A kinetic study of the thermal decomposition process of potassium metabisulfite: Estimation of distributed reactivity model

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1 Journl of Physics nd Chemistry of Solids 69 (28) A kinetic study of the therml decomposition process of potssium metbisulfite: Estimtion of distributed rectivity model B. Jnković,, S. Mentus, M. Jnković b Fculty of Physicl Chemistry, University of Belgrde, Studentski trg 12 16, P.O. Box 137, 111 Belgrde, Serbi nd Montenegro b Rdition nd Environmentl Protection Deprtment, Institute Vinč, P.O. Box 522, 111 Belgrde, Serbi nd Montenegro Received 19 September 27; received in revised form 19 December 27; ccepted 28 Jnury 28 Abstrct The therml decomposition kinetics of potssium metbisulfite ws studied by thermogrvimetric (TG) nd differentil thermogrvimetric (DTG) techniques using non-isotherml experiments. The pprent ctivtion energy (E ) is determined using the differentil (Friedmn) isoconversionl method. The results of the Friedmn s isoconversionl nlysis of the TG t suggests tht the investigted decomposition process follows single-step rection nd the observed pprent ctivtion energy ws determined s kj mol 1. A kinetic rte eqution ws derived for the decomposition process of potssium metbisulfite with contrcting re model, f() ¼ 2(1 ) 1/2, which is estblished using the Mlek s kinetic procedure. The vlue of pre-exponentil fctor (A) is lso evluted nd ws found to be A ¼ min 1. By pplying the Miur s procedure the distributed rectivity model (DRM) for investigted decomposition process ws estblished. From the dependence versus E, the experimentl distribution curve of pprent ctivtion energies, f(e ), ws estimted. By pplying the non-liner lest-squres nlysis, it ws found tht the Gussin distribution model (with distribution prmeters E ¼ kj mol 1 nd s ¼ 1.5 kj mol 1 ) represents the best rectivity model for describing the investigted process. Using the Miur s method, the A vlues were estimted t five different heting rtes nd the verge A vlues re plotted ginst E. The liner reltionship between the A nd E vlues ws estblished (compenstion effect). Also, it ws concluded tht the E vlues clculted by the Friedmn s method nd estimted distribution curve, f(e ), re correct even in the cse when the investigted decomposition process occurs through the single-step rection mechnism. r 28 Elsevier Ltd. All rights reserved. Keywords: A. Inorgnic compounds; C. Thermogrvimetric nlysis (TGA); D. Surfce properties 1. Introduction Potssium metbisulfite, K 2 S 2 O 5, is white crystlline powder with pungent sulfur odor. K 2 S 2 O 5 is lso chemiclly very similr to sodium metbisulfite [1]. Even t room temperture it delibertes gseous sulfur dioxide (SO 2 ) thus cting s potent ntioxint, protecting both the color, nd delicte flvors of wine [1], nd my be used s the ctivtor in the prticulr polymeriztion processes [2,3]. The decomposition my be described by the following chemicl eqution: K 2 S 2 O 5ðsÞ! K 2 O ðsþ þ 2SO 2ðgÞ ", (1) Corresponding uthor. Tel./fx: E-mil ddress: bojnjn@ffh.bg.c.yu (B. Jnković). where the potssium monoxide (K 2 O) is solid slt, wheres the SO 2 is gs. Mlnchuk investigted experimentlly the decomposition of sodium metbisulfite [4]. It ws found tht the therml decomposition of sodium metbisulfite in ir tmosphere involves two mjor weight chnges before the finl formtion of sodium sulfte. The first presented n endothermic process, in which SO 2 is evolved, leving residue of sodium sulfite. The second chnge leds to the formtion of sodium sulfte by oxition of the sulfite [4]. There re, however, the intermedite decomposition rections, occurring t the second chnge, which led to the formtion of elementl sulfur nd to incomplete recovery of the originl sulfur in the finl sulfte product [4]. Bogushevich et l. [5] nlyzed the nture of thermlly induced ion-rdicls ppering in K 2 S 2 O 5 subjected to X-ry irrdition. In ddition, /$ - see front mtter r 28 Elsevier Ltd. All rights reserved. doi:1.116/j.jpcs

