Dielectric properties of binary systems 9. Excess permittivities as the sum of several possible contributions.

Journal of Mohxdur Liquids, 45 (1990) 237-252 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

DIELECTRIC

PF?OPEHTIES OF BINAHY

AS THE SUM OF SEVERAL

ADRIAN

HUGO

POSSIBLE

BUEF', MARIA

Departamento

de Buenos

1430 Buenos

Aires.

REBOLLO

Facultad

Aires,

9. EXCESS

FERMITTIVITIES

CONTRIBUTIONS.

BERTA

de Ffsica,

Universidad

SYSTEMS

237

PAZ AND JOSE LUIS

de Ciencias

FabellCn

Exactas

I.

Ciudad

of

the

TOURON

y Naturales,

Universitarla,

Argentina.

(Received 11 October 1969) ABSTKACT

A

term

representing

present

in a binary

viously

proposed.

This

excesses

dielectric o-xylene,

carbon

rearrangements solution

was

improvement

in systems

308.15

K. and carbon

51C.lS

I:.

gave

a

containing

tetrachloride

different

introduced

in

a

species

model

pre-

description

good

carbon

tetrachloride

of +

+

ethylbenzene

at

2YG.15

K

and

tetrachloride

+ mesitylene

at

298.15

K

and

INTKODUCTION

A simple describe when

model

excess

model

adjusts

properties

specific

interactions

very well

systems

p-xylene,

wherein

vacant

to the

type complex

of

case

proposed

been

dielectrrc

there exist

donor-acceptor

has

However the existence

among

ccl.

exist

atom

the

is

and the

to

syste.ms

when

The a

specifically

interactions *

I.2

component=.

benzene,

in CC1

work

liquid

values

This

with

specific

pre*/ious

binary

experimental

3d level of the chloride

the aromatic

in

is present.

containing there

in

1:l the

toluene

or

between

the

n

cloud

of

hydrocarbons'. the proposed and magnitude

model

could

not account

of dielectric

excess

0167-7322/90/$03.500 1990 Elsevier Science Publishers B.V.

succesfully

in

some

for systems

238 that should with

be similar

o-xylene,

attributed

phenomena

The

present.

latter

could

include

the

consequences

per

unit

spectroscopic

thermodynamic

functionss-'"

of the systems

the presence

of interactions

in previous

work.

vious

to systems

model

include

terms

species

present

small

and refractive

indices

this meant

EXFERIMENTAL

as

and

question to

those

was

a

excess indicate

described of the pre-

reexamined

values

dielectric

Since

none

available

to

molecular

and,

above

in the Ccl4

work

all,

high

in

the

irregular

it

molar

volumes

although

in

some

in the literature. molecular

of the dielectric accounted

+ mesitylene

found

are very

precision

previous

description

ideality

were

permittivities,

with adequate

arrangement

behaviour

accurately

of

the

for

the

system.

PART

Reaction

grade

liquids

In dark

bottles

under

over metalic

sodium.

Purity

kept

4

usefulness

of a term that represents

lead to a complete

found

have

and

of the various

from

to measure

duplicating

The inclusion

=.*/sterns studied

in

the

rearrangements

and the density necessary

excess

extend

are needed.

was considered

cases

to

departures

measurements

literature

different

in the liquid.

To observe precision

of

volume

of this kind the model

representing

be

that may be

that should

analysis

that are similar

Therefore

account

of the system.

temperature',

Melting

can

into

effects

molecules

ccl4

This

takes

only

any other

on their number

the permittivity

those containing

mesitylene.

model

of the component

influence

affect

the

namely or

disregarding

distributions

a distinct result

in principle,

ethylbenzene,

to the fact that

association

spatial

or

were dry

twice

fractionally

nitrogen.

was better

than

99.9%

and

distilled

0-xylene

was

ref luxed

through

molar

GPC. Solutions

were

prepared

a 5 x 10-' g precision.

by weighing

The error

to be less than 1 Y 10W4. Temperature trolled weights,

to within obtained

picnometer".

