ORIGINALPAPER Investigation of dielectric relaxation in dipolar liquids S Sahoo* Department of Electronics and Communication Engineering, National Institute of Technology Jamshedpur, P.O. Jamshedpur, Jharkhand 831014, India Received: 03 April 2018 / Accepted: 28 January 2019 Abstract: A graphical method has been used to evaluate the double relaxation time s 1 and s 2 for rotation of the flexible part and whole molecule of four butyl alcohols in p-xylene under 2.50 GHz (S-Band), 9.313 GHz (X-Band), 16.20 GHz (Ku-Band) and 23.98 GHz (K-Band) electric field at 25 °C using Fro ¨hlich and Debye model. The fixed s 1 and s 2 obtained from graphical method at those frequencies agree well with the reported average s’s. This reveals s’s are independent of the electric field frequencies signifying the material properties of chemical systems in identical environment. This method is making no approximation, and the infinite number of solutions clearly shows that observation at one single frequency is not sufficient to determine the correct values of s 1 and s 2 . The dipole moments l 1 and l 2 are measured at all the frequencies in terms of graphically obtained s 1 and s 2 and reported s. Estimated penetration depth indicates development of a new simple and rapid sensor for determination of alcohol concentration. Keywords: Dielectric relaxation; Dipole moment; Binary mixture; Relaxation time PACS Nos.: 77.22 Gm; 72.80. Le 1. Introduction Dielectric spectroscopy is a versatile experimental tool and dramatically developed in the last three decades [1–3]. It covers the extraordinary spectral range from 10 -6 to 10 12 Hz in recent years. As a simple, rapid and nondestructive measuring technique, broadband dielectric spectroscopy provides information about dielectric response of material to electromagnetic field and enables researchers to make sound contribution to contemporary problems in modern science and engineering by correlating dielectric properties with other physico-chemical properties of test material. Broadband dielectric spectroscopy technique has been successfully applied to diverse fields such as pharmaceu- tical science [4], polymer science [5], electrochemistry [6], colloid science [7], thin film [8], industrial material char- acterization [9], ceramic [10], agri-food sector [11] and electrical and electronic industry [12]. Frequency-depen- dent permittivity of material shows dielectric relaxation or dielectric dispersion under ac fields as a measure of polarization. Alcohols are hydrogen-bonded polymer-like molecule and extensively used in various field of science and technology [13]. Due to high electronegativity of oxygen atom, O–H bond in alcohol is highly polar. Alco- hols usually show a, b and c relaxation under hf electric field [13]. The dilute solutions of polar substances in nonpolar solvents allow solute molecule to be examined in a quasi-isolated state, and the behavior is less affected by the dipolar field [14]. Among various existing models, Debye [15] and Fro ¨hlich models [16] are simpler, straightforward and more topical to understand relaxation phenomena. Crossley et al. [17] showed double relaxation time due to end-over-end rotation of the whole as well as flexible part of some long-chain alcohols dissolved in nonpolar solvent p-xylene under hf GHz electric field at 25 °C. He intended to predict s 1 and s 2 , using Cole–Cole plot based on approximation and semi-empirical method. Mansingh and Kumar [18] presented a graphical technique to determine s 1 and s 2 for a pure polar liquid using Fro ¨hlich model in terms of measured permittivity e under different frequencies at a single temperature. However, no such technique has been applied so far to predict s 1 and s 2 of butyl alcohols dissolved in a nonpolar solvent using fre- quency variation method in terms of complex orientational susceptibility v  ij  . In this context, the purpose of the present paper is to introduce a graphical method to estimate *Corresponding author, E-mail: swagatdebmsit@yahoo.co.in Indian J Phys https://doi.org/10.1007/s12648-019-01437-3 Ó 2019 IACS