Dielectric Relaxation of Ethanol and N-Methyl Acetamide Polar Mixture in C6H6 at 9.90 Ghz

PRAMANA c Indian Academy of Sciences Vol. 83, No. 4 — journal of October 2014 physics pp. 579–595

Dielectric relaxation of ethanol and N-methyl acetamide polar mixture in C6H6 at 9.90 GHz

S SAHOO1,TRMIDDYA2 and S K SIT3,∗ 1Department of Electronics & Instrumentation Engineering, Dr. Meghnad Saha Institute of Technology, P.O. Debhog, Haldia, Purba Medinipore 721 657, India 2Department of Physics, Jadavpur University, Kolkata 700 032, India 3Department of Physics, Dr. Meghnad Saha Institute of Technology, P.O. Debhog, Haldia, Purba Medinipore 721 657, India ∗Corresponding author. E-mail: [email protected]

MS received 30 March 2013; revised 11 February 2014; accepted 25 February 2014 DOI: 10.1007/s12043-014-0813-7; ePublication: 27 September 2014 Abstract. Debye relaxation times τjk and dipole moments μjk of binary (jk) polar mixtures of ethanol (EtOH) and N-methyl acetamide (NMA) dissolved in benzene(i) are studied by studying conductivity of solution at 9.90 GHz for different temperatures, different mole fractions xj of ethanol and different weight fractions wjk of the mixtures, respectively. The variation of τjk−xj from linear slope of imaginary (σij k ) against real (σij k ) part of total conductivity ∗ (σij k ) curve reveals solute–solute (dimer) or solute–solvent (monomer) molecular associations up to xj = 0.0−0.3 and thereafter, solute–solvent molecular associations. τjks from the ratio of slopes of σij k−wjk and σij k −wjk curves exhibit solute–solvent molecular association for all xj s which are ◦ consistent with the μjk−xj curves at all temperatures except at 35 C. This signiﬁes the validity of both the proposed methods in estimating τ and μ. The molecular dynamics of the polar mixture are ascertained from Eyring rate theory. Theoretical dipole moments from bond angles and bond moments (μtheo) are also calculated to predict associational aspects.

Keywords. Relaxation time; dipole moment; solute–solute association; solute–solvent association; hf conductivity.

PACS Nos 77.22.Gm; 72.80.Le; 77.22.d

1. Introduction

The study of structure and associated behaviour of binary polar molecules (jk) dissolved in non-polar solvents (i) through the dielectric relaxation phenomena involved are with measurement of conductivity [1–3] under gigahertz (GHz) electric ﬁeld. This is very important now [4], because of its increasing applications in new electrotechnology which is used in agriculture and food industry [5]. Dielectric measurements also have uses in

Pramana – J. Phys., Vol. 83, No. 4, October 2014 579 S Sahoo, T R Middya and S K Sit package design, process control and physical chemical analysis [5]. Dielectric relaxation data from microwave absorption studies are expected to throw light on various molecular associations because of the capacity of microwaves to detect weaker molecular association [6]. There are several methods to study dielectric relaxation to get relaxation time τjk, τj or τk and dipole moment μjk,μj or μk of polar solutes jk, j or k either of pure liquids or binary polar–nonpolar liquid mixtures. The μjks of nonassociating liquids are better represented by the Onsager equation [7]. Kirkwood [8] and Fröhlich [9] equations, on the other hand, agree well in associating liquids with the predetermined value of correlation factor g related to the structure of liquids. Of the above, Debye theory [10]which is very simple and straightforward is invariably used to calculate τjk and μjk of binary polar–nonpolar liquid mixture. It is very easy to measure the conductivity of a solution in the laboratory by a Klystron or a radio frequency Hartley oscillator. The existence of free ions in the polar–nonpolar liquid mixture under radio frequency electric field is respon- sible for conductivity in the solution [1]. In the GHz region, the conductivity is involved with the bound molecular charge of the polar–nonpolar liquid mixture. Kumar et al [11] measured the real εij k and imaginary εij k parts of complex high-frequency relative permit- ∗ tivity εij k of binary (jk) polar mixtures of ethanol (EtOH) and N-methyl acetamide (NMA) for different mole fractions xj s of EtOH and weight fractions wjks of the binary polar mixtures at 25, 30, 35 and 40◦C under 9.90 GHz electric field. They used Gopalakrishna’s single-frequency concentration variation method [12] to measure τjk and μjk to get information on the associational behaviour of the ternary mixture as well as molecular dynamics of the systems from the standpoint of Eyring’s rate theory [13]. We, however, thought to extensively study the aforesaid systems in terms of the measured real ∗ σij k and imaginary σij k parts of high-frequency complex conductivity σij k under the same state of molecular environment [11] within the framework of Debye model for binary polar–nonpolar liquid mixture. Both the polar molecules are associative in nature, where Onsager equation [7] may be a better choice due to the strong intermolecular interactions as a result of short-range forces produced by hydrogen bonding in solution. But the resulting expression cannot be solved easily because of the presence of the quadratic ∗ term εij k . Earlier, an extensive study was undertaken [4] on the binary mixture of N,N- dimethyl acetamide (DMA) and acetone (Ac) in C6H6, using Debye–Smyth model and employing conductivity measurement technique at 9.88 GHz electric field. However, no such rigorous study has been made so far, to check the applicability of Debye model for the (EtOH + NMA) binary polar mixture dissolved in C6H6 in terms of σij k s of solution under GHz electric field. Alcohols and amides are, however, standard examples for multimodal dielectric spectra, reflecting non-Debye behaviour. In particular, near 10 GHz, there is a strong secondary relaxation mode, in addition to primary Debye process. Nevertheless, Debye relaxation is equally applicable for amide and alcohol binary polar mixture [14] dissolved in nonpolar solvent under X band electric field in formulating adequate model for obtaining the information about the relaxation process. NMA, the nonaqueous protophilic H-bond donor solvent having high value of dielectric constant and dipole moment, constitutes the basis of protein and enzymes. NMA and EtOH are good constituents of binary polar mixture to form solute–solute (dimer) and solute– solvent (monomer) molecular associations. Ethanol (EtOH), an amphiprotic hydroxylic solvent, which behaves like a polymer due to the formation of hydrogen bonding among themselves has wide applications in industry. Earlier, a study [15] was undertaken on

