Dielectric relaxation of ethanol and N-methyl acetamide polar mixture in C 6 H 6 at 9.90 GHz

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1 PRAMANA c Indian Academy of Sciences Vol. 83, No. 4 journal of October 2014 physics pp Dielectric relaxation of ethanol and N-methyl acetamide polar mixture in C 6 6 at 9.90 Gz S SAOO 1,TRMIDDYA 2 and S K SIT 3, 1 Department of Electronics & Instrumentation Engineering, Dr. Meghnad Saha Institute of Technology, P.O. Debhog, aldia, Purba Medinipore , India 2 Department of Physics, Jadavpur University, Kolkata , India 3 Department of Physics, Dr. Meghnad Saha Institute of Technology, P.O. Debhog, aldia, Purba Medinipore , India Corresponding author. swagatdebmsit@yahoo.co.in MS received 30 March 2013; revised 11 February 2014; accepted 25 February 2014 DOI: /s ; epublication: 27 September 2014 Abstract. Debye relaxation times ( ) ( ) τ jk and dipole moments μjk of binary (jk) polar mixtures of ethanol (EtO) and N-methyl acetamide (NMA) dissolved in benzene(i) are studied by studying ( ) conductivity of solution at 9.90 Gz ( for different ) temperatures, different mole fractions xj of ethanol and different weight fractions wjk of the mixtures, respectively. The variation of τ jk x j from linear slope of imaginary (σ ) against real (σ ) part of total conductivity (σ ) curve reveals solute solute (dimer) or solute solvent (monomer) molecular associations up to x j = and thereafter, solute solvent molecular associations. τ jk s from the ratio of slopes of σ w jk and σ w jk curves exhibit solute solvent molecular association for all x j s which are consistent with the μ jk x j 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 (μ theo ) are also calculated to predict associational aspects. Keywords. Relaxation time; dipole moment; solute solute association; solute solvent association; hf conductivity. PACS Nos Gm; Le; 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 (Gz) 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

2 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 τ jk, τ j or τ k and dipole moment μ jk,μ j or μ k of polar solutes jk, j or k either of pure liquids or binary polar nonpolar liquid mixtures. The μ jk s 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 τ jk and μ jk 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 artley oscillator. The existence of free ions in the polar nonpolar liquid mixture under radio frequency electric field is responsible for conductivity in the solution [1]. In the Gz region, the conductivity is involved with the bound molecular charge of the polar nonpolar liquid mixture. Kumar et al [11] measured the real ε and imaginary ε parts of complex high-frequency relative permittivity ε of binary (jk) polar mixtures of ethanol (EtO) and N-methyl acetamide (NMA) for different mole fractions x j s and weight fractions w jk s of the binary polar mixtures at 25, 30, 35 and 40 C under 9.90 Gz electric field. They used Gopalakrishna s single-frequency concentration variation method [12] to measure τ jk and μ jk 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 σ and imaginary σ parts of high-frequency complex conductivity σ 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 ε. Earlier, an extensive study was undertaken [4] on the binary mixture of N,Ndimethyl acetamide (DMA) and acetone (Ac) in C 6 6, using Debye Smyth model and employing conductivity measurement technique at 9.88 Gz electric field. owever, no such rigorous study has been made so far, to check the applicability of Debye model for the (EtO + NMA) binary polar mixture dissolved in C 6 6 in terms of σ s of solution under Gz electric field. Alcohols and amides are, however, standard examples for multimodal dielectric spectra, reflecting non-debye behaviour. In particular, near 10 Gz, 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 -bond donor solvent having high value of dielectric constant and dipole moment, constitutes the basis of protein and enzymes. NMA and EtO are good constituents of binary polar mixture to form solute solute (dimer) and solute solvent (monomer) molecular associations. Ethanol (EtO), 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

