Dipole moment of molecules determined from dielectric measurements in very dilute solutions of a dipole liquid in a nondipole liquid

103

Journal of Molecular Liquids, 59 (1994) 103-113 Elsevier Science B.V.

Dipole

moment

in

very

J.

J.

of

dilute

molecules

determined

solutions

of

from

a dipole

dielectric in

liquid

measurements

a nondipole

liquid

Makosz

Institute of Physics, Silesian Unversity, Katowice. (Received 28 April 1993; in revised form 25 June 1.993) A formula

is

given

for liquid

molecules

of

dielectric

measurements

dipole

liquid

basing

on

Scholte’s

a in

Onsager

liquids:

from dilute

liquid.

The

an

for

interest

is

formula

the found

account

for

ethyl

measurement

from

was

into

obtained

of

of

shape

dichloromethane,

and also

obtained

taking

were

moment

solution

ellipsoidal

results

o-xylene,

dipole data

very theory

for

Satisfactory

nitrobenzene

a

a nondipole

the

of

derived in

correction

molecules.

calculation

Poland.

of

dipole

four

tested

acetate taken

data

and

from

the

literature. INTRODUCTION. Considerable the

dipole

moments 1

solutions molecules

. A

reliable

would

make

values

of

dipole

tested

in

the

knowing

value

A number

considered

as

causes

this,

for

polarisation factor. are

On the not

the

these

doubts,

in

ultimate

theory

0167-7322/!94/$07.00

moment

endeavoured

theory paper

accurate Scholte’s

as

of that

and

then

magnitude

of

formulae

for

a

to

further for

the

attempt

of

atomic

molecule

shape

theory,

still

liquid. was

moment

cavity

reserved

be

(capacitance)

dipole

dipole

ellipsoidal

yet several

value

Onsager

the

principle

cannot

permittivity

describing formula

In

undoubtedly the

the

0 1994 - Elsevier Science B.V. All rights - C

SSDI 0167-7322@4)00725

be

molecules)

they

are

and also

correct cannot

derive

about

seem

obtain which

the

but

There

in of

examined.

to

improving

of

made moments

measurements.

measurements would

to

the

may be

dielectric

liquid

dipole

liquids

of

uncertainty

present

and

in

dipole

have

determination

importantly,

molecules

always

It

a satisfactorily

Onsager

most

from

hand,

the

determining

satisfactory.

accurate.

is

the

2-9

the

measurements

measurements

other

tested

other

for

in

(disintegration

including the

dielectric

molecule

are

entirely

used, obtain

state

moments

of

now very

from

of

obtained

evinced

from

possible,

authors

dipole

results

it

various

of

still

method

moments

with

molecules’

liquids

gaseous

the

interaction

the

of

10-12

Despite made basing

.This

to on

is

to

104

certain The

extent

a continuation

immediate

where

stimulus

applying

dipole

this

moment

measurements In

calculated

required

the

first

case

relative

errors

Measurements

for

four

dipole for

of

for

satisfactory Studies

situation

cases

gases’

the

fraction

0,005

reasonable small

of

to

is

suppose

for

in

give

it

liquids of

differing

were

calculated

made

and

from

solutions.

under

normal large.

conditions.

Debye

or

cm3 is

of

3 10

number).

19

. In

This

considering

worth

to

solution

in

concentrations in

used Onsager

correspond

example

(Loschmidte

The

Formulae

satisfactorily gases.For

is

is

values

markedly been

are

molecules

a similar

it calculated

large

dilute

for

101’

of

The dipole

and

simplified

formulae

2.7

sum

case

moments

gases

and T in

that

concentrations

to

in

general

dipole

conditions

from

13.14.16

tetrachloride

number

normal

as

distances

in

E, P,

dichloromethane-carbon under

so

the

were

solvents.

obtained

that

simplified

between

second

medium

conducted

to are

for

than

data)

moments

dipole

inter-molecular

, these

relations

literature

had previously

were

similar

Ref.13

value

8.15

data

the

small, chosen

were

permittivity 2.17

formulae

is the

in

measurements

reported

here

In both

from

two different

were

results

in

a different

literature

Additionally,

which

and R.R.Birges. cited

formula.

represent

Solvents

A.B.Myers results

made and dipole

in

to

permittivity.

liquids

these

for

as

of

the

we obtained

positive, were

liquids, so

moments.

values

this

work by

(calculations

is

dipole

selected

the

from

for

negative. were

of

was provided 14 same formula

mole a

makes

gas it

solutions

of

solution

of

manner.

