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Isoconversional Kinetic Analysis of Decomposition of Nitroimidazoles: Friedman Method vs. Flynn-Wall-Ozawa Method M. Venkatesh, Pasupala Ravi, and Surya P Tewari J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp407526r • Publication Date (Web): 12 Sep 2013 Downloaded from http://pubs.acs.org on September 16, 2013

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The Journal of Physical Chemistry

Isoconversional Kinetic Analysis of Decomposition of Nitroimidazoles: Friedman method vs. Flynn-Wall-Ozawa method M. Venkatesh, P. Ravi* and Surya P. Tewari Advanced Centre of Research in High Energy Materials University of Hyderabad, Hyderabad 500 046, India ABSTRACT We have investigated the decomposition kinetics of imidazole, 2-nitroimidazole and 4nitroimidazole using TG-DTA technique under nitrogen atmosphere. Isoconversional methods were used for the evaluation of kinetic parameters from the kinetic data of different heating temperatures. The Friedman method provided comparably higher values of activation energy than the Flynn-Wall-Ozawa method. Imidazole, 2-nitroimidazole and 4-nitroimidazole were decomposed by the multi step reaction mechanism evident from the non-linear relationship of activation energy and the conversion rate. The NO2 elimination and nitro-nitrite isomerization are expected to be competitive reactions in the decomposition of 2-nitroimidazole and 4nitroimidazole. The present study may be helpful in understanding how the position of NO2 group affects the decomposition kinetics of substituted imidazoles. Keywords: Nitroimidazoles; Kinetics; Mechanism; Thermal analysis

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I. INTRODUCTION Imidazoles have been used as dyes, fine chemicals, radiosensitizers, antibacterial, antifungal, antiprotozoal and antiepileptic drugs, and agrochemical pesticides, and recently as high energy materials.1These are simple heteroaromatic compounds having hydrogen bond donor group (i.e., N-H, pyrrole like nitrogen atom) and hydrogen acceptor group (i.e., N3 atom, pyridine like nitrogen, where numeral 3 stands for the position of N-atom). Nitration of imidazole using nitric acid or nitric-sulfuric acid mixture leads to substitution in the 4-position. 2-Nitroimidazole was synthesized from the sulfate or hydrochloride salt of 2-amonoimidazole using alkali metal nitrites (e.g., KNO2, NaNO2).2 N-Nitroimidazoles were isomerized into C-nitroimidazoles in chlorobenzene at moderate temperature. C-Nitroimidazoles were formed quantitatively however in some instances denitration of N-nitroimidazoles during thermal isomerization was observed.3 Several researchers have used metal nitrates or impregnated metal nitrates to prepare Cnitroimidazoles in higher yields.4,5 The measurement of kinetics and the associated Arrhenius parameters are the essential aspects of the characterization of materials. The macrothermal kinetics of imidazole derivatives to reveal stability, sensitivity and performance have been reported elsewhere.6-8 The molecular frameworks of imidazole, 2-nitroimidazole and 4-nitroimidazole are shown in Figure 1. Nitroimidazoles are known to undergo peculiar decomposition mechanism.9 The reaction would follow: (i) NO2 elimination, (ii) nitro-nitrite isomerization, and (iii) a step-wise mechanism involving initial ring opening followed by bond dissociation with a concerted hydrogen shift. Homolysis of one or more bonds between the ring atoms and their substituents leaving the ring intact or exchange of two adjacent ring substituents followed by breakdown of the imidazole ring have also been proposed. However one of these initiation events may predominate under a given set of experimental conditions, competition among these pathways is likely depending upon the physical environment and the excess energy available. Infra red spectroscopy (IR), thermogravimetry (TG), differential thermal analysis (DTA), differential scanning calorimetry (DSC), and T-jump/FT-IR spectroscopy have been used for the measurement of kinetics and the Arrhenius parameters of the decomposition of materials. TG and DTA techniques involve the continuous measurement of physical property such as 2