2 1924 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) K 2 S 2 O 5 ws used for the electron spin resonnce study of the sulfur dioxide rdicl nion (SO 2 d ) [6]. From the literture survey, it ws concluded tht the therml decompositions of metbisulfites re studied very scrcely. The present uthors re given first complete kinetic nlysis (determintion of full kinetic triplet (Arrhenius prmeters (A nd E ) nd rection model function, f())) of the therml decomposition of K 2 S 2 O 5 by the following presented methods: () differentil isoconversionl (model-free) method [7] nd (b) M lek s kinetic procedure [8 1]. Also, in this pper, the distributed rectivity model (DRM) for investigted decomposition process ws estblished. For estimting the DRM for considered process, the Miur s procedure [11,12] ws used. 2. Experimentl Therml decomposition of K 2 S 2 O 5 (Merck, 99.5%, powder) ws studied by thermogrvimetry using TA SDT 296 thermoblnce, enbling simultneous recording of TGA nd DTA curves. The verge mss of smples ws bout 1571 mg. Purging gs ws nitrogen ( vol%) t flowing rte of 9 ml min 1. The furnce temperture rose linerly t heting rtes: 2.5, 5, 1, 15 nd 3 1C min 1, in the temperture rnge from n mbient one up to 6 1C. The originl mss loss versus temperture (TG) curves obtined t constnt heting rte were trnsformed into the degree of conversion () versus temperture curves by mens of the following eqution: ¼ m m t, (2) m m f where m t represents the mss of the smple t rbitrry time t (or temperture T), wheres m nd m f re the mss of the smple t the beginning nd t the end of the process, respectively. 3. Kinetic study The governing eqution for kinetic nlysis of solid-stte decomposition cn be expressed s ¼ kðtþf ðþ, (3) dt where t is the time, k(t) the temperture-dependent rte constnt nd f() represents the differentil conversion function (rection model). The rection models my tke vrious nlyticl forms nd some of them used in this work re listed in Tble 1. The explicit temperture dependence of the rte constnt is introduced by replcing k(t) with the Arrhenius eqution, which gives dt ¼ A exp E f ðþ, (4) where A is the pre-exponentil (frequency) fctor, E is the pprent ctivtion energy nd R is the gs constnt. In the cse of non-isotherml rection, the pplied heting rtes re constnt nd the temperture cn be expressed s T ¼ T +bt (T is the initil temperture) in which the constnt heting rte, b, is given s dt/dt ¼ b. Using this trnsformtion, Eq. (4) cn be converted into b dt ¼ A exp E f ðþ. (5) The use of Eq. (5) supposes tht kinetic triplet (A, E, f()) describes the time evolution of physicl or chemicl chnge. Tble 1 The bsic kinetic models nd properties of y() nd z() functions Kinetic models Symbol f() g() y() z() Johnson Mehl Avrmi JMA(n) n(1 )[ ln(1 )] 1 1/n [ ln(1 ) 1/n ] Concve for no1, liner for n ¼ 1, mximum for n Phse-bounry controlled rection (contrcting re, i.e., bidimensionl shpe or one-hlf order kinetics) Phse-bounry controlled rection (contrcting volume, i.e., tridimensionl shpe or two-thirds order kinetics) Two-dimensionl diffusion (bidimensionl prticle shpe) Vlensi eqution R2, F1/2 2(1 ) 1/2 [1 (1 ) 1/2 ] Convex.75 R3, F2/3 3(1 ) 2/3 [1 (1 ) 1/3 ] Convex.74 D2 1/[ ln(1 )] (1 ) ln(1 )+ Concve.834 Three-dimensionl diffusion (tridimensionl prticle shpe) Jnder eqution D3 3(1 ) 1/3 /2[(1 ) 1/ 3 1] [1 (1 ) 1/3 ] 2 Concve.74 Three-dimensionl diffusion (tridimensionl prticle shpe) Ginstling Brounshtein D4 3/2[(1 ) 1/3 1] (1 2/3) (1 ) 2/3 Concve.776