3 Dielectric relaxation of ethanol and N-methyl acetamide NMA in C 6 6 at different temperatures for studying the molecular dynamics through the relaxation phenomenon using conductivity technique. The solvent EtO, on the other hand, shows double relaxation times τ 2 and τ 1, due to the rotation of the whole and the flexible part of the molecule under Gz 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 τ jk,τ j and τ k as well as μ jk,μ j and μ k 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 τ 2 and τ 1 at all the frequencies of 6 6 Imaginary part of conductivity " (ohm -1 m -1 ) 4 2 I(e) I(d) I(b) I(c) m System (I):- in benzene at 25 C Imaginary part of conductivity " (ohm -1 m -1 ) 4 2 II(e) II(d) II(b) II(c) II(a) System (II):- in benzene at 30 C 0.04, Real part of conductivity (ohm -1 m -1 ) 0.04, Real part of conductivity (ohm -1 m -1 ) 4 4 Imaginary part of conductivity " (ohm -1 m -1 ) 2 III(e) III(d) III(b) III(c) III(a) System (III):- in benzene at 35 C Imaginary part of conductivity " (ohm -1 m -1 ) 2 IV(e) IV(d) IV(b) IV(c) IV(a) System (IV):- in benzene at 40 C , Real part of conductivity (ohm -1 m -1 ) , Real part of conductivity (ohm -1 m -1 ) Figure 1. The linear plot of σ against σ of (EtO + NMA) polar mixture in C 6 6 for different x j and temperature under 9.88 Gz electric field. (I), (II), (III), (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0x j, respectively. Pramana J. Phys., Vol. 83, No. 4, October

4 S Sahoo, T R Middya and S K Sit 24.33, 9.25 and 3.00 Gz electric field [17]. They also show material property at three different frequencies [17]. 2. Experimental procedure N-methyl acetamide (NMA), ethanol (EtO) and C 6 6 are all good-quality samples purified 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, w jk s dissolved in the non-polar solvent, C 6 6. The X-band microwave was used to measure ε, ε ij or ε ik and ε, ε ij and 40 C, respectively [11]. The measured ε ±1.67%, respectively. or ε and ε ik at different w jks and at 25, 30, 35 are accurate within ±0.5% and 6 6 Imaginary part of conductivity " (ohm -1 m -1 ) 4 2 I(b) I(a) I(d) I(c) I(e) System (I):- in benzene at 25 C Imaginary part of conductivity " (ohm -1 m -1 ) 4 2 II(b) II(c) II(a) II(e) System (II):- in benzene at 30 C 4 4 Imaginary part of conductivity " (ohm -1 m -1 ) 2 III(b) III(c) III(a) III(e) System (III):- in benzene at 35 C Imaginary part of conductivity " (ohm -1 m -1 ) 2 IV(b) IV(a) IV(c) IV(e) System (IV):- in benzene at 40 C Figure 2. The variation of imaginary part of conductivity, σ ( 1 m 1 ) against weight fractions w jk s of binary polar mixture (EtO + NMA) dissolved in C 6 6 for different x j and temperature under 9.88 Gz electric field. (I), (II), (III), (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0x j, respectively. 582 Pramana J. Phys., Vol. 83, No. 4, October 2014

5 Dielectric relaxation of ethanol and N-methyl acetamide 3. Theoretical formulations The σ due to displacement current of a binary polar liquid mixture dissolved in nonpolar solvent(i) for given w jk s of solute is [4] σ = ( σ + ) jσ, (1) where σ (= ωε 0ε ) and σ (= ωε 0ε ) are just functions of permittivity in the real and imaginary parts of complex conductivity σ related to ε = ε jε, j being a complex number = 1. The total hf conductivity σ of the ternary solution is σ = ωɛ 0 (ɛ 2 + ɛ 2 ) = (σ 2 + σ 2 ), (2) " (ohm -1 m -1 ) I(a) " (ohm -1 m -1 ) II(a) conductivity of I(b) I(c) I(d) conductivity of II(b) II(c) II(d) Real part part I(e) System (I):- in benzene at 25 C 0 Real II(e) System (II):- in benzene at 30 C Real part of conductivity " (ohm -1 m -1 ) III(a) III(b) III(c) III(d) III(e) System (III):- in benzene at 35 C Real part of conductivity " (ohm -1 m -1 ) IV(b) IV(a) IV(c) IV(d) IV(e) System (IV):- in benzene at 40 C 0 0 Figure 3. The variation of real part of conductivity σ ( 1 m 1 ) against weight fractions w jk s of binary polar mixture (EtO + NMA) dissolved in C 6 6 for different x j and temperature under 9.88 Gz electric field. (I), (II), (III), (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0x j, respectively. Pramana J. Phys., Vol. 83, No. 4, October