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weight, volume, heat capacity, etc., as sample temperature is increased at a predetermined rate. It is possible to calculate the kinetic constants from these techniques by making a number of patterns at different heating rates. Several methods are known to calculate the kinetic parameters of solid state reactions based on the Arrhenius rate law.10-14 The recommendations of International Confederation for Thermal Analysis and Calorimetry (ICTAC) offer guidance for reliable evaluation of kinetic parameters from the data obtained by thermogravimetry, differential scanning calorimetry and differential thermal analysis.15-22 The Arrhenius equation relates the rate constant of a reaction to temperature through the activation energy and preexponential factor. Generally activation energy and pre-exponential factor are assumed to be constant however in some solid-state reactions these kinetic parameters may vary with the progress of the reaction. This variation can be detected by isoconversional methods. These methods yield effective activation energy as a function of the extent of conversion and permit to draw reliable mechanistic conclusions. The model dependent method needs thermal analysis measurement however it suffers from an inability to determine the reaction model uniquely. On the other hand, the model independent isoconversional methods avoid the problems originated from the ambiguous evaluation of the reaction model.

Figure 1: Molecular frameworks of imidazoles In order to understand the initial decomposition steps and overall mechanism of compounds, it is necessary to separate and elucidate their intra- and intermolecular behavior and properties. The first step in chemical-to-mechanical energy transformation should involve the breaking of a molecular chemical bond. Even if the condensed high density phase behavior and mechanism are different from the molecular one, the initial bond rupture or weakening for the isolated molecule is an essential step for elucidation of the entire decomposition process. Second, many imidazoles and intermediate species may decompose in gas phase on a timescale that 3



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insures isolation. Initiation of the decomposition reaction can occur by rapid heating, arcs, sparks or shocks. All of these initiation methods can generate gas phase species whose molecular chemistry can play an important role in the overall mechanism and kinetics of decomposition of imidazoles. The present study aims to aid in the design of imidazoles for various applications by the decomposition dynamics and kinetics from isoconversional analysis. This is certainly the first step in the elucidation of the release of stored energy and for the synthesis of new energetic imidazoles. We have investigated the decomposition kinetics of imidazole, 2-nitroimidazole and 4-nitroimidazole at different heating temperatures using TG–DTA technique under nitrogen atmosphere. II. EXPERIMENTAL DETAIL 2.1. Thermal analysis The sample (~1 mg) taken in alumina crucible and the reference were heated from 25 ◦C to 500 ◦C on the TA instruments (Q600 SDT) under nitrogen environment (flow rate of 100 cm3/min) as the purge and protective gas. The reference was an empty alumina crucible. Non-isothermal TGA runs were conducted at heating rates of 2.5, 5, 10, 15, and 20 ◦C per minute. 2.2. Kinetic analysis The kinetic methods used in thermal analysis have been derived for single reactions. For systems involving multiple reactions the inappropriate applications of kinetic methods can lead to misleading results. However it has been shown that the isoconversional methods can give meaningful activation energy values in the wide range of circumstances. These methods permit a model independent estimate of the activation energy. The rate constant for the solid state decomposition reaction was assumed to follow the Arrhenius rate law. The extent of conversion (α) has been computed from the weight loss data using the reported standard methods. ∆α of 0.01 and a ∆α of 0.025 were used to compute the activation energy from the differential and the integral methods respectively. For comparison and plotting, constant values were shown at an interval of 0.025. The most common differential isoconversional method is that of Friedman.11 It is the most straightforward way to evaluate the effective activation energy (Ea) as a function of the 4


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extent of reaction (α). The magnitude of rate constant (k) is determined by temperature (T) and is usually described by the following equation:

where, f(α) is the reaction model (i.e., conversion function), α is the conversion function (it should be noted that α ranges from 0 to 1), β is the heating rate (i.e., β = dT/dt = constant), A is the pre-exponential factor, R is the universal gas constant. The reaction model is unknown at the outset of the analysis. There are a significant number of reaction models however all can be reduced to three major types: accelerating, decelerating and sigmoidal (i.e., autocatalytic). Each of these types has a characteristic reaction profile or kinetic curve, the terms frequently used to describe a dependence of α or dα/dt on t or T. Such profiles are readily recognized for isothermal or non-isothermal data and the kinetic curve shape is determined by the reaction model alone. Friedman’s method applies the logarithm of conversion rate as a function of the reciprocal temperature at different degrees of conversion. Friedman’s equation is obtained by simple rearrangement of Eq. (1)

