Dielectric behaviour of aprotic polar liquid dissolved in non-polar solvent under static and high frequency electric field

Dielectric behaviour of aprotic polar liquid dissolved in non-polar solvent under static and high frequency electric field

S Sahoo¹*, T R Middya² & S K Sit³

1Department of Electronics & Instrumentation Engineering, ³Department of Physics

Dr. Meghnad Saha Institute of Technology, P O Debhog, Haldia, Dist Purba Medinipore, West Bengal, India, 721657

2Department of Physics, Jadavpur University, Kolkata, West Bengal, India

3E -mail : swapansit @ yahoo. co.in

Received 29 November 2011; revised 4 January 2012; accepted 11 January 2012

Dielectric behaviour of aprotic polar liquids (j) like N,N dimethylformamide (DMF), N,N dimethylacetamide (DMA) and acetone (Ac) has been studied under static as well as 9.987, 9.88 and 9.174 GHz electric field employing Debye theory of polar-non polar liquid mixture in terms of measured İ′ij and imaginary İ″ij part of complex relative permittivity İij*, static 0ij and high frequency İij for different wj’s of solute dissolved in non polar solvent at 27°C temperature. Double relaxation times 2 and 1 due to whole molecule and part of the polar molecule have also been estimated analytically using the complex high frequency orientational susceptibility Ȥij* (= İij*−İij) from measured data for DMF and DMA in C6H6 and CCl4 as well as acetone in C6H6 and CCl4 solvent, respectively at 27°C. Out of the six systems, three systems show double relaxation time 2 and 1 and dipole moment 2 and 1. The estimated ’s and IJ’s agree excellently well with the reported and measured values from ratio of slope and linear slope method. The dipole moments 0s’s in static electric field are also compared with ȝj’s in hf method. The relative contributions c1 and c2 due to IJ1 and 2 have been calculated from Fröhlich equation as well as graphical plot of χ′_ij/χ0ij −wj and ″ij/0ij −wj curve at wj0. Solute-solute and solute-solvent molecular associations are ascertained in different molecular environment.

Keywords: Double relaxation times, Dipole moment, Monomer, Dimer

1 Introduction

Amides have attracted the attention of a large number of researchers^1-4 because of their high dielectric constant and wide biological applications.

Amides are pervasive in nature and technology as structural materials. The amide linkage is easily formed which confers structural rigidity and resists hydrolysis. Moreover, amide linkages constitute a defining molecular feature of proteins. The secondary structure is a part to the hydrogen bonding abilities of amides. N,N-dimethylformamide (DMF), N,N-dimethyl acetamide (DMA) are recognized as non-aqueous dipolar aprotic solvent. Acetone (Ac) on the other hands is a good aprotic solvent for the manufacturer of smokeless powder and used as raw materials for the production of idoform and chloroform. Dielectric relaxation studies of polar solutes in non-polar solvent using microwave absorption technique are expected to throw some light on various type of molecular association because of the capacity of microwaves to detect weak molecular association^5-7. Dhull and Sharma^8,9 measured dielectric constant (İ′ij), dielectric loss (İ″ij) of dilute solution of N,N-dimethyl-

formamide (DMF), N,N-dimethylacetamide (DMA) in benzene, dioxane and carbon tetrachloride using standing wave technique at 25,35,45,55°C under 9.987 GHz electric field to calculate dielectric relaxation time (), dipole moment (ȝ), energy parameters (F, H, S) at various temperatures and weight fractions of solutes dissolved in non- polar solvents from their measured data. They proposed for monomer and dimmer association in various solvent in terms of measured IJ and ȝ. They compared the evaluated energy parameters with corresponding viscosity parameters to show that the dielectric relaxation process like viscous flow can be considered as a rate process.

The existence of double relaxation phenomenon of DMF, DMA and Ac dissolved in benzene or carbon tetrachloride has been studied at 27°C for different w_j’s of solutes in terms of measured real ′ij (İ′ij−İij) and imaginary ″ij (İ″ij) parts of high frequency orientational susceptibility ij* (İij−İij) and 0ij (İ0ij − İij) which is real from single frequency susceptibility measurement technique¹⁰. This study offers to get the double relaxation times 2 and 1 due to rotation of the

whole and flexible part of the polar molecules under high frequency electric field as well as dipole moment 2 and 1 to enable one to get information on intra and intermolecular interactions and their structures. To calculate IJ₂, IJ₁ and ȝ₂, ȝ₁ accurate measurement of İ_0ij and İij are needed. The static dipole moments ȝ0s’s under static and low frequency electric field were estimated in terms of slope a₁ of static experimental parameter X_ij[={(ε0ij−ε∞ij)}/{(ε0ij+2)(ε∞ij+2)}] against w_j within the frame work of Debye model of polar-non polar liquid mixture.