580 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide

NMA in C6H6 at different temperatures for studying the molecular dynamics through the relaxation phenomenon using conductivity technique. The solvent EtOH, on the other hand, shows double relaxation times τ2 and τ1, due to the rotation of the whole and the ﬂexible part of the molecule under GHz electric ﬁeld from single-frequency measurement [16]. It is worthwhile to see how far the conductivity technique is applicable within the framework of Debye model for ternary polar–nonpolar liquid mixture like earlier [4]. The purpose of the present paper is to study molecular dynamics of the system in terms of τjk,τj and τk as well as μjk,μj and μk using conductivity technique and to see how far they agree with the reported τs from Gopalakrishna’s method [13]orτs from double relaxation phenomenon along with associational behaviour involved in them. Moreover, the normal alcohols exhibit double relaxation times τ2 and τ1 at all the frequencies of

1.36 1.36 ) ) 1.34 1.34 -1 -1 m m -1 -1 I(e) (ohm (ohm 1.32 1.32 " ijk " ijk I(d) m I(b) II(e) 1.3 1.3 II(a) II(d) II(b) I(c) II(c)

1.28 1.28 System (I):- (NMA+ EtOH) System (II):- in benzene at 25 C (NMA+ EtOH) Imaginary part of conductivity 1.26 for various x of EtOH 1.26 j Imaginary part of conductivity in benzene at 30 C for various x of EtOH j

1.24 1.24 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Real part of conductivity , (ohm-1m-1) Real part of conductivity , (ohm-1m-1) ijk ijk

1.34 1.34 ) 1.32 ) 1.32 -1 -1 m m -1 -1 III(b) (ohm 1.3 (ohm 1.3 " ijk III(e) " ijk

III(d) III(a) IV(e) IV(a) III(c) IV(d) 1.28 1.28 IV(b) IV(c)

1.26 1.26 System (III):- System (IV):- (NMA+ EtOH) (NMA+ EtOH) in benzene at 35 C in benzene at 40 C 1.24 1.24 Imaginary part of conductivity for various x of EtOH Imaginary part of conductivity for various x of EtOH j j

1.22 1.22 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 Real part of conductivity , (ohm-1m-1) Real part of conductivity , (ohm-1m-1) ijk ijk Figure 1. The linear plot of σij k against σij k of (EtOH + NMA) polar mixture in C6H6 for different xj of EtOH and temperature under 9.88 GHz electric ﬁeld. (I) , (II) , (III) , (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0xj of EtOH, respectively.

Pramana – J. Phys., Vol. 83, No. 4, October 2014 581 S Sahoo, T R Middya and S K Sit

24.33, 9.25 and 3.00 GHz electric ﬁeld [17]. They also show material property at three different frequencies [17].

2. Experimental procedure

N-methyl acetamide (NMA), ethanol (EtOH) and C6H6 are all good-quality samples puri- ﬁed and distilled through a long vertical fractionating column [11]. The middle fraction of the sample was collected and then mixed for preparing the binary polar mixture of weight fractions, wjks dissolved in the non-polar solvent, C6H6. The X-band microwave was used to measure εij k , εij or εik and εij k , εij or εik at different wjks and at 25, 30, 35 ◦ and 40 C, respectively [11]. The measured εij k and εij k are accurate within ±0.5% and ±1.67%, respectively.

