Chapter 1

INTRODUCTION

1.1 General

1.2 Excess Volume of Binary Liquid Mixtures

1.3 Viscosity of Binary Liquid Mixtures

1.4 Ultrasonic Velocity of Binary Liquid Mixtures

1.5 Spectroscopic Properties of Binary Liquid Mixtures

1.6 Present work

References

CHAPTER 1

INTRODUCTION

1.1 General :

The science of solution chemistry is very complex. It needs for its

clarification the help of many branches of science namely mathematical physics,

thermodynamics, statistical mechanics, electrostatistics and hydrodynamics.

Numerous experimental methods have been employed to explore the information

from the study of solutions. Although many of the important fundamental principles

of electrochemistry had been discovered in the last decades of 18th century and the

first 80 years of the 19th century, it was not until 1887 that an organized theoretical

and experimental investigation of conducting solutions was begun. This was brought

about by the monumental discovery of vant's Hoff [1] that solutions which readily

conduct electric current possess freezing points, boiling points, osmotic pressures and

vapour pressures characteristics of a special class of systems, and the simultaneous

and even more important discovery of Arrhenius [2] that such systems contain

electrically charged particles or ions.

It was vant's Hoff who first applied the powerful methods of thermodynamics

to solutions in a systematic manner. His treatment, however, lacked the generality

which might have been achieved at that time if the system of thermodynamics

developed by Gibbs [3] ten years earlier had been employed. Gibbs great treatise

provided all the essential basic principles required for the thermodynamics of

solutions.

The most important contribution of thermodynamics has been to reduce all

measurements of system in equilibrium to the determination of a single

thermodynamic function.

1

Traditional theories of solutions dwell exclusively on two aspects of liquid

mixtures. One of these is the entropy associated with dispersion of the two molecular

species, or of their constituent elements in the case of complex molecules among one

another. A lattice model often serves as the device for estimating this

"combinational" entropy. The other aspect relates to the interactions between

neighbouring molecules and, in particular, to the difference in the interactions

between unlike and like neighbour pairs. Treatment of the properties of the liquid

mixtures has progressed little beyond the level of interpretation possible within the

framework supported by these two considerations alone [4,5].

The equilibrium properties of a liquid are strongly dependent on what may be

loosely called its local structure, often expressed in terms such as packing density,

free volume or more exactly in terms of the radial distribution function. In as much as

this local structure depends on the forces between molecules and on the forms and

volumes of the molecules, in general, it will change with the composition. This

change in turn will be reflected in the thermodynamic properties of the mixture.

Contributions of this nature have either been ignored altogether, or correction to a

state of null volume change on mixing has been adopted as a means of compensating

for the effects referred to [5]. By this device, the various properties of the mixtures

are altered by the changes they would sustain if the volumes were adjusted to the

value linearly interpolated between the volumes of the pure components. It will be

apparent, however, that adjustments of one thermodynamic quantity (e.g. volume) in

this manner will not, in general, effect a simultaneous correction of others (e.g. the

free energy or that part of it relating to the local structure) to their linearly

interpolated values. The choice of volume as the property to be "conserved" is

arbitrary, and there is no assurance that nullifying volume change obviates

consideration of other characteristic properties of the liquid.

2

More sophisticated treatments [6,7] of liquid mixtures derive their conceptual

basis from (a) the cell model for liquids and (or) from (b) the postulations of a

universal form for the intermolecular potential expressed by εij = ε∗ij φ(rij/r*ij),

where rij is the distance between centers of molecules i and j, ε∗ij and r*ij are

characteristic parameters for the pair, and φ(rij/r*ij) is a universal function of its

argument The corresponding states approach, including conformal theory, proceeds

from the latter of these premises [7]. In so far as giving account of experimental result

is concerned, these approaches have failed to establish decisive advantage over

treatments recalled in the preceding paragraphs. Reasons, therefore, undoubtedly

relate to limitations of the cell model and to severe departures from propositions (b)

above for component molecules which differ appreciably in size, shape, or

composition.