The value of dα/dt is obtained numerically using ∆α= 0.025 and linear interpolation of the experimental data. The plot of ln(dα/dt) versus 1/T at constant α for a set of β values gives a family of straight line with slope −Eα/R. This model-free method can be applied to the data sets obtained at different heating rates βi and/or different temperatures, Ti. Friedman’s method may lead to erroneous estimates of the activation energy however isoconversional integral methods seems to be a safer alternative for the calculation of meaningful activation energy values. The integral method was given by Flynn and Wall22 and Ozawa12,23 independently. The major advantage of this method is that it does not require any assumptions concerning the form of the kinetic equation other than the Arrhenius type temperature dependence. The Flynn–Wall–Ozawa method is a model-free method which involves measuring the temperatures corresponding to fixed values of α from experiments at different heating rates, β and plotting ln(α) against 1/T and the slopes of such plots give −Eα/R. If Eα varies with α, the 5



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results should be interpreted in terms of multi-step reaction mechanisms. The Arrhenius rate law Eq. (1) was integrated and then Doyle approximation24 was applied to obtain Eq. (3). The plot of lnβ versus 1/T gives straight line with slope −1.052 Ea/R.

where g(α) is the integral form of kinetic model (i.e., g(α) = kt). Thus, for α = constant, a plot of lnβ versus 1/T obtained from thermal curves recorded at several heating rates should be a straight line whose slope allows evaluation of the activation energy. As per the pre-exponential factor value is concerned, its value can be obtained from the intercept if the form of the integral conversion function g(α) is known. For x < 20 (i.e., x = Ea/RT), Doyle’s approximation leads to errors higher than 10%. For such cases, Flynn25,26 suggested corrections in order to obtain correct activation energy values. The Flynn–Wall–Ozawa method is potentially suited for use in systems where many reactions are occurring such that the activation energy varies with time. However, the method is predicted to fail if reactions of widely different type (and hence having very different activation energies) are occurring simultaneously. Competitive reactions which have different products also render the method inapplicable. In addition the Flynn–Wall–Ozawa method is less precise than the Friedman’s method. It was demonstrated that if the activation energy depends on the degree of conversion its values obtained by isoconversional differential and integral methods are different.27-29 Dowdy30,31 showed that for the systems of competitive or independent reactions both the Friedman and the Flynn–Wall–Ozawa methods lead to different values of the activation energy. On the other hand if Eα is independent on α then the two methods lead to practically the same activation energy value. For this reason a comparison of the results from the two methods is helpful to check on their accuracy. III. RESULTS AND DISCUSSION Thermal analysis is concerned with thermally stimulated processes (i.e., the processes that can be initiated by a change in temperature). The rate can be parameterized in terms of temperature, extent of conversion and pressure however the majority of kinetic methods consider the rate to 6


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be a function of temperature and extent of conversion. The physical properties measured by thermal analysis methods are not species-specific and usually cannot be linked directly to specific reactions of molecules. Thus the value of extent of conversion typically reflects the progress of the overall transformation of a reactant to products. The gaseous products of thermal decomposition can be reactive toward the decomposing substance causing autocatalysis as frequently seen in the decomposition of nitro compounds. Bernstein et al9 studied the NO and NO2 channels in the decomposition of 2-nitroimidazole and 4-nitroimidazole using UV photon spectroscopy. Li et al9 established the NO2 channel in the decomposition of 4-nitroimidazole catalyzed by Pb(NO3)2 using thermolysis/RSFT-IR spectroscopy. We have used the DTA thermograms for kinetic analysis of imidazole, 2-nitroimidazole and 4-nitroimidazole. Accordingly the DTA analysis has been performed at five different heating rates of 2.5, 5, 10, 15, and 20 ◦C per minute so as to obtain five peak values to generate the kinetic parameters. TG-DTA of imidazole, 2-nitroimidazole and 4-nitroimidazole are presented in Figure 2. For the Arrhenius type of kinetic equation the primary objective is to determine experimentally the frequency factor, activation energy and reaction model or conversion functions. All isoconversional methods take their origin in the isoconversional principle that states that the reaction rate at constant extent of conversion is only a function of temperature.14 These are often called as model-free methods as they do not need to identify the reaction model. They assume that the conversion dependence of the rate obeys some f(α) model. The temperature dependence of the isoconversional rate can be used to evaluate isoconversional values of activation energy without assuming or determining any particular form of the reaction model. These methods reveal the complexity of the process in the form of a functional dependence of activation energy and extent of conversion. The evaluated Ea dependencies by such methods allow for meaningful mechanistic and kinetic analyses as well as for reliable kinetic prediction. A significant variation of Ea with α indicates that a process is kinetically complex to describe the kinetics of thermally stimulated processes. We have calculated the Ea values for α values varying 0.05-0.95 with a step of 0.05 and found the dependencies of Ea vs. α. The Flynn–Wall–Ozawa method has been known to give meaningful values of activation energy in wide range of circumstances. The Friedman method is related to the Flynn–Wall– 7