Aprotic polar solute (j) dissolved in benzene is usually showed¹¹ double and single relaxation mechanism under ~ 10 GHz electric field. The purpose of the present paper is to study the occurrence of double relaxation mechanism of six systems at 27°C temperature and different wj’s of solutes using susceptibility measurement technique and thereby to predict structure, shape, size of polar molecule and various molecular association like solute-solvent (monomer) and solute-solute (dimer). It is worthwhile to investigate how far measured relaxation times IJ2

and IJ1 and dipole moment 2 and ȝ1 agree with reported IJ’s and ȝ’s from Gopalakrishna’s method as well as static 0s and to see whether a part of the molecule or whole molecule is rotating under high frequency electric field within the frame work of Debye model of polar-non polar liquid mixture.

2 Experimental Details

The aprotic polar liquids DMF, DMA and Ac (E.Merck) and the solvents C6H6 and CCl4 were used after distillation. The solutions of different concentrations were made by mixing a certain weight of solute with solvent using electronic balance and micro pipet. Agilent E4980A precision LCR meter has been used to measure 0ij and İij of six systems under investigation. The frequency range of LCR meter is 49 Hz to 5 MHz. The values of İ′ij and İ″ijfor a given wj’s of solutes under different frequency of MHz range have been carefully measured to draw the Cole-Cole semicircular arc plot to get accurate values of İ0ij and İij. The values of İ′ij and İij are, however, extracted from the measured data^8,9 at the desired concentration using least squares fitting procedure.

All the measured data are presented in Table 1.

3 Theory

3.1 Static dipole moment µµµµ0s

The static dipole moment µ0s of a polar solute (j) dissolved in solvent (i) under static or low frequency

electric field at temperature T, K within the frame work of Debye model⁸ is given by:

2

0 0 0

0 0 0

1 1 1 1

2 2 2 2 9

ij ij i i s j

ij ij i i B

N c K T

ε ε ε ε µ

ε ε ε ε ε

∞ ∞

∞ ∞

− − − −

− = − +

+ + + + ^…(1)

where ε₀ is the absolute permittivity of free space = 8.854×10⁻¹² Fm⁻¹.

The molar concentration c_j of the polar solute can be expressed in terms of weight fractions wj’s of polar solute as:

ij j

j j

c w M

= ρ …(2)

Again, the density ij of the binary solution is written as :

(1 ) 1

ij i wj

ρ =ρ −γ ⁻ …(3)

Eq. (1) can now be written as :

0 0

0 0

2

1 0

( 2)( 2) ( 2)( 2)

(1 )

27

ij ij i i

ij ij i i

i s

j j

j B

N w w

M k T

ε ε ε ε

ε ε ε ε

ρ µ γ

ε

∞ ∞

∞ ∞

−

− −

+ + = + +

+ −

2 2

2

0 0

27 27

i s i s

ij i j j

j B j B

N N

X X w w

M k T M k T

ρ µ ρ µ

ε ε γ

= + + …(4)

Eq. (4) is a polynomial equation of X_ij against w_j. On differentiation of Eq. (4) with respect to wj and at w_j →0 one gets:

1/ 2

0 1

0

27 _{j B}

s

i

M k Ta N µ ε

ρ

ª º

=« »

¬ ¼ …(5)

where a1 is the slope of Xij −wj curve at wj →0. The curves of Xij−w_j are shown in Fig. 1. M_j being the molecular weight of polar solute. All other symbols are expressed in SI units¹³.