The definition of the cell, consisting of neighbour molecules in fixed array

about the central "wanderer" erroneously, ascribed as crystal-like characteristics to

the liquid. Each molecule is required to perform duel, mutually inconsistent rolls. It

must function both as a fixed neighbour and as the wanderer within its own cell.

Thus, not only the cell model incorporate the acknowledged deficiencies of the

Einstein model for solids, but it also takes account of those features which set a liquid

apart from a solid. These short comings of the cell model have been stressed by

Hildebrand et al. [4,5].

By computing the mean intermolecular energy for a set of molecules in

perfect array, each being assigned to the center of its cell, the cell model prescribes a

dependence on the volume which is too great. This error can be seen to be an

inevitable consequence of the order implied by this model and would follow for any

acceptable representation of the intermolecular energy for a pair of molecules. That,

the energy (E) and volume (V) relationship according to the cell model is at variance

3

with experiment, has been abundantly shown [5-8] by analysis of (δΕ /δV)T

coefficients.

The intermolecular energy is usually discussed on the basis of the familiar

Lennard-Jones potential [5] operating between molecular centers. Even in

comparatively simple poly-atomic molecules e.g. CH4 or CCl4, the acentric

distribution of polarizable electrons necessitates fairly drastic modification of this

potential. Kihara [9], Hamann-Lambert [10], and Pitzer [11] have offered modified

intermolecular potential for poly-atomic (globular) molecules, especially those

approximating spherical symmetry in form. Pitzer replaces each molecule with a

smooth distribution of interacting elements (electrons), these being distributed

uniformly either on the surface of a spherical core or throughout the volume of the

core. In either case a Lennard-Jones interaction is ascribed to each pair of elements,

one from the distribution for each of two neighbouring molecules, and the total

interaction is obtained by integrating over the receptive cores. The form of the

potential is modified considerably by acentricity irrespective of which the two models

is used. Both the attractive and the repulsive terms are rendered more steeply

dependent on the distance between molecular centers [10,11], but to a degree which is

highly dependent on the particular molecule.

An extension of considerations which suggests itself as basis for treating the

intermolecular energy in liquids, consists of integrating the interactions of elements of

the core of one molecule with the elements of all surrounding molecules, these later

being treated as a continuum, occupying the space outside the cavity reserved for the

molecule in question. The result obtained departs markedly from the form of

intermolecular energy according to the theory of Lennard-Jones and Devonshire [12].

For a ratio of core to cavity diameters greater than 1/5, the energy is approximately

proportional to the density, it depends also on a simple function of the cavity

diameter. In as much as the form of the potential depends on parameters peculiar to

4

the molecular species, it does not lend itself to reduction to a parametric expression

such as is required to sustain a low of corresponding states [12]. Limitations [13] of

the corresponding states scheme advanced by Prigogine and co-workers [6] are

probably related to considerations of this nature.

In the limit of very large particles such that the range of intermolecular

interactions, attractive as well as repulsive, is small compared to the molecular

diameter and to the distance between boundaries of the domains of neighbouring

molecules, the intermolecular energy can be treated as arising effectively from the

interactions between the surfaces of adjoining molecules. The calculations described

briefly above support an account of intermolecular energy on this basis and they

indicate further that this manifest-naive approximation should be satisfactory even for

small poly-atomic molecules such as CCl4. Certainly, this approximation which has a

long history of usage in solution theory, is preferable to the central force potentials of

the Lennard-Jones type for virtually all molecules of interest. It offers the additional

advantage of being adaptable to treatment on non-spherical molecules and of

mixtures of molecules differing in size.

Flory et al. [14] have explored the application of a comparatively simple

partition function suitable for liquids comprising chain molecules to homologues of

the normal paraffin hydrocarbon series, H-(CH2)n-H with n>5. A coherent

correlation of the properties of the pure hydrocarbons has been achieved which, as it

involves relationships expressed in algebraic form, is much to be preferred over the

various corresponding states schemes which have been propounded [6,13].

The same partition function has been adopted to mixtures of straight-chain

hydrocarbons [14]. Thermodynamic properties of these mixtures are thus related to

parameter obtained from equation of state characteristics of the pure component

hydrocarbons. The peculiar patterns of the excess chemical potentials and the excess

enthalpies for these systems are well explained by the theory. Especially striking is

5

the excellent agreement between calculated and observed chemical potentials for a

variety of systems at different temperatures with arbitrary choice of a single

parameter for all.

