteromolecukr interactions and dispersion forces in the systems.

Khanwakr etalMused Flory's theory to develop a new model to predict the

ultrasonic velocity in any composition of a binary liquid mixture from the pure

component data, both with and without a knowledge of its equimolar density.

The efficacy of this model is shown to be much better than that of the Flow

model developed by Pandey. Molecular interaction studies in bina y liquid

mixtures of o-khlorophenol, ~h loropheno l , chlorobenzene and nitrobenzene in

benzene were carried out by Belsare et a185 Oswal et a/& carried out the

molecular interaction studies in binary mixtures of ethyl ethanoate with

ch loroa lkanes from sound velocities, isentropic cornpressibilities and excess

volumes. Analysis of excess functions indicated the existence of specific

interaction between ethyl ethanoate and chlorwlkanes. They also compared the

experimental sound velocities with the values evaluated using FLT and CFT.

Chennarayappa et a187 investigated the binary mixtures of n-methyi

cyclohexylamine with alcohols at 303.15 K. Based on the negative values of

excess isentropic cornpressibility , they predicted the presence of hydrogen

bonded interaction between unlike molecules in these mixtures. Srinivasutu

et studied the kentropic cornpressibility and its excess value in the binary

, liquid mixtures of l, l, l -trichloroethane with l-alcohol at 303.15 K and the

results suggest that the strudure breaking effect is dominant in the mixtures.

Singh et alg9 studied the acoustical behaviour of some organometallic-

tetrahydrofuran binay liquid mixtures at 45OC. A large number of acoustical and

thermodynamic parameters, and excess functions were evaluated and the results

were used to interpret the relative order of the acceptor strength of the butyltins.

Pandey etdgO evaluated cllhasonic velocity using RT, CFT, NI? and IMR in the

binary mixtures of 1,1,2,2-tetrachloroethane with benzene, toluene, pxylene,

acetone and cyclohexane at 298.15 and 308.15 K, and showed that IMR gives

the minimum deviation for all the systems except acetone.

Rao et a19' studied the thermodynamic properties of toluene + n a b n o l s

at 30°C. The results showed that the effects of interaction among the

components produce a greater steric impediment as the chain length of alcohols

increases. Ultrasonic studies of methanol solutions of benzophenone and

2,Q.dichlorophenol were carried out by Blokhra et U b n i c study of the

anomalous behaviour of higher aliphatic ahhols was carried out by Srivastava

et alw The results showed that the strength of interadion increases with increase

in chain length of almhols. ~rimstava~ evaluated ultrasonic velocities using RT,

CFT, NR and IMF3 in the binay liquid mixtures of anisole with aniline,

benzoniirile, nitrobenzene and ~hlorophenol and showed that the theoretical

velocity values are in good agreement with experimental velocity values. Dewan

et alg5 studied the binary mixtures of ethyl benzene with nitroalkanes and nitriles

at 303.15 K, using isentropic compressibility , interrnolecu lar free length, R~o's

constant and Van der Waak' constant. The experimental ultrasonic velocities

were compared with values predicted using ET, Cm, FPT and NR.

Ramanjappa et al% studied the excess sound velocity and excess specific

acoustic impedance behaviour of liquid rnixtures-ethers + nAeptane. The

solute-solvent interactions in these mixtures were explained on the basis of

excess functions. Ultrasonic studies in polar liquid mixtures of triethylamine with

ethanol, n-propanol, n-butanol, phenol and -resol were carried out by

Rajendran et al-he results suggest the existence of strong hydrogen bonding

interaction between NH2 a d OH groups. Rao et aig8 investigated the binary

mixtures of acetonitrile with some amines at 303.15 K based on excess isentropic

cornpressibility values and the results were used to estimate the strength of

complex formation between unlike molecules. Internal pressure and its excess

values for the binary liquid mixtures of triethyl amine with ethanol, n-propanol,

n-butanol, phenol and -resol were evaluated by ~ajendran.'' The resuhs

pointed out the fad that the excess internal pressure values provide useful

information in the study of intermolecular interaction in binary liquid mixtures.