3.2 Double relaxation times ττττ2 and ττττ1 and relative contributions c₁ and c₂

Bergmann et al¹⁵. suggested a graphical method to get τ1 and τ2 of a polar liquid mixture dissolved in benzene (i) in terms of measured χ′ij, χ″ij and χ_0ij under different frequency of GHZ electric field and temperature T, K as:

'

1 2

2 2 2 2

0 1 1 1 2

ij ij

c c

χ

χ ⁼ +ω τ ⁺ +ω τ ^…(6)

0.002 0.004 0.006 0.008 0.010 0.012 0.01

0.02 0.03

(VI)

(V) (IV)

(III) (II)

(I)

X ij

w_j

Fig. 1 — Variations of static experimental parameter Xijagainst weight fractions wj’s of different polar solutes dissolved in non polar solvent under static electric field at 27^°C temperature.(I) — — for DMF+C6H6 (II) — — for DMF+CCl4 (III) — — for DMA+ C6H6 (IV) —  — for, DMA+ CCl4, (V) — — for Ac+ C6H6 (VI) — — for Ac+ CCl4,respectively

"

1 2

1 2 2 2 2 2

0 1 1 1 2

ij ij

c c

χ ωτ ωτ

χ ⁼ +ω τ ⁺ +ω τ ^…(7)

where c₁, c₂ are the relative contributions due to two broad Debye type dispersions such that c1 + c2 = 1.

Eqs (6) and (7) are solved for c1 and c2 to get a straight line equation as :

( )

' "

0 2

2 1 1 2

' '

ij ij ij

ij ij

χ χ χ

ω τ τ ω τ τ

χ χ

− = + − …(8)

where ω τ

(

2+τ1

)

and −ω τ τ² _{1 2} are the slopes and intercepts of Eq. (8) obtained by least squares fitting procedures of variables (χ0ij−χ′ij)/χ′ij plotted against χ″_ij / χ′ij for different w_j’s under a given angular frequency ω(=2πf). The intercepts and slopes are justified up to four decimal place along with τ’sfrom double relaxation phenomenon, are presented in Table 2.

τ’s were also calculated from the linear slope of χ″ij

against χ′ij of Fig. 2 as suggested by Murthy et al¹⁵.

"

' ij ij

d d

χ ωτ

χ ^{= …(9)}

Both χ″ij and χ′ij are the functions of wj’s. To avoid polar-polar interactions one could use the ratio of slopes of χ″ij −wj and χ′ij − wj curves at wj →0 to measure τ as shown in Figs 3 and 4.

0.0 0.2 0.4 0.6 0.00

0.05 0.10 0.15

(III) (IV)

(VI) (II)

(I) (V) χij

''

χ_ij^'

Fig. 2 — Straight line plot of ij against ij of different polar solutes in non polar solvent at 27°C temperature under ∼10 GHz electric field. (I) — — for DMF+C6H6 (II) — — for DMF+CCl4 (III) — — for DMA+ C6H6 (IV) —  — for DMA+ CCl4, (V) — — for Ac+ C6H6 (VI) — — for Ac+

CCl4,respectively

0.002 0.004 0.006 0.008 0.010 0.012

0.00 0.05 0.10 0.15

(V)

(VI)

(IV)

(III) (I)

(II)

χij

''

w_j

Fig. 3 — The plot of ij against weight fractions wj’s of different polar liquids in non polar solvents at 27°C temperature under

∼10 GHz electric field. (I) — — for DMF+C6H6 (II) — — for DMF+CCl4 (III) — — for DMA+ C6H6 (IV) —  — for DMA+ CCl4, (V) — — for Ac+ C6H6 (VI) — — for Ac+ CCl4, respectively

"

0 '

0

j

j

ij

j w

ij

j w

d dw

d dw χ

χ ωτ

→

→

§ ·

¨ ¸

¨ ¸

© ¹

§ · =

¨ ¸

¨ ¸

© ¹

…(10)

0.005 0.010 0.015 0.020

0.0 0.2 0.4 0.6

(V) (VI)

(IV)

(III) (II)

(I) χij

'

wj

Fig. 4 — Variation of χ′ij against weight fractions wi’s of different polar solutes in non- polar solvent at 27°C temperature under ∼10 GHz electric field. (I) — — for DMF+C6H6 (II) — — for DMF+CCl4 (III) — — for DMA+ C6H6 (IV) —  — for, DMA+ CCl4, (V) — — for Ac+ C6H6 (VI) — — for Ac+ CCl4 respectively.

All the τ’s including the most probableτ₀= τ τ_{1 2}, reported τ due to Gopalakrishna’s method, symmetrical τ_s and characteristics τ_cs are placed in Table 2. The values of τ’s are significant up to two decimal place.