The previous formulation [14,15] was addressed specifically to chain

molecules and to mixtures of unrelated type. One of the merits of the theory is its

adaptability to mixtures of molecules differing in size and shape. Calculations

performed to date encourage the expectation that it may be broadly applicable to

mixtures of homopolar molecules [16].

1.2 Excess volumes of binary liquid mixtures :

Experimental determination [17-19] of excess functions for suitably chosen

liquid mixtures serves as a valuable check of the predictions of different theories of

solutions. The most sophisticated are (i) the theory of Flory et al. [12,16]; (ii) cell

theory of Prigogine [6,20].The cell theory assumes a solid like structure and the

Lennard-Jones and Devonshire potential. Flory's theory is based on the reduced

theorem of state derived from simple consideration of molecules in the mixtures

differing in shape and size.

1.2.1. Flory's Theory ;

The VE of mixing is related to the characteristic volume V* for the

components in the mixture by;

VE = νΕcal (x1V*1 + x2V*2) --1

where νΕcal is the excess calculated reduced volume which is given by

νΕcal = (ν0)7/3[4/3 − (ν0)1/3]−1(Τ− Τ0) --2

where ν0 , T and T0 are ideal reduced volumes, the reduced temperature of the

mixtures and the ideal reduced temperature. These quantities can be evaluated in the

following manner;

ν0=φ1ν1+φ2ν2 --3

6

Τ0 = [(ν0)1/3 − 1]/(ν0)4/3 --4

νi = [1 + {(αiΤ)/3}/(1 + αiΤ)]3 i = 1and 2 --5

V*i = Vi /νi --6

φ1 = 1 - φ2 = N1V*1/(N1V*1 + N2V*2) --7

Where α is the coefficient of volume expansion. The reduced temperature T for the

mixture is given by;

T = [(φ1P*1T1 + φ2P*2T2)/(φ1P*1 + φ2P*2 )]

[ 1 - (φ1φ2χ12)/(φ1P*1 + φ2P*2 )]-1 --8

where χ12 is pair interaction parameter and P*i ( i = 1 and 2) are the characteristic

pressure given by;

P*i = αiTνi2/(kT)i --9

where (kT)i is the isothermal compressibility for component i in the mixtures.

1.2.2 Cell Theory of Prigogine[18];

The expression for VE is given by;

VE/(x1x2) = (3/2)V1ρ[θ(x1 - x2) + δ/2 + 11ρ/4] +

Τ(dV1/dT)[ - 2θ + 9ρ2 + θ2 - (3/4)δ2 + θδ(1 + 2x2) −

(3/2)θρ + (9/4)ρδ + (3/2)θρ(x1 - x2)] +

(T2/2) (d2V1/dT2)[ θ2 - (3/4)δ2 + θδ(1 + 2x2)] --10

The characteristic parameters for the pure components were calculated from

the critical constant using the relations:

1 + δ = TcB/ Tc

A = (PcA Vc

B)/( PcB Vc

A) --11

(1 + ρ)3 = VcB/Vc

A = (PcA Tc

B)/( PcB Tc

A) --12

assuming that each component of the mixture obeys the theorem of corresponding

states.

1.3 Viscosity of binary liquid mixtures :

The predication of the viscosity of liquid mixtures is a goal of long standing,

with both theoretical and practical importance. A truly fundamental theory would

7

predict the viscosity, along with other thermodynamic and transport properties, from

knowledge of the intermolecular forces and radial distribution function alone. Such a

program has had appreciable success in application to pure, simple liquids such as the

liquefied rare gases [21]. For solutions, however, although the general theory has

been formulated [22], it has not yet been reduced successfully to numerical results.

One is thus forced to approximate approaches of which two general types may

be distinguished. The first is that of continuum hydrodynamics whose application to

molecular problem is identified with the names of Einstein and Stokes. This

approach, in which the discrete molecular nature of the solvent is neglected, has been

remarkably successful in explaining the viscosity of dilute solutions of high polymers.