THEORY. According two

liquids,

to one

a dipole

other

c-1 Z-E In originating

= this

the of

Onsager

which

liquid

formula

pd -

the

“2”)

N2[(~r,)2

+

is

directing

polarization

a nondipole

(index

N,(P,),

from

is

theory, is

+ (P,),

the

liquid

(index

expressed

by

the

a

” 1” )

and

pa

(1) of

-

the

formula’

+ PI

mean value

field,

of

is

induced the

polarization mean

value

of

105

induced the

polarization

mean value

of

In order know

cavity

us assume

the

that

of

in

cavity

solvent

and

the

61

=

A,

This

-

E

is

the

-

serve

to

calculate

in

solutions

a

may be

the

in

few

molecules

solution

dipole of

of

dipole

of

words,

composed

molecules

approximation close

assumption

permits

also

field

(camp.

(4.1).

field

in

nearest

its

surroundings

reaction

field

EIf =

f,

the

field,

the

the

molecules solvent.

molecules

taken

the

of

be

to

expressed

form

14

Ref.2. one

replaced

by

in

agreement

with

zero

Ref.2

in

El

-

solvent

the

assumption,

c*E,.

modification Ref.a).The of

in

(2.84)

is

surroundings, formed

of

the

dipole and

solvent

formula

moment in

induces

a

case

the

Hence

the

our

molecules.

for

.

(~~-1) ’

taking

our

El s,+(l-c,)Aa reaction

to

(4.45)

si+(l-cl)A,

1 = I-faaa -

are

A,(l-A,)

&

The directing

E,

has

similar

is

a concentration

reaction nearest

(2.76)

rather

permittivity

This

for

factor

the

reaction

Ref.2):

nondipole

shape

from

solution

This

where

only

to

(2)

cavity

differs

permittivity. since

liquid.

necessary

concentrations

dielectric

dipole

is

E

E~+C~-~~)A~

formula

that

a few

of

the

tested

it

is

form:

E,

where

only

in

the

/.J -

measurements

In other are

and

field.

will

feasible solvents.

layer

field

of

and applied

dielectric

zero)

field

terms

formula

final

virtually

by a thick

The

reaction

a molecule

field

from

nondipole

the

individual

technically

the

concentration

surrounded

the

molecules

lowest

molecules

of

the

reaction

field,

moments

from

moment

calculate

the

with

in

dipole

to

Let dipole

(of

originating

assumption,

now has

the

form:

E

field

(4)

factor

has

the

form

(camp.

(4.45)

106

f

=abc

a,

-

aai

=

while

A,, (l-A,i)

3

ai

(‘1-l) (5)

‘,+(l-E,lA,i

polarisability

has

these

latter

cavity. first

electric

to

a,

b,

the

c -

the

are

semiaxes

/~z- mean value

calculate

determine

(6)

energy

of

of

the

permanent

the

of

the

dipole

dipole

i da1

ellipso

we

moment, moment

an

in

field‘

w=

-

L’(Q),

tak i ng

Then

Ref .2:

abc

formulae

In order

must

(2.105)

form

q-1 3[1+(+l)Aai]

In

the

into

account

formula

(4)

for

the

induced

the

directing

field

we

(Ed)a

obtain 2

In

Onsager

that

parts, from

the

the

is

polarization

directing

permanent

dipole

will

exhibit

this

is

3&1Q*

Induced

polarization

has

form

(camp.

of

the

(l-f,la,l)

reaction field

molecule,

the

from

polarization by

the

polarization

The reaction

moment

only

=

from

field.

expressed

(P,),

the

theory

the

formul a (camp.

field’ is

hence

and

with

solvent field.

(5.82)

of

two

polarization

associated the

directing (5.81),

consists

the

molecules In

our

case

Ref .2)

1

(2s,+l) of (5.83)

the

’ dipole

Ref.2)

molecules

consists

of

two

terms

and

107

E

=iaa2 (pd)2

+

(PR)2

Formula substitution c-l 4n

and

3El

This

Nla,

2s,+1

=

tested

2

of

the

form

1

N,IJ~

from in

formula and adi

instead

of

we obtain

this

fai

with

(10)

is

where

the

defined

6,

the

putting

a2 -

6,,

is

the

referring

to

have

On the for

of

formula

is

/J, the

cited

(5.84)

dipole

moment

of

magnitudes

II

the

El

E-61

and

formulae

(5)

in

&2(+5)

@2

dipole

magnitude

(11)

2e,+s;

molecules

I

in

the

solution

relation 3

as

in

of

assumption

made, i.e.

the to

radius

papers

by

A,,

the

formula

magnitudes curve

si

the the

= Aa2= =

molecule.

dipole that

shape: when E -

the

of

2.8,14

induced

polarisation

a spherical

tangent

given

2sr+l

of

this

= (4n/3)a2N2

mean value

e2 = 0,

to

---

following

6,

From measurements, slope

analogous

2

coefficient

the

assumed,

molecules correct

volume by

1 -

=

additionally (10)

.2a~2)2~&,+(l-E,)A,21

respect

l+(+l)A,, 9,

(l-f

formula

OD

is

after

El

the

E~+(“~-E~)A,~

and

solution,

(9)

molecule.

and

where

dilute

.2Qa2

a

+ 3KT

slightly

~~+(l-ci)A,~

(10)

l-f,2a,2

+

magnitude

Transforming (6)

(l-f

)2

pl=O).

