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Effect of chloride dopant on the kinetics of the thermal decomposition of sodium oxalate
Thermochimica Acta 537 (2012) 25–30
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Effect of chloride dopant on the kinetics of the thermal decomposition of sodium oxalate K. Muraleedharan, M. Jose John 1 , M.P. Kannan, V.M. Abdul Mujeeb ∗ Department of Chemistry, University of Calicut, Kerala 673635, India
a r t i c l e
i n f o
Article history: Received 3 January 2012 Received in revised form 10 February 2012 Accepted 24 February 2012 Available online 5 March 2012 Keywords: Contracting cylinder equation Diffusion controlled mechanism Isothermal thermogravimetry Prout–Tompkins equation Sodium oxalate Chloride doping
a b s t r a c t The thermal decomposition kinetics of sodium oxalate (Na2 C2 O4 ) has been studied as a function of concentration of dopant, chloride, at five different temperatures in the range 783–803 K under isothermal conditions by thermogravimetry (TG). The TG data were subjected to both model free and model fitting methods of kinetic analysis. The results obtained from model fitting methods of kinetic analysis shows that no single kinetic model describes the whole ˛ versus t curve with a single rate constant throughout the decomposition reaction. Separate kinetic analysis shows that Prout–Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model, and corresponding activation energy values were evaluated. The diffusion of Na+ ions occupying normal lattice sites and interstitial sites was greatly affected by a change in the concentration of defects. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Thermal decomposition of metal oxalates has been the subject of many researches, both from a practical and theoretical viewpoint [1–3]. Duval [4] has summarized the thermogravimetric data for the drying and ignition temperature of a large number of metal oxalates. Galwey and Brown [5] has identified and discussed the studies on the thermal decomposition of silver oxalate. Dollimore [6] has made an excellent review on the thermal decomposition and stability of many oxalates. A review on the literature of the thermal behavior of inorganic oxalates reveals that except yttrium oxalate, all undergo thermal decomposition before melting and the decomposition kinetics are not complicated except in the case of a few. The decomposition invariably involves the C C bond breaking and in many cases the C C bond cleavage is the rate determining step [7]. Górski and Kra´snicka [7] proposed that the decomposition in oxalates begins with the heterolytic dissociation of C C bond forming CO2 and CO2 2− . The cleavage may be heterolytic to produce CO2 and CO2 2− [7] or hemolytic to produce two CO2 − anions [8]. In silver oxalate [9], the transfer of an electron from the C2 O4 2− to the cation is the first stage of the decomposition which leads to the rupture of
∗ Corresponding author. Tel.: +91 494 2401144x413; fax: +91 494 2400269. E-mail address: [email protected] (V.M. Abdul Mujeeb). 1 Present address: Department of Chemistry, St. Josephs College, Devagiri, Calicut, Kerala, India. 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2012.02.031
the C C bond [10]. Chaiyo et al. [11] studied the thermal decomposition of Na2 C2 O4 using non-isothermal TG–DTA, XRD, and SEM; performed the kinetic analysis of the non-isothermal decomposition data using the iso-conversional methods, proposed by Ozawa and KAS, and possible conversion functions have been estimated by the Liqing–Donghua method [12]. The objective of our investigations is to study the role of lattice defects on solid state decomposition kinetics of alkali metal oxalates with a view to controlling the reactivity of solids in general. As solid-state reactions often occur between crystal lattices or with molecules that must permeate into lattices where motion is restricted and may depend on lattice defects [13], the solids under investigation are subjected to pretreatments such as doping, precompression, and pre-heating, to modify the magnitude and nature of lattice defects. It has been reported that pre-treatments affect the rate and temperature of decomposition of oxalates [14–16]. The first two factors generally increase the rate and decrease the decomposition and dehydration temperatures. The effects of pretreatments on decomposition kinetics provide valuable information regarding the topochemistry of the solid and the kinetics and mechanism of the solid state reactions. In continuation of our work on metal oxalates [17–19], in the present paper we describe the effect of chloride dopants on the kinetics of thermal decomposition of sodium oxalate. Doping of ionic solids with ions of different valences not only introduces impurity ions into the lattice but also changes the vacancy concentration so as to restore the electrical charge balance
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of the lattice. Thus doping Na2 C2 O4 with Cl− causes an increase in the concentration of cation vacancies. In ionic solids the following relationships holds good at a given temperature. [+] [−] = constant
(1)
[+] [I + ] = constant
(2)
where [+], [−] and [I+ ] represent concentration of cation vacancy, anion vacancy and interstitial, respectively. Thus an increase in the concentration of cation vacancies will be accompanied by a decrease in the anion vacancies as per Eq. (1) and a decrease in the concentration of interstitials as per Eq. (2). This principle can be utilized for arriving probable mechanism of decomposition of solids doped with alliovalent ions.
2. Experimental 2.1. Materials All the chemicals used in the present study were of AnalaR grade samples of Merck. NaCl is used for doping chloride. Like earlier workers [20–25], the doped samples were prepared by the method of co-crystallization. Chloride doped samples of sodium oxalate were prepared as per the following procedure. 10 g of sodium oxalate was dissolved in 230 ml of distilled water at boiling temperature in a 500 ml beaker. 10 ml of a solution containing the desired quantity of Cl− is added to the hot solution so as to achieve a total volume of 240 ml. The solution, containing desired concentration of the dopant, was then cooled slowly to room temperature. The beaker containing the solution was covered using a clean uniformly perforated paper and kept in an air oven at a temperature of 333 K over a period of 6–7 days to allow slow crystallization by evaporation. The resulting crystals were removed; air dried, powdered in an agate mortar, fixed the particle size in the range 106–125 m and kept in a vacuum desiccator. The doped samples were prepared at five different concentrations, viz. 10−5 , 10−4 , 10−3 , 10−2 , 10−1 , and 1 mol%.
2.2. Thermogravimetric analysis Thermogravimetric measurements in static air were carried out on a custom-made thermobalance fabricated in this laboratory [22,23], a modified one of that reported by Hooley [26]. A major problem [27] of the isothermal experiment is that a sample requires some time to reach the experimental temperature. During this period of non-isothermal heating, the sample undergoes some transformations that are likely to affect the succeeding kinetics. The situation is especially aggravated by the fact that under isothermal conditions, a typical solid-state process has its maximum reaction rate at the beginning of the transformation. So we fabricated a thermobalance particularly for isothermal studies, in which loading of the sample is possible at any time after the furnace has attained the desired reaction temperature. The operational characteristics of the thermobalance are, balance sensitivity: ±1 × 10−5 g, temperature accuracy: ±0.5 K, sample mass: 5 × 10−2 g, atmosphere:static air and crucible:platinum. Thermal decomposition of sodium oxalate was found to be very slow below 783 K and very fast above 803 K. The decomposition was thus studied in the range 783–803 K. The loss in mass of sodium oxalate was measured as a function of time (t) at five different temperatures (T), viz., 783, 788, 793, 798 and 803 K.
