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

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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 mix- tures 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 associa- tion [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 cor- relation 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, how- ever, 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 interac- tions 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 solu- tion 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].
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