The relevant the

N2Qa

differs

(K= 1,2.

has

1

l-falaal

formula

in Ref.2

reordering

&lE

f.2%2

polarization

total

for

(1)

P2 + 3KT

(1-f,2a,2)(2e,+1)

=

l/3

(t

(It in

dipole

and

solvent

, and s1aDy El). above

0

(c--Er)/@2*(W@2)@

and

-

E,)

are vs.

was

formula

quoted

(As/A% ) 92+o of

terms

is

found 9,

at

accurately

from the

2

.O’ the

point

108

@2

0.

=

the

This

is

derivation

then

has

the of

the

magnitude

the

that

formula.

satisfies

The

the

final

assumption

formula

for

the

made

dipole

in

moment

form

a:KT(2c,+l) P2 =-

cl [E~+(~-E~)A~~I Let

us now compare a.14 .A11 these

in papers

this

formula

formulae

obtained

with

may be written

in

the

final

the

form

formulae

(13)

where

A

and B are

the

same

in

three

formulae

and have

the

form

2

a:KT(2cl+l)

A=

all

EI+(E;-EI)Aa2

3cf [EI+(l-EI)Aa21 I I+@;-l)A,,

1 (14)

The

three c,

formulae

c2 c3

=

3(2c;+1)/(2s1+1)’

=

3E,/(2E1+1)

these

These

Table

nondipole give

For dipole

is

the

moment

formula

by Ci

for

from (7a)

Ci,

that

is:

Ref.8

from

Ref.14

(14). the

of

value

dipole of

expressions

solvent

for

calculated

moment

permittivity.

various

values

El

I. El most

often

molecules

same value found

(11)

in values of

same measurement is

expression

(12),

governed

liquids

dipole the

the

formulae

values

the

formula

difference

in

from

signifies

formulae

the

formulae

seen

For cl=1

of

in

the in

in

differences

may be

only in

The magnitude from

differ

= 1

from

in

for

the

data formula

has

the dipole the (12).

a value

gaseous

close state

to (all

-

moment).

greatest

value

of

2.

three molecule

109

EVALUATION OF RESULTS AND DISCUSSION In

the

made for

experiments

conducted

measurements

following

solutions:

o-xylene,

the

acetate

and nitrobenzene

Measurements OH-302

were

performed

precision

6425

(Wayne

from

II

were

experimental

the

calculated

dipole

gives

the

values

results

greatest

are

moment

in

values

equally

the

in

as

gaseous

the from

dielectrics

for

from

pentane.

on a Hungarian Component

in

a

made

Analyser

range

for

tested

dipole

moments.

satisfactory

as

In

the

molar

of

(12).

value

For

those the

In

CH,Cl,

these

for

values

three

cases of

from

(12) last

of the

two

dipole nearest

dipole

are

known

also

Formula

III

is

and

1 iquids

values

Table

(AE/A@~)~ +.

.

given.

remaining

are

state

formula

the are

of

18-22

papers

moment s

state.

which

taken data

gaseous

calculated

earlier made

in

and 15

and on a Precision were

were ethyl

0.003+0.15.

required

the

permittivity

tetrachloride

described

Kerr).Measurements

data

In Table

as

dielectrometer

concentration Additional

carbon

in

of

dichloromethane,

moments out

set

the

experiment.

As

2

may be

seen

absolute

from

value

summing

is

found

As mentioned obtai

ned

than

ant icipated

that

the

zero,

on the slope

wh ile

TABLE I.

for

Values

in

the

basis

of

13

of

.This the

the for

relative the

percentage

third

introduction,

the

calculations becomes

from

curve

(E -

every

other

concentration

Ci’as

function

of

vs.

solvent

Formula

=

c2

= 3(2e;+

C3 = 3&,/(2ci+

1)/(2s,+ 1)

1)’

of

literature

the

smallest

e2 has

dipole data

when a

it

than

larger

remembered

zero

permittivity E,=2

moment

are

is

minimum

greater

El=1

1

Cl

values

understandable ~1)

errors,

sum.