Its application to solutions in which both components are of comparable size is less

appropriate.

The second general approach is to correlate the viscosity of the mixtures with

properties of the pure components and with thermodynamic parameters

characteristics of the interactions between components. In simplest form, the

interactions may be neglected and simple additive relation assumed. One such

relation commonly used is;

lnη = x1lnη1 + x2lnη2 -- 13

where η is the viscosity of the solution, x1, x2, η1 and η2 are the mole fractions

and viscosities of the two components, respectively, in a binary mixture. However, it

will be noted that this equation and other similar ones, predict monotonic increase or

decrease of viscosity with composition. Such monotonicity is often not observed in

practice It is, therefore, generally necessary to take explicit account of interactions.

There are two major semi-empirical theories of liquid viscosity. The first is

the absolute reaction rate theory of Eyring et al. [23]. This relates the viscosity to the

free energy needed for a molecule to overcome the attractive force field of its

neighbour, so that it can jump (flow) to a new equilibrium position. Thus, the

8

deviation of the mixture viscosity from equation 1.1 should be related to the free

energy, more precisely, the excess free energy of mixing [24, 25]. The second semi-

empirical theory is the free volume theory [26-28], which relates the viscosity to the

probability of occurrence of an empty neighbouring site into which a molecule can

jump. This probability is exponentially related to the free volume of the liquid, so

deviations from equation 1.1 can be attributed to variations in the free volume of the

solution.

Macedo and Litovitz [29] have argued that neither of these theories are

entirely adequate in its own right and that better results for pure liquids are obtained

by combining them. Thus, the probability for viscous flow is taken as the product of

the probabilities of acquiring sufficient activation energy and of the occurrence of an

empty site. It has been shown [30] that the assumptions of these two probabilities are

independent, and may be multiplied, is incorrect for one-dimensional liquids. While

this conclusion also presumably holds in three dimensions, it will be of interest to

investigate the consequences of the assumptions of independent probabilities for

viscosities of liquid mixtures in the treatment that follows.

The free energy and free volume data required in these viscosity theories may

occasionally be available directly from experiment. This is often not the case,

however, particularly for the free volume whose operational definition is in any event

some what ambiguous [29]. They have, therefore, preferred to obtain the

thermodynamic parameters from a statistical thermodynamic theory of liquid

mixtures proposed by Flory et al. [14-16, 31]. This theory, which bears some

similarities to the corresponding states theory of Prigogine et al. [6], treats the

properties of mixtures in terms of reduced properties of the pure components and a

single interaction parameter. It, thus, has a minimum of adjustable parameters. The

theory is applicable to mixtures of molecules of different sizes and lays particular

9

stress on equation of state contributions to the thermodynamic excess functions which

are of central importance in determining the free volume of the solution.

Use of theoretical expressions for the thermodynamic properties of mixtures

has the further advantage that an equation for the intrinsic viscosity or the rate of

change of viscosity with concentration at infinite dilution of one component can be

explicitly formulated by expanding the thermodynamic functions in a power series in

concentration and keeping only the first non-trivial terms.

Several empirical and semi-empirical relations have been used to represent the

dependence of viscosity on concentration of components in binary liquid mixtures.

A number of workers have proposed a number of equations for the calculation

of the viscosity of mixtures. Irving [32,33] surveyed more than fifty equations for

describing the viscosity of binary liquid mixtures. He recommends the one-constant

Grunberg-Nissan [34] equation which has been widely applicable, yet reasonably

accurate, for predicting absolute viscosity. The equation reported by him is

lnηm = x1lnη1 + x2lnη2 + x1x2d --14

where d may be regarded as an approximate measure of the strength of the interaction

between the components.

Tamura and Kurata [35] gave the equation of the form;

ηm = x1φ1η1 + x2φ2η2 + 2(x1x2 φ1φ2)1/2Τ12 --15

where φ1 and φ2 are the volume fractions of components 1 and 2, respectively, T12 is

Tamura and Kurata constant.

Hind et al.[36] proposed following equation;

ηm = x12η1 + x22η2 + 2x1x2 Η12 --16

where Η12 is an interaction parameter.