3 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) Upon integrtion Eq. (5) gives Z gðþ ¼ f ðþ ¼ A Z T exp E dt b T A Z T exp E dt b ¼ AE Rb Z x expð xþ x 2 dx ¼ AE pðxþ, (6) Rb where g() is the integrl form of the rection model nd p(x) is the temperture integrl, for x ¼ E /, which does not hve nlyticl solution. To overcome this difficulty, the temperture integrl hs been solved using pproximtion methods, series, expnsions, nd numericl solution methods [13]. IfT is low, it my be resonbly ssumed tht T -, so tht the lower limit of the integrl on the right-hnd side of Eq. (6), T, cn be pproximted to be zero Apprent ctivtion energy estimtion Isoconversionl (model-free) method The im of the kinetic nlysis of solid-stte rections is the selection of the f() nd g() functions, which give the best pproximtion of experimentl t. The disdvntge tht the severl kinetic models provide similr description of the studied processes is cused by the strong interreltion between the used kinetic functions [14,15]. Often the choice of n pproprite model bsed on dditionl informtion, e.g., morphologicl studies, is hmpered by the discrepncies between the rel process nd idelized models. The model-independent (model-free) kinetic nlysis, on the other hnd, leds to n estimtion of the pprent ctivtion energy without the definition of detiled model for the rection pthwy. This seems to be the wy of choice to bypss the model-inherent problems. But lso in this cse ssumptions re necessry for scientificlly useful result. For instnce, one ssumption is tht the sme product is obtined irrespective of the heting rte. Accordingly, the isoconversionl methods, which llow for model-independent estimtes of the pprent ctivtion energy t progressive degrees of conversion by conducting multiple experiments t different constnt heting rtes, re highly recommended in order to obtin relible kinetic description of the investigted process [14]. The differentil isoconversionl method suggested by Friedmn [7] is bsed on Eq. (5) in the logrithmic form: " # ln b i dt ;i ¼ ln½a f ðþš E ;. (7) The pprent ctivtion energy (E ) is determined from the slope of the plot of ln[b i (/dt),i ] versus 1/T, t constnt vlue. Subscript i is the ordinl number of n experiment performed t given heting rte. This method is rther ccurte becuse it does not include ny mthemticl pproximtions Rection model determintion Mlek s kinetic procedure The isoconversionl method cn be pplied without knowledge of true f() function. But this function must be invrint for ll heting rtes. If this bsic ssumption is not fulfilled, n pprent E vlue would be clculted, which differs from the ctul vlue. The invrince cn be exmined by the method which is offered by M lek [8 1]. He hs suggested tht f() function is proportionl to the y() nd z() functions tht cn simply be obtined by simple trnsformtion of thermogrvimetric (TG) t. In non-isotherml conditions, these functions re defined s yðþ ¼ dt exp E, (8) zðþ ¼p E T dt b, (9) where p(e /) is the expression of the temperture integrl. It ws suggested tht p(e /) my be ccurtely estimted by mens of the fourth rtionl expression of Senum nd Yng [16]: x 3 þ 18x 2 þ 88x þ 96 pðxþ ¼ x 4 þ 2x 3 þ 12x 2 þ 24x þ 12, (1) where x is reduced pprent ctivtion energy (E /). For prcticl resons, the y() nd z() functions re normlized within the (, 1) rnges. However, s evident from Eqs. (8) nd (9) for clcultions of y() nd z() functions it is necessry to know the pprent ctivtion energy in the cse of non-isotherml conditions. Thus, by plotting the y() dependence, normlized within the (, 1) rnge, the shpe of the function f() is obtined. The y() function is therefore chrcteristic for given rection model, nd it cn be used s dignostic tool for rection model determintion. The mthemticl properties of the y() function for bsic kinetic models re summrized in Tble 1. The z() function hs mximum t 1 p for ll rection models summrized in Tble 1. This prmeter hs chrcteristic vlues for bsic rection models nd these vlues re summrized in Tble 1. If there re considerble differences in the shpe of the y() nd z() functions then, we cn conclude tht the ssumption in which the rection model ws considered to be single-step model hs not fulfilled. The clculted model-independent vlue of the pprent ctivtion energy delivers n unmbiguous choice of the pproprite kinetic model. A non-liner regression nlysis with fixed pprent ctivtion energy vlue or n nlysis using y() ndz() functions [8] re suitble.