1.36 1.36 ) ) 1.34 -1 1.34 -1 m I(a) m -1 -1

(ohm II(a) (ohm 1.32

1.32 " ijk ijk "

II(e) 1.3 1.3 I(d) I(c) I(e) II(c) 1.28 I(b) 1.28 System (I):- II(b) (NMA+ EtOH) System (II):- (NMA+ EtOH) 1.26 in benzene at 25 C Imaginary part of conductivity 1.26 Imaginary part of conductivity for various x of EtOH in benzene at 30 C j for various x of EtOH j

1.24 1.24 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Weight fraction w Weight fraction w jk jk

1.34 1.34 ) ) 1.32 1.32 -1 -1

m IV(a) m III(a) -1 -1 (ohm (ohm 1.3 1.3 " ijk ijk " III(e)

1.28 1.28 IV(c) IV(e) III(c) III(b) 1.26 1.26 IV(b) System (III):- System (IV):- (NMA+ EtOH) (NMA+ EtOH) Imaginary part of conductivity Imaginary part of conductivity 1.24 1.24 in benzene at 35 C in benzene at 40 C for various x of EtOH for various x of EtOH j j

1.22 1.22 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Weight fraction w Weight fraction w jk jk −1 −1 Figure 2. The variation of imaginary part of conductivity, σij k ( m ) against weight fractions wjks of binary polar mixture (EtOH + NMA) dissolved in C6H6 for different xj of EtOH and temperature under 9.88 GHz electric ﬁeld. (I) , (II) , (III) , (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0xj of EtOH, respectively.

582 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide

3. Theoretical formulations

∗ The σij k due to displacement current of a binary polar liquid mixture dissolved in nonpolar solvent(i) for given wjks of solute is [4] ∗ σij k = σij k + jσij k , (1) where σij k (= ωε0εij k ) and σij k (= ωε0εij k ) are just functions of permittivity in the real σ ∗ ε∗ = ε − jε and imaginary parts√ of complex conductivity ij k related to ij k ij k ij k , j being a complex number = − 1. The total hf conductivity σij k of the ternary solution is √ √ 2 2 2 2 σij k = ω0 (ij k + ij k ) = (σij k + σij k ), (2)

0.04 0.04

0.035 0.035 ) ) -1 0.03 -1 0.03 m I(a) m -1 -1 II(a) (ohm 0.025 (ohm 0.025 ijk " " ijk y y t t i I(c) i II(c) v v i i t 0.02 t 0.02 c c u I(b) u d d II(b) n n o I(d) o c c II(d) f 0.015 f 0.015 o o t t r r a a p p l l a 0.01 a 0.01 e e R I(e) R II(e) System (I):- System (II):- (NMA+ EtOH) (NMA+ EtOH) 0.005 0.005 in benzene at 25 C in benzene at 30 C for various x of EtOH for various x of EtOH j j 0 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Weight fraction w Weight fraction w jk jk

0.035 0.035

0.03 0.03 ) ) -1 III(a) -1

m IV(a) 0.025 m 0.025 -1 -1 (ohm III(c) (ohm " ijk ijk " IV(c) 0.02 0.02

III(b) IV(b) III(d) 0.015 0.015 IV(d)

0.01 0.01 Real part of conductivity III(e) conductivity of part Real System (III):- IV(e) System (IV):- 0.005 (NMA+ EtOH) 0.005 (NMA+ EtOH) in benzene at 35 C in benzene at 40 C for various x of EtOH for various x of EtOH j j 0 0 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035

Weight fraction w Weight fraction w jk jk −1 −1 Figure 3. The variation of real part of conductivity σij k ( m ) against weight fractions wjks of binary polar mixture (EtOH + NMA) dissolved in C6H6 for different xj of EtOH and temperature under 9.88 GHz electric ﬁeld. (I) , (II) , (III) , (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0xj of EtOH, respectively.

Pramana – J. Phys., Vol. 83, No. 4, October 2014 583 S Sahoo, T R Middya and S K Sit

9 where ω = 2πf, f is the frequency of the electric ﬁeld = 9.90 × 10 Hz and ε0 = −12 −1 absolute permittivity of free space = 8.854 × 10 F · m .Ineqs(1)and(2)ofσij k s, there are no free ions or electrons in the solution and the displacement current is the only factor to contribute to the total conductivity σij k of the ternary mixture. Again, σij k is related to σij k by

σij k = σ∞ij k + (1/ωτjk)σij k , (3) where τjk is the relaxation time of binary polar mixture at wjk → 0 for constant conductivity σ∞ij k of the solution. Differentiation of eq. (3) with respect to σij k yields

dσij k /dσij k = 1/ωτjk. (4) The straight line of eq. (4)ofσij k –σij k (ﬁgure 1) represents a convenient method to obtain τjk at wjk → 0. The ratio of slopes of σij k –wjk and σij k –wjk curves as shown

−12 × 10 10

(III) 7

jk (II) (III) 5

(IV) 4 (I) (I) (II)

3 (IV)

1 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 x j

Figure 4. The variation of τjks of binary polar mixture (EtOH + NMA) in C6H6 with mole fraction xj of EtOH at different temperatures under 9.90 GHz electric ﬁeld. (I) ; at 25◦C, (II) ; at 30◦C, (III) ; at 35◦C and (IV) ; at 40◦C for ratio of slopes (—-) and Murthy et al (·····), respectively.