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Ozawa method inasmuch as they both rely on the use of several different heating rates. These methods provide separate values of activation energy at different levels of conversion independent of the form of the kinetic equation. Imidazoles have characteristic reaction profile or kinetic curve on plotting α or dα/dt against t or T. The sigmoidal shape represents the processes whose initial and final stages corresponds to the accelerating and decelerating behavior respectively. The numerical values of g(α) has not shown any significant variation with β giving rise to a single dependence of g(α) values on α. The Eα values obtained according to the Friedman and the Flynn–Wall–Ozawa methods are plotted as function of α of imidazoles as shown in Figure 3. The values of activation energy of imidazole (1) have been decreased to 49.6 kJ mol-1 (Friedman method) and 52.1 kJ mol-1 (Flynn–Wall–Ozawa method) with the extent of conversion. The activation energy required for the decomposition of imidazole according to the Friedman and the Flynn–Wall–Ozawa methods are 75.7 kJ mol-1 and 71.6 kJ mol-1 respectively. The non-linear relationship of activation energy with the conversion rate indicates that imidazole is expected to be decomposed by multi step kinetics. The plausible decomposition paths of imidazole (1) are shown in Scheme 1. Vinylcarbene is likely to be the major intermediate in the decomposition of imidazole.1 The mechanism was partly based on the reactions of 3H-imidazole and vinyldiazo compound. Two competitive reactions such as cyclization to 3H-imidazole and nitrogen extrusion first one being lower in energy are likely to occur. The relatively unstable vinylcarbene rearranges into the propyne which is thermoneutral decomposition. The N2 elimination is likely to play a major role in the decomposition kinetics of imidazole.

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4-Nitroimidazole

2-Nitroimidazole

Imidazole

Figure 2: TG-DTA of imidazoles at heating rate 5 ◦C per minute.

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4-Nitroimidazole

2-Nitroimidazole

Imidazole

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Scheme 1: Plausible pathways of the decomposition of imidazole. 11



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2-Nitroimidazole (2) has some weight loss below 287 ◦C (m.p) as seen from Figure 2. The activation energies were increased to 89 kJ mol-1 (Friedman method) and 93.5 kJ mol-1 (Flynn–Wall–Ozawa method) and then decreased with the extent of conversion (Figure 3). The activation energy required for the decomposition of 2-nitroimidazole according to the Friedman and the Flynn–Wall–Ozawa methods are 75 kJ mol-1 and 71.2 kJ mol-1 respectively. The plausible decomposition paths of 2-nitroimidazole are summarized in Scheme 2. The NO2 elimination and the NO elimination after the nitro-nitrite isomerization seem to be the major decomposition pathways. The decomposition of 2-nitroimidazole begins with the split of C-NO2 bonds, and the dissociated product NO2 destroy the undecomposed parent compound instantaneously, and finally all the ring C=N, C=C, C-H and N-H bonds shall be broken concurrently into NO2, CO2 and CO. The HONO elimination is less than the NO2 elimination and the nitro-nitrite isomerization. For 2-nitroimidazole the HONO elimination is even less likely due to its exceptional stability/or aromaticity (i.e., sextet of π-electrons). Therefore the NO2 elimination and the nitro-nitrite isomerization are presumably to play foremost role in the decomposition kinetics. 4-Nitroimidazole (3) has good thermal stability with no weight loss observed up to 303 ◦C (dec. point). The weight loss of 4-nitroimidazole begins around 200 ◦C with the most rapid weight loss at 230 ◦C. The compound underwent maximum weight loss from 200 ◦C to 303 ◦C. The estimated activation energies are slightly increased and then decreased to 65.6 kJ mol-1 (Friedman method) and 61.8 kJ mol-1 (Flynn–Wall–Ozawa method) with the extent of conversion. The activation energy required for the decomposition of 4-nitroimidazole according to the Friedman and the Flynn–Wall–Ozawa methods are 120 kJ mol-1 and 114.7 kJ mol-1 respectively. Scheme 3 summarizes the plausible decomposition paths of 4-nitroimidazole. The decomposition of 4-nitroimidazole was proposed to begin with the split of C-NO2 bonds, whose product NO2 destroyed the undecomposed 4-nitroimidazole instantaneously, and lastly all the other C=N, C=C, C-H and N-H bonds of the 1,3-diazole ring were broken concurrently.32 The NO2 elimination and the NO elimination have been the major decomposition pathways in the decomposition of 4-nitroimidazole. Also, the HONO elimination is far less likely possible due to its exceptional stability of 4-nitroimidazole.