4 1926 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) Determintion of the pre-exponentil (frequency) fctor Bsed on the determined pprent ctivtion energy (E ) nd rection (conversion) model (g()), the A vlue cn be clculted from Eq. (6), in ccornce with dependence g() versus E p(x)/rb. For clcultion the A vlue for the investigted decomposition process, the fourth rtionl expression of Senum nd Yng [16] for p(x) function ws used. Also, knowing the vlue of the pprent ctivtion energy nd the kinetic model, the pre-exponentil fctor cn be clculted from Eq. (11) [8]: A ¼ bx p Tf ð p Þ expðx pþ, (11) where x p ¼ E / p (T p is the pek temperture on corresponding differentil thermogrvimetric, DTG curve), f ()is the differentil form of the kinetic model [df()/], p is the degree of conversion corresponding to the mximum on DTG curve nd p represents the mximum of DTG curve. 4. Determintion of distributed rectivity model For estimtion the DRM for investigted non-isotherml decomposition process of potssium metbisulfite, the Miur s procedure [11,12] is used. In ccornce with this procedure, the cumultive weight loss cn be expressed by the following eqution: m m t m ¼ 1 Z 1 ¼ exp A Z t exp E dt f ðe Þ de, (12) where f(e ) is distribution curve of the pprent ctivtion energy nd A is the pre-exponentil (frequency) fctor corresponding to the E vlue. The distribution curve f(e ) is normlized to stisfy Z 1 f ðe Þ de ¼ 1. (13) Specific mthemticl forms of f(e ) ppering in the literture re the Gussin [17 19], Weibull[2] nd Gmm distributions [21 25]. The distribution cn lso be finite discrete distribution of rbitrry form, in which cse the integrl in Eq. (12) would be replced with summtion [26,27]. Knowingf(E )nda, we cn clculte the chnge in for ny heting profile. In generl cse, the pre-exponentil fctor (A) is ssumed to be constnt to void the complexity of the nlysis. However, the ssumption of constnt A vlue my not be vlid when f(e ) spreds over wide rnge of E vlues, since tht A nd f(e ) re interrelted [18]. The procedure for estimtion both f(e ) nd A cn be summrized in the following few items [11,12]: () Mesure versus T reltionships t lest three different heting rtes. (b) Clculte the vlues of /dt t severl but sme vlues t the different heting rtes, then mke Friedmn plots (ln[b(/dt)] versus 1/T) t the sme vlues using the reltionship in Eq. (7). (c) Determine the pprent ctivtion energies from the Friedmn plots t different levels of, then plot ginst the pprent ctivtion energy (E ). (d) Differentite the versus E reltionship by E to give f(e ), since the following reltion holds pproximtely: ¼ 1 Z 1 E f ðe Þ de ¼ Z E f ðe Þ de. (14) (e) Clculte A corresponding to ech E vlue t ll heting rtes b i (i ¼ 1, 2, 3, y) using the following eqution [12]: :545b i E A 2 ¼ exp E (15) nd then employ the verge A vlue s true A vlue. Eq. (15) ws obtined when pproximting Eq. (12) by Eq. (14). No priori ssumptions were required for the functionl forms of f(e ) nd A(E ). In other words, we could estimte A nd E t ny levels of by using the bove procedure. 5. Results nd discussion The TG nd DTG curves of the decomposition process of potssium metbisulfite smples obtined t different heting rtes (2.5, 5, 1, 15 nd 3 1C min 1 ) re shown in Fig. 1() nd (b). The effect of heting rte on the TG behvior of K 2 S 2 O 5 smples in nitrogen tmosphere is presented in Fig. 1. Lowering of the heting rte brings the rection system closer to equilibrium conditions nd minimizes the effects of het trnsfer nd therml lg. As result, the rection strts nd ends t lower tempertures, nd decomposition occurs over nrrower temperture rnge. The observed TG curves show n symmetric chrcter (Fig. 1()) nd were moves to higher tempertures with increse in heting rte. Fig. 2 shows the reltionships of versus T t five different heting rtes (b ¼ 2.5, 5, 1, 15 nd 3 1C min 1 ). Fig. 2 shows the temperture rnge in which the decomposition process occurs t considered vlues of heting rtes (145 1CpTp275 1C). From Fig. 2, it cn be observed tht ll T curves t ll considered heting rtes hs the sme shpes. Vlues of pek temperture (T p ) nd the degree of conversion t mximum rection rte ( p ), t vrious heting rtes re presented in Tble 2. Incresing of heting rte leds to increse of the pek temperture vlue (T p ) from 21 to 25 1C. On the other