A continuous distribution of τ’s between two extreme values of τ2 and τ1 for three systems inspires one to calculate c₁ and c₂ from Eqs (6) and (7) as follows :

(

²

)

' "

2 1

0 0

1

2 1

1

ij ij

ij ij

c

χ χ

α α

χ χ

α α

§ ·

− +

¨ ¸

¨ ¸

© ¹

= − …(11)

(

²

)

1 2

0 0

2

2 1

" '

ij ij 1

ij ij

c

χ χ

α α

χ χ

α α

§ ·

¨ − ¸ +

¨ ¸

© ¹

= − …(12)

where α₁=ωτ₁andα₂ =ωτ₂ such thatα₂ >α₁. The experimental c1 and c2 were calculated from the parabolic fitted curve of χ″ij /χ0ij and χ′ij /χ0ij against w_j at wj →0 as shown in Fig. 5. The theoretical c1 and c2 were also calculated in terms of χ′ij /χ0ij and χ″ij/χ0ij

following Fröhlich’s equations¹⁷ as:

2 2 2 2 2

0 1

' 1 1

1 ln

2 1

ij

ij A

χ ω τ

χ ω τ

ª + º

= − « »

¬ + ¼ …(13)

0.002 0.004 0.006 0.008 0.010 0.012 0.86

0.88 0.90

χij ''/χ

0ij

(III) (II) (I)

χij ' /χ0ij

w_j

0.30 0.32 0.34 0.36 (III)

(II)

(I)

Fig. 5 — Variations of χ′ij / χ0ij and χ″ij / χ0ij against weight fraction wj of DMF and DMA at 27°C temperature under 9.987 GHz electric field (I) — — and … … for DMF+CCl4

(II) — — and … … for DMA+ C6H6 (III) — — and

…… for DMA+ CCl4 respectively

( ) ( )

1 1

2 1

0

" 1

tan tan

ij

ij A

χ ωτ ωτ

χ

− −

ª º

= ¬ − ¼ …(14)

where A= Fröhlich’s parameter = ln (τ₂/τ₁).

3.3 Symmetric and asymmetric distribution parameter γγγγ and į

The three systems i.e DMF in CCl4, DMA in C6H6

and DMA in CCl4 for different w_j’s of solute exhibiting molecular non-rigidity are expected to show symmetric or asymmetric distribution of relaxation parameters as:

( )

¹

0

* 1

1

ij

ij j s ^γ

χ

χ ⁼ + ωτ ⁻ …(15)

( )

0

* 1

1

ij

ij j cs ^δ

χ

χ ⁼ + ωτ …(16)

where γ= symmetric and δ = asymmetric distribution parameters related to symmetric τs and characteristic relaxation times τcs, respectively.

Eq. (15), on simplification of real and imaginary parts yields :

1

0 0

' ' "

2tan 1

"

ij ij ij

ij ij

ij

χ χ χ

γ π χ χ χ

−

ª§ · º

«¨ ¸ »

= − −

«¨ ¸ »

© ¹

¬ ¼

…(17)

1

' 1

1 1 cos sin

" 2 2

ij s

ij

χ γπ γπ γ

τ ω χ

ª ­°§ · § · § ·½°º−

« ¨ ¸ »

= ««¬ ®°¯¨© ¸¹ ¨© ¸¹− ¨© ¸¹¾°¿»»¼

…(18)

where

'

0 ij

ij

χ χ ^and

"

0 ij

ij

χ

χ are obtained from Fig. 5 at

j 0 w → .

On simplification of Eq. (16) further, one gets:

( ) ^{( )}

( )

0

log ' cos

1log(cos )

ij ij

χ χ φδ

φ φ φδ

ª º

« »

¬ ¼

= …(19)

( ) ( )

( )

0

0

"

tan '

ij ij

ij ij

χ χ φδ

χ χ

= …(20)

where tan φ = ωτ_cs.

Measured parameter of [log{( χ′ij/ χ0ij)/cos(φδ)}]/φδ of Eqs (19) and (20) are estimated and the value of φ is ascertained from the theoretical curve of 1/φ log(cosφ) against φ¹¹. į can also be found out from the known φ of Eq. (20).