2.3. Kinetic analysis 2.3.1. Model free (isoconversional) methods Isoconversional methods have their origin in the single-step kinetic equation: d˛ = Ae−E/RT f (˛)h dt where E is the activation energy, A is the Arrhenius pre-exponential factor, f(˛) is the reaction model or conversion function, R is the gas constant, T is the temperature, t is the time, and ˛ is the extent of conversion. The fundamental assumption of isoconversional methods is that a single-step kinetic equation is applicable only to a single extent of conversion and to the temperature region related to this conversion. That is, isoconversional methods describe the kinetics of the process by simultaneously using multiple single step kinetic equations. The temperature dependence of the isoconversional rate can be used to evaluate the values of the activation energy, E␣ without assuming/determining the reaction model. The isoconversional principle lays a foundation for a large number of isoconversional computational methods. They can generally be split in two categories: differential and integral [28]. The most common differential isoconversional method is that of Friedman [29], in which ln[(d˛/dt)i ] is plotted against 1/Ti , measured at the same value of ˛i , from ˛ versus t curves at different isothermal reaction temperatures, Ti , and the activation energy values were evaluated from the slope of the plot. Under integral isoconversional method [10] the plot of ln t (t being the time required for reaching a given value of ˛ at a constant temperature T) versus the corresponding reciprocal of the temperature (1/T) would lead to the activation energy for the given value of ˛. 2.3.2. Model fitting methods Historically model-fitting methods were widely used because of their ability to directly determine the kinetic triplet. On the other hand, isoconversional methods do not compute a frequency factor nor determine reaction models which are needed for a complete kinetic analysis. In solid state kinetics, mechanistic interpretations usually involve identifying a reasonable reaction model [30] because information about individual reaction steps is often difficult to obtain. A model can describe a particular reaction type and translate that mathematically into a rate equation. Many models have been proposed in solid-state kinetics and these models have been developed based on certain mechanistic assumptions. Solid-state kinetic reactions can be mechanistically classified as nucleation, geometrical contraction, diffusion and reaction order models [10]. In the present work we have subjected kinetic analysis of TG data of all doped samples studied, by weighted linear least squares method, to all kinetic models presented in [10]. 3. Results and discussion The experimental mass loss data obtained from TG were transformed in to ˛ versus t data as reported earlier [25], in the range ˛ = 0.05–0.95 with an interval of 0.05, at all temperatures studied. Typical ˛ versus t curve for the thermal decomposition of chloride doped, at different dopant concentrations, sodium oxalate at 793 K is shown in Fig. 1. Similar types of ˛ versus t curve were obtained at all other temperature studied (not shown). The nature of the ˛ versus t curves (sigmoid) remain unchanged on doping. Kinetic analysis of the TG data of the chloride-doped sodium oxalate samples, in the range ˛ = 0.05–0.95, were accomplished through the Friedman’s [10,29] differential model free method, by plotting ln[(d˛/dt)i ] against 1/Ti , and the activation energy values were evaluated from the slope of the plot. The values of E, standard
-1
α 1.0
0.5
0.0
210
195
180
210
195
180
A
B
15
0.4
30
Nil -5 10 mol % -4 10 mol % -3 10 mol % -2 10 mol % -1 10 mol % 0 10 mol %
0.2
t / min
α 0.6
60
-5
10 mol % -4 10 mol % -3 10 mol % -2 10 mol % -1 10 mol % 1 mol %
1.0
Table 1 Values of E, standard deviation (SD) and r obtained from Friedman’s differential isoconversional method for the thermal decomposition of chloride-doped sodium oxalate samples at different dopant concentrations. ˛
Dopant concentration/mol% 10−4
10−5 E/kJ mol 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
201.3 198.1 196.6 195.4 196.6 195.3 196.1 193.1 189.8 188.1 184.6 184.2 183.0 182.3 180.6 178.2 177.6 175.4
−1
SD
−r
E/kJ mol
0.0750 0.1060 0.0740 0.0228 0.0960 0.0543 0.0588 0.0588 0.0921 0.0746 0.0630 0.0868 0.0883 0.0508 0.0952 0.0742 0.0759 0.2345
0.9561 0.9181 0.9907 0.9851 0.9873 0.9807 0.9901 0.9802 0.9709 0.9702 0.9421 0.9231 0.9138 0.9231 0.9013 0.9023 0.9325 0.8893
199.3 197.1 196.8 196.0 194.3 194.1 193.4 193.0 193.2 192.1 189.5 187.4 185.6 184.4 183.9 181.2 180.7 178.4
10−2
10−3 −1
SD
−r
E/kJ mol
0.1739 0.0320 0.1542 0.0881 0.1089 0.0321 0.0880 0.0741 0.0825 0.1232 0.0725 0.1526 0.0969 0.0826 0.0884 0.1061 0.1378 0.1818
0.9043 0.9898 0.9015 0.9801 0.9012 0.9897 0.9875 0.9897 0.9801 0.9091 0.9849 0.9147 0.9754 0.9812 0.9891 0.9209 0.9148 0.9014
201.5 199.7 198.6 196.5 195.2 194.0 192.8 191.4 188.3 186.8 184.6 182.8 181.7 180.5 180.0 178.4 177.4 176.8
−1
10−1 −1
SD
−r
E/kJ mol
SD
−r
E/kJ mol
0.2057 0.1270 0.1081 0.0603 0.0684 0.0793 0.0608 0.0488 0.0700 0.1219 0.0681 0.0808 0.0927 0.1761 0.0686 0.1049 0.0337 0.1262
0.9092 0.9012 0.9135 0.9859 0.9818 0.9896 0.9857 0.9868 0.9823 0.9014 0.9875 0.9127 0.9012 0.9001 0.9526 0.9120 0.9895 0.9107
203.4 199.6 197.1 196.6 196.0 194.7 193.6 192.0 190.9 189.8 188.7 187.8 186.0 185.8 184.5 182.1 180.2 179.9
0.1132 0.1090 0.1122 0.0768 0.0291 0.0643 0.1393 0.0340 0.0639 0.0264 0.0991 0.1321 0.0346 0.0664 0.0588 0.0816 0.0608 0.1384
0.9012 0.9156 0.9019 0.9803 0.9871 0.9795 0.9120 0.9891 0.9808 0.9859 0.9218 0.9017 0.9879 0.9816 0.9846 0.9648 0.98727 0.9025
206.8 200.0 197.7 195.5 195.3 193.6 192.1 190.0 189.0 187.3 185.6 185.1 184.4 183.9 181.1 179.9 177.4 177.8
1 −1
SD
−r
E/kJ mol−1
SD
−r
0.1241 0.0502 0.0735 0.0090 0.0928 0.0937 0.0808 0.0843 0.0515 0.0927 0.0873 0.0534 0.0952 0.1405 0.0733 0.1101 0.1815 0.2613
0.9128 0.9745 0.9753 0.9909 0.9802 0.9958 0.9890 0.9896 0.9870 0.9891 0.9819 0.9872 0.9799 0.9014 0.9874 0.9100 0.8901 0.8802
204.2 199.0 196.2 195.3 194.6 193.1 192.0 190.9 189.1 188.3 187.9 185.1 183.6 182.2 180.7 179.2 178.1 177.7
0.0312 0.1910 0.1292 0.0262 0.0688 0.0332 0.0780 0.0663 0.1087 0.1179 0.0304 0.0569 0.0568 0.0968 0.1470 0.1056 0.2065 0.0373
0.9895 0.9123 0.9028 0.9857 0.9825 0.9879 0.9856 0.9799 0.9023 0.9011 0.9892 0.9854 0.9862 0.9749 0.9018 0.9107 0.8907 0.9901
K. Muraleedharan et al. / Thermochimica Acta 537 (2012) 25–30
45
0.8
Fig. 1. Typical ˛ versus t curve for the thermal decomposition of chloride-doped (at different dopant concentrations) sodium oxalate at 793 K.
E / kJ mol
deviation (SD) and correlation coefficient (r) values obtained for all chloride-doped sodium oxalate samples are given in Table 1. The ˛–t data, in the range of ˛ = 0.05–0.95, of the isothermal decomposition of chloride-doped sodium oxalate samples were also subjected to integral isoconversional studies. The values of apparent activation energy, as a function of ˛, were evaluated from the slope obtained by plotting ln t versus the corresponding reciprocal of the temperature (1/T). The values of activation energy obtained for the thermal decomposition of all chloridedoped sodium oxalate samples at different conversions are given in Table 2 and the dependence of E on conversion is shown in Fig. 2. Examination of Tables 1 and 2 and Fig. 2 reveals that the activation energy is not constant through the entire conversion range studied, its value first decreases – though not in a steady/systematic manner – and stabilizes towards the end. This indicates that in the range, ˛ = 0.05–0.45, the thermal decomposition reaction requires more activation energy. Examination of Table 1 and Fig. 2A shows that the Friedmann’s differential isoconversional method resulted poor correlation at most of the conversions.
-1
0.0
Fig. 2. Dependence of E on ˛ obtained for the differential (A) and integral (B) isoconversional methods for the thermal decomposition of chloride-doped sodium oxalate.