To predict the viscosity of binary liquid mixture, the equations based on three

body interaction model have been suggested. The one amongst these is McAllister's

equation [37].

10

lnνm = x13lnν1 + x23lnν2 + 3x12x2lnν12 + 3x1x22lnν21 + L --17

where the term

L = - ln[x1 + (x2M2)/M1] + 3x12x2ln[2/3 + M2/(3M1)] +

3x1x22ln[1/3 + 2M2/(3M1)] + x23ln(M2/M1) --18

where ν1, ν2 , νm, x1 and x2 have the usual meaning. The above equation consists of

two adjustable parameters namely ν12, and ν21, which are determined by a least

squares method. The term L is computed from a knowledge of composition of the

mixture and molecular weights of the pure components.

Heric [38] expression is

lnηm = x1lnη1 + x2lnη2 + x1lnΜ1 + x2lnΜ2 +

ln(x1Μ1 + x2Μ2) + δ12 --19

where δ12 = α12x1x2 is a term representing departure from a non

interacting system and α12 = α21 is the interaction parameter. Either α12 or α21 can

be expressed as a linear function of composition:

α12 = β'12 + β''12(x1 − x2) --20

From an initial guess of the values of coefficients β'12 and β''12, the values of α12

are computed.

The excess Gibbs free energy of flow, G*E, is given by Eyring [23] equation;

G*E = RT [ln(ηV) − x1ln(η1V1) - x2ln(η1V2)] --21

where Vi is the molar volume of ith component.

Katti and Chaudhari [39] suggested following equation;

log(ηmVm) = x1log( η1V1) + x2log( η2V2) + x1x2[Wvis/(RT)] --22

where Wvis is defined as interaction energy for the activation of flow.

The next step lies in the study of the thermodynamic properties of viscous

flow. The energy of activation of the viscous flow, ∆G*, was calculated by using the

Eyring [40] viscosity equation;

η = hN/Vme [∆G* / (RT)] --23

11

where h is the Plank's constant, N is the Avogadro's number, T is absolute

temperature and R is gas constant.

Now it is possible to write :

∆G* = ∆H* - T∆S* --24

where ∆H* and ∆S* are the enthalpy and the entropy of activation of viscous flow,

respectively.

By combining equation 23 and 24, following relation is obtained:

lnηVm = [ln(hN) − ∆S*m/R] + [∆H*m/(RT)] --25

1.4 Ultrasonic velocity of binary liquid mixtures :

Ultrasonic velocity measurement through liquid mixtures of non-electrolytes

provide an excellent tool to investigate inter and intramolecular interactions between

like and unlike molecules.

There have been a number of studies on the measurements of ultrasonic

velocities and isentropic compressibilities of liquid-liquid mixtures as the deviations

from the rectilinear dependence of velocities and compressibilities on the mole

fractions, throw much light on the physico-chemical behaviour of liquid mixtures

such as molecular association and dissociation as well as the strength of interactions

between the components. It has been found that a number of derived parameters from

ultrasonic sound velocity such as isentropic compressibility, Ks, molar sound velocity

[41], R, specific acoustic impedance, Z, intermolecular free length [42],

Lf provide better insight in the understanding of molecular interactions in pure

liquids and binary liquids which are given by following relations;

Ks = 1/(ρU2) --26

R = (M/ρ) U1/3 --27

Z = ρU --28

Lf = K(Ks)1/2 --29

12

where M is the average molecular weight, K is the temperature dependent constant

whose values are 1.976 x 10-6, 1.995 x 10-6, 2.008 x 10-6 and 2.030 x 10-6 at 298.15,

303.15, 308.15 and 313.15 K respectively, Lf is the free length of the ideal mixture.

1.4.1. Empirical relations for ultrasonic velocity :

As the sound velocity in liquid mixtures is known to be a quantity which

depends on concentration in a variety of manner according to the nature of each

component liquid, it becomes of considerable interest and importance if one can

establish a formula to predict the sound velocity in liquid mixtures. This, however, is

not an easy task considering of the various manners of the concentration in some

cases. So it becomes necessary to employ one formula for some mixtures and other

formula for other mixtures, even if one succeeds to obtain some approximate

formulas to represent the sound velocity.

