Kinetic analysis of DTG data from master curves

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analysis of DTG data from master curves

Kinetic

J_ M

Acra, 24 (1978) 186189 Scicnrifk Publishing Company, Amsterdam - Printed in The Ndhaiads

CRIADO

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Deprtmn~nto

(Ft.seivcd 7 June 1977)

The aim of the present note is to develop a series of master curves for an easy and quick anaiysis of the mechanism of thermal decomposition reaction of solids from DTG data_ It is well known’ that the reaction rate of the above named reactions is given by the equation:

where I is the reacted fraction; t, the time; f(z) a function depending on the reaction mechanism; A, the pre-exponential factor of Arrhenius; E, the activation ener_ey; R, the gas constant and T, the absoiute temperature, If the temperature of the sampIe increases at a constant rate, j3, eqn (1) can be integrated’ and becomes: ART=

&)

=

T-e

-

EIRi

From eqns (1) and (2), we obtain:

RT’dz gbJ = -xjF-dt

1

(3)

f(2)

which for z = O-5 becomes: (4)

whereTo-5and

(dz,Wf~_, are, respectively, the temperature From eqns (3) and (4), it is very easy to obtain:

where (I[=

I/f(OS) - g(OS)] is a constant

and the rate when z = 0.5,

for a given mechamsm.

Fig

I_ Redlpccdrate--~~ mast= cunxs of difkrcnt reaction mechanismsof thcnnal ckornposition of

solids_

If we consider

that TfT,_,

is close to unity, eqr. (5) shows

that the plot of

“reduced rate“ [i-e_, (dz/d?)/(dz!dt)O_5] against I &ves a series of master curves that depend neither on the kinetic parameters nor on the heating rate but only on the reaction mechanism. The equations of the master curves obtained are included in Table i and plotted in Fig_ I. We can see that it is not possible to distinguish between the mechanism R, and D, (see the nomenclature in Table I). On the other hand, it is impossible

to discern between a first-order

reaction and the Avrami-Erofeev

mecha-

nism by means of these curves_ A similar conclusion was reached by analyzing TG data in a prior publication3. The method developed in the present work has the advantage of allowing the quick selection of a singe mechanism or, in the worst case, a small group of themIn this way, the work required for performing the kinetic analysis and to determine the acti-ation energy of the reaction is considerably shortened. In order to check the master curves, the DTG diagram of CaC03 obtained under vacuum* and included in Fis 2 has been analyzed_ The values of (TIT,_,)’ [(dx/df)/(dz/df)o_J calculated from Fig_ 2 are plotted versus 3~in Fig 3. We can see that the experimental data fit very well the master curve of the R3 mechanism, in good a_greement with the conclusion previously reached3 from the analysis of i.~+ thermal and TG data of the thermal decomposition of the same sample of CaCO,

189

Fig 2 TG and DTG diagrams of th,wmal dexmpositian of C&OS obtained undo a czcuum of lo-’ torr and a heating rate of 12-C min-1.

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47

6-3

als

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is Fig_

1 2 3 4 5

3, Checking of the master cmve azormsponding to a & nuxbnkn_

J. H. sharp and s. A. wal!wonh, Ad Ch., 41(1969) 2060. k W. Coats and J. R&fern. iV&rre, 