3.4 Dipole moments µµµµjk from susceptibility measurement technique

The imaginary part of dielectric orientational susceptibility χ″ij as a function of wj of a binary polar mixture can be written as¹⁰ :

( )

2 2

"

2 2 0

27 1 2

ij j j

ij ij j

j B j

N w

M K T

ρ µ ωτ

χ ε

ε ω τ

§ ·

= ¨¨© + ¸¸¹ +

…(21) On differentiation of Eq. (21) w.r. to w_j and at infinite dilution i.e wj0 yields:

( )

" 2

2 2 2

0 0

27 1 2

j

ij i j j

i

j w j B j

d N

dw M K T

χ ρ µ ωτ

ε ω τ ε

→

§ · § ·

= +

¨ ¸ ¨ ¸

¨ ¸ ¨ + ¸

© ¹ © ¹

…(22) where µj is the dipole moment of polar solute of molecular weight Mj; The other symbols carry usual meaning in SI unit as mentioned elsewhere¹⁰.

On comparison of Eqs (10) and (22), one gets:

( )

' 2

2 2 2

0 0

1 2

27 1

j

ij i j

i

j w j B j

d N

dw M K T

χ ρ µ

ε ω τ ε

→

§ · § ·

= +

¨ ¸ ¨ ¸

¨ ¸ ¨ + ¸

© ¹ © ¹

…(23)

Eq. (23) yields dipole moment µj as:

( )

1 2 0

2

27

2

j B

j

i i

M K T

N b

ε β

µ ρ ε

ª º

=« »

« + »

¬ ¼

...(24)

where β (significant up to four decimel place) is the slope of χ′ij−w_j curve at wj0 and b is a dimensionless parameter. They are placed in Table 3.

All the µ’s justified up to two decimal place along with theoretical and experimental contributions c1 and c₂ are placed in Table 3.

4 Results and Discussion

The measured İ′ij, ij″, İ0ij and ij for different wj’s of solute are given in Table 1. The concentration of the polar solute for each dilute solution of polar-non polar liquid mixture are made extremely low. In that case, one polar unit is sufficiently apart from the other so that a polar unit may be considered as quasi- isolated validating the applicability of Debye theory for polar molecule.

The static dipole moment 0s’s are estimated from the slope of Xij−wj curve of Fig. 1. The ȝ0s’s thus estimated are placed in Table 1 along with slope a1 of Xij−wj curve, reported and estimated ’s as well as theoretical ȝ theo’s. As evident from Fig. 1 that polarization increases gradually with the rise of wj’s of solute under static field. Similar nature of curve(III) and (V) exhibiting almost same slope and intercepts may be due to their same polarity as observed¹⁵.The system DMA in CCl4 (II), however, shows maximum polarization in comparison to other system. This is probably due to solute-solute (dimer) molecular association at higher concentration region.

At infinite dilution i.e wj→0, the same polar molecule in different non- polar solvents environment yields different polarization probably due to solvent effect¹⁸. The estimated values of 0s’s are agree excellently well with the reported ’s of Gopalakrishna’s method¹⁹ in the high frequency electric field signifying the fact that the frequency of the electric field affects a little in determining ’s as observed⁷. It is evident from Table 2 that three systems out of six systems exihibit double relaxation times 2 and 1. The values of ’s from linear slope of ȤijƎ− Ȥij' curve of Fig. 2 following the procedure of Murthy et al ¹³. agree excellently well and placed in Table 2. The values of ’s have also been calculated from the ratio of slopes of Ȥij −wj and Ȥij−wj curves of Eq. (10) and

H C N CH₃ CH₃ O

8.47 C.m 1.08C.m 8.53C.m

H C

O N CH₃

CH₃ Cl C Cl Cl Cl

10.96 C.m 2.31C.m

13.37C.m H₃C C

O N CH₃

H₃C C O

N CH₃ Cl C Cl Cl Cl

8.96 C.m 3.5C.m

11.2C. m

12.46 C.m 4.86C.m

9.62C. m

H₃C C O

CH₃ 4.03C.m

7.02 C.m 0.68 C.m

0.31 C.m 1.45 C.m

1.45C.m

0.88 C.m 9.09 C.m

1.32 C.m

1.87C.m 1.87 C.m

0.89 C.m 7.43 C.m

CH₃ 1.08 C.m 1.53 C.m

1.53C.m

1.23 C.m 10.33 C.m

CH3 1.5 C.m 2.13 C.m

2.31C.m

0.48 C.m 0.48

C.m 4.03 C.m (i)

(ii)