5 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) (dm/dt)/% C Cmin -1 1 Cmin Cmin -1 3 Cmin Temperture, T/ C Tble 2 Vlues of T p nd p for decomposition process of potssium metbisulfite determined by thermogrvimetric nlysis t different heting rtes Heting rte, b (1C min 1 ) T p (1C) p Mss loss/% Cmin Cmin Cmin -1 3 Cmin Temperture, T/ C In [β i (d/dt),i ]/min Fig. 1. TG () nd DTG (b) curves for the therml decomposition process of potssium metbisulfite smples in nitrogen tmosphere Cmin -1 1 Cmin Cmin -1 3 Cmin /T /K -1 Fig. 3. Typicl Friedmn s isoconversionl plots for the determintion of n pprent ctivtion energy t different conversion levels, for the nonisotherml decomposition process of potssium metbisulfite Temperture, T/ C Fig. 2. The experimentl conversion ( T) curves for the therml decomposition process of potssium metbisulfite smples in nitrogen tmosphere, t the different heting rtes. hnd, the vlues of p vry in the rnge of.73p p p.74. The vlues of p t 2.5 nd 5 1C min 1 re equl ( p ¼.73), while the vlue of p t 1, 15 nd 3 1C min is little higher ( p ¼.74). It cn be pointed out, tht Lee nd Dollimore [28] re estblished the procedure for choosing rection model from the degree of conversion t the mximum rection rte ( p ). This pproch hs not gined wide use. Therefore, Vyzovkin nd Wight [15] hve recommended using isoconversionl methods insted of modelistic pproches. The non-isotherml decomposition process of potssium metbisulfite ws nlyzed by differentil (Friedmn) isoconversionl method. A typicl Friedmn plots, constructed to evlute the slopes d(ln b(/dt))/d(1/t), re presented in Fig. 3. If the conversion mechnisms re the sme t ll conversion lvels, the isoconversion lines would ll hve the sme slopes. From Fig. 3, we cn observe tht the isoconversionl lines t ll considered conversion lvels (see the inset in Fig. 3) hve lmost the sme slopes. The dependence of pprent ctivtion energy (E )on the degree of conversion ()(E plot) for non-isotherml decomposition process of potssium metbisulfite obtined

6 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) E /kjmol Fig. 4. Determined pprent ctivtion energy ( ) nd pprent isoconversionl intercepts (&) s function of degree of conversion. The solid continuous lines represents the simulted trends of both, the pprent ctivtion energy nd isoconversionl intercept with the degree of conversion. by Friedmn s method is presented in Fig. 4. The sme figure (Fig. 4) lso shows the dependence of the pprent isoconversionl (Friedmn) intercepts (Eq. (7)) on the degree of conversion () for the investigted decomposition process. The symbols ( ) nd (&) represent directly clculted vlues of pprent ctivtion energies nd isoconversionl intercepts from Friedmn s eqution, respectively. On the other hnd, the full lines which re showed t the sme figure, represents the simulted trends of both, the pprent ctivtion energy nd isoconversionl intercept with the degree of conversion. The simulted lines hve been drwn to better expose the chnges of E vlues with progress of during the trnsformtion. It ws observed from Fig. 4 tht the pprent ctivtion energy ws not relly chnged nd lmost independent with respect to the level of conversion. This suggests tht the non-isotherml decomposition process of potssium metbisulfite follow single-step rection. The pprent ctivtion energy ws determined s E ¼ kj mol 1. It should be noticed tht this result ws obtined without ny knowledge of the rection model, f(). Furthermore, the vrition of y() nd z() functions with conversion re indicted in Figs. 5 nd 6, clculted using Eqs. (8) nd (9), respectively. We normlized the vlues of both y() nd z() within (, 1) intervl under non-isotherml conditions for the decomposition process of potssium metbisulfite. The shpes of the y() nd z() plots re the prcticlly unchnged with respect to heting rte. For clcultions of the bove functions, the pprent ctivtion energy vlue In[Af()], A /min -1 y() Cmin -1 1 Cmin Cmin Fig. 5. Normlized y() function obtined by trnsformtion of TG t for the decomposition process of potssium metbisulfite t the different heting rtes (b ¼ 2.5, 5, 1, 15 nd 3 1C min 1 ). z() Cmin -1 1 Cmin Cmin -1 3 Cmin Fig. 6. Normlized z() obtined by trnsformtion of TG t for the decomposition process of potssium metbisulfite t the different heting rtes (b ¼ 2.5, 5, 1, 15 nd 3 1C min 1 ). of E =122.4 kj mol 1 evluted from Friedmn s method ws used. The conversions, in which the y() nd z() functions exhibit the mximum vlues ( m nd 1 p, respectively) for the different heting rtes, re listed in Tble 3.