6 S Sahoo, T R Middya and S K Sit where ω = 2πf, f is the frequency of the electric field = z and ε 0 = absolute permittivity of free space = F m 1.Ineqs(1) and(2) ofσ 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 ( ) σ of the ternary mixture. Again, σ is related to σ by σ + (1/ωτ jk )σ (3) where τ jk is the relaxation time of binary polar mixture at w jk 0 for constant conductivity σ of the solution. Differentiation of eq. (3) with respect to σ dσ /dσ = 1/ωτ jk. (4) The straight line of eq. (4) ofσ σ (figure 1) represents a convenient method to obtain τ jk at w jk 0. The ratio of slopes of σ w jk and σ w jk curves as shown (III) 6 jk 5 (III) (II) 4 (I) (II) (IV) (I) 3 (IV) x j Figure 4. The variation of τ jk s of binary polar mixture (EtO + NMA) in C 6 6 with mole fraction x j at different temperatures under 9.90 Gz 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

7 Dielectric relaxation of ethanol and N-methyl acetamide Table 1. Ratio of slopes of σ w jk and σ ) curve of eq. (4), estimated τ jk from eqs (5) and(4), reported τjk from GK method, average τjk = (τj xj + τkxk), coefficients a, b, c of (μjk xj ) and (τjk xj ) curves from eq. (5) + NMA binary polar mixture dissolved in benzene for different mole fractions, xj s and temperatures under 9.90 Gz electric field. w jk curves of eq. (5), linear slope of (σ σ Ratio of slopes Reported Coefficients of: (a) τjk Mole fraction of (σ Temp. xj sofetoin (σ w jk)/ Linear slope of Estimated τjk,τj, τjk,τj,τk in Average τjk = xj ;(b)μjk w jk) (σ ) τ k in psec psec from (τj xj + τkxk) xj curves System ( C) the mixture at wjk 0(eq.(5)) curve (eq. (4)) From eq. (5) Fromeq.(4) GK method in psec from eq. (5) EtO (a) NMA in C (b) EtO (a) NMA in C (b) EtO (a) NMA in C (b) EtO (a) NMA in C (b) Pramana J. Phys., Vol. 83, No. 4, October

8 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 ( dσ ) /( dσ ) = 1, (5) dw jk w jk 0 dw jk w jk 0 ωτ jk where τ jk x j curves at different temperatures are shown in figure 4. The constituent polar molecules mixed in appropriate proportions yield average τ jk as τ jk = τ j x j + τ k x k, (6) where x j and x k are mole fractions of ethanol (j)andnma(k) having relaxation times τ j and τ k, respectively. All the τs along with reported values are shown in table Total conductivity (ohm -1 m -1 ) 2 I(b) I(a) I(d) I(c) I(e) System (I):- in benzene at 25 C Total conductivity (ohm -1 m -1 ) 2 II(b) II(a) II(c) II(e) System (II):- in benzene at 30 C 4 4 Total conductivity (ohm -1 m -1 ) 2 III(b) III(c) III(a) III(e) System (III):- in benzene at 35 C Total conductivity (ohm -1 m -1 ) 2 IV(b) IV(a) IV(c) IV(e) System (IV):- in benzene at 40 C Figure 5. The variation of total conductivity, σ ( 1 m 1 ) against weight fractions, w jk s of binary polar mixture (EtO + NMA) dissolved in C 6 6 for different x j and temperature under 9.88 Gz electric field. (I), (II), (III), (IV) and (V) for 0.0, 0.3, 0.5, 0.7 and 1.0x j of EtO, respectively. 586 Pramana J. Phys., Vol. 83, No. 4, October 2014