1 Y lC~-' K. as indicated,

on a Nettler

in mole

Density and

fractions

balance is

In all measurements was the

calculated

volumes

with

estimated was

con-

from

measured

the in

a

239

TAE!LE 1:

DENSITII~

(6) I PERMITTIVITIES

(6). AND KEFRACTIVE

INDICES

(nl,) FOR 'THE PURE LIOIJIDS.

f%RMITTIVITY

DENSITY,g/ml EXF"T'. LIT.

COMF'U.

REI-RACTIVE INDEX

LIT.

EXPT.

EXPT.

2.22,6b

LIT.

C’T

1 ,J@4:30

1 .s84.~:3a .

2.22'79

1.45739

1.45739=

ox ET

0.87596

0.87596=

2.56::y

l.S:,289

1 ..__k LiW'8c? u

O.l36264

0.86264=

2. 392<1

1 .4 9-L IL. '>'J 1 .493250

ME

0.86111

0.86111=

2. 2'73<1>2.27496

1.49605

1.49604=

.3:J8 .15 k:

CT

The static with

an error

type Bausch -5 5x1'1 .

indices

PC Lomb

Measured liquids

permittivity

.

was measured

1.45110

as

already

described'.

less than 3 x lo-' for a?1 concentrations.

Refractive

pure

2.2079

1.56542

for sodium

precision

density,

refractometer

permittivity

at 2913.15 E, 308.15

ble 1 together

the literature

light were

measured

with

an error

and refractive

K and cSlI3.15K

values

at 298.15

on an

K.

ABBE

less than

indices

of

the

are shown

in

Ta-

240 HESLILTS

AND

The of

DISCUSSIClN

excess

values

permittivity,

line,

at

the

shown

in

Table

The

three

from

calculated

density

and

experimental

refractive

temperatures

indices for

and

measurements

for

all

the

sodium

D

concentrations

are

2.

following

relations

were

used

to

calculate

excesses:

(1) E

n

2

2

=n

D

0

-4

D

n

A

2

wherein

E)

v

n D'

refractive f rat

tion

of

and

the

pure

@O

0

-4

D

and

molar

the

ccmponents.

:
(31

respectively:

are

volume,

components

2 D B

m'

index,

n

B

A

S

ideal

(A,B!

fraction

volume

Subscripts

permittivity,

refer

to

the

and

molar

solution

(sj

s

E

The

errors

temperatures ml :‘mol

in are

E

E

,

less

n

2

and

D than

V

,5

x

E

for

;,:>-4,

all 3

concentrations

x 1,:,-4

and

and

S

1 o- =

x

.

E3ch fitted

set

through

using

the

for

o-f results le:!st

squares,

different

the with

temperatures

points

all

equal

iy

Wi3S

weighted,

equation:

j=n

y=,

zA(l-zAj

j-i

C

a,

(l-2

:

j=i

)

*

E

wherein

Y E represents

reoresen

ts

standard

fraction

with whole not

4(Ye)

examination

a difference volume range the

case

positive

for

ethylbenrene

excesses

q5: or

deviations

Carefcl shows

all

in

excess. of

x “, for are

shown

of

the

former

concentrations

with

the

ccl4 and

with

latter

+

sign

in

for (E and

, 0.

Table

and for

(VE

m

inversion

1,

n EL) all

for

m

)) aj

z

A

and

3.

are

data

in

Table

excess

as

compared

positive

over

it

is

negative Ccl4

+

3

the

This

temperatures.

because

slightly

Ve

Coefficients

dielectric

E

and

ni

experimental

mesitylene, a

.cE

component

behaviour

The

i

large for

o-xylene.

is

and ccl4

+

241

TABLE

2:

EXF'ERIMENTAL

EXCESS

PERMITTIVITIES

fW.lD EXCESS

MOLAR

VCILUMES f :<0

lo4 c=

CCL

1(:I 4 n2 D

4

E lo3

v,’

104

tE

ml/m01

1 (I! 4

n z D

10

3

0-uXYLENE f:)

43 69 97 1 10 124 127 130 122 106 e3 50 30 (3

1) r:r. !)[3"it %.

c' I.1t6 ::: I0 (Z, .34. . 1I "' (1) "31:) 58 t:) .3 7'70 0 .4706 0 .526 1 ().6f:)JU C).69 10 0.7731 I.') . 135otr C). Y4.16 1

(:, 1.3 ,.,1.> LL .I :9 37 42 43 45 44 x.3 .32 19 12 C)

0 9 11 6 4 1 -6 -9 -11 -16 -13 -11 _( 7 0

v ,”

ml/m01

0 33 se 01 98 106 1 10 111 104 70 70 4'7 ?.I c LJ (.)