584 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide × from jk × τ jk jk ) τ 5 μ curves curves from ) j ;(b) j x j x – x − – 30 12 jk 10 ), estimated (τ 4 10 and ) ) = j k x x k jk − τ τ jk + j (μ ) curve of eq. ( x j s of EtOH and temperatures under 9.90 ij k of j σ (τ x − in Average k ij k a, b, c σ ,τ j ,τ jk ) GK method in psec from eq. ( 4 , coefficients ,τ ) j k x ,τ k τ ), linear slope of ( jk τ 5 + )Fromeq.( j in psec psec from 5 x k j (τ = jk τ curves of eq. ( jk )) From eq. ( )τ 4 w ij k σ − − ij k σ ij k Linear slope of Estimated and )) curve (eq. ( jk 5 w )/ )(σ jk − jk w w ij k 0(eq.( from GK method, average − σ − jk → ij k τ ij k (σ jk (σ Ratio of slopes Reported Coefficients of: (a) w NMA binary polar mixture dissolved in benzene for different mole fractions, + ), reported 4 Ratio of slopes of 0.50.71.0 4.76170.5 3.95160.7 5.61491.0 3.94043 4.23129 4.40410.5 5.30085 5.64880.7 3.38 7.67231.0 4.07 2.86 4.12133 4.08 4.44484 7.17590.5 3.80 5.67301 5.41670.7 3.65 3.03 9.44891.0 2.85 3.81 2.10 3.59 4.1693 3.90 2.95 4.48543 5.6742 3.62 5.8901 4.27 4.8430 2.83 2.24 3.71 9.9228 2.97 3.71 2.86 (b) 10.69 3.50 4.40537 –6.30 1.70 2.77 4.57772 3.86 2.39 3.58 6.35507 3.40 2.83 2.73 2.88 3.32 (b) 2.10 3.61 13.64 1.62 3.41 –9.36 3.65 2.63 2.60 3.51 5.70 2.53 4.10 3.51 1.70 3.32 (b) 9.03 2.43 6.99 –9.28 2.55 2.18 1.62 (b) 14.23 –13.26 5.63 )and( )ofEtOH sofEtOHin 5 5 j Mole fraction of x Table 1. GHz electric field. eqs ( eq. ( C) the mixture at 25 0.0 2.8287 3.55458 5.68 4.52 4.13 5.68 (a) 4.98 –7.02 5.50 30 0.035 3.4268 0.040 3.51539 1.6570 0.0 4.69 3.63046 4.57 4.6206 9.70 4.02 3.84528 4.43 4.69 3.48 3.91 (a) 4.18 –4.36 4.18 2.61 9.70 3.80 (a) 8.94 –21.26 14.73 3.48 (a) 3.14 –0.25 –0.93 ◦ Temp. + + + + 6 6 6 6 H H H H 6 6 6 6 System ( EtOH EtOH EtOH EtOH NMA inC 0.3 11.3476 3.38552 1.42 4.75 4.48 4.83 NMA inC 0.3NMA inC 10.9883 0.3NMA inC 3.52548 8.4507 0.3 1.46 3.61139 4.56 7.6545 1.90 4.37 3.49883 4.45 3.91 2.10 4.26 4.59 7.30 4.15 2.92

Pramana – J. Phys., Vol. 83, No. 4, October 2014 585 S Sahoo, T R Middya and S K Sit in ﬁgures 2 and 3 may be a better choice to eliminate polar–polar interactions at higher concentrations in a given solvent dσij k dσij k 1 = , (5) dwjk w dwjk w ωτjk jk→0 jk→0 where τjk–xj curves at different temperatures are shown in ﬁgure 4. The constituent polar molecules mixed in appropriate proportions yield average τjk as

τjk = τj xj + τkxk, (6) where xj and xk are mole fractions of ethanol (j)andNMA(k) having relaxation times τj and τk, respectively. All the τs along with reported values are shown in table 1.

1.36 1.36

1.34 1.34 I(a) ) ) -1 -1 II(a) m m

-1 1.32 -1 1.32 (ohm (ohm ijk ijk II(e) 1.3 1.3 I(d) I(e) I(c) II(c) 1.28 1.28 I(b) Total conductivity Total conductivity II(b) System (I):- System (II):- (NMA+ EtOH) 1.26 1.26 (NMA+ EtOH) in benzene at 25 C in benzene at 30 C for various x of EtOH for various x of EtOH j j

1.24 1.24 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Weight fraction w Weight fraction w jk jk

1.34 1.34

1.32 1.32 IV(a) )

) III(a) -1 -1 m m

-1 1.3

-1 1.3 (ohm (ohm ijk ijk

1.28 1.28 III(c) IV(c) IV(e) III(e)

1.26 1.26 III(b) IV(b) Total conductivity Total conductivity System (III):- System (IV):- (NMA+ EtOH) (NMA+ EtOH) 1.24 1.24 in benzene at 35 C in benzene at 40 C for various x of EtOH for various x of EtOH j j

1.22 1.22 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 Weight fraction w Weight fraction w jk jk − − Figure 5. The variation of total conductivity, σij k ( 1 m 1) against weight fractions, wjks of binary polar mixture (EtOH + NMA) dissolved in C6H6 for different xj of EtOH and temperature under 9.88 GHz electric ﬁeld. (I) , (II) , (III) , (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0xj of EtOH, respectively.

586 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide

By differentiating eq. (3) with respect to wjk and assuming σij k ≈ σij k in the high- frequency region at wjk → 0, one gets 1 dσij k β = . (7) ωτjk dwjk wjk→0

Here β is the slope of σij k –wjk curve as shown in ﬁgure 5. The σij k of a binary polar–nonpolar liquid mixture of wjk at T Kisgivenby[3] Nρ μ2 2 ij k jk ω τjk σ = ε ij k + 2 ε∞ij k + 2 wjk. (8) ij k 2 2 0 27MjkKBT 1 + ω τjk

Differentiating eq. (8) with respect to wjk and comparing with eq. (7)forwjk → 0, one gets

1/2 27MjkKBTβ μjk = , 2 (9) Nρi(εi + 2) ωb 2 2 where b is the dimensionless parameter = 1/(1 + ω τjk) and Mjk is the molecular weight of the binary polar mixture = Mj xj + Mkxk. The other terms in eq. (9) carry usual signiﬁcance [4]. The μjk–xj and μjk–t curves are sketched in ﬁgures 6 and 7, respectively along with theoretical dipole moment (μtheo) from bond angles and bond

−29 × 10 1.5

1.4

1.3

1.2

1.1 (III)

jk 1 (III)

0.9 (I) (I) (II) 0.8 (II)

0.7

0.6

0.5 -0.2 0 0.2 0.4 0.6 0.8 1 1.2 x j

Figure 6. The variation of μjks of binary polar mixture (EtOH + NMA) in C6H6 with mole fraction xj of EtOH at different temperatures under 9.90 GHz electric ﬁeld. (I) ; at 25◦C, (II) ; at 30◦C, (III) ; at 35◦C and (IV) ; at 40◦C for ratio of slopes (—) and Murthy et al (···) respectively.

Pramana – J. Phys., Vol. 83, No. 4, October 2014 587 S Sahoo, T R Middya and S K Sit

−29 × 10 1.5

1.4

1.3

1.2 (I) (I) 1.1 (IV)

jk 1 (IV)

(II) 0.9 (III) (II) (III) 0.8

0.7 (V) 0.6 (V)

0.5 24 26 28 30 32 34 36 38 40 42 t in C

Figure 7. The variation of dipole moment μjk in Coulomb·metre (C·m) with temper- ◦ ature t in C for different xj of EtOH of (EtOH + NMA) binary mixture under 9.90 GHz electric field. (I) ; , (II) ; , (III) ; , (IV) ; and (V) ; for 0.0, 0.3, 0.5, ___ 0.7 and 1.0xj of EtOH from ratio of slopes ( ) and linear slope (···) methods, respectively. moments in figure 8. All the μs are placed in table 2. The molecular dynamics of the polar mixture are ascertained from linear plot of ln(τjkT)vs. 1/T curve of figure 9 assuming the rotation of the molecule under gigahertz electric field as a rate process [13]. The values of Fτ , Sτ and Hτ are given in table 3.

4. Results and discussion

The normalized measured σij k datapoints within the error bar at different wjksof(EtOH + NMA) mixture for various xj s of EtOH are utilized to estimate τsandμs dissolved in nonpolar solvents C6H6 for different experimental temperatures at 9.90 GHz electric field by adopting MATLab programming and using least squares fitting technique. τsare also estimated from the slope of linear relation σij k against σij k of figure 1 at different xj s of EtOH and experimental temperatures. The graphs are, however, perfectly linear and the correlation coefficient r of straight line of eq. (3)is−1 ≤ r ≤+1. Neverthe- less, they are found to deviate from linearity in the higher concentration region for system II (⎯•⎯) at 25, 30, 35 and 40◦C, respectively. This indicates the validity to use the ratio of slopes of σij k –wjk and σij k –wjk curves at wjk → 0 to estimate τ as shown in figures 2 and 3, where polar–polar interactions are almost eliminated. The straight lines in figure 1 are parallel indicating their same polarity [18] in solvent benzene as evident

588 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide

(i) O H 4.86 C.m 10.33 1.5 4.33 C.m C.m 15.44 C.m CH CH 3 C N 3 C.m 14.66 1.23 1.5 2.13 C.m C.m C.m C.m

(ii) H 1.30 C.m 3.40 C.m CH3 C O 1.23 3.33 C.m C.m ° H 105 H

(iii) CH3 H C H O CH 105° 3 jk = = ° C 14.71 108.64 NMA H N EtOH O k CH j 3 H

(iv) H

CH3 C O H 105° H

105° H H O C CH3

Figure 8. Theoretical dipole moments μtheos from available bond angles and bond moments (multiples of 10−30 C·m) along with solute–solvent, solute–solute and self- molecular associations: (i) NMA–C6H6, (ii) EtOH–C6H6, (iii) EtOH–NMA and (iv) EtOH–EtOH self-association.

Pramana – J. Phys., Vol. 83, No. 4, October 2014 589 S Sahoo, T R Middya and S K Sit from τsoftable1. The straight lines for xj = 0.0 (I) and xj = 0.3 (II) of EtOH in figure 1 are flat to yield higher τs, whereas almost constant τs of smaller magnitude are found to occur for xj = 0.5–1.0 of ethanol when compared with the results available for −1 −1 binary polar liquids [11]. As evident from figures 2 and 3, the curves of σij k in m against wjk are parabolic like σij k –wjk curves. Figures show that σij k and σij k exhibit larger magnitudes at xj = 0.0 for different wjks of solutes and found to decrease gradually up to xj = 1.0 of EtOH for all the temperatures. This is probably due to the maximum and minimum polarization of NMA and EtOH, because of the high and low absorption of high-frequency electric energy. The dipole moments μjks in Coulomb·metre (C·m) are estimated in terms of slopes βsofσij k –wjk curves and dimensionless parameter bs −1 −1 from eq. (9). The total high-frequency conductivity σij k in m due to displacement current in the mixture are plotted against wjk at different experimental temperatures to get parabolic curves as shown in figure 4. The curves are similar to σij k –wjk curves ∼ of figure 2 validating the approximation σij k = σij k in eq. (3). The estimated τjksare

Table 2. Slopes of (σij k –wjk) curve of eq. (7), dimensionless parameters b, estimated and reported dipole moments μjk in Coulomb·metre (C·m), average dipole moments μjk = μj xj + μkxk, theoretical dipole moments μtheo from bond angles and bond moments of of EtOH + NMA binary polar mixture dissolved in benzene for different mole fractions xj s of EtOH and temperatures under 9.90 GHz electric ﬁeld.

Mole fraction Slopes of Dimensionless parameters xj sof (σij k –wjk) bbb 2 2 2 2 2 2 Temp EtOH in curve = 1/(1+ τjk) = 1/(1+ τjk) =1/(1+ τjk) System (◦C) the mixture (eq. (7)) (eq. (5)) (eq. (4)) (eq. (6))

(I) EtOH 25 (a) 0.0 8.3265 0.8890 0.9267 0.8890 + NMA (b) 0.3 4.8702 0.9923 0.9197 0.9171 in C6H6 (c) 0.5 5.2870 0.9577 0.9395 0.9341 (d) 0.7 7.8651 0.9398 0.9471 0.9495 (e) 1.0 4.2712 0.9693 0.9657 0.9693

(II) EtOH 30 (a) 0.0 13.1376 0.9216 0.9252 0.9216 + NMA (b) 0.3 8.8667 0.9918 0.9255 0.9441 in C6H6 (c) 0.5 5.4181 0.9510 0.9444 0.9573 (d) 0.7 10.9942 0.9695 0.9517 0.9690 (e) 1.0 4.2629 0.9832 0.9699 0.9832

(III) EtOH 35 (a) 0.0 4.3158 0.7331 0.9294 0.7331 + NMA (b) 0.3 8.2726 0.9862 0.9288 0.8291 in C6H6 (c) 0.5 6.8496 0.9810 0.9455 0.8883 (d) 0.7 10.5100 0.9670 0.9528 0.9389 (e) 1.0 4.4306 0.9889 0.9720 0.9889

(IV) EtOH 40 (a) 0.0 14.0811 0.9552 0.9367 0.9552 + NMA (b) 0.3 7.0971 0.9832 0.9246 0.9680 in C6H6 (c) 0.5 5.9853 0.9699 0.9510 0.9755 (d) 0.7 7.5446 0.9591 0.9545 0.9820 (e) 1.0 3.9062 0.9899 0.9758 0.9899

590 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide

Table 2. (Continued.)

Estimated dipole Theoretical moments μjk × 1030 Reported Average dipole moment 30 30 in C·m μjk × 10 dipole moment μtheo × 10 Eqs (5)& Eqs(4)& Eqs(6)& in C·m μjk = (μj xj +μkxk) from bond angles System (9)(9)(9) ×1030 in C·m and bond moments

(I) EtOH 11.27 11.04 11.27 12.47 11.27 15.44 + NMA 7.69 7.99 10.46 9.73 in C6H6 7.81 7.89 9.93 8.71 14.71 9.17 9.14 9.39 7.68 6.14 6.15 8.57 5.80 6.14 3.40

(II) EtOH 14.09 14.07 11.16 12.07 14.09 15.44 + NMA 10.52 10.89 10.40 11.71 in C6H6 8.04 8.07 9.89 10.13 14.71 10.82 10.92 9.37 8.55 6.17 6.21 8.58 5.77 6.17 3.40

(III) EtOH 9.18 8.15 12.62 11.84 9.18 15.44 + NMA 10.33 10.64 11.19 8.33 in C6H6 9.02 9.19 10.35 7.77 14.71 10.74 10.82 9.60 9.21 6.36 6.41 8.62 5.70 6.36 3.40 (IV) EtOH 14.71 14.71 11.14 11.74 14.71 15.44 + NMA 9.71 10.00 10.44 12.11 in C6H6 8.59 8.68 9.96 10.38 14.71 9.25 9.27 9.46 8.64 6.04 6.08 8.69 5.63 6.04 3.40 plotted against xj s of ethanol at different temperatures as seen in figure 5. τs from figure 1 and table 1 are found to increase from xj = 0.0 to 0.3 of EtOH and then decrease gradually indicating the solute–solute (dimer) or solute–solvent (monomer) molecular association up to xj = 0.0–0.3 and thereafter, rupture of dimer occurs to facilitate solute– solvent (monomer) molecular association up to xj = 1.0 of EtOH as observed in [11]. The estimated τs from eq. (4) are in excellent agreement with the reported τs[11] due to Gopalakrishna method [13]. The plot of estimated τsagainstxj from eq. (5)offigures2 and 3 is however, concave in nature. This is probably due to the occurrence of solute– solvent (monomer) molecular association at higher concentration due to break-up of solute–solute molecular association as polar–polar interactions are almost eliminated with the use of eq. (5). The average τjks of the constituent binary polar mixtures are calculated using simple mixing rule to place them in table 1. All the τs agree with the reported τ [11] due to Gopalakrishna method [13], signifying the applicability of both the methods. It is evident from table 1 that τs in general from eq. (4) decrease with increase in temperature [11] due to faster rotation according to Debye relaxation unlike eq. (5). The interaction of the adjacent polar groups of binary mixture hindering molecular rotation probably leads to departure from Debye behaviour. The estimated μjks from both the methods are plotted against xj s of ethanol at different temperatures as shown in figure 6 to get the parabolic curves. Unlike system (III), all the curves are concave and in excellent

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-19.5

-20

(I) (II) (I) -20.5 (III)

T) (IV) jk (IV) (III) ln( (V) -21

(II)

(V) -21.5

-22 3.15 3.2 3.25 3.3 3.35 3.4 1/T −3 × 10

Figure 9. Linear plot of ln(τjkT)against1/T curve of (EtOH + NMA) binary polar mixture in C6H6 under 9.90 GHz electric field. (I) ; , (II) ; , (III) ; , (IV) ; and (V) ; for 0.0, 0.3, 0.5, 0.7 and 1.0xj of EtOH from ratio of slopes (—) and linear slope (······) methods, respectively. agreement with each other. This probably signifies the solute–solute (dimer) associations for larger τs happening initially and then, rupture of dimer takes place to favour solute– solvent molecular association up to xj = 1.0 for smaller τs according to eq. (9). This type of behaviour further demands little dependence of τ to estimate μ rather than slope β of σij k –wjk curve as evident from eq. (9). The variations of μjk against temperature (t)in ◦C are plotted in figure 7 to show the highest asymmetric nature due to associative pair (NMA+EtOH) in benzene for all xj s of EtOH except xj = 0 with the rise of temperature probably due to stretching of bond angles. A fraction of associative pair will break as EtOH or NMA with the increase in temperature to yield smaller μ for monomer. The theoretical dipole moment (μtheo) of the polar molecule is estimated from the available bond angles and bond moments of N ← CH3,C⇐ O, CH3 ← C, C ← N, C → OandO→ Hof2.13×10−30, 10.33×10−30,1.23×10−30,1.5×10−30, 3.334×10−30 and 1.30×10−30 C·m making an angle 105◦ with the bond axis as seen in table 2.The solute–solvent (monomer) and solute–solute (dimer) associational behaviours of the polar molecules are plotted in figure 8. The solute–solvent (monomer) association may occur due to the interaction of the π delocalized electron cloud in benzene ring and the frac- tional positive charge (δ+) at the site of N and C atoms of NMA or H atom of –O–H group

592 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide in EtOH. Solute–solute (dimer) molecular association occurs due to the interaction of two adjacent atoms of slightly opposite polarity of diverse polar entity, as shown in ﬁgure 8iii. Self-association may also occur between two similar polar molecules (ﬁgure 8iv). Oppo- site polarity develops between two atoms of a substituent polar group due to the inherent inductive, mesomeric and electromeric effects in them [4]. The molecular dynamics of the polar mixtures are ascertained from the standpoint of rate theory of Eyring’s equation [13].

− Sτ/R ln(tjkT)= ln(Ae ) + Hτ /RT , (10) where Fτ= Hτ –T Sτ . Equation (10) is a straight line of ln(τjkT)vs.1/T (ﬁgure 9) to yield thermodynamic energy parameters such as free energy of activation, ( Fτ ), enthalpy of activation ( Hτ ) and entropy of activation ( Sτ ). The values of Fτ are higher and lower at xj = 0.0 and 0.3, respectively, although they exhibit almost constant values for 0.5, 0.7 and 1.0xj of EtOH, respectively, as seen in table 3. This may be

Table 3. Intercepts and slopes ln(τjkT)against1/T curve, Hτ in kJ/mole, Fτ in kJ/mole and Sτ in J/mole·K treating the rotation of the binary polar mixture as γ the rate process, γ = ( Hτ / Hη), Debye factor τjkT/η, Kalman factor τjkT/η and coefﬁcients a, b, c of μjk– t curves of EtOH + NMA binary polar mixture dissolved in benzene for different mole fractions xj of EtOH and temperatures under 9.90 GHz electric ﬁeld.

System Mole fraction Temp. Intercepts and Hτ Fτ Sτ ◦ xj of EtOH ( C) slopes of ln(τjkT)(kJ/mole) (kJ/mole) (J/mole·K) in the mixture vs. 1/T × 103,eq.(5)

EtOH + NMA 0.0 25 −23.5827 1030.3690 8.5624 8.8207 −0.8667 in C6H6 30 8.5283 0.1125 35 10.571 −6.5214 40 8.1181 1.4193 EtOH + NMA 0.3 25 −11.6179 −2981.6596 −24.778 5.3876 −101.2256 in C6H6 30 5.5898 −100.2226 35 6.3982 −101.2202 40 6.8043 −100.9007 EtOH + NMA 0.5 25 −26.0835 1607.6311 13.359 7.5352 19.5445 in C6H6 30 7.897 18.0277 35 6.8198 21.2326 40 7.5805 18.4631 EtOH + NMA 0.7 25 −23.2989 786.2578 6.5338 7.9953 −4.9043 in C6H6 30 7.2741 −2.4432 35 7.5415 −3.2719 40 7.9956 −4.6703 EtOH + NMA 1.0 25 −31.9648 3285.1622 27.300 7.1216 67.7117 in C6H6 30 6.5051 68.6290 35 6.1136 68.7860 40 6.1294 67.6368

Pramana – J. Phys., Vol. 83, No. 4, October 2014 593 S Sahoo, T R Middya and S K Sit

Table 3. (Continued.)

System γ from ln Hη = ( Hτ /γ ) Debye factor Kalman factor Coefﬁcients of γ (τjkT)vs.lnη (kJ/mole) τjkT/η ×106 τjkT/η μjk–t curve curve from abc eqs (11)&(5)

EtOH + NMA 0.77 11.12 2.82 5.12 36.57 −1.65 0.03 in C6H6 2.52 4.50 5.64 9.95 2.17 3.78 EtOH + NMA −2.71 9.14 0.71 7.86 −29.62 2.36 −0.03 in C6H6 0.78 6.98 1.10 7.76 1.31 7.57 EtOH + NMA 1.52 8.79 1.68 7.95 −0.56 0.50 −0.01 in C6H6 1.96 9.56 1.30 6.58 1.76 9.14 EtOH + NMA 0.72 9.07 2.02 2.53 −22.29 2.04 −0.03 in C6H6 1.53 1.88 1.73 2.09 2.07 2.46 EtOH + NMA 2.98 27.30 1.42 3.40 2.66 0.23 −0.01 in C6H6 1.13 3.04 0.99 3.02 1.01 3.42 due to the fact that the dielectric relaxation process involves the rotation of the participat- ing polar constituents to a different extent. Enthalpies of activation ( Hη) for the viscous flow of the solvent are higher for all the systems except xj = 0.5 of EtOH. Difference in enthalpy of activation for dielectric relaxation and viscous flow processes indicates different types of bonding and breaking of bonds to a different extent. Entropy of a system, on the other hand, measures its orderness. Entropy of activation ( Sτ ) are positive for xj = 0.5 and 1.0 of ethanol, unlike other systems. The negative values of Sτ indicate that the activated states are more ordered than the normal state, whereas reverse is true for the negative Sτ . The estimated values of γ indicate the solvent environment around the solute molecule from the relation [3] γ τjk = Aη /T, (11) where γ = Hτ / Hη is the slope of ln(τjkT)vs.lnη linear relation having coefficient of viscosity η of solvent benzene. For the system xj = 0.3, γ is negative and behaves as solid phase rotator. The other systems do not behave as solid phase rotator as γ > 0.55 [18]. The different behaviours of EtOH + NMA mixture for various xj s of ethanol may be attributed to the solute–solute association of polar mixtures in different molecular γ environment. Both the Debye factor (τjk/η) and Kalman factor (τjkT/η ) are found to be almost constant with temperature. This indicates that the relaxation mechanism could be better represented by using both Debye and Kalman equations, respectively.

594 Pramana – J. Phys., Vol. 83, No. 4, October 2014 Dielectric relaxation of ethanol and N-methyl acetamide

5. Conclusions

The normalized measured conductivity datapoints within the error bar are analysed by adopting MATLab programming and using least squares ﬁtting procedure. The structures of the polar liquid molecules EtOH and NMA dissolved in benzene as well as their molecular association are inferred from high-frequency conductivity measurement of solution of 9.90 GHz and 25, 30, 35 and 40◦C temperatures using Debye theory. The measurement technique proposes the simultaneous estimation of μ in terms of τ by using ratio of slopes of σij k –wjk and σij k –wjk curves at wjk → 0 as well as linear slope of σij k –σij k curves. The observations are in accordance with the reported ones validating the proposed method. Solute–solute and solute–solvent molecular interactions in the ternary mixtures are proposed on the basis of a plot of τ and μ against xj of EtOH and associated aspects are displayed from the standpoint of μtheo. Molecular dynamics of liquid mixture are also ascertained using Eyring rate theory equation. This reveals that relaxation mechanism follows both Debye and Kalmann equations.

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