9 Dielectric relaxation of ethanol and N-methyl acetamide By differentiating eq. (3) with respect to w jk and assuming σ σ in the highfrequency region at w jk 0, one gets β = 1 ( dσ ). (7) ωτ jk dw jk w jk 0 ere β is the slope of σ w jk curve as shown in figure 5. The σ of a binary polar nonpolar liquid mixture of w jk at T Kisgivenby[3] σ = Nρ ( ) μ 2 jk ω 2 τ jk (ε0 27M jk K B T 1 + ω 2 τjk )( ε + 2 ) w jk. (8) Differentiating eq. (8) with respect to w jk and comparing with eq. (7) forw jk 0, one gets [ ] 27Mjk K B Tβ 1/2 μ jk = Nρ i (ε i + 2) 2, (9) ωb where b is the dimensionless parameter = 1/(1 + ω 2 τjk 2 ) and M jk is the molecular weight of the binary polar mixture = M j x j + M k x k. The other terms in eq. (9) carry usual significance [4]. The μ jk x j and μ jk t curves are sketched in figures 6 and 7, respectively along with theoretical dipole moment (μ theo ) from bond angles and bond jk (III) (III) (I) (I) (II) (II) x j Figure 6. The variation of μ jk s of binary polar mixture (EtO + NMA) in C 6 6 with mole fraction x j at different temperatures under 9.90 Gz 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

10 S Sahoo, T R Middya and S K Sit jk (I) (I) (IV) (IV) (II) (II) (III) (III) (V) (V) t in C Figure 7. The variation of dipole moment μ jk in Coulomb metre (C m) with temperature t in C for different x j of (EtO + NMA) binary mixture under 9.90 Gz electric field. (I) ;, (II) ;, (III) ;, (IV) ; and (V) ; for 0.0, 0.3, 0.5, 0.7 and 1.0x j 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(τ jk T)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 F τ, S τ and τ are given in table Results and discussion The normalized measured σ datapoints within the error bar at different w jk sof(eto + NMA) mixture s are utilized to estimate τs andμs dissolved in nonpolar solvents C 6 6 for different experimental temperatures at 9.90 Gz electric field by adopting MATLab programming and using least squares fitting technique. τsare also estimated from the slope of linear relation σ against σ of figure 1 at different x j s and experimental temperatures. The graphs are, however, perfectly linear and the correlation coefficient r of straight line of eq. (3) is 1 r +1. Nevertheless, 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 σ w jk and σ w jk curves at w jk 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

11 Dielectric relaxation of ethanol and N-methyl acetamide (i) C 3 O C.m C.m C.m C N C C.m C.m C.m 4.86 C.m C.m C.m (ii) 0 C.m 3.40 C.m C 3 C O C.m C.m 105 (iii) C 3 C 105 O C 3 N C O C 3 NMA k = jk = EtO j (iv) C 3 C O O C C 3 Figure 8. Theoretical dipole moments μ theo s from available bond angles and bond moments (multiples of C m) along with solute solvent, solute solute and selfmolecular associations: (i) NMA C 6 6, (ii) EtO C 6 6, (iii) EtO NMA and (iv) EtO EtO self-association. Pramana J. Phys., Vol. 83, No. 4, October

12 S Sahoo, T R Middya and S K Sit from τs oftable1. The straight lines for x j = 0.0 (I) and x j = 0.3 (II) in figure 1 are flat to yield higher τs, whereas almost constant τs of smaller magnitude are found to occur for x j = of ethanol when compared with the results available for binary polar liquids [11]. As evident from figures 2 and 3, the curves of σ in 1 m 1 against w jk are parabolic like σ w jk curves. Figures show that σ and σ exhibit larger magnitudes at x j = 0.0 for different w jk s of solutes and found to decrease gradually up to x j = 1.0 for all the temperatures. This is probably due to the maximum and minimum polarization of NMA and EtO, because of the high and low absorption of high-frequency electric energy. The dipole moments μ jk s in Coulomb metre (C m) are estimated in terms of slopes βs ofσ w jk curves and dimensionless parameter bs from eq. (9). The total high-frequency conductivity σ in 1 m 1 due to displacement current in the mixture are plotted against w jk at different experimental temperatures to get parabolic curves as shown in figure 4. The curves are similar to σ w jk curves of figure 2 validating the approximation σ = σ in eq. (3). The estimated τ jk sare Table 2. Slopes of (σ w jk ) curve of eq. (7), dimensionless parameters b, estimated and reported dipole moments μ jk in Coulomb metre (C m), average dipole moments μ jk = μ j x j + μ k x k, theoretical dipole moments μ theo from bond angles and bond moments of + NMA binary polar mixture dissolved in benzene for different mole fractions x j s and temperatures under 9.90 Gz electric field. Mole fraction Slopes of Dimensionless parameters x j sof (σ w jk ) b b b Temp EtO in curve = 1/(1+ϖ 2 τjk 2 ) = 1/(1+ϖ 2 τjk 2 ) =1/(1+ϖ 2 τjk 2 ) System ( C) the mixture (eq. (7)) (eq. (5)) (eq. (4)) (eq. (6)) (I) EtO 25 (a) NMA (b) in C 6 6 (c) (d) (e) (II) EtO 30 (a) NMA (b) in C 6 6 (c) (d) (e) (III) EtO 35 (a) NMA (b) in C 6 6 (c) (d) (e) (IV) EtO 40 (a) NMA (b) in C 6 6 (c) (d) (e) Pramana J. Phys., Vol. 83, No. 4, October 2014