0

6 10 7 .z 0 -4 -7 -9 -15 -12 -11 -5 1:)

c-l

,t.

E

Irlt.

E E

n

z

”

VE in E L

The magnitude follow

for

of cE

the sequence:

solutions

the

Ccl4 + a-xylene

are

and

different

> Ccl4 + ethylbenzene

ccl.

> r

+ mesitylene related

at 248.15

through

K.

a similar

The

experimental

sequence

data

but the differences

for

ni among

are the

243 systems

On the other

are smaller.

are sequenced

as: Ccl.

hand

+ mesitylene

the absolute

> Ccl*

values

+ ethylbenzene

for

V

:::, CC1

.

I m +

o-xylene. E

the largest

For both cE and nz around

equimolar

asymmetry

due

There

concentrations,

to the difference

are however

systems.

For

increases

slightly

substantial + o-xylene decrease smaller

individual

large

than

in excess

the

volumes.

of liquids

considered and B are

the individual

The permittivity

over

and

monomers

present

ponding

total i

are used

causes

of

work"'.

the

Consequently

in the pure

state,

and AF the complex

specie.%

is then described

c. I.=i

+N

of molecules

the permittivity

t = 1 + 4 n

per ml

of

and a

+N

re(aAB-

a* -

(6)

(7)

(e) i

a. L

i = A,B

(9)

becomes:

n N 1,

%I

each

are the corresand a * SaP AB Now, when the following relations

of the mixture

No (c - 1)/(4 A A

A

for-

15)

AB "*lB)

e

+4nN*

is

by:

No + No A

a

A, B and AH. Wherein

N::= NA + NAB Nz= NB + NAB I=

4 a

dielectric

:

N

a

range.

II

in the solution

increase

is

for CC1

a large temperature

system:

of the system

polarizabilities.

hand

is much

as in previous

component

excess

there

but the latter

behaviour

N * , NB and NIB are the number

species

slight

dielectric

On the other

excesses,

&=1+4n(NAuA+Npa

where

the

A and EC, non-associated

to be a three

a

occur

for the various

increases,

a temperature

systems

origin

they are tpeated

exists

differences

while

and volume

for the other

explain

there

temperature

and Ccl. + ethylbenzene

excesses,

med.

with

decrease

although

from ideality

in size of the species.

meritylene

+

1

in dielectric

To

mixture

cc1

some

departure

)

+NP"

(c,,- 1)/(4

n Nl ) e

245

where

N

is the

AV

Avogadro

number

and NAB is

the

number- of moles

per ml. of sa1ution.

A totally frequency

similar

equation

n

2

be

obtained

for

high

the

I “,

D

/

(VI”

+

m

The equation

thus

the first

two terms,

the second

vz, A

a:,-

+ 4nN *v17_ (

while

can

permittivi*ies: L

a:

found

(16)

for the dielectric on the molar

consequence

a

I

1

-a:

one depends

is

1)

of

excess excess

the

comprises

volume

( V' 1 m complex.

existing

I when

Therefore,

be positive,

a complex

negative

each contributing responsible

forms

in a mixture

or non-existent, The

term.

for dielectric

.sp and n:

depending

complex

excess

both

on the

related

are

terms

E

when ‘J

only

=

0.

could

value

0”

of

solely

other m be positive, VE can negative or m null. This last possibilzty only occurs when VE = 0. m A negative excess volume ( Vf X 0 ! implies the existence of hand

the term

depending

on

more

molecules

per unit

volume

Therefore

behaviour. compared

with

charges

per unit

contrltution In order

il&) with IJ *a

be

there are more charges

the ideal

to the permittivity

that would

and there

case,

excess.

volume

Converseiy

as compared

case

the per

the

in

ideal

volume,

unit

is a positive

when V", 30 there are

to

the

ideal

as

contribution

case

fewer

and

the

is negative. to compare

the values

the experimental

calculated

data, thf values

from eqns.

of

kA*s" a:,,

(15) and a:s

and

are needed.