Amlaguppi et a1. '00 studied the molecular interactions in the binary mixtures of

methyl acetoacetate with benzene, toluene, m-xylene, 1,3,5-trimethylbenzene

and methoxybenzene at 298.15 K, 303.15 K and 308.15 K, based on excess

viscosity and excess Gibbs' free energy values.

Rajendran et allo1 investigated the thermodynamic properties of anline-

alcoholmixtures at 303.15K, and the sign and magnitude of the excess

thermodynamic properties were used to study the nature and strength of

interaction between unlike molecules. UItrwnic studies in binary mixhres of

2-butoxyethanol with benzene, toluene, o-xylene, m-xylene, p-xylene,

chlorobenzene, bromobenzene and nitrobenzene at 303.15 were carried out by

Prasad et allM The excess cornpressibility values were used to study the

molecular interactions in these mixtures. Padmasree ef a/lm investigated the

binary mixture of ethyl acetate in n-butanol at 303.15, 313.15 and 323.15 K

based on the excess values of the molar volume, intermolecular free length,

compressibility , internal pressure, enthalpy and viscosity. The results show that.

interactions between unlike molecules are predominant in the binary mixture at

a11 temperatures besides interstitial site occupation. Rout et allM studied the

molecular interaction in the binary mixtures of acetylacetone from excess velocity

and viscosity values. The excess fundions indicate the existence of specific

interaction of acetylacetone with benzene and CC&. Chauhan et allo5 studied

the acetonitrile + propylene carbonate mixture at 25 and 45°C based on excess

values of compressibility, viscosity and volume. The results show the existence of

strong dipoledipole interactions in the binary mixture. Reddy et allM evaluated

ultrasonic velocity using K T and CFT in the binary mixtures of acetophenones,

4-chloroacetophenone and 2-hydroxyacetophenone with isopropanol as the

common component in the temperature range 308.15323.15 K. They have

shown that both theories applies successfully, yet Cm appears to have an edge

over FLT in all the systems.

Chauhan et allo7 studied the binary mixtures of methanol with dimethyl

sulphoxide and dimethyl forrnamide at 25, 35 and W C based on excess

compressibifity and excess viscosity values. Variations of these excess functions

were discussed from the viewpoint of intermolecular interactions and its

structural consequences. Nikam et al.'OB studied the acoustical properties of

nibobenzene-alcohol binary mixtures at 298.15 K and 303.15 K, based on the

excess values of compressibility and intemlecuhr free length, and the results

were linked with the intermolecular interactions. Lafuente et allDg investigated

the binary mixture of an isomer of chlorobutane and an isomer of butanol based

on excess compressibility values. Ultrasonic studies in binay mixtures of

acetonitrile + propylene carbonate at different temperatures were carried out by

Chauhan et a/"' Bhavani et all1' studied the excess sound velocity and excess

specific acoustic impedance of the binary Liquid mixtures containing acetonitrile

at 298.15K. Uhsonic investigation of molecular association in binary mixtures

of carboxylic acids in dioxane was carried out by Gupta et a1.112 at temperatures

25, 35. and 45°C. The results were explained on the basis of the acoustical

parameters like compressibility, specific acoustic impedance and intermolecular

free length. Haribabu et a1113 studied certain hydrogen bonded binay liquid

mixtures based on excess values of thermodynamic functions. Ultrasonic study of

molecular interadion in binary liquid mixtures with CC4 as common component

was carried out by Jayahmar et d114 bjendran115 investigated the binary

mixtures of n-heptane with isomeric alcohols at 298.15 K based on the excess

values of molar volume, internal pressure and enthalpy of the mixtures.