Some formulae have been proposed [43-45] for the sound velocity in liquid

mixtures, Schaffs [43] considered the sound velocity in ideal solutions to be a linear

function of the weight percentages of the mixtures. Natta et. al. [44] showed that a

better agreement with experiment is attained by the formula;

V = 1/{[(1 -P)/(ρΑ VA) + (P)/(ρΒ VB)] ρ} --30

where ρ means the density and P the weight fraction of the liquid B, and V, the

corresponding sound velocity. This formula is based on the assumption that the sound

velocity is the same as in the case when the two component liquids are separated in

two layers and the directions of propagation of the sound is perpendicular to the

interface. The formula proposed by Danusso [45] for ideal mixtures;

U = (1/ρ)[(1 -P)/(ρ2Α V2A) + (P)/(ρ2Β V2B)]-1/2

= (1/ρ){(1/M)[(nAMA)/(ρ2Α V2A) - (nBMB)/(ρ2Β V2B)]-1/2} --31

had been found to hold true for some mixtures, but not necessarily in others.

Here,

M = nAMA + nBMB --32

13

means the mean molecular weight of the mixture. The quantities with suffixes A and

B mean the corresponding quantities for the component liquids A and B, respectively,

and nA and nB are the mole fractions of the component liquids. The ideal mixture

defined here is the mixture without volume change. So Nomoto [46] had additivity of

the molar volume

V = nAVA + nBVB --33

and the density became

ρ = M/V = (nAMA + nBMB)/( nAVA + nBVB) --34

For non- ideal liquids, however, the formula 31 does not hold true. Danusso

[47] had investigated the deviation from ideal velocity formula of the sound velocity

in many mixtures and obtained some results of interest, especially the approximate

proportionality amongst the percentage deviations of the quantities U (sound

velocity), V (Molar volume) and B (= Danusso's molecular compressibility), defined

as;

B = V β --35

where β means the adiabatic compressibility.

Poupko [48] has performed a theoretical analysis of the sound velocity based

on Prigogine et al.'s theory of the liquid mixtures [49] and derived the result;

∆V/V = K(∆β/β ) --36

where K is a constant for each mixture. This, however, furnishes only an order of

magnitude, explanation for the deviation from ideality of the molar volume and the

adiabatic compressibility (or sound velocity).

1.4.2. Nomoto's relation :

The formula proposed by Nomoto [46] is based on the assumption of the

linearity of the molecular sound velocity versus molar fractions and the additivity of

the molar volumes in liquid mixtures. The deviation from linearity of the molecular

sound velocity has been investigated by Nomoto and it has been reported that some

14

mixtures, especially the mixtures of the hydrocarbons and those of two monovalent

alcohols, exhibit the linear dependency on concentration with an accuracy, usually

not exceeding 0.3%.

Nomoto investigated the additivity of the molar volumes in those mixtures for

which the deviation from linearity of the molecular sound velocity is small, and it was

revealed that a great part of these mixtures had also a good additivity relationship of

the molar volume. So he could establish an empirical formula for the sound velocity

in liquid mixtures based on the assumption of the linearity of the molecular sound

velocity;

R = x1R1 + x2 R2 --37

where R1 and R2 are the molar sound velocities whose mole fractions are x1 and x2

respectively. The molar sound velocity (R), also known as Rao's constant, is related

to sound velocity (U) and density (ρ) by the relation 32.

Hence, the sound velocity (U) is given by;

U = (R/V)3 = [(x1R1 + x2 R2 )/(x1V1 + x2 V2 )]3 --38

An alternative formula:

The linearity of the molecular compressibility of Wada [50]

W = M/ρx β-1/7/ ρ= U2/7/ ρ6/7 --39

is somewhat better than the linearity of the molecular sound velocity, it is possible to

make an empirical formula using this relation and assuming the additivity of the

molar volume. The formula, however, becomes somewhat complicated, and

numerical computation of some examples revealed that the practical result is not so

improved because of the increased stages of the numerical computation involved.