13 Dielectric relaxation of ethanol and N-methyl acetamide Table 2. (Continued.) Estimated dipole Theoretical moments μ jk Reported Average dipole moment in C m μ jk dipole moment μ theo Eqs (5) & Eqs(4) & Eqs(6) & in C m μ jk = (μ j x j +μ k x k ) from bond angles System (9) (9) (9) in C m and bond moments (I) EtO NMA in C (II) EtO NMA in C (III) EtO NMA in C (IV) EtO NMA in C plotted against x j s of ethanol at different temperatures as seen in figure 5. τs from figure 1 and table 1 are found to increase from x j = 0.0 to 0.3 and then decrease gradually indicating the solute solute (dimer) or solute solvent (monomer) molecular association up to x j = and thereafter, rupture of dimer occurs to facilitate solute solvent (monomer) molecular association up to x j = 1.0 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 τs againstx j 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 τ jk s of the constituent binary polar mixtures are calculated using simple mixing rule to place them in table 1. All the τs agree with the reportedτ [11] dueto Gopalakrishnamethod [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 μ jk s from both the methods are plotted against x j 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 Pramana J. Phys., Vol. 83, No. 4, October

14 S Sahoo, T R Middya and S K Sit (III) (I) (II) (I) ln( jk T) -21 (IV) (IV) (V) (III) (II) (V) /T 10 3 Figure 9. Linear plot of ln(τ jk T)against1/T curve of (EtO + NMA) binary polar mixture in C 6 6 under 9.90 Gz electric field. (I) ;, (II) ;, (III) ;, (IV) ; and (V) ; for 0.0, 0.3, 0.5, 0.7 and 1.0x j from ratio of slopes ( ) and linear slope ( ) methods, respectively. agreement with each other. This probably signifies the solute solute (dimer) associations for larger τ s happening initially and then, rupture of dimer takes place to favour solute solvent molecular association up to x j = 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 σ w jk curve as evident from eq. (9). The variations of μ jk against temperature (t) in C are plotted in figure 7 to show the highest asymmetric nature due to associative pair (NMA+EtO) in benzene for all x j s except x j = 0 with the rise of temperature probably due to stretching of bond angles. A fraction of associative pair will break as EtO or NMA with the increase in temperature to yield smaller μ for monomer. The theoretical dipole moment (μ theo ) of the polar molecule is estimated from the available bond angles and bond moments of N C 3,C O, C 3 C, C N, C OandO of , , , , and 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 fractional positive charge (δ+) at the site of N and C atoms of NMA or atom of O group 592 Pramana J. Phys., Vol. 83, No. 4, October 2014

15 Dielectric relaxation of ethanol and N-methyl acetamide in EtO. 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). Opposite 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]. ln(t jk T)= ln(ae Sτ/R ) + τ /RT, (10) where F τ = τ T S τ. Equation (10) is a straight line of ln(τ jk T)vs. 1/T (figure 9) to yield thermodynamic energy parameters such as free energy of activation, ( F τ ), enthalpy of activation ( τ ) and entropy of activation ( S τ ). The values of F τ are higher and lower at x j = 0.0 and 0.3, respectively, although they exhibit almost constant values for 0.5, 0.7 and 1.0x j, respectively, as seen in table 3. This may be Table 3. Intercepts and slopes ln(τ jk T)against1/T curve, τ in kj/mole, F τ in kj/mole and S τ in J/mole K treating the rotation of the binary polar mixture as the rate process, γ = ( τ / η ), Debye factor τ jk T/η, Kalman factor τ jk T/η γ and coefficients a, b, c of μ jk t curves + NMA binary polar mixture dissolved in benzene for different mole fractions x j and temperatures under 9.90 Gz electric field. System Mole fraction Temp. Intercepts and τ F τ S τ x j ( C) slopes of ln(τ jk T) (kj/mole) (kj/mole) (J/mole K) in the mixture vs. 1/T 10 3,eq.(5) EtO + NMA in C EtO + NMA in C EtO + NMA in C EtO + NMA in C EtO + NMA in C Pramana J. Phys., Vol. 83, No. 4, October