E / kJ mol
27
0.0337 0.0214 0.0511 0.0540 0.0487 0.0425 0.0415 0.0419 0.0430 0.0421 0.0375 0.0360 0.0352 0.0346 0.0362 0.0350 0.0316 0.0340 0.0294 0.9849 0.9931 0.9962 0.9951 0.9957 0.9955 0.9956 0.9967 0.9975 0.9979 0.9978 0.9980 0.9981 0.9987 0.9982 0.9985 0.9986 0.9990 0.9973 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
194.8 192.1 184.6 182.3 179.0 177.0 177.0 175.1 175.2 174.3 173.7 172.7 172.3 171.9 171.6 172.2 172.4 172.2 172.4
0.0355 0.0141 0.0286 0.0241 0.0205 0.0241 0.0244 0.0201 0.0163 0.0161 0.0161 0.0176 0.0151 0.0155 0.0150 0.0145 0.0140 0.0125 0.0055
0.9951 0.9989 0.9951 0.9967 0.9975 0.9966 0.9965 0.9976 0.9984 0.9985 0.9985 0.9982 0.9987 0.9986 0.9987 0.9988 0.9989 0.9991 0.9998
203.0 200.0 198.4 196.9 193.9 190.8 187.3 184.5 180.7 177.1 175.1 174.7 174.6 174.6 173.4 173.2 173.2 172.3 173.0
0.0528 0.0474 0.0411 0.0446 0.0418 0.0343 0.0299 0.0297 0.0271 0.0260 0.0226 0.0232 0.0164 0.0163 0.0174 0.0170 0.0188 0.0234 0.0210
0.9894 0.9904 0.9922 0.9910 0.9919 0.9943 0.9956 0.9955 0.9962 0.9965 0.9974 0.9972 0.9986 0.9987 0.9985 0.9985 0.9982 0.9974 0.9979
205.9 199.9 196.2 193.1 190.3 186.3 183.1 181.3 178.2 178.0 176.7 176.5 175.1 174.3 174.3 174.8 174.2 173.8 174.0
0.0458 0.0885 0.0932 0.0875 0.0749 0.0663 0.0638 0.0614 0.0564 0.0550 0.0551 0.0536 0.0505 0.0516 0.0461 0.0433 0.0415 0.0383 0.0377
0.9922 0.9693 0.9613 0.9666 0.9748 0.9785 0.9798 0.9809 0.9830 0.9839 0.9837 0.9844 0.9860 0.9858 0.9887 0.9901 0.9911 0.9926 0.9927
203.4 198.1 196.1 193.2 190.5 189.0 185.6 182.2 179.2 176.3 175.3 176.5 175.8 174.1 174.2 173.0 173.1 172.7 172.0
0.0886 0.0545 0.0549 0.0615 0.0628 0.0581 0.0575 0.0468 0.0428 0.0424 0.0404 0.0384 0.0341 0.0341 0.0352 0.0353 0.0353 0.0334 0.0257
0.9772 0.9856 0.9850 0.9795 0.9777 0.9810 0.9808 0.9871 0.9889 0.9891 0.9904 0.9914 0.9935 0.9936 0.9930 0.9930 0.9931 0.9937 0.9962
205.5 201.4 199.3 197.8 196.1 193.5 190.8 187.7 185.1 180.4 178.5 178.0 177.2 177.9 178.9 177.5 176.9 176.1 176.5
0.0723 0.0520 0.0361 0.0397 0.0358 0.0357 0.0345 0.0297 0.0252 0.0227 0.0234 0.0223 0.0212 0.0176 0.0212 0.0191 0.0187 0.0159 0.0259
208.5 200.0 194.8 192.4 190.7 188.0 185.7 183.7 180.1 176.7 175.0 175.7 176.6 176.6 175.4 175.3 176.8 175.9 175.8
SD 1
E/kJ mol−1 r SD E/kJ mol−1 E/kJ mol−1 SD
r E/kJ mol−1
SD
r
E/kJ mol−1
SD
r
E/kJ mol−1
SD
r
10−1 10−2 10−3 10−4 10−5
Dopant concentration/mol% ␣
Table 2 Values of E, standard deviation (SD) and r obtained from the integral isoconversional method for the thermal decomposition of chloride-doped sodium oxalate samples at different dopant concentrations.
0.9961 0.9981 0.9877 0.9855 0.9878 0.9903 0.9909 0.9906 0.9899 0.9906 0.9925 0.9932 0.9935 0.9938 0.9933 0.9938 0.9948 0.9941 0.9951
K. Muraleedharan et al. / Thermochimica Acta 537 (2012) 25–30
r
28
Fig. 3. The dependence of rate constant on dopant concentration (I: acceleratory stage and II: deceleratory stage) for the thermal decomposition chloride doped sodium oxalate.
The results of kinetic analysis of the TG data of the doped samples, in the range ˛ = 0.05–0.95, by the method of model fitting, revealed that no single kinetic equation describes the whole ˛ versus t curve with a single rate constant as observed with pure sample [18]; the acceleratory stage (˛ < 0.5) of the thermal decomposition reaction is best described with Prout–Tompkins equation {ln [˛/(1 − ˛)] = kt} and the deceleratory stage (˛ > 0.5) with contracting cylinder equation [1−(1−˛)1/2 = kt] with separate rate constants, k1 and k2 . Such a description of reaction kinetics using different rate laws for different ranges of conversion is not unusual in solid-state reactions. For instance Philips and Taylor used Prout–Tompkins equation to describe the acceleratory region of the decomposition of potassium metaperiodate (KIO4 ) and the contracting sphere equation for the decay stage [31]. It has also been reported that under isothermal conditions KIO4 decomposes via two stages; the Prout–Tompkins equation best describes the acceleratory stage and the deceleratory stage proceeds according to contracting cylinder law [22,24,32]. The acceleratory stage in the decomposition of lithium perchlorate followed Prout–Tompkins rate law whereas the decay stage followed the monomolecular model [33]. Similarly both the acceleratory and decay regions of the thermal decomposition of sodium perchlorate and of potassium bromate were well described by the Prout–Tompkins relation with separate rate constants [34]. Several other authors [35–39] also have described the reaction kinetics for the same solid using different rate laws for different ranges of ˛. The values of rate constants, k1 and k2 , obtained from model fitting method respectively to Prout–Tompkins model (acceleratory stage) and contracting cylinder model (deceleratory stage) for the thermal decomposition of all samples of chloride-doped sodium oxalate studied are given in Table 3. The dependence of k1 and k2 on dopant concentration at different temperatures is shown in Fig. 3. Table 3 (and also Fig. 3) show that the dopant, Cl− , which produces cation vacancies in the Na2 C2 O4 lattice, desensitize the rate of the decomposition up to a certain concentration of the dopant and then the rate begins to increase slowly with further increase in the dopant concentration. However, the rate remained lower than that of the pure sample even when the dopant concentration is increased to 1 mol%. The desensitizing effect shows the same pattern in both acceleratory and deceleratory stages at all the temperatures examined. The activation energies for both the acceleratory (model: PT) and deceleratory (model: R2) stages of thermal decomposition of all chloride-doped samples of sodium oxalate studied were evaluated from Arrhenius plots. The values of E, standard deviation (SD),
K. Muraleedharan et al. / Thermochimica Acta 537 (2012) 25–30
29
Table 3 Values of rate constants, k1 and k2 , obtained from model fitting respectively to Prout–Tompkins (PT) model (acceleratory stage) and contracting cylinder model (deceleratory stage) for the thermal decomposition chloride doped sodium oxalate. T/K
103 × Rate constant/min
Dopant concentration/mol% 10−5
10−4
10−3
10−2
10−1
1
0
783
k1 k2
1.83 0.451
1.77 0.404
1.74 0.386
1.73 0.375
1.86 0.463
1.92 0.486
1.97 0.469
788
k1 k2
2.12 0.542
2.07 0.483
2.03 0.465
2.01 0.454
2.14 0.567
2.23 0.587
2.29 0.569
793
k1 k2
2.51 0.651
2.44 0.589
2.37 0.556
2.33 0.542
2.53 0.672
2.55 0.703
2.65 0.682
798
k1 k2
2.92 0.777
2.81 0.706
2.66 0.666
2.65 0.647
2.90 0.799
2.96 0.841
3.07 0.828
803
k1 k2
3.36 0.941
3.23 0.852
3.12 0.791
3.14 0.781
3.37 0.973
3.50 1.040
3.58 0.991
Table 4 Values of E, standard deviation (SD), error and correlation coefficient (r) obtained from Arrhenius plot for the acceleratory and deceleratory stages of the thermal decomposition of chloride doped sodium oxalate samples at different dopant concentrations. Dopant concentration/mol%
Nil 10−5 10−4 10−3 10−2 10−1 1
Acceleratory stage (˛ = 0.05–0.45)
Deceleratory stage (˛ = 0.5–0.95)
E/kJ mol−1
SD
Error
−r
E/kJ mol−1
SD
Error
−r
155.5 160.5 157.8 150.4 153.5 156.0 155.1
0.0038 0.0073 0.0080 0.0119 0.0108 0.0075 0.0118
0.1494 0.2900 0.3168 0.4728 0.4292 0.2989 0.4692
0.9999 0.9997 0.9996 0.9990 0.9992 0.9996 0.9991
195.7 191.4 195.7 187.6 190.4 191.1 196.6
0.0036 0.0051 0.0056 0.0022 0.0048 0.0105 0.0124
0.1445 0.2032 0.2222 0.0855 0.1924 0.4158 0.4941
0.9999 0.9999 0.9999 0.9999 0.9999 0.9995 0.9994