A convenient alternative method consists in employing the linearity of the

quantity

N = MU1/3/ρ5/6 = Rρ1/6 --40

15

which shows as good in a linearity of concentration dependence as molecular

compressibility (of Wada) (of Nomoto [51] ), namely;

N = nANA + nBNB --41

This gives, together with the additivity of the molar volume equation 38 the

velocity formula

U = N3/(M1/2V5/2)

= (nANA + nBNB)3/[(nANA + nBNB)1/2 ( nAVA + nBVB)5/2] --42

This formula, though some what better than the formula in equation 43, is of

the same order of accuracy with equation 38 and, therefore, not to be recommended

because of the complexity.

1.4.3 Van Dael's relation :

According to Vangeel [52] assumption the adiabatic compressibility (βs) of

the mixture is given by;

βs (im) = φ1ν1βs(1)/νim + φ2ν2βs(2)/νim --43

where φ and ν represent volume fraction and specific heat ratio, respectively.

Equation 48 holds true if the mixture is an ideal one and also ν1 + ν2 = ν im, it can be

transformed into a linear combination if the additional assumption V1 = V2 is made

[53].

βs (im) = x1βs(1) + x2βs(2) --44

On the basis of equation 44 Van Deal's expression for sound velocity in binary

mixtures may be written as;

1/[(x1M1 +x2M2)(U2im )] = x1/(M1U21) + x2/(M2U22) --45

where M1 and M2 are molecular weights of component 1 and 2, respectively.

1.4.4 Free length theory :

According to Eyring and Hirschfelder [54] the intermolecular free length Lf

is defined as;

16

Lf = 2Va/Y --46

where Va, the available volume is equal to (VT – V0), where VT and V0 are molar

volumes at absolute temperature and absolute zero temperature, respectively, Y, the

surface area per mole is given by;

Y = (36 πN V20 )1/3 --47

and

V0 = VT [1 - (T/Tc)]0.3 --48

where Tc and N are critical temperature and Avogadro’s number, respectively.

The intermolecular free length in case of binary liquid mixture can be

expressed as;

Lf(mix) = 2{[Vmix - (x1V0(1) + x2V0(2))]/(x1Y1 + x2Y2)} --49

The sound velocity in mixtures can be evaluated from Jacobson's formula

[55,42];

Umix = K/(Lf(mix)ρ1/2

(mix)) --50

here, K is a temperature dependent constant.

1.4.5 Collision factor theory:

Schaffs [56,57] on the basis of CFT gave the following relation for sound

velocity in liquids;

U = U∞ S rf = U∞ S B/V --51

where U∞ = 1600 ms-1, S is collision factor and rf (rf = B/V) is space filling factor,

B is actual volume of the molecule per mole and V is molar volume.

Nutsch- Kuhnikies [58] extended the concept to binary liquid mixtures as;

Umix = U∞ (x1S1 + x2S2)[(x1B1 + x2B2)/Vm] --52

The actual volume of molecule per mole for pure components was calculated

using the relation;

B = (4/3)(πr3mΝ) --53

17

where N is Avogadro number, rm, the molecular radius can be calculated from the

following relation [53]:

d5/2 = [1/(7.21 x 1019][(Vσ1/4/Tc1/4)] --54

In equation 54, d is molecular diameter, V, σ, and Tc stand for molar volume,

surface tension and critical temperature, respectively. The surface tension of liquid

has been evaluated using the relation 55.

σ = 6.3 x 10-4 x ρ x U3/2 --55

1.4.6 Comparison :

Sound velocity had been evaluated in binary liquid mixtures by Nomoto [46]

and Bhimsenchar et al. [59] using Nomoto's relation. Several workers [60-63] studied

the relative merits of both the relations for computation of sound velocity in binary

and ternary liquid mixtures and mixtures of molten salts. Sheshadri et al. [64,65],

Prasad and Reddy [66], Mishra and Pandey [67] compared the merits and demerits of

both the free length theory(FLT) and collision factor theory(CFT) as applied to binary

mixtures.

Sheshadri et al [64,65] have found FLT to give better results whereas Mishra

and Pandey [67] observed that CFT is better than FLT for evaluation of sound

velocity. Investigation of interaction in liquids becomes difficult when experimental

data other than sound velocity and density are unknown. Van Dael and Vangeel [52]

had considered non ideality in terms of the ratio U2expt/U2im with mole fraction

(Uexp and Uim refer to the experimental and ideal mixture velocities, respectively).