(iii)

(iv)

(v)

δ δ

δ δ

H C N CH₃

CH₃ O

δ

H C N CH₃

CH₃ O

δ

H C

O N CH₃

CH3

H C

O N CH₃

CH₃ Cl

C Cl Cl Cl H₃C C

O

CH₃ 9.09

C.m 1.08

C.m 1.08 C.m 9.09 C.m (vi)

H₃C C O

CH₃

H₃C C O

CH₃ (vii)

(viii)

(ix)

δ

δ

δ δ

δ

Fig. 6 — Theoretical dipole moments µtheo’s from available bond angles and bond moments (multiples of 10^-30 cm) along with solute-solvent and solute-solute molecular associations (i) DMF- C6H6, (ii) DMF+CCl4, (iii) DMA+ C6H6, (iv) DMA+ CCl4, (v) Ac+ C6H6, (vi) Ac+ CCl4, (vii) DMF-DMF, (viii) DMA-DMA, (ix) Ac-Ac

are shown in Figs 3 and 4, respectively. All the values of Fig. 3 are found to increase with wj’s under high frequency electric field. This type of nature indicates the absorption of electric energy with the increase of solute concentration. The absorption is the maximum for DMF in CCl4 (II) and minimum for Ac in CCl4(V). Fig. 4 shows the convex nature of all the curves indicating the highest asymmetric nature of the polar molecule at w_j≅0.015 probably due to solute- solute molecular association of the polar liquids.

Table 2, however, presents that IJ1’s of three systems and 2’s of three systems exhibiting mono-relaxation behaviour which agree well with the reported and measured values. Most probable τ₀= τ τ_{1 2}, symmetric IJs and characteristic IJcs are also estimated and placed in Table 2 along with symmetric distribution parameters γ and asymmetric distribution parameters for comparison. This fact signifies that double relaxation phenomena offer better understanding of relaxation behaviour of polar solutes in non- polar solvents by yielding microscopic as well as macroscopic relaxation⁸.

The dipole moments µ₂ and µ₁ due to 2 and 1 in terms of slope β of χ′ij−wj curve (Fig. 4) and dimensionless parameter b are estimated and placed in Table 3. They are compared with the measured µ’s from ratio of slopes as well as linear slope method. In all the cases,the agreement is better signifying the validity of the method adopted here. The relative contributions c₁ and c₂ due to τ₁ and τ₂ are also estimated from FrÖhlich’s Eqs (13) and (14) as well as graphical plots of χ′ij/χ0ij and χ″ij/χ0ijagainst w_j of wj→0 of Fig. 5. In both the cases, c1+ c2 ≅1 as evident from Table 3. Table 3 also presents that measured and reported values of µ’s agree well with the estimated values of µ1’s of three systems and µ2’s of other three systems showing single relaxation behaviour. This fact reveals that a part of the molecule is rotating under high frequency electric field^10,11. The theoretical dipole moments theo’s of the polar molecules are ascertained the available bond angles and bond moments of 2.13×10^-30 cm, 1.5×10⁻³⁰ cm, 10^-30 cm, 1.23×10⁻³⁰ cm, 10.33×10^-30 cm of N←CH3, C←N, C←H, CH3←C, and C⇐O substituent polar groups as shown in Fig. 6. It is evident from Table 3 that estimated values of µ’s are slightly greater in solvent CCl4 than C6H6. This is probably due to the solute- solvent association of polar molecules with CCl4

attributed by the interaction of dipolar solute with a C-Cl dipole whose local field is not cancelled by other

dipoles. In solvent C6H6 too, interaction of the fractional +ve charge on N-atom of amides or C atom in acetone with the π delocalized electron cloud of benzene ring may be responsible for solute-solvent association.

5 Conclusions

The simple Debye model of polar-non polar liquid mixture, thus, satisfactorily explains the dielectric behaviour of amides and acetone under static and high frequency electric field in terms of measured relaxation parameter İij’s and ij’s. Double relaxation phenomenon of aprotic polar liquid is predicted for DMA in C6H6 and CCl4 as well as DMF in CCl4

alone. Estimated values of µ2 and µ1 are compared with the static 0s under low frequency field as well as measured and reported µ’s in GHz range. This agreement is good signifying the validity of the method. Solute-solute (dimmer) and solute-solven (monomer) molecular associations are ascertained in different solvent environment.

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