error and correlation coefficient (r) obtained from Arrhenius plot for both stages of the thermal decomposition of all chloride-doped sodium oxalate samples studied are given in Table 4. Examination of Table 4 reveals that doping does not alter the Activation energy of the thermal decomposition of sodium oxalate. Diffusion of the cation and/or the anion towards the potential sites, where they can react, usually determines the reaction rate of solid state decompositions. Migration of ions is greatly influenced by the defect structure of the solid. Since the size of the cation is significantly smaller than that of the anion in the oxalate systems, Frenkel defect structure is expected to dominate in these solids. For instance, silver oxalate has been shown to have Frenkel defect structure [10]. No such literature is available on sodium oxalate. However, from size considerations (Na+ is much smaller than Ag+ ), it may be assumed that sodium oxalate is also a solid with Frenkel defect structure. Diffusion of ions can occur mainly in two ways: vacancy mechanism and interstitial mechanism. Both will have their own contributions, but depending upon the characteristic of the solid one may dominate over the other. Due to larger size, migration of C2 O4 2− will be negligible in comparison with Na+ and hence the rate of oxalate decomposition will be controlled by diffusion of cation. The possible diffusion processes taking place during the thermal decomposition of sodium oxalate, diffusion of Na+ ions occupying normal lattice sites and diffusion of Na+ ions occupying the interstitial sites, will be greatly affected by a change in the concentration of defects leading to a complex reactivity of the solid. Doping of sodium oxalate with Cl− results in an increase in the concentration of cation vacancies and we observed, in the present investigation, that doping with Cl− ions results in a decrease of the rate of thermal decomposition (Table 2). According to Eq. (2), an increase in the concentration of cation vacancies results in a decrease of the concentration of Na+ interstitials. This is due to the sucking [40] of interstitials to the normal lattice sites. The decrease in the concentration of interstitials and filling up of vacancies by
these vanishing interstitials result in a decrease of the diffusion rate of cation, and thereby the decomposition rate. This accounts for the observed initial decrease of decomposition rate. But, when the sucking of interstitials into the normal vacant lattice sites is complete, further increase in the concentration of dopants results in a sudden increase in the concentration of cation vacancies, which promote the diffusion of Na+ . This amounts to an increase of decomposition rate and accounts for the increase of rate observed at higher concentrations.
4. Conclusions The thermal decomposition and kinetics of sodium oxalate as a function of dopant (chloride) concentration is investigated by thermogravimetry in the temperature range 783–803 K under isothermal conditions. The TG data were subjected to both model free and model fitting methods of kinetic analysis. We observed that, from model fitting methods, no single kinetic equation fitted the whole ˛ versus t curve with a single rate constant throughout the reaction. Separate kinetic analysis of the acceleratory and deceleratory stages of the thermal decomposition data revealed that the acceleratory stage is best fitted with Prout–Tompkins model (a model developed on the assumption of branching nucleation) and the contracting cylinder model (a model in which the advancement of interface into the bulk of the reactant particle proceeds only from the edges of the crystal surfaces upon which nucleation occurs or simply speaking the inward movement of the interface is two dimensional/cylindrical in nature) best describes the deceleratory stage. The correspondence of acceleratory stage of the decomposition with Prout–Tompkins model indicates that the nucleus growth takes place by propagation of chains. The decrease of the rate in the decay period is likely to be due to the merging of these chains, leading to the kinetics in accordance with the contracting cylinder model.
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The possible diffusion processes taking place during the thermal decomposition of sodium oxalate, diffusion of Na+ ions occupying normal lattice sites and diffusion of Na+ ions occupying the interstitial sites, was greatly affected by a change in the concentration of defects leading to a complex reactivity of the solid. References [1] B.V. L’vov, Kinetics and mechanism of thermal decomposition of nickel, manganese, silver, mercury and lead oxalates, Thermochim. Acta 364 (2000) 99–109. [2] H.S. Gopalakrishna Murhty, M. Subba Rao, T.R. Narayanan Kutty, Thermal decomposition of titanyl oxalates—II: Kinetics of decomposition of barium titanyl oxalate, J. Inorg. Nucl. Chem. 7 (1975) 1875–1878. [3] B.S. Patra, S. Otta, S.D. Bhattamisra, A kinetic and mechanistic study of thermal decomposition of strontium titanyl oxalate, Thermochim. Acta 441 (2006) 84–88. [4] C. Duval, Inorganic thermogravimetric analysis, 2nd ed., Elsevier, Amsterdam, The Netherlands, 1963. [5] A.K. Galwey, M.E. Brown, An appreciation of the chemical approach of V. V. Boldyrev to the study of the decomposition of solids, J. Therm. Anal. Calorim. 90 (2007) 9–22. [6] D. Dollimore, The thermal decomposition of oxalates. A review, Thermochim. Acta 117 (1987) 331–363. [7] A. Górski, A.D. Kra´snicka, The importance of the CO2 2− anion in the mechanism of thermal decomposition of oxalates, J. Therm. Anal. Calorim. 32 (1987) 1229–1241. [8] M.V.V.S. Reddy, K.V. Lingam, T.K. Gundu Rao, Radical studies in oxalate systems: E.S.R. of CO2 − in irradiated potassium oxalate monohydrate, Mol. Phys. 42 (1981) 1267–1269. [9] A.G. Leiga, Decomposition of silver oxalate. II. Kinetics of the thermal decomposition, J. Phys. Chem. 70 (1966) 3260–3267. [10] A.K. Galwey, M.E. Brown, Thermal Decomposition of Ionic Solids, Elsevier, Amsterdam, 1999. [11] N. Chaiyo, R. Muanghlua, S. Niemcharoen, B. Boonchom, P. Seeharaj, N. Vittayakorn, Non-isothermal kinetics of the thermal decomposition of sodium oxalate Na2 C2 O4 , J. Therm. Anal. Calorim. 107 (2012) 1023– 1029. [12] J.J. Zhang, N. Ren, J.H. Bai, Non-isothermal decomposition reaction kinetics of the magnesium oxalate dehydrate, Chin. J. Chem. 24 (2006) 360–364. [13] A.J.E. Welch, Solid–solid reactions, in: W.E. Garner (Ed.), Chemistry of the Solid State, Academic Press, New York, 1955 (Chapter 12). [14] C. Sciora, J.C. Mutin, Traitement mecanique des materiaux III Consequences du broyage sur la reactivite ulterieure de quelques hydrates, J. Therm. Anal. Calorim. 20 (1981) 125–139. [15] C. Sciora, J.C. Mutin, Traitement mecanique des materiaux I—Modification de Phases que provoque le broyage application au cas d’une serie d’oxalates hydrates, J. Therm. Anal. Calorim. 19 (1980) 365–376. [16] M. Rossberg, E.F. Khairetdinov, E. Linke, V.V. Boldyrev, Effect of mechanical pretreatment on thermal decomposition of silver oxalate under nonisothermal conditions, J. Solid State Chem. 41 (1982) 266–271. [17] K. Muraleedharan, P. Labeeb, V.M. Abdul Mujeeb, M.H. Aneesh, T. Ganga Devi, M.P. Kannan, Effect of particle size on non-isothermal decomposition of potassium titanium oxalate, Z. Phys. Chemie 225 (2011) 169–181. [18] M. Jose John, K. Muraleedharan, M.P. Kannan, T. Ganga Devi, Thermal decomposition and kinetics of sodium oxalate, J. Serb. Chem. Soc., submitted for publication.