L complex

can be obtained formation.

neglected because decided

Atom

or taken

from the equilibrium polarizabilities

as

5%

they do not usually to

neglect

them

of

the

exceed

(

constant aI*)

can

electronic this value.

because

they

of

the

either

shown

In our

will

not

case

we

affect

have

the

E 1 to

4

for all systems,

CCl~ molar

be

polarizabllities,

calculations. In Figs.

AB

the

calcc!lated

at the three

curves

for

temperatures,

2

and

I-I' D

as a function

are

of

concentrations. The equilibrium constants li:*,used were of calorimetric origin S.6.B I while a' and ~1 were calculated *a *e using the excesses from the curve fitted at 298.15 I( at equimolar

246

0.014 0.013 0.012 0.01 I 0.01 0.039 0.00-Y 0.007 0.006 0.005 O.OV4 0.0‘33 0.002 V.C.?l 0 0.2

0.4

0.6

0.8

1

molar frustions of corbvn tctroohlw~c

Fig.

Excess

1:

tetrachloride Ca?culated:

static

permlttivity

system. -

(cE)

Experimental

:

for +

the

(398.15

o-xylene k.),

x

+

carbon

(3l38.15

C’:)*I

.

V.014 0013

-

0012

-

V.Vll

-

G.01 V.Vo9 O.VC=30.307 O.VGb -

Fig.

3:

the

o-xylene

(378.15

Excess

K),

permittivitty

+

carbon

x (3X3.15

C:);

at

optical

frequencies

tetrachloride Calculated:

sys tern. -

.

In

2

E:

D

Experimental

for

)

:

+

247

0.014 0.013

-

0.012

-

0.011

-

0.01

-

o.oc¶

-

o.OQu 0.007

-

0.006

-

0.005

-

0.004

-

o.w3

-

0

0.2

0.4

w.

Fig.

3:

Excess

cat-ban

static

K);

Calculated:

Excess

ethylbenzene (298.15

I(),

Fermi +

::

1

*

for

Experimental

0.6

0.4 froctiar

ttivi

carbon

(508.15

.

the :

+

ethylbenzene

+

(293.1s

X

K),

.

mdur

4:

0.3

tctrcc~lcrkk

(CC)

system.

0.2

Fig.

Qf cnrbal

permittivity

tetrachloride

(X8.15

*xc

molar fmctions

ty

of arbn

at

0.8

optical

frequences

tetrachloride IO;

1

tetrnchlw&

Calculated:

system. --

.

(nD‘=) Experimental

far

the :

+

248

0.314 OX.1 3 O.G12 0.01 1 O.Cl

-

O.Oca cGw

-

0:+?7

-

O.‘OC6 o.w!i

-

0x4

-

-4 0.2

0.4 molar fmdion

Fig.

Excess

5:

carbon

static

K);

-

6.2

0

_

6:

Excess

mesitylene (298.1s

+ K),

:

mesitylene

the +

(29E.15

+

k.),

;<

1

0.8

tstmshloridc

optical

frequencies

tetrachloride K);

TOP-

0.6 of cwbw

at

carbon

:< (318.13

1

.

factions

permittivity

(2)

Experimental

0.4 mu&r

Fig

ty

ttivi

system.

Calculated:

0.8

of corbcn tctrochlode

permi

tetrachloride

(gl8.13

0.6

Calculated:

system.

-

.