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Scheme 2: Plausible pathways of the decomposition of 2-nitroimidazole. 13



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Scheme 3: Plausible pathways of the decomposition of 4-nitroimidazole. 14


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The non-linear relationship of activation energy with the conversion rate indicates the possibility of multi step kinetics seen in case of 2-nitroimidazole and 4-nitroimidazole. For 2nitroimidazole and 4-nitroimidazole the NO and HONO eliminations are less likely than for 1,3,5-trinitroperhydro-1,3,5-triazine (RDX) and octahydro-1,3,5,7-tetranitro-1,3,5,7-tetrazocine (HMX). Further the branching ratio between these two pathways will depend on many factors like enthalpy, entropy, temperature, catalyst, and so on. 2-Nitroimidazole and 4-nitroimidazole yield N2, NO, NO2, H2 and HCN as the most abundant gaseous decomposition products apart from small amount of HN3. The rate of decomposition of imidazole, 2-nitroimidazole and 4nitroimidazole found to be autocatalytically increasing over the temperature. The C-NO2 and NNO2 bonds of nitroimidazoles have been assumed to be the trigger sites of decomposition in such compounds.21,32 The numerical values of activation energy obtained using isoconversional methods showed variations. These variations are presumably due to the approximation of temperature integral used in the derivations of the relations of the kinetic methods. The values activation energy calculated using the Friedman method for imidazoles are comparably higher than those values obtained from the Flynn-Wall-Ozawa method. We speculate that the activation energy, pre-exponential factor and the effective reaction order are strongly dependent on the experimental conditions. The stability order of compounds based on the calculated values of activation energy may be written as: 4-nitroimidazole > 2-nitroimidazole > imidazole. IV. SUMMARY AND CONCLUSION The thermal decomposition kinetics of imidazole, 2-nitroimdazole and 4-nitroimidazole has been investigated using TG–DTA technique under nitrogen atmosphere at the flow rate 100 cm3/min. The values of activation energy have been estimated using the Friedman method and the FlynnWall-Ozawa method. These isoconversional methods seem to be helpful in providing the mechanistic clues. However the mechanistic clues obtained from such methods are not yet the reaction mechanism rather a path to it that can further be followed using species-specific experimental techniques. The values of activation energy obtained using the Friedman method and the Flynn-Wall-Ozawa method showed variations. These variations are probably due to the approximation of the temperature integral that were used in the derivations of the relations of non-linear isoconversional kinetic methods. Imidazole, 2-nitroimdazole and 4-nitroimidazole 15



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were decomposed by multi step kinetics evident from the non-linear relationship of activation energy with the conversion rate. The C-nitroimdazoles represents different dynamics and kinetics and thus the NO2 elimination and the nitro-nitrite isomerization will compete with each other for the decomposition mechanism. The activation energy, pre-exponential factor and the effective reaction order are strongly dependent on the experimental conditions. The present study may be helpful in understanding the decomposition kinetics of several imidazole derivatives. ASSOCIATED CONTENT Supporting Information Figures of additional experimental data is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author * Tel:. +91-40-23134303, Fax- +91-40-23012800; E-mail: [email protected]. ACKNOWLEDGEMENTS We are very grateful to the reviewers for their useful suggestions and enlightening comments. The support of this work by Defence Research Development Organization, India through Advanced Centre of Research in High Energy Materials is gratefully acknowledged. REFERENCES (1) Larina, L.; Lopyrev, L. Nitroazoles: Synthesis, Structure and Applications; Springer: New York, 2009. (2) Beaman, A. G.; Caldwell, N.; Duschinky, R. 2-Nitroimdiazoles and Process. 1996, US Patent No. 3,287,468. (3) Bulusu, S.; Damavarpu, R.; Autera, J. R.; Behrens Jr. R.; Minier, L. M.; Villanuera, J.; Jayasuriaya, K.; Axenard, T. Thermal Rearrangement of 1,4-Dinitroimidazole to 2,4Dinitroimidazole: Characterization and Investigation of the Mechanism by Mass Spectrometry and Isotope Labeling. J. Phys. Chem. 1995, 99, 5009-5015. (4) Phukan, K.; Devi, N. Greener and Versatile Synthesis of Bioactive 2-Nitroimidazoles using Microwave Irradiation. J. Chem. Pharm. Res. 2011, 3, 1037-1044. 16


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(5) Badgujor, D. M.; Talwar, M. B.; Asthana, S. N.; Mahulikar, P. P. Novel Synthesis of Biologically Active Nitro Heterocyclic Compounds. J. Sci. Ind. Res. 2008, 67, 54-57. (6) Gutowski, K. E.; Rogers, R. D.; Dixon, D. A. Accurate Thermochemical Properties for Energetic Materials Applications. I. Heats of Formation of Nitrogen-Containing Heterocycles and Energetic Precursor Molecules from Electronic Structure Theory. J. Phys. Chem. A 2006, 110, 11890-11897. (7) Gutowski, K. E.; Rogers, R. D.; Dixon, D. A. Accurate Thermochemical Properties for Energetic Materials Applications. II. Heats of Formation of Imidazolium-, 1,2,4-Triazolium, and Tetrazolium Based Energetic Salts from Isodesmic and Lattice Energy Calculations, J. Phys. Chem. B 2007, 111, 4788-4800. (8) Li, X. H.; Zhang, R. Z.; Zhang, X. Z. Computational Study of Imidazole Derivative as High Energetic Materials. J. Hazard. Mater. 2010, 183, 622-631. (9) Yu, Z.; Bernstein, E. R. Experimental and Theoretical Studies of the Decomposition of New Imidazole Based Energetic Materials: Model Systems. J. Chem. Phys. 2012, 137, 114303111430311. (10) Lesnikovich, A. I.; Ivashkevich, O. A.; Lyutsko, V. A.; Printsev, G. V.; Kovalenko, K. K.; Gaponik, P. N.; Levchik, S. V. Thermal Decomposition of Tetrazole: Part I. Programmed Heating. Thermochim. Acta. 1989, 145, 195–202. (11) Friedman, H. L. Kinetics of Thermal Degradation of Char-forming Plastics from Thermogravimetry. Application to a Phenolic Plastic. J. Polym. Sci. C. 1965, 50, 183–195. (12) Ozawa, T. A New Method Analyzing Thermogravimetric Data. Bull. Chem. Soc. Jpn. 1965, 38, 1881–1886. (13) Kissinger, H. E. Reaction Kinetics in Differential Thermal Analysis. Anal. Chem. 1957, 29, 1702–1706. (14) Brown, M. E.; Maciejewski, M.; Vyazovkin, S.; Nomen, R.; Sempere, J.; Burnham, A.; Opfermann, J.; Strey, R.; Anderson, H. L.; Kemmler et al. Computational Aspects of Kinetic Analysis: Part A: the ICTAC Kinetics Project Data, Methods and Results. Thermochim. Acta. 2000, 355, 125–143.

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Isoconversional Kinetic Analysis of Decomposition ... - ACS Publications

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