[19] M. Jose John, K. Muraleedharan, M.P. Kannan, T. Ganga Devi, Effect of semiconducting metal oxide additives on the kinetics of thermal decomposition of sodium oxalate under isothermal conditions, Thermochim. Acta, (2012) doi:10.1016/j.tca.2012.02.001. [20] J.N. Maycock, V.R. Pai Verneker, Role of point defects in the thermal decomposition of ammonium perchlorate, Proc. R. Soc. Lond. 307A (1968) 303–315. [21] V.V. Boldyrev, V.V. Alexandrov, A.V. Boldyreva, V.I. Gritsan, Y.Y. Karpenko, O.P. Korobeinitchev, E.F. Panfilov, V.N. Khairetdinov, On the mechanism of the thermal decomposition of ammonium perchlorate, Combust. Flame 15 (1970) 71–77. [22] M.P. Kannan, K. Muraleedharan, Kinetics of thermal decomposition of sulphate doped potassium metaperiodate, Thermochim. Acta 158 (1990) 259–266. [23] K. Muraleedharan, M.P. Kannan, Effects of dopants on the isothermal decomposition kinetics of potassium metaperiodate, Thermochim. Acta 359 (2000) 161–168. [24] K. Muraleedharan, M.P. Kannan, T. Gangadevi, Thermal decomposition of potassium metaperiodate doped with trivalent ions, Thermochim. Acta 502 (2010) 24–29. [25] V.M. Abdul Mujeeb, K. Muraleedharan, M.P. Kannan, T. Ganga Devi, Influence of trivalent ion dopants on the thermal decomposition kinetics of potassium bromate, Thermochim. Acta 525 (2011) 150–160. [26] J.G. Hooley, A recording vacuum thermobalance, Can. J. Chem. 35 (1957) 374–380. [27] S. Vyazovkin, C.A. Wight, Kinetics in solids, Annu. Rev. Phys. Chem. 48 (1997) 125–149. [28] S. Vyazovkin, A.K. Burnham, J.M. Criado, L.A. Pérez-Maqueda, C. Popescu, N. Sbirrazzuoli, ICTAC kinetics committee recommendations for performing kinetic computations on thermal analysis data, Thermochim. Acta 520 (2011) 1–19. [29] H.L. Friedman, Kinetics of thermal degradation of char-forming plastics from thermogravimetry. Application to a phenolic plastic, J. Polym. Sci., Part C 6 (1964) 183–195. [30] M.E. Brown, Stocktaking in the kinetic cupboard, J. Therm. Anal. Calorim. 82 (2005) 665–669. [31] B.R. Philips, D. Taylor, Thermal decomposition of potassium metaperiodate, J. Chem. Soc. (1963) 5583–5590. [32] K. Muraleedharan, M.P. Kannan, T. Gangadevi, Effect of metal oxide additives on the thermal decomposition kinetics of potassium metaperiodate, J. Therm. Anal. Calorim. 100 (2010) 177–182. [33] M.M. Markowitz, D.A. Boryta, The decomposition kinetics of lithium perchlorate, J. Phys. Chem. 65 (1961) 1419–1424. [34] F. Solymosi, Structure and Stability of Salts of Halogen Oxyacids in the solid phase, John Wiley & Sons, London, 1977. [35] R.A.W. Hill, A diffusion chain theory of the decomposition of inorganic solids, Trans. Faraday Soc. 54 (1958) 685–690. [36] S.R. Mohanty, D. Patnaik, Effects of admixtures of potassium bromide on the thermal decomposition of potassium bromate, J. Therm. Anal. Calorim. 35 (1989) 2153–2159. [37] B.C. Das, D. Patnaik, Effect of anion doping on the thermal decomposition of potassium bromate, J. Thermal Anal. Calorim 61 (2000) 879–883. [38] M.P. Kannan, V.M. Abdul Mujeeb, Effect of dopant ion on the kinetics of thermal decomposition of potassium bromate, React. Kinet. Catal. Lett 72 (2001) 245–252. [39] K. Muraleedharan, V.M. Abdul Mujeeb, M.H. Aneesh, T. Ganga Devi, M.P. Kannan, Effect of pre-treatments on isothermal decomposition kinetics of potassium metaperiodate, Thermochim. Acta 510 (2010) 160–167. [40] J.E. Spice, Chemical Binding and Structure, Pergamon Press, New York, 1964.
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Effect of chloride dopant on the kinetics of the thermal decomposition of sodium oxalate K. Muraleedharan, M. Jose John 1 , M.P. Kannan, V.M. Abdul Mujeeb ∗ Department of Chemistry, University of Calicut, Kerala 673635, India
a r t i c l e
i n f o
Article history: Received 3 January 2012 Received in revised form 10 February 2012 Accepted 24 February 2012 Available online 5 March 2012 Keywords: Contracting cylinder equation Diffusion controlled mechanism Isothermal thermogravimetry Prout–Tompkins equation Sodium oxalate Chloride doping
a b s t r a c t The thermal decomposition kinetics of sodium oxalate (Na2 C2 O4 ) has been studied as a function of concentration of dopant, chloride, at five different temperatures in the range 783–803 K under isothermal conditions by thermogravimetry (TG). The TG data were subjected to both model free and model fitting methods of kinetic analysis. The results obtained from model fitting methods of kinetic analysis shows that no single kinetic model describes the whole ˛ versus t curve with a single rate constant throughout the decomposition reaction. Separate kinetic analysis shows that Prout–Tompkins model best describes the acceleratory stage of the decomposition while the decay region is best fitted with the contracting cylinder model, and corresponding activation energy values were evaluated. The diffusion of Na+ ions occupying normal lattice sites and interstitial sites was greatly affected by a change in the concentration of defects. © 2012 Elsevier B.V. All rights reserved.
1. Introduction Thermal decomposition of metal oxalates has been the subject of many researches, both from a practical and theoretical viewpoint [1–3]. Duval [4] has summarized the thermogravimetric data for the drying and ignition temperature of a large number of metal oxalates. Galwey and Brown [5] has identified and discussed the studies on the thermal decomposition of silver oxalate. Dollimore [6] has made an excellent review on the thermal decomposition and stability of many oxalates. A review on the literature of the thermal behavior of inorganic oxalates reveals that except yttrium oxalate, all undergo thermal decomposition before melting and the decomposition kinetics are not complicated except in the case of a few. The decomposition invariably involves the C C bond breaking and in many cases the C C bond cleavage is the rate determining step [7]. Górski and Kra´snicka [7] proposed that the decomposition in oxalates begins with the heterolytic dissociation of C C bond forming CO2 and CO2 2− . The cleavage may be heterolytic to produce CO2 and CO2 2− [7] or hemolytic to produce two CO2 − anions [8]. In silver oxalate [9], the transfer of an electron from the C2 O4 2− to the cation is the first stage of the decomposition which leads to the rupture of
∗ Corresponding author. Tel.: +91 494 2401144x413; fax: +91 494 2400269. E-mail address: [email protected] (V.M. Abdul Mujeeb). 1 Present address: Department of Chemistry, St. Josephs College, Devagiri, Calicut, Kerala, India. 0040-6031/$ – see front matter © 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.tca.2012.02.031
the C C bond [10]. Chaiyo et al. [11] studied the thermal decomposition of Na2 C2 O4 using non-isothermal TG–DTA, XRD, and SEM; performed the kinetic analysis of the non-isothermal decomposition data using the iso-conversional methods, proposed by Ozawa and KAS, and possible conversion functions have been estimated by the Liqing–Donghua method [12]. The objective of our investigations is to study the role of lattice defects on solid state decomposition kinetics of alkali metal oxalates with a view to controlling the reactivity of solids in general. As solid-state reactions often occur between crystal lattices or with molecules that must permeate into lattices where motion is restricted and may depend on lattice defects [13], the solids under investigation are subjected to pretreatments such as doping, precompression, and pre-heating, to modify the magnitude and nature of lattice defects. It has been reported that pre-treatments affect the rate and temperature of decomposition of oxalates [14–16]. The first two factors generally increase the rate and decrease the decomposition and dehydration temperatures. The effects of pretreatments on decomposition kinetics provide valuable information regarding the topochemistry of the solid and the kinetics and mechanism of the solid state reactions. In continuation of our work on metal oxalates [17–19], in the present paper we describe the effect of chloride dopants on the kinetics of thermal decomposition of sodium oxalate. Doping of ionic solids with ions of different valences not only introduces impurity ions into the lattice but also changes the vacancy concentration so as to restore the electrical charge balance
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of the lattice. Thus doping Na2 C2 O4 with Cl− causes an increase in the concentration of cation vacancies. In ionic solids the following relationships holds good at a given temperature. [+] [−] = constant
(1)
[+] [I + ] = constant
(2)
where [+], [−] and [I+ ] represent concentration of cation vacancy, anion vacancy and interstitial, respectively. Thus an increase in the concentration of cation vacancies will be accompanied by a decrease in the anion vacancies as per Eq. (1) and a decrease in the concentration of interstitials as per Eq. (2). This principle can be utilized for arriving probable mechanism of decomposition of solids doped with alliovalent ions.
