Calculation of the Relaxation Time and the Activation Energy Close to the Lower Phase Transition in Imidazolium Perchlorate


Phase transition
Ising model
relaxation time
activation energy
imidazolium perchlorate

How to Cite

Yurtseven, H., A. Kiraci, & N. Kara. (2021). Calculation of the Relaxation Time and the Activation Energy Close to the Lower Phase Transition in Imidazolium Perchlorate. Journal of Basic & Applied Sciences, 17, 79–86.


The temperature dependence of the relaxation time of imidazolium perchlorate (Im-ClO4) was calculated from the pseudospin-phonon coupled (PS) and the energy fluctuation (EF) models close to the first-order phase transition temperature of 247 K. This calculation was performed in terms of the proton second moment M2 that was associated with the order parameter which was predicted from the mean-field theory. Our results were in good agreement with the observed data. In addition, values of the activation energy were deduced in terms of the Arrhenius plot using our calculated values of the relaxation time from both PS and EF models.


Anderson EB, Long TE. Imidazole- and imidazoliumcontaining polymers for biology and material science applications. Polymer 2010; 51(12): 2447-2454.

Riduan SN, Zhang Y. Imidazolium salts and their polymeric materials for biological applications. Chem Soc Rev 2013; 42(23): 9055.

Zhao L, Zhang C, Zhuo L, Zhang Y, Ying JY. Imidazolium Salts: A Mild Reducing and Antioxidative Reagent. J Am Chem Soc 2008; 130(38): 12586-12587.

Hanke CG, Price SL, Lynden-Bell RM. Intermolecular potentials for simulations of liquid imidazolium salts. Molec Phys 2001; 99(10): 801-809.

Zhang Y, Chan JYG. Sustainable chemistry: imidazolium salts in biomass conversion and CO2 fixation. Energy Environ Sci 2010; 3(4): 408-417.

Lee S. Functionalized imidazolium salts for task-specific ionic liquids and their applications. Chem Commun 2006; 37(31): 1049-1063.

Seoud OAE, Koschella A, Fidale LC, Dorn S, Heinze T. Applications of ionic liquids in carbohydrate chemistry: A window of opportunities. Biomacromolecules 2007; 8(9): 2629-2647.

Yu B, Zhou F, Hu H, Wang C, Liu W. Synthesis and properties of polymer brushes bearing ionic liquid moieties. Electrochim Acta 2007; 53(2): 487-494.

Ma H, Gao W, Wang J, Wu T, Yuan G, Liu J, et al. Ferroelectric polarization switching dynamics and domain growth of triglycine sulfate and imidazolium perchlorate. Adv Electron Mater 2016; 2: 1600038.

Gao W, Chang L, Ma H, You L, Yin J, Liu J, et al. Flexible organic ferroelectric films with a large piezoelectric response. NPG Asia Mater 2015; 7(6): e189.

Hu Y, Guo Z, Ragonese A, Zhu T, Khuje S, Li C, et al. A 3Dprinted molecular ferroelectric metamaterial. PNAS 2020; 117(44): 27204-27210.

Zhang Y, Liu Y, Ye HY, Fu DW, Gao W, Ma H, et al. A molecular ferroelectric thin film of imidazolium perchlorate that shows superior electromechanical coupling. Angew Chem Int Ed 2014; 126: 5164-5168.

Zhu X, Du M, Feng J, Wang H, Xu Z, Wang L, et al. High- Efficiency perovskite solar cells with imidazolium- based ionic liquid for surface passivation and charge transport. Angew Chem Int Ed 2021; 60: 4238-4244.

Pająk Z, Czarnecki P, Szafrańska B, Małuszyńska H, Fojud Z. Ferroelectric ordering in imidazolium perchlorate. J Chem Phys 2006; 124(14): 144502.

Czapla Z, Dacko S, Kosturek B, Waskowska A. Dielectric and optical properties related to phase transitions in an imidazolium perchlorate [C3N2H5ClO4] crystal. Phys Stat Sol B 2005; 242: 122-124.

Przesławski J, Czapla Z. Calorimetric studies of phase transitions in imidazolium perchlorate crystal. J Phys Cond Mat 2006; 18(23): 5517-5524.

Kiraci A, Yurtseven H. Damping constant and the relaxation time calculated for the lowest-frequency soft mode in the ferroelectric phase of Cd2Nb2O7. Optik 2016; 127: 11497- 11504.

Kiraci A, Yurtseven H. Temperature dependence of the Raman frequency, damping constant and the activation energy of a soft-optic mode in ferroelectric barium titanate. Ferroelectrics 2012; 432:14-21.

Yurtseven H, Kiraci A. Calculation of the damping constant and the relaxation time for the soft-optic and acoustic mode in hexagonal barium titanate. Ferroelectrics 2012; 437: 137- 148.

Kiraci A, Yurtseven H. Calculation of the Raman frequency, damping constant (linewidth) and the relaxation time near the tetragonal-cubic transition in PbTiO3. Optik 2017; 14231: 1- 319.

Karacali H, Kiraci A, Yurtseven H. Calculation of the Raman frequency and the damping constant of a coupled mode in the ferroelectric and paraelectric phases in KH2PO4. Phys. Stat Sol B 2010; 247: 927-936.

Yurtseven H, Kiraci A. Damping constant (linewidth) and the relaxation time of the Brillouin LA mode for the ferroelectricparaelectric transition in PbZr1-x TixO3. IEEE Trans Ultrason Ferroelectr Freq Control 2016; 63: 1647-1655.

Yurtseven H, Kiraci A. Temperature dependence of the damping constant and the relaxation time close to the tetragonal-cubic phase transition in SrZrO3. J Mol Struct 2017; 1128: 51-56.

Yurtseven H, Kiraci A. Damping constant and the inverse relaxation time calculated as a function of pressure using the X-ray diffraction data close to the cubic-tetragonal phase transition in SrTiO3. Ferroelectrics 2019; 551: 143-151.

Kiraci A, Yurtseven H. Analysis of the integrated intensity of the central peaks calculated as a function of temperature in the ferroelectric phase of lithium tantalite. Therm Sci 2018; 22(1): 221-227.

Laulicht I, Luknar N. Internal-mode line-broadening by proton jumps in KH2PO4. Chem Phys Lett 1977; 47(2): 237-240.

Laulicht I. On the drastic temperature broadening of hard mode Raman lines of ferroelectric KDP type crystals near TC. J. Phys Chem Sol 1978; 39(8): 901-906.

Lahajnar G, Blinc R, Zumer S. Proton spin-lattice relaxation by critical polarization fluctuations in KH2PO4. Phys Condens Matter 1974; 18(4): 301-316.

Schaack G, Winterfeldt V. Temperature behavior of optical phonons near TC in triglycine sulphate and triglycine selenite. Ferroelectrics 1977; 15(1): 35-41.

Bartoli FJ, Litovitz TA. Raman scattering: Orientational motions in liquids. J Chem Phys 1972; 56(1): 413-425.

Pajak Z, Czarnecki P, Wasicki J, Nawrocik W. Ferroelectric properties of pyridinium periodate. J Chem Phys 1998; 109: 6420-6423.

Pajak Z, Czarnecki P, Małuszynska H, Szafranska B. Ferroelectric properties of pyridinium fluorosulfonate. J Chem. Phys 2000; 113: 848-853.

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