1.2.3 Ternary mixtures

Chaturvedi et d116 studied the ternary mixtures--benzene + cyclohexane + methanol, benzene + cyclohexane + ethanol and benzene + cyclohexane + butanol-based on the ultrasonic velocity, density, adiabatic

compressibility, free volume and excess functions. Molecular interactions in these

mixtures were explained on the basis of excess compressibility values. Pandey

et all" studied the molecukr interadion in the ternary rnixtur-clohexane

+ acetone + ethanol, cyclohexane + acetone + butanol, benzene + acetone + chloroform and cyclohexane + benzene + CCb--ultrasonically. The relative

merits of NR and IMR in predicting sound velocity in these ternary mixtures were

evaluated. It was found that, the velocity predicted using NR gives better

agreement with the experimental values when compared with the velocity

predicted using IMR Pmsad et a P 8 studied sound velocities and related

properties in ternary mixtures of exylene. Excess values of adiabatic

cornpressibility, intermolecukr free length and free volume were used to

investigate the molecu br interactions in these ternary mixtures.

Rastogi et studied the thermodynamic properties of ternay mixtures

of cyclohexane, aromatics, and halomethanes based on ex- volume. It was

found that the molecular interactions in these mixtures are due to the weakening

of donor-acceptor interadion between halomethanes and aromatics by

cyclo hexane. Prakash et al. investigated the molecular interactions in ternary

mixtures-methanol + acetonitrile + CCL, methanol + cyclohexane + chloroform and methanol + acetonitrile + benzene. They used the excess

values of adiabatic compressibility , intemolecu kr free length and available

volume to show the presence of molecular interaction between components of

the mixture. 13astogi12 studied the thermodynamic properties of some ternary

mixtures and it was found that the addition of a third component weakens the

molecular interaction and tema y mixture tends to approach the ideal behaviour.

Mdecular interaction study in ternay liquid mixt.~res--benzene + chlorobenzene + toluene, benzene + bromobenzene + toluene and acetone + chlorobenzene + toluene- carried out by Prakash et allZL Excess values of

cornpressibility , intermolecular free length, available volume and free volume

were used to investigate the molecular interactions in these ternary mixtures.

Acoustic properties of ternary mixtures of some commonly known liquids, viz.

ethanol + n-propanol + water, were studied by ~arasirnham.'~~ it was found

that, the variation of transit time and absorption coefficient, with variation in the

concentration of a component of the mixture, can be represented by a quadratic

equation, typical of a relaxation process. Naidu et studied the ultrasonic

behaviour of ternary mixtures of methyl ethyl ketone with n+onane and

l-alkanols. The molecular interactions in these mixtures were explained in tern

of structure breaking and structure making effects of the common components.

Agnihotri ~ t a 1 . l ~ ~ Studied the molecular interaction and other t h e d y n a m i c

properties ultrasonically in ternary mixtures of cumene using excess values of

cornpressibility and intermolecular free lengh. ~hanwalkar"~ made an

ultmsonic and rheological study in binary and temary mixtures based on the

excess values of compressibility, volume and Gibbs' free energy. The analysis of

the resuh suggests that, all the excess values can be fitted to the same anawcal

expression.

Pandey el allZ7 observed fairly good agreement between the velocity

values evaluated using FLT and the experimental values in temary mixtures-

acetone + toluene + CC& and acetone + benzene + toluene. Pandey et allz8

used Floy's statistical theory to obtain a relation for excess volume of temay

mixtures. It was found that, there is excellent agreement between the

experimental and theoretical excess volumes, both in magnitude and sign.

Rai et allz9 evaluated ultrasonic velocity in the ternary mixtures-n-pentane + nhexane + benzene, nhexane + yclohexane + benzene and cyclohexane + n-heptane + toluene- using FLT, Cm, FPT, NR and IMR at 298 K and

compared the velocity with the experimental value. They observed that the

theoretical velocity d u e s are in good zcgeement wit!! experimental mlues in a!!

the mixtures. A comparative kudy of the sound velocities evaluated using NR, 130 - IMR, CFI and FLT was made by Pandey et al. In two temay mixtures-

acetone + toluene + CC4 and benzene + acetone + toluene-t 303.15 K It

was found that, there exists good agreement between the theoretical and

experimental velocity values. Kannappan et a1 l3' measured ultrasonic velocity in

the temay mixtures of benzene, toluene and 1-4 dioxane with cyclohexane in

c'hloroform and compared with the velocity calculated using FPT. They

observed good agreement between theoretical and experimental velocity values. f

Khanwalkar13' used Flory's statistical theory to develop a model for predicting

the ultrasonic velocity in ternary liquid mixtures from only the pure component

parameters. The efficacy of this model was found to be better than that of the

Roy model developed by Pandey. Kannappan et computed theoretically

the ultrasonic velocity using KT, Cm, NR and IMR in the ternary mixtures and

the theoretical velocity values were compared with the experimental values.