16 S Sahoo, T R Middya and S K Sit Table 3. (Continued.) System γ from ln η = ( τ /γ ) Debye factor Kalman factor Coefficients of (τ jk T)vs.lnη (kj/mole) τ jk T/η 10 6 τ jk T/η γ μ jk t curve curve from a b c eqs (11) &(5) EtO + NMA in C EtO + NMA in C EtO + NMA in C EtO + NMA in C EtO + NMA in C due to the fact that the dielectric relaxation process involves the rotation of the participating polar constituents to a different extent. Enthalpies of activation ( η ) for the viscous flow of the solvent are higher for all the systems except x j = 0.5. 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 ( S τ ) are positive for x j = 0.5 and 1.0 of ethanol, unlike other systems. The negative values of S τ indicate that the activated states are more ordered than the normal state, whereas reverse is true for the negative S τ. The estimated values of γ indicate the solvent environment around the solute molecule from the relation [3] τ jk = Aη γ /T, (11) where γ = τ / η is the slope of ln(τ jk T)vs.lnη linear relation having coefficient of viscosity η of solvent benzene. For the system x j = 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 + NMA mixture s of ethanol may be attributed to the solute solute association of polar mixtures in different molecular environment. Both the Debye factor (τ jk /η) and Kalman factor (τ jk T/η γ ) 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

17 5. Conclusions Dielectric relaxation of ethanol and N-methyl acetamide 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 EtO and NMA dissolved in benzene as well as their molecular association are inferred from high-frequency conductivity measurement of solution of 9.90 Gz 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 σ w jk and σ w jk curves at w jk 0 as well as linear slope of σ σ 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 x j and associated aspects are displayed from the standpoint of μ theo. Molecular dynamics of liquid mixture are also ascertained using Eyring rate theory equation. This reveals that relaxation mechanism follows both Debye and Kalmann equations. References [1] S N Sen and R Ghosh, J. Phys Soc. 33, 838 (1972) [2] N Ghosh, R C Basak, S K Sit and S Acharyya, J. Mol. Liquids 85, 375 (2000) [3] S Sahoo and S K Sit, Indian J. Phys. 84, 1549 (2010) [4] S Sahoo, K Dutta, S Acharyya and S K Sit, Pramana J. Phys. 70, 543 (2008) [5] M S Venkatesh and G S V Raghavan, Canadian BioSystem Engg. 47, 7.15 (2005) [6] D Singh, N Thakur and D R Sharma, Indian J. Phys. 85(7), 1417 (2011) [7] L Onsager, J. Am. Chem. Soc. 58, 1486 (1936) [8] J G Kirkwood, J. Chem. Phys. 7, 911 (1939) [9] Fröhlich, Theory of dielectrics (Oxford University Press, Oxford, 1949) [10] P Debye, Polar molecules, Chemical Catalogue, 1929 [11] R Kumar, V S Rangra, D R Sharma, N Thakur and N S Negi, Z. Naturforsch. 62a, 213 (2007) [12] A Sharma and D R Sharma, J. Phys. Soc. 61, 1049 (1992) [13] Eyring, S Glasstone and K J Laidler, Theory of rate process (McGraw ill, New York, 1941) [14] R Jain, N Bhargava, K S Sharma and D Bhatnagar, Indian J. Pure & Appl. Phys. 49, 401 (2011) [15] U Saha and S Acharyya, Indian J. Pure & Appl. Phys. 32, 346 (1994) [16] S K Sit and S Acharyya, Indian J. Phys. 70B, 19 (1996) [17] K Dutta, A Karmakar, S K Sit and S Acharyya, J. Mol. Liquids 128, 161 (2006) [18] S Sahoo and S K Sit, Mater. Sci. Engg. B 163, 31 (2009) Pramana J. Phys., Vol. 83, No. 4, October