El-3

(11)

Ref.8

1

1

1

(7a)

Ref.14

1

1.08

1.16

(12)

(14)

1

1.20

1.28

value it

takes

at a

110

TABLE II. (cccl

Experimetal = 2.227, 4

Molecule

data

sc

a2

cm o-xylene

0.22

4.80

* “0

1.5028

‘ref

0.6223

dichloro-

0.33

2.55

1.4215

vents

B

*t

8

14

Pl

iJ3(12)

p2

0.0124

CtlHlO

ccvap=

298K

sol23

x10,

in D at

12

3

A

moments

= 1.836)

s 5

and dipole

CCI,

0.32

0.55

0.58

0.62

C,H,,

0.62

0.52

0.57

0.65

/~,=0,54

/.1,=0.58

H3=0.64

0.0826’27

methane

ccl,

4.11

1.49

1.56

1.65

CH,Cl 2

C,H,,

4.20

1.54

1.59

1.68

PVaP

=

1.6225

ethyl-

pi=1.52

0.33

3.90

1.3728

C4H,02 =

ni tro-

ccl,

3.24

C,H,,

3.16

22

1.78

1.52

0.18

4.07

1.5499

1.61

1.52 u1=1.52

benzene

1.58 ~~~1.60

ccl,

19.15

3.92

(3.84) C,H,,17.41

4.12

***

Values

parameter

in

magnitude

depending

brackets of

atomic

were

(4.04)

(4.28

4.09

4.32

(3.89)

(4.02)

(4.25

/12=4.11

(3.87)

-

4.36

3.95

pi=3.94

***

1.68 /.r3=1.69

0.5630

PvCI.p = 4.2829

a ref

1.70

(0.69)31’32

C6H5N02

*

/.1~=1.67

0.3228

acetate

hi%P

/J2=1.58

,u3=4.34

(4.03)

(4.27)

on ET = (1 + a,,,)ni

found

polarization

when shown

taking in brackets.

into

account

the

111

TABLE III. (a raf bi

-

Average

-depending [(cc,

-

literature

and

corrected

on sy = (l+a,,,)ni.

n -

dipole number

of

moments

in D

solvents,

PY*p)/PY.plw

Molecule Iodomethane

14

(CH,I)

14

PVaP

aref

1.64

0.22

3

1.49

1.57

1.66

-9

-4

1

1.62

0.08

2

1.52

1.58

1.67

-6

-2

3

1.50

0.08

4

1.36

1.43

1.51

-9

-5

1

1.44

0.13

3

1.31

1.37

1.45

-8

-4

1

n

II:

v2

cc,(lZ)

b,

b

2

b

3

Dichloromethane (CH&lz)* Dibromomethane (CHzBrr)

l4

1,2-dichloroethane 16 (C$-I,Cl2)

Ethyl

acetate

1-butanol

(C,HaS)z)*

(C,Hr,O)

lo

1.78

0.32

2

1.52

1.60

1.69

-15

-10

1.60

0.07

4

1.46

1.52

1.61

-9

-5

-5 1

1.66

0.08

3

1.57

1.65

1.74

-5

-1

5

0.01

4

1.66

1.74

1.84

-2

2

8

(-6)

(-2)

(4)

Fluorobenzene 16 (C,H,F)

Chlorobenzene 13 (C,H,Cl)

1.70

(0.10)

(1.59)(1.67)(1.77)

Bromobenzene (C6H5Br) ’ 3

1.70

0.01

4

(0.08)

1.64

1.72

1.82

-3

(1.58)(1.66)(1.76)

1

7

(-7)

(-2)

(3) -5

Iodobenzene (C6HSI) ’ 3 *

0-xylene

(CsH,,)

1.71

0.05

3

1.44

1.51

1.62

-16

-12

0.62

0.01

2

0.54

0.58

0.64

-13

-6

3

4.14

0.64

4

3.91

4.08

4.32

-5

-1

4

1.49

0.19

3

1.40

1.47

1.58

-6

-1

6

* 4.28

0.56

2

3.94

4.11

4.34

-8

-4

1

(3.87)

(4.03)

(4.27)

(-10)

-6

0.2

Benzonitrile (C,H,CN) Aniline

l3 13

(C,H,NH,)

Nitrobenzene

(C,H,NO,)

(0.69) b,= * **

Measurements Values magnitude

in of

-120(-130)**, from

this

b,=

-54 (-63)

,

b3=

35(26)

paper

brackets

were

atomic

polarization

found

when shown

taking in

brackets.

into

account

the

112

greater

value.

necessary.

values

(As/&s)

the

from

of

in

the

formula

(Ac/&z)+z+O

This

of

give

for

the

a

necessary

in

for

can

formulae

is

Hence values

Recapitulating, best

it

0,.

literature

values

magnitude

the

discussed

From calculations

specific these

For

to

effect,

estimate

moments

dipole

of

moment

measurements

of

and

is

is

for values

next

in which

orientational

zero

(AE/A@~)

calculations

dipole

only

slope

putting

needed

the

values.

presented

formula

(12)

gives

results. work

was partly

supported

by

the

grant

from

KBN.

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