They observed that, though four theories give satisfactory resuhs for temay

mixtures, NR is best suited for the prediction of ultrasonic velocity.

Kannappan et al.134 evaluated ultrasonic velocity using FIT in the ternary

mixtures of carboxylic acids with triethylamine in benzene and found fairly Qood agreement between the experimental and theoretical velocity values.

Shukla eta^'^^ investigated the ternary mixtures at 300C based on the excess

internal pressure values. It was found that, the excess internal pressure values

provide useful information in the study of intermolecular interaction in ternary

liquid mixtures. Kannappan et al investigated the molecular interaction in

temay mixtures of acetic acid, propionic acid and butyric acid with aniline, and

acetic acid and propionic acid with pyridine in a nonpolar sobent benzene. The

excess values of compressibility, intermolecular free length, free volume and

internal pressure were used to estimate the strength of interaction in these

mixtures. Ultrasonic studies in tema y mixtures containing pchlorotoluene ,

nheptane and l-alcohok at 303.15 K were carried out by Sivakumar et

They used the excess cornpreaibility values t~ evaluate the nature and extent of

interactions between the co&ponents of these mixtures. Burghate et ail3 made

a comparative study of molecular interactions in binary and temay mixtures of

diethylamine, butyric acid, triethykmine, propionic acid and benzene. Excess

values of cornpressibility, intermolecular free length and internal pressure were

used to explain the extent of intermolecular interactions in these mixtures.

~ a j e n d r a n ' ~ ~ studied the excess enthalpies of ternary liquid mixtures of benzene,

toluene, chlorobenzene and 1,Mioxane with cyclohexane in chloroform from

the internal pressure data. He also determined the excess enthalpy values using

nay's theoy. A good agreement between the excess enthalpy values evaluated

from internal pressure data and those obtained using Fbry theoy is observed in

a1 the ternary mixtures. Swain et studied the molecular interaction in

temay mixtures of tri-n-butyl phosphate, benzene and CChbased on the excess

viscosity values.

1.2.4 Acoustic nonlinearity parameter (WA)

Adler et all4' obtained the nonlinearity parameter for water and m-xylene

b ~ d on the optical determination of the second harmonic component of a

distorted 3 MHz ultrasonic wave at various frequencies and initial pressure

amplitudes. ~agelberc~'" measured the velocity of sound in water over a wide

range of temperatures and pressures, and calculated the nonlinearity parameter

BIA in the temperature range from O" to 80OC and at pressures of about

10000 kg/cm2. The usefulness of B/A in studying the Liquid state was discussed.

Lisnyanskii et studied the relationship between the structure of aqueous

solutions of tertiay buty l alcohol and the nonlinearity parameter. Narayana

e t a P 4 studied the nonlinear acoustical properties of n-amyl alcohol. They

obtained the B/A values of n-amyl alcohol over 273 K to 373 K temperature

range and 0 to %.5 MPa pressure range. Sound velocities and %/A in

fluorocarbon fluids were studied by Madigosky et al.145 Very low sound velocities

and very high B/A values were observed in these fluorocarbon fluids. Ultrasonic

determination of the nonlinearity parameter B/A for some biological media was

carried out by Law et allM ~ n d o ' ~ ~ derived an empirical rehfior. for

nonlinearity of liquids using thermodynamic constants. ~ h a m a ' ~

made an attempt to relate the nonlinearity acoustical parameter with Rao's

acoustical parameter. cobb14' discussed the finite amplitude method for the

determination of the acoustic non linearity parameter B/A in liquids. Law et al l"

compared the finite amplitude and thermodynamic methods of WA

measurements in biological materials. It was found that, the agreement achieved

between the two methods is within a fraction of a percent for liquid samples and

within 10 % for the soft tissues studied. ~ ~ f e 1 ' ~ l derived a relation which gives

the effective nonlinearity parameter of a system of immiscible liquids. Cain

etall= discussed the ultrasonic methods of measurement of the nonlinearity

parameter in fluid like media. They suggested several improvements on

ultrasonic B/A measurement techniques. Hartmann et a1 calculated the B/A

parameters for n a k n e liquids. It was found that, the n-alkane chain length

dependence of B/A is not straight forward but tends to decrease as the chain

length increases.