7 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) Tble 3 The conversions, in which the y() nd z() functions exhibit the mximum vlues ( m nd 1 p, respectively) for different heting rtes Heting rte, b (1C min 1 ) m 1 p As ws noticed, the t in Tble 3 which hs been extrcted from Figs. 5 nd 6, showtht m nd 1 p vlues wekly depend on the heting rte. The mxim of y() nd z() plots fll into the smll rnge of.3p m p.8 nd :73p 1 p p:75, respectively. The y() functions shows the convex behvior, wheres the mxim of z() functionshs vlues from.73 to.75, which corresponds to the R2 kinetic model (Tble 1). The most probble kinetic model for decomposition process of potssium metbisulfite is therefore R2 model (with ccommotion prmeter n ¼ 2). By introducing the derived rection model, g() ¼ 1 (1 ) 1/2, into Eq. (6), Eq. (16) is obtined: 1 ð1 Þ 1=2 ¼ AE pðxþ. (16) Rb The plot of [1 (1 ) 1/2 ] ginst (E /Rb)p(x) t the different heting rtes is constructed in Fig. 7. By using Eq. (16), the A vlue ws determined from the slope of the fitted line shown in Fig. 7. For contrcting re model (R2 with n ¼ 2) nd E ¼ kj mol 1, the pre-exponentil (frequency) fctor ws found to be A ¼ min 1 (ln A ¼ 27.95). The obtined vlue of ln A is in good greement with verge vlue of Friedmn isoconversionl intercept (ln[af()] ¼ 28.4; Fig. 4). The vlues of f ( p ) (for R2 kinetic model) nd preexponentil fctors (A) clculted from Eq. (11) t ll considered heting rtes re listed in Tble 4. From Tble 4, it cn be observed tht very good greement exists between the clculted vlues of A (including nd verge vlue) from the bove mentioned eqution nd the vlue of A estimted from Eq. (16). Therefore, the corresponding kinetic eqution for describing the non-isotherml decomposition process of potssium metbisulfite is given by b dt ¼ 1: exp 122:4 ½2ð1 Þ 1=2 Š, (17) where 2(1 ) 1/2 represent the differentil form of phsebounry controlled rection model. As we mentioned in introduction section, the degree of conversion () is relted to f(e ) by Eq. (14). Therefore, f(e ) is given by differentiting Eq. (14) by E s f ðe Þ¼. (18) de [1-(1-) 1/2 ] E+ 2.E-13 4.E-13 6.E-13 8.E-13 E p(x)/βr Fig. 7. Determintion of A vlue by plotting [1 (1 ) 1/2 ] ginst E p(x)/ br t n ¼ 2 for the decomposition process of potssium metbisulfite t the different heting rtes (b). Tble 4 Vlues of f ( p ) (R2 or F1/2 kinetic model) nd A clculted from Eq. (11) t different heting rtes (b) for decomposition process of potssium metbisulfite b (1C min 1 ) f ( p ) A (min 1 ) Averge This eqution shows tht f(e ) cn be obtined by differentiting the versus E reltionship, which my be deduced from Fig. 4. The grphiclly estimted distribution curve, f(e ), for the investigted decomposition process is presented in Fig. 8. From Fig. 8, it cn be observed tht the estimted curve (Eq. (18)) for investigted process represents the very shrply nd symmetricl distribution curve. The obtined distribution curve does not show the brod pek nd the pprent ctivtion energy does not spreds in the lrge E intervl. The pek position is plced in unique point t E,p ¼ kj mol 1. These results indictes tht f(e ) cn be represented by single Gussin distribution. By pplying the non-liner lest-squres nlysis the Gussin rectivity model is founded for considered system, nd cn be presented in form of Eq. (19): f ðe Þ¼ð2pÞ 1=2 s 1 exp ðe E Þ 2 2s 2, (19)

8 193 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) f (E )/molkj f(e )/molkj Clculted curve (Gussin).5.5 Estimted curve E /kjmol -1 Fig. 8. The estimted distribution curve, f(e ), from the dependence versus E for the decomposition process of potssium metbisulfite. where E nd s represents the men pprent ctivtion energy nd stnrd devition, respectively. Using the conventionl non-liner lest-squres nlysis, the following vlues of Gussin distribution prmeters re obtined: E ¼ kj mol 1 nd s ¼ 1.5 kj mol 1. It cn be pointed out, tht obtined vlue of E is very similr to the vlue of E clculted by the differentil (Friedmn) isoconversionl method (122.4 kj mol 1 ). Fig. 9 shows the comprison between the estimted distribution curve nd clculted distribution curve ssuming the Gussin model (Eq. (19)). It cn be seen from Fig. 9 tht exist very good greement between estimted distribution curve (Eq. (18)) nd clculted distribution curve with Gussin function (Eq. (19)). After this nlysis, the A vlues were estimted using Eq. (15) t the five heting rtes, nd the verge vlues of A re plotted ginst E in Fig. 1. From Fig. 1, we cn see tht the compenstion effect [29,3] holds between the A vlues nd E. The ppernce of compenstion effect shows tht only one rection model is presented [31]. The A vlue vries from n order of 1 1 to n order of 1 13 min 1, nd this result shows tht A cnnot be ssumed s constnt for the investigted nonisotherml decomposition process. However, we cn see from Fig. 1 tht the gretest number