The theory had been successfully applied to evaluate sound velocity in binary liquid

mixture by several workers [58, 64-67].

Furthermore, interactions in binary liquid mixtures have been extensively

studied by Aminabhavi et. al. [68], Oswal et.al. [69], Nikam et. al. [70], Low and

Moelwyn- Hughes [71], Pandey et. al. [72], Benson et. al. [73], Sheshadri et. al. [74],

18

Dalmas and Turrell [75] and several others, from a knowledge of excess

thermodynamic functions and some acoustical parameters.

1.5 Spectroscopic properties of bianry liquid mixtures :

In the field of organic spectroscopy several advances have been made during

this period. Infrared Spectroscopy (IR) is one of the leading method in spectroscopy

and an important tool of the organic chemist. An IR is widely used for:

i) identification & determination of structure; ii) determining the purity & quantitative

analysis; iii) following the course of reaction; iv) hydrogen bonding; v) molecular

geometry & conformational analysis; vi) chemistry of organic polymers; and vii)

reactions of reactive species like free radicals and ions. Infrared radiation is absorbed

by organic molecules and converted into energy of molecular vibration. In IR

spectroscopy, an organic molecule is exposed to infrared radiation. When the radiant

energy matches the energy of a specific molecular vibration, absorption occurs.

1.6 Present work :

Accurate knowledge of thermodynamic mixing properties of binary mixtures

has great relevance in theoretical and applied areas of research. These data are needed

for design processes in chemical, petrochemical and pharmaceutical industries.

Usually, for nonideal mixtures, direct experimental measurements are performed over

the entire composition range. Many times predictive methods for the excess quantities

would be more useful than the direct experimental measurements especially when

quick estimates are needed. Most empirical approaches for calculating the excess

properties attempt to explain solution nonidealities in terms of specific and

nonspecific intermolecular interactions.

These specific and nonspecific intermolecular interactions are sensitive to

composition, temperature and presence of different functional groups in the mixtures

19

under investigation. Group contribution methods are powerful tools for the prediction

of thermodynamic and transport properties of liquid mixtures, in particular the excess

molar volume, and deviation function in viscosity and in ultrasonic velocities. The

knowledge of the group contribution parameters of the solvent is useful in

formulating solvent mixtures for specific applications.

In order to investigate specific and nonspecific interactions between

constituent molecules of binary mixtures of t-butanol with methyl benzoate, ethyl

benzoate, benzyl benzoate, diethyl ether, di-isopropyl ether, di-n-butyl ether, anisole,

phenetole and benzyl ether, measurements of densities, viscosities and ultrasonic

velocities as a function of mixture composition, temperature of measurements and

nature of function groups through these mixtures are made.

Alcohols are strongly self-associated molecules [76] through hydrogen

bonding and for binary solutions rich in alcohols, three dimensional network of

hydrogen bond is believed to be present [7,77].

From the measured values of density, viscosity and ultrasonic velocity of the

binary t-butanol with methyl benzoate,ethyl benzoate, benzyl benzoate, diethyl ether,

di-isopropyl ether, di-n-butyl ether, anisole, phenetole and benzyl ether excess molar

volume (VE), deviation in viscosity (∆η),have been calculated. The various

interaction parameters such as Grunberg-Nissan (d), Tamura Kurata (T12), Hind et al.

(H12), Heric (δ12), McAlliester (ν12 and ν21) and Katti-Chaudhri (Wvis) are

calculated.

From the ultrasonic velocity measurements, the values of isentropic

compressibility (Κs), intermolecular free length (Lf), specific acoustic impedance (Z),

have also been calculated along with their excess parameters. In addition to these

ultrasonic properties, molar sound velocity (R), have been calculated. All these

parameters are related to type and extent of intermolecular interactions in binary and

ternary liquid mixtures.

20

An attempt is also made to calculate theoretical ultrasonic velocity values of

binary mixtures by using Nomoto's relation, CFT, FLT and Van Dael relation and

compared with those experimental observed.

21

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