Ymhwmmi et all" made a physicochernical evaluation of the nonlinearity

parameter B/A for media predominantly composed of water. ~ n d o ' ~ ' derived a

relation for the prediction of nonlinearity parameter B/A of a liquid from the

Percus-Yevick equation. It was found that, the calculated values of B/A are in

fairly good agreement with the experimental vaiues. Sarvazyan et studied

the acoustic nonlinearity parameter B/A of aqueous solutions of. some amino

acids and proteins. Chalikian studied the temperature dependence of the

acoustic nonlinearity parameter of aqueous solutions of amino acids. sehgall"

developed simple relations that relate acoustic nonlinearity parameter to the

molecular properties, namely internal pressure, free energy of binding, the

effective Van der Waak' constants, the translational diffusion coefficient and the

rotational correlation time.

The literature survey shows that ultrasonic studies have been done in a

variety of Liquids, and binary and ternary liquid mixtures. It reveals the fad that

Ule ultrasonics has been a subject of active interest during the' recent past. - *

5

Recent literature on ultrasonic studies shows that ultrasonics still exists as a

potential tool in evaluating the intermolecular interactions in binary and ternary

liquid mixtures.

1.3 Present study

Molecular interaction studies were carried out in the binary mixtures of

toluene + n-alkanol and in the ternary mixtures of methyl ethyl ketone and

toluene with n-alkanols by making use of literature values of ultrasonic velocity

in these binay and ternary mixtures. Experimental measurement of ultrasonic

velocity. density and viscosrty were carried out in the following binary and

ternary systems at different temperatures 30,35 and W C .

Binary mixtures:

System I

1. Acetonitrile + Methanol

2. Bermnitrile + Methanol

3. Acetonitrile+Toluene

4. Bermnitrile + Toluene System II

1. Methyl Ethyl Ketone + Methanol

2. Methyl Phenyl Ketone + Methanol

3. MethylEthy!Ketone+Toluene

4. Methyl Phenyl Ketone + Toluene

Ternary mixtures:

S-m I

1. Methyl Ethyl Ketone + Toluene + Methanol

2. Methyl Ethyl Ketone + Toluene + Ethanol

3. Methyl Ethyl Ketone + Toluene + Propanol

System II

1. Methyl~hen~l~one+Toluene+Methanol

2. Methyl Phenyl Ketone + Toluene + Ethanol

3. Methyl Phenyl Ketone + Toluene + Propanol

The experimental velocity values were compared with the values predicted using

Jacobson's free length theory, Schaaffs' collision factor theory, Fiory-Patterson

theory, Nornoto's relation and Van Dael's ideal mixture relation and the

efficiency of each theory in predicting ulirasonic velocity was studied. Various

thermo-acoustical parame ten like 'kentropic compressibility , internal pressure,

intemolecubr free length, specific acoustic impedance, molar volume, free

volume, available volume, enthalpy, surface tension and degree of molecular

interaction were computed. Excess values of isentropic cornpressibi lity , internal

pressure, intermolecular free length, specific acoustic impedance, viscosity,

enthalpy and Gibbs' free energy were evaluated. The sign and magnitude of

these excess functions were used to evaluate the nature, type and strength of

intermolecular interactions present in the binary and ternary mixtures. The Rao's

constant, Wada's constant and Van der Waals' constant of the binary and

temay mixtures were computed at different temperatures and dependence of

these constants on temperature was studied. The thermal expansivity , isobaric

heat capacity, isochoric heat capacity, ratio of specific heats, isothermal

compressibility and acoustic nonlinearity parameter @/A) were calculated

theoretically for the binary and temay Liquid mixtures.

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