of A vlues were grouped bout the order of 1 12, which corresponds to the nrrow rnge of E (E ¼ kj mol 1 ). This result is in greement with order of A clculted using Eqs. (11) nd (16). To exmine the vlidity of the presented Gussin rectivity model, the experimentl T curves t b=1 nd 3 1C min 1 were compred with the clculted curves E /kjmol -1 Fig. 9. Comprison of the estimted (Eq. (18)) nd clculted (Eq. (19)) f(e ) curves for the non-isotherml decomposition process of potssium metbisulfite. A/min -1 1E13 1E12 1E E /kjmol -1 Fig. 1. Estimted verge vlues of pre-exponentil (frequency) fctors from five different heting rtes (Eq. (15)) s function of pprent ctivtion energy, for the decomposition process of potssium metbisulfite. for the non-isotherml decomposition process of potssium metbisulfite, s shown in Fig. 11. The clculted curves ws obtined by numericlly integrting Eq. (12) using the evluted f(e ) (Eq. (19)) nd A versus E reltionship estimted by the bove procedure. It cn be pointed out,

9 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) Experimentl (1 Cmin -1 ) Experimentl (3 Cmin -1 ) Clculted (Gussin distribution) Clculted (Gussin distribution) Temperture, T/ C 26 Fig. 11. Comprison between the experimentl conversion ( T) curves nd conversion curves reproduced using clculted f(e ) in the form of Gussin distribution (with prmeters: E ¼ kj mol 1 nd s ¼ 1.5 kj mol 1 ) for the pproximted R2 (F1/2) rection model, t b ¼ 1 nd 3 1C min 1. tht clculted T curves re evluted from the fct tht the specific nture of A E compenstion lw cuses the integrtion of the Gussin distribution of the first-order rection to look like s one-hlf order rection (R2 or F1/2). Nmely, this pproximtion is necessry becuse the vlue of pre-exponentil fctor (A) does not strictly constnt (which is the bsic condition for integrtion of the Gussin distribution). In ddition, this devition is more expressive t the lower nd t the higher vlues of degree of conversion () (Figs. 4 nd 1). Fig. 11 clerly shows tht exist good greement between the experimentl nd clculted T curves, which indictes tht Gussin rectivity model cn be pplied for nlyzing of non-isotherml decomposition process of potssium metbisulfite. It cn be pointed out tht Eqs. (14) nd (15) implicitly ssume tht the E vlues differ for different vlues. The f(e ) distribution curve used in the model clcultion (Eq. (19) nd Fig. 9) stisfy this ssumption, but lmost the sme E vlue cn be obtined for considered rnge of when we pplied the bove clcultion method. In tht cse, single-step rection covers the considered rnge nd the A vlue cn be estimted directly from the Friedmn s eqution (Eq. (7)) if the rection model is known (determined the nlyticl form of f() function). The extreme cse when the bsolutely the sme E vlue is obtined for ll considered vlues does not occurs in investigted decomposition process of potssium metbisulfite. Nmely, if we look Fig. 4 crefully, we cn observe tht the obtined E vlues does not ly on strictly one stright line, but vry bout tht imgined stright line. It cn be observed tht mentioned devitions re higher t the beginning nd t the end of investigted decomposition process ( ¼.5.1 nd ¼.8.95, respectively), but these devitions re in the limits of experimentl error. On the other hnd, vrition in pprent ctivtion energy could be observed for both elementry nd complex rections. An elementry rection could show vrible pprent ctivtion energy during its progress due to the heterogeneous nture of the solid smple, which could cuse systemtic chnge in rection kinetics due to product formtion, crystl defect formtion, intr-crystlline strin or the other similr effects. It cn be pointed out, tht Friedmn method tends to overestimte the men pprent ctivtion energy t midconversion (E,FR ¼ kj mol 1 4E ¼ kj mol 1 ). Therefore, the increse in A bove the true vlue t midconversion cn be interpreted s needed compenstion effect required to recover the correct overll rectivity (Fig. 1). In ddition, it ws showed tht the Friedmn method cn be pplied to rections which cn be described by nrrow distribution of pprent ctivtion energies (sp4% of E vlue) [17]. From the results given bove, we cn conluded tht the Friedmn method represents the pproprite kinetic method for the isoconversionl (model-free) nlysis of the investigted decomposition process. In fct, from the results obtined by pplying the Friedmn s method, we were estblished the nrrow distribution curve of pprent ctivtion energies, f(e ), which corresponds to the Gussin distribution of rectivity with so4% of E vlue (s ¼ 1.2% of E ; see the vlues of s nd E ). Accordingly, these results confirm the sttement, tht the Friedmn s method cn be pplied for the rections which cn be described with nrrow distribution of pprent ctivtion energies. We cn concluded tht the E vlues clculted by the Friedmn s method nd estimted distribution curve, f(e ), re correct even in the cse when the investigted decomposition process occurs through the single-step rection mechnism. For the non-isotherml decomposition process of potssium metbisulfite in nitrogen tmosphere, the following kinetic triplet ws obtined: E ¼ kj mol 1, A ¼ min 1 nd the phse-bounry model f() ¼ 2(1 ) 1/2, which is ssocited with n inwrd dvncement of the rection interfce from the crystl s edges (with n ¼ 2 for rections spreding in two dimensions). If the surfce growth is much fster thn the rte of penetrtion into the crystl, then coherent interfce is formed between the decomposed outer lyers nd rectnt. If the propgting interfce penetrtes into undecomposed rectnt t constnt rte, then the kinetics is governed by phse-bounry controlled rection (for vlue of ccommotion prmeter n ¼ 2, the considered rection ws spreds in two dimensions (over surfce)) [32]. The eqution of phse-bounry rection model often provides n excellent fit to the decy period of decomposition nd

10 1932 B. Jnković et l. / Journl of Physics nd Chemistry of Solids 69 (28) is prticulrly effective when surfce nucletion nd surfce growth occur rpidly nd internl nucletion either does not occur or occurs only very slowly. The investigted decomposition process cn be well described by the single Gussin rectivity model with following prmeters: E ¼ kj mol 1 nd s ¼ 1.5 kj mol 1. It ws estblished tht the vlue of men pprent ctivtion energy (E ) is in good greement with vlue of E evluted from the Friedmn s isoconversionl method (122.4 kj mol 1 ), which corresponds to the middle prt of conversion (for E.5). 6. Conclusions The kinetics of the non-isotherml decomposition of potssium metbisulfite ws ccurtely determined from series of thermonlyticl experiments t different constnt heting rtes. The pprent ctivtion energy (E ) ws clculted by differentil (Friedmn) isoconversionl method without previous ssumption regrding the conversion model fulfilled by the rection. It ws found tht the pprent ctivtion energy is prcticlly constnt in the considered rnge (for.5pp.95), nd this suggesting tht the investigted decomposition ws single-step process with vlue of E ¼ kj mol 1 obtined by Friedmn method. By pplying the Mlek s procedure, the pproprite rection model chrcterizing the process studied ws estblished. The y() ndz() functions exhibit mxim t m nd 1 p, respectively. The mxim fll into the smll rnge of.3p m p.8 nd :73p 1 p p:75, respectively. From the results obtined by Mlek s procedure, the contrcting re geometricl model (R2) (where the rdil direction predomintes) represents the most probble kinetic model for describing the decomposition process of potssium metbisulfite. By pplying the Miur s procedure, the DRM for investigted decomposition process ws estblished. From dependence versus E, the experimentl distribution curve of pprent ctivtion energies, f(e ), ws estimted. From the bsic chrcteristics of estimted f(e ), it ws concluded tht the investigted non-isotherml decomposition process cn be represented by single Gussin distribution. By pplying the non-liner lest-squres nlysis the Gussin rectivity model is founded for considered system with following distribution prmeters: E ¼ kj mol 1 (the men pprent ctivtion energy) nd s ¼ 1.5 kj mol 1 (stnrd devition). It ws estblished, tht the vlue of E is similr to the vlue of E clculted by the differentil (Friedmn) isoconversionl method. By pplying the Miur s procedure, the A vlues were estimted t five different heting rtes nd the verge A vlues re plotted ginst E. The liner reltionship between the A nd E vlues ws estblished (compenstion effect). Also, it ws estblished tht the E vlues clculted by the Friedmn s method nd estimted distribution curve, f(e ), re correct even in the cse when the investigted decomposition process occurs through the single-step rection mechnism. As the finl conclusion, the following kinetic triplet: E ¼ kj mol 1, A ¼ min 1 (ln A ¼ 27.95), f() ¼ 2(1 ) 1/2 nd the Gussin distribution rectivity model (f(e ) ¼ (2p) 1/2 s 1 exp[ (E E ) 2 /2s 2 ]) with prmeters E ¼ kj mol 1 nd s ¼ 1.5 kj mol 1 were estblished for the non-isotherml decomposition process of potssium metbisulfite. Acknowledgments The study ws prtilly supported by the Ministry of Science nd Environmentl Protection of Serbi, under the following Projects 14225, (S. Mentus) nd 1425 (M. Jnkovic ). References [1] McGrw-Hill Professionl, Encyclopedi of Science nd Technology, 1th ed., 27. [2] S. Rjvidy, R. Bjpi, A.K. Bjpi, Morphologicl, therml nd nneled micro-hrdness chrcteriztion of geltin bsed interpenetrting networks of polycrylonitrile: hrd biopolymer, Bull. Mter. Sci. 28 (25) [3] T.J. Mder-Sntn, F.V. Moreno, Grft polymeriztion of methyl methcrylte onto short lether fibers, Polym. Bull. 42 (1999) [4] M. Mlnchuk, Therml nlysis of sodium metbisulfite, Anl. Chim. 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