(ni

E

)

for

Experimental

the

:

+

1 I:,

concentration. 4

All

were

and

used

temperatures

The excess

calculated find

values

the

the entire

the Ccl.

mixture

range

+ o-xylene

with

and at high

frequencies

etnylbenzene.

changes

to thermal

comple::

species

temperature

should

Likewise prrmittivity

the with

be interpreted

since

per

all

a

on

excess

for

ccl‘

the

mixtl_!res

substantially

hand

in

terms

the offer

o-xylene

4

for CC1

similar 7.

the

system.;1

and

ccl4

,+

mesitylene

4

4

+

deseribed

are

for all

to

CCl.

in Fig.

changes

calculated

temperature

in the first

decrease

in

in the CCll

decrease

that of the complex

excess.

systems model

number

the

increase

an

in

excess

+ mesitylene

oppose

its term each

as of in

excesses.

the

static

system,

of the term related

depending

contributions

in

in dielectric

incremerit

two

of the proposed

Therefore

the contribution The

all

value.

volume.

temperature

in the resulting

due

formin

on the basis

unit

(15) and

of

ethylbenzene

are

and to the change

small

through

in this case

increase

with

cause

+

l

s13n as can be seen

change

effects

rearrangement. than

Table

for

K with eqns.

at lcw frequencies

can be interpreted

da_teboth

laryer

excesses

behaviour

other

e :.: c es s

the experimental

The excess

species

On the

only

The excess

than

mentioned

and CC1

influence

this mode!

for 298.15

excesses

the two

The temperature

is higher

in

of concentrations.

but of opposite

contributions,

correctly

are shown

theoretical

experimental

have Vc zz 0 their dielectric m intermolecular associations. mesitylene

CD)

P AB

parameters

the

calculated

correctly

over

Since

to

A3 (cm3)

cx

and concentrations.

(16) describe systems

these

z3

absolute ( Fig. other

can

to the

va:ue

is

7 1) so that there

is

an

250 As

for

excess

with

values

are

the

optical

frequencies

temperature

is

somewhat

larger

an

expected, the

increase but

trend

is

in

al though as

experimental the

observed

predicted.

0

Fig.

7 :

for

the

Severa

tcmpe.ratures. 298.15

1

K,

+

Terms (1’)

( ‘3) .-I 248.15

K,

to

contributions

mesitylene

related

318.15

(2’)

K.

318.15

to Terms

the

excess

static

tetrachloride

carbon

specie5

the related

to

permittivity

system -rearrangement

the

both

at :

(1)

formation:

complex

I(.

COMCL’JS I UNS

1)

An

improved

excesses

in

One

of

treatment

This

complex 2)

solutions

depends

consequence

on

is the

the is

composed

formation

arrangements able

tc

describe

two

perfectly

prdposed

to

predict

of of

complexes

of

the

and

different

excesses

even

the

dielectric

distinct the species in

parts.

other

-the-

is

a

p-resent. absence

of

formation.

The

range

equakon

proposed of

reference

equation

temperatures temperature.

predicts provided

the a:.

dielectric and

~1 re

behaviour are

known

in for

a a

251

3) In the mixtures

examined

explained

if existence

Otherwise

calculated

4) The description

the species

understanding

of excess

resulting

present

in

when only

only

is

different

accepted.

and

excesses

several

interactions

provides

behaviour

be

do not coincide.

as the sum of

from

experimental

can

mixture

solution

a

ideality

excesses

permittivities

of its dielectric

conclusions

from

in the

and experimental

contributions

partial among

deviations

of complexes

a

avoids

detailed erroneous

are considered.

ACKNOWLEDGMENTS

We are greatly for detailed

indebted

and helpful

to Dr. MA::imo BarCn,

this Department,

discussions.

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1

A. H. Buep

2

Il. B. Rebollo 38

3

(1988)

and M. Barbn,

J. R. Goates

M. L. McGlashan,

6

P.J.

7

E. B. Ewing,

(196Y)

9

and A. H. Budge,

and J. M. Prausnitz,

5

8

Chem.,

92 (1988) 840. J. Mol. Liquids,

J. Phys.

Chem.,

66

1387.

4. R Anderson 1339 &A_.

Chem.

J. Phys.

A. H. Fuep and M. Far&n,

225.

J. B. Ott, (1962)

Paz,

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