2. Experimental 2.1. Materials All the chemicals used in the present study were of AnalaR grade samples of Merck. NaCl is used for doping chloride. Like earlier workers [20–25], the doped samples were prepared by the method of co-crystallization. Chloride doped samples of sodium oxalate were prepared as per the following procedure. 10 g of sodium oxalate was dissolved in 230 ml of distilled water at boiling temperature in a 500 ml beaker. 10 ml of a solution containing the desired quantity of Cl− is added to the hot solution so as to achieve a total volume of 240 ml. The solution, containing desired concentration of the dopant, was then cooled slowly to room temperature. The beaker containing the solution was covered using a clean uniformly perforated paper and kept in an air oven at a temperature of 333 K over a period of 6–7 days to allow slow crystallization by evaporation. The resulting crystals were removed; air dried, powdered in an agate mortar, fixed the particle size in the range 106–125 m and kept in a vacuum desiccator. The doped samples were prepared at five different concentrations, viz. 10−5 , 10−4 , 10−3 , 10−2 , 10−1 , and 1 mol%.
2.2. Thermogravimetric analysis Thermogravimetric measurements in static air were carried out on a custom-made thermobalance fabricated in this laboratory [22,23], a modified one of that reported by Hooley [26]. A major problem [27] of the isothermal experiment is that a sample requires some time to reach the experimental temperature. During this period of non-isothermal heating, the sample undergoes some transformations that are likely to affect the succeeding kinetics. The situation is especially aggravated by the fact that under isothermal conditions, a typical solid-state process has its maximum reaction rate at the beginning of the transformation. So we fabricated a thermobalance particularly for isothermal studies, in which loading of the sample is possible at any time after the furnace has attained the desired reaction temperature. The operational characteristics of the thermobalance are, balance sensitivity: ±1 × 10−5 g, temperature accuracy: ±0.5 K, sample mass: 5 × 10−2 g, atmosphere:static air and crucible:platinum. Thermal decomposition of sodium oxalate was found to be very slow below 783 K and very fast above 803 K. The decomposition was thus studied in the range 783–803 K. The loss in mass of sodium oxalate was measured as a function of time (t) at five different temperatures (T), viz., 783, 788, 793, 798 and 803 K.
2.3. Kinetic analysis 2.3.1. Model free (isoconversional) methods Isoconversional methods have their origin in the single-step kinetic equation: d˛ = Ae−E/RT f (˛)h dt where E is the activation energy, A is the Arrhenius pre-exponential factor, f(˛) is the reaction model or conversion function, R is the gas constant, T is the temperature, t is the time, and ˛ is the extent of conversion. The fundamental assumption of isoconversional methods is that a single-step kinetic equation is applicable only to a single extent of conversion and to the temperature region related to this conversion. That is, isoconversional methods describe the kinetics of the process by simultaneously using multiple single step kinetic equations. The temperature dependence of the isoconversional rate can be used to evaluate the values of the activation energy, E␣ without assuming/determining the reaction model. The isoconversional principle lays a foundation for a large number of isoconversional computational methods. They can generally be split in two categories: differential and integral [28]. The most common differential isoconversional method is that of Friedman [29], in which ln[(d˛/dt)i ] is plotted against 1/Ti , measured at the same value of ˛i , from ˛ versus t curves at different isothermal reaction temperatures, Ti , and the activation energy values were evaluated from the slope of the plot. Under integral isoconversional method [10] the plot of ln t (t being the time required for reaching a given value of ˛ at a constant temperature T) versus the corresponding reciprocal of the temperature (1/T) would lead to the activation energy for the given value of ˛. 2.3.2. Model fitting methods Historically model-fitting methods were widely used because of their ability to directly determine the kinetic triplet. On the other hand, isoconversional methods do not compute a frequency factor nor determine reaction models which are needed for a complete kinetic analysis. In solid state kinetics, mechanistic interpretations usually involve identifying a reasonable reaction model [30] because information about individual reaction steps is often difficult to obtain. A model can describe a particular reaction type and translate that mathematically into a rate equation. Many models have been proposed in solid-state kinetics and these models have been developed based on certain mechanistic assumptions. Solid-state kinetic reactions can be mechanistically classified as nucleation, geometrical contraction, diffusion and reaction order models [10]. In the present work we have subjected kinetic analysis of TG data of all doped samples studied, by weighted linear least squares method, to all kinetic models presented in [10]. 3. Results and discussion The experimental mass loss data obtained from TG were transformed in to ˛ versus t data as reported earlier [25], in the range ˛ = 0.05–0.95 with an interval of 0.05, at all temperatures studied. Typical ˛ versus t curve for the thermal decomposition of chloride doped, at different dopant concentrations, sodium oxalate at 793 K is shown in Fig. 1. Similar types of ˛ versus t curve were obtained at all other temperature studied (not shown). The nature of the ˛ versus t curves (sigmoid) remain unchanged on doping. Kinetic analysis of the TG data of the chloride-doped sodium oxalate samples, in the range ˛ = 0.05–0.95, were accomplished through the Friedman’s [10,29] differential model free method, by plotting ln[(d˛/dt)i ] against 1/Ti , and the activation energy values were evaluated from the slope of the plot. The values of E, standard
-1
α 1.0
0.5
0.0
210
195
180
210
195
180
A
B
15
0.4
30
Nil -5 10 mol % -4 10 mol % -3 10 mol % -2 10 mol % -1 10 mol % 0 10 mol %
0.2
t / min
α 0.6
60
-5
10 mol % -4 10 mol % -3 10 mol % -2 10 mol % -1 10 mol % 1 mol %
1.0
Table 1 Values of E, standard deviation (SD) and r obtained from Friedman’s differential isoconversional method for the thermal decomposition of chloride-doped sodium oxalate samples at different dopant concentrations. ˛
Dopant concentration/mol% 10−4
10−5 E/kJ mol 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
201.3 198.1 196.6 195.4 196.6 195.3 196.1 193.1 189.8 188.1 184.6 184.2 183.0 182.3 180.6 178.2 177.6 175.4
−1
SD
−r
E/kJ mol
0.0750 0.1060 0.0740 0.0228 0.0960 0.0543 0.0588 0.0588 0.0921 0.0746 0.0630 0.0868 0.0883 0.0508 0.0952 0.0742 0.0759 0.2345
0.9561 0.9181 0.9907 0.9851 0.9873 0.9807 0.9901 0.9802 0.9709 0.9702 0.9421 0.9231 0.9138 0.9231 0.9013 0.9023 0.9325 0.8893
199.3 197.1 196.8 196.0 194.3 194.1 193.4 193.0 193.2 192.1 189.5 187.4 185.6 184.4 183.9 181.2 180.7 178.4
10−2
10−3 −1
SD
−r
E/kJ mol
0.1739 0.0320 0.1542 0.0881 0.1089 0.0321 0.0880 0.0741 0.0825 0.1232 0.0725 0.1526 0.0969 0.0826 0.0884 0.1061 0.1378 0.1818
0.9043 0.9898 0.9015 0.9801 0.9012 0.9897 0.9875 0.9897 0.9801 0.9091 0.9849 0.9147 0.9754 0.9812 0.9891 0.9209 0.9148 0.9014
201.5 199.7 198.6 196.5 195.2 194.0 192.8 191.4 188.3 186.8 184.6 182.8 181.7 180.5 180.0 178.4 177.4 176.8
−1
10−1 −1
SD
−r
E/kJ mol
SD
−r
E/kJ mol
0.2057 0.1270 0.1081 0.0603 0.0684 0.0793 0.0608 0.0488 0.0700 0.1219 0.0681 0.0808 0.0927 0.1761 0.0686 0.1049 0.0337 0.1262
0.9092 0.9012 0.9135 0.9859 0.9818 0.9896 0.9857 0.9868 0.9823 0.9014 0.9875 0.9127 0.9012 0.9001 0.9526 0.9120 0.9895 0.9107
203.4 199.6 197.1 196.6 196.0 194.7 193.6 192.0 190.9 189.8 188.7 187.8 186.0 185.8 184.5 182.1 180.2 179.9
0.1132 0.1090 0.1122 0.0768 0.0291 0.0643 0.1393 0.0340 0.0639 0.0264 0.0991 0.1321 0.0346 0.0664 0.0588 0.0816 0.0608 0.1384
0.9012 0.9156 0.9019 0.9803 0.9871 0.9795 0.9120 0.9891 0.9808 0.9859 0.9218 0.9017 0.9879 0.9816 0.9846 0.9648 0.98727 0.9025
206.8 200.0 197.7 195.5 195.3 193.6 192.1 190.0 189.0 187.3 185.6 185.1 184.4 183.9 181.1 179.9 177.4 177.8
1 −1
SD
−r
E/kJ mol−1
SD
−r
0.1241 0.0502 0.0735 0.0090 0.0928 0.0937 0.0808 0.0843 0.0515 0.0927 0.0873 0.0534 0.0952 0.1405 0.0733 0.1101 0.1815 0.2613
0.9128 0.9745 0.9753 0.9909 0.9802 0.9958 0.9890 0.9896 0.9870 0.9891 0.9819 0.9872 0.9799 0.9014 0.9874 0.9100 0.8901 0.8802
204.2 199.0 196.2 195.3 194.6 193.1 192.0 190.9 189.1 188.3 187.9 185.1 183.6 182.2 180.7 179.2 178.1 177.7
0.0312 0.1910 0.1292 0.0262 0.0688 0.0332 0.0780 0.0663 0.1087 0.1179 0.0304 0.0569 0.0568 0.0968 0.1470 0.1056 0.2065 0.0373
0.9895 0.9123 0.9028 0.9857 0.9825 0.9879 0.9856 0.9799 0.9023 0.9011 0.9892 0.9854 0.9862 0.9749 0.9018 0.9107 0.8907 0.9901
K. Muraleedharan et al. / Thermochimica Acta 537 (2012) 25–30
45
0.8
Fig. 1. Typical ˛ versus t curve for the thermal decomposition of chloride-doped (at different dopant concentrations) sodium oxalate at 793 K.
E / kJ mol
deviation (SD) and correlation coefficient (r) values obtained for all chloride-doped sodium oxalate samples are given in Table 1. The ˛–t data, in the range of ˛ = 0.05–0.95, of the isothermal decomposition of chloride-doped sodium oxalate samples were also subjected to integral isoconversional studies. The values of apparent activation energy, as a function of ˛, were evaluated from the slope obtained by plotting ln t versus the corresponding reciprocal of the temperature (1/T). The values of activation energy obtained for the thermal decomposition of all chloridedoped sodium oxalate samples at different conversions are given in Table 2 and the dependence of E on conversion is shown in Fig. 2. Examination of Tables 1 and 2 and Fig. 2 reveals that the activation energy is not constant through the entire conversion range studied, its value first decreases – though not in a steady/systematic manner – and stabilizes towards the end. This indicates that in the range, ˛ = 0.05–0.45, the thermal decomposition reaction requires more activation energy. Examination of Table 1 and Fig. 2A shows that the Friedmann’s differential isoconversional method resulted poor correlation at most of the conversions.
-1
0.0
Fig. 2. Dependence of E on ˛ obtained for the differential (A) and integral (B) isoconversional methods for the thermal decomposition of chloride-doped sodium oxalate.
E / kJ mol
27
0.0337 0.0214 0.0511 0.0540 0.0487 0.0425 0.0415 0.0419 0.0430 0.0421 0.0375 0.0360 0.0352 0.0346 0.0362 0.0350 0.0316 0.0340 0.0294 0.9849 0.9931 0.9962 0.9951 0.9957 0.9955 0.9956 0.9967 0.9975 0.9979 0.9978 0.9980 0.9981 0.9987 0.9982 0.9985 0.9986 0.9990 0.9973 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95
194.8 192.1 184.6 182.3 179.0 177.0 177.0 175.1 175.2 174.3 173.7 172.7 172.3 171.9 171.6 172.2 172.4 172.2 172.4
0.0355 0.0141 0.0286 0.0241 0.0205 0.0241 0.0244 0.0201 0.0163 0.0161 0.0161 0.0176 0.0151 0.0155 0.0150 0.0145 0.0140 0.0125 0.0055
0.9951 0.9989 0.9951 0.9967 0.9975 0.9966 0.9965 0.9976 0.9984 0.9985 0.9985 0.9982 0.9987 0.9986 0.9987 0.9988 0.9989 0.9991 0.9998
203.0 200.0 198.4 196.9 193.9 190.8 187.3 184.5 180.7 177.1 175.1 174.7 174.6 174.6 173.4 173.2 173.2 172.3 173.0
0.0528 0.0474 0.0411 0.0446 0.0418 0.0343 0.0299 0.0297 0.0271 0.0260 0.0226 0.0232 0.0164 0.0163 0.0174 0.0170 0.0188 0.0234 0.0210
0.9894 0.9904 0.9922 0.9910 0.9919 0.9943 0.9956 0.9955 0.9962 0.9965 0.9974 0.9972 0.9986 0.9987 0.9985 0.9985 0.9982 0.9974 0.9979
205.9 199.9 196.2 193.1 190.3 186.3 183.1 181.3 178.2 178.0 176.7 176.5 175.1 174.3 174.3 174.8 174.2 173.8 174.0
0.0458 0.0885 0.0932 0.0875 0.0749 0.0663 0.0638 0.0614 0.0564 0.0550 0.0551 0.0536 0.0505 0.0516 0.0461 0.0433 0.0415 0.0383 0.0377
0.9922 0.9693 0.9613 0.9666 0.9748 0.9785 0.9798 0.9809 0.9830 0.9839 0.9837 0.9844 0.9860 0.9858 0.9887 0.9901 0.9911 0.9926 0.9927
203.4 198.1 196.1 193.2 190.5 189.0 185.6 182.2 179.2 176.3 175.3 176.5 175.8 174.1 174.2 173.0 173.1 172.7 172.0
0.0886 0.0545 0.0549 0.0615 0.0628 0.0581 0.0575 0.0468 0.0428 0.0424 0.0404 0.0384 0.0341 0.0341 0.0352 0.0353 0.0353 0.0334 0.0257
0.9772 0.9856 0.9850 0.9795 0.9777 0.9810 0.9808 0.9871 0.9889 0.9891 0.9904 0.9914 0.9935 0.9936 0.9930 0.9930 0.9931 0.9937 0.9962
205.5 201.4 199.3 197.8 196.1 193.5 190.8 187.7 185.1 180.4 178.5 178.0 177.2 177.9 178.9 177.5 176.9 176.1 176.5
0.0723 0.0520 0.0361 0.0397 0.0358 0.0357 0.0345 0.0297 0.0252 0.0227 0.0234 0.0223 0.0212 0.0176 0.0212 0.0191 0.0187 0.0159 0.0259
208.5 200.0 194.8 192.4 190.7 188.0 185.7 183.7 180.1 176.7 175.0 175.7 176.6 176.6 175.4 175.3 176.8 175.9 175.8
SD 1
E/kJ mol−1 r SD E/kJ mol−1 E/kJ mol−1 SD
r E/kJ mol−1
SD
r
E/kJ mol−1
SD
r
E/kJ mol−1
SD
r
10−1 10−2 10−3 10−4 10−5
Dopant concentration/mol% ␣
Table 2 Values of E, standard deviation (SD) and r obtained from the integral isoconversional method for the thermal decomposition of chloride-doped sodium oxalate samples at different dopant concentrations.
0.9961 0.9981 0.9877 0.9855 0.9878 0.9903 0.9909 0.9906 0.9899 0.9906 0.9925 0.9932 0.9935 0.9938 0.9933 0.9938 0.9948 0.9941 0.9951
K. Muraleedharan et al. / Thermochimica Acta 537 (2012) 25–30
r
28
Fig. 3. The dependence of rate constant on dopant concentration (I: acceleratory stage and II: deceleratory stage) for the thermal decomposition chloride doped sodium oxalate.
The results of kinetic analysis of the TG data of the doped samples, in the range ˛ = 0.05–0.95, by the method of model fitting, revealed that no single kinetic equation describes the whole ˛ versus t curve with a single rate constant as observed with pure sample [18]; the acceleratory stage (˛ < 0.5) of the thermal decomposition reaction is best described with Prout–Tompkins equation {ln [˛/(1 − ˛)] = kt} and the deceleratory stage (˛ > 0.5) with contracting cylinder equation [1−(1−˛)1/2 = kt] with separate rate constants, k1 and k2 . Such a description of reaction kinetics using different rate laws for different ranges of conversion is not unusual in solid-state reactions. For instance Philips and Taylor used Prout–Tompkins equation to describe the acceleratory region of the decomposition of potassium metaperiodate (KIO4 ) and the contracting sphere equation for the decay stage [31]. It has also been reported that under isothermal conditions KIO4 decomposes via two stages; the Prout–Tompkins equation best describes the acceleratory stage and the deceleratory stage proceeds according to contracting cylinder law [22,24,32]. The acceleratory stage in the decomposition of lithium perchlorate followed Prout–Tompkins rate law whereas the decay stage followed the monomolecular model [33]. Similarly both the acceleratory and decay regions of the thermal decomposition of sodium perchlorate and of potassium bromate were well described by the Prout–Tompkins relation with separate rate constants [34]. Several other authors [35–39] also have described the reaction kinetics for the same solid using different rate laws for different ranges of ˛. The values of rate constants, k1 and k2 , obtained from model fitting method respectively to Prout–Tompkins model (acceleratory stage) and contracting cylinder model (deceleratory stage) for the thermal decomposition of all samples of chloride-doped sodium oxalate studied are given in Table 3. The dependence of k1 and k2 on dopant concentration at different temperatures is shown in Fig. 3. Table 3 (and also Fig. 3) show that the dopant, Cl− , which produces cation vacancies in the Na2 C2 O4 lattice, desensitize the rate of the decomposition up to a certain concentration of the dopant and then the rate begins to increase slowly with further increase in the dopant concentration. However, the rate remained lower than that of the pure sample even when the dopant concentration is increased to 1 mol%. The desensitizing effect shows the same pattern in both acceleratory and deceleratory stages at all the temperatures examined. The activation energies for both the acceleratory (model: PT) and deceleratory (model: R2) stages of thermal decomposition of all chloride-doped samples of sodium oxalate studied were evaluated from Arrhenius plots. The values of E, standard deviation (SD),
K. Muraleedharan et al. / Thermochimica Acta 537 (2012) 25–30
29
Table 3 Values of rate constants, k1 and k2 , obtained from model fitting respectively to Prout–Tompkins (PT) model (acceleratory stage) and contracting cylinder model (deceleratory stage) for the thermal decomposition chloride doped sodium oxalate. T/K
103 × Rate constant/min
Dopant concentration/mol% 10−5
10−4
10−3
10−2
10−1
1
0
783
k1 k2
1.83 0.451
1.77 0.404
1.74 0.386
1.73 0.375
1.86 0.463
1.92 0.486
1.97 0.469
788
k1 k2
2.12 0.542
2.07 0.483
2.03 0.465
2.01 0.454
2.14 0.567
2.23 0.587
2.29 0.569
793
k1 k2
2.51 0.651
2.44 0.589
2.37 0.556
2.33 0.542
2.53 0.672
2.55 0.703
2.65 0.682
798
k1 k2
2.92 0.777
2.81 0.706
2.66 0.666
2.65 0.647
2.90 0.799
2.96 0.841
3.07 0.828
803
k1 k2
3.36 0.941
3.23 0.852
3.12 0.791
3.14 0.781
3.37 0.973
3.50 1.040
3.58 0.991
Table 4 Values of E, standard deviation (SD), error and correlation coefficient (r) obtained from Arrhenius plot for the acceleratory and deceleratory stages of the thermal decomposition of chloride doped sodium oxalate samples at different dopant concentrations. Dopant concentration/mol%
Nil 10−5 10−4 10−3 10−2 10−1 1
Acceleratory stage (˛ = 0.05–0.45)
Deceleratory stage (˛ = 0.5–0.95)
E/kJ mol−1
SD
Error
−r
E/kJ mol−1
SD
Error
−r
155.5 160.5 157.8 150.4 153.5 156.0 155.1
0.0038 0.0073 0.0080 0.0119 0.0108 0.0075 0.0118
0.1494 0.2900 0.3168 0.4728 0.4292 0.2989 0.4692
0.9999 0.9997 0.9996 0.9990 0.9992 0.9996 0.9991
195.7 191.4 195.7 187.6 190.4 191.1 196.6
0.0036 0.0051 0.0056 0.0022 0.0048 0.0105 0.0124
0.1445 0.2032 0.2222 0.0855 0.1924 0.4158 0.4941
0.9999 0.9999 0.9999 0.9999 0.9999 0.9995 0.9994
error and correlation coefficient (r) obtained from Arrhenius plot for both stages of the thermal decomposition of all chloride-doped sodium oxalate samples studied are given in Table 4. Examination of Table 4 reveals that doping does not alter the Activation energy of the thermal decomposition of sodium oxalate. Diffusion of the cation and/or the anion towards the potential sites, where they can react, usually determines the reaction rate of solid state decompositions. Migration of ions is greatly influenced by the defect structure of the solid. Since the size of the cation is significantly smaller than that of the anion in the oxalate systems, Frenkel defect structure is expected to dominate in these solids. For instance, silver oxalate has been shown to have Frenkel defect structure [10]. No such literature is available on sodium oxalate. However, from size considerations (Na+ is much smaller than Ag+ ), it may be assumed that sodium oxalate is also a solid with Frenkel defect structure. Diffusion of ions can occur mainly in two ways: vacancy mechanism and interstitial mechanism. Both will have their own contributions, but depending upon the characteristic of the solid one may dominate over the other. Due to larger size, migration of C2 O4 2− will be negligible in comparison with Na+ and hence the rate of oxalate decomposition will be controlled by diffusion of cation. The possible diffusion processes taking place during the thermal decomposition of sodium oxalate, diffusion of Na+ ions occupying normal lattice sites and diffusion of Na+ ions occupying the interstitial sites, will be greatly affected by a change in the concentration of defects leading to a complex reactivity of the solid. Doping of sodium oxalate with Cl− results in an increase in the concentration of cation vacancies and we observed, in the present investigation, that doping with Cl− ions results in a decrease of the rate of thermal decomposition (Table 2). According to Eq. (2), an increase in the concentration of cation vacancies results in a decrease of the concentration of Na+ interstitials. This is due to the sucking [40] of interstitials to the normal lattice sites. The decrease in the concentration of interstitials and filling up of vacancies by
these vanishing interstitials result in a decrease of the diffusion rate of cation, and thereby the decomposition rate. This accounts for the observed initial decrease of decomposition rate. But, when the sucking of interstitials into the normal vacant lattice sites is complete, further increase in the concentration of dopants results in a sudden increase in the concentration of cation vacancies, which promote the diffusion of Na+ . This amounts to an increase of decomposition rate and accounts for the increase of rate observed at higher concentrations.
4. Conclusions The thermal decomposition and kinetics of sodium oxalate as a function of dopant (chloride) concentration is investigated by thermogravimetry in the temperature range 783–803 K under isothermal conditions. The TG data were subjected to both model free and model fitting methods of kinetic analysis. We observed that, from model fitting methods, no single kinetic equation fitted the whole ˛ versus t curve with a single rate constant throughout the reaction. Separate kinetic analysis of the acceleratory and deceleratory stages of the thermal decomposition data revealed that the acceleratory stage is best fitted with Prout–Tompkins model (a model developed on the assumption of branching nucleation) and the contracting cylinder model (a model in which the advancement of interface into the bulk of the reactant particle proceeds only from the edges of the crystal surfaces upon which nucleation occurs or simply speaking the inward movement of the interface is two dimensional/cylindrical in nature) best describes the deceleratory stage. The correspondence of acceleratory stage of the decomposition with Prout–Tompkins model indicates that the nucleus growth takes place by propagation of chains. The decrease of the rate in the decay period is likely to be due to the merging of these chains, leading to the kinetics in accordance with the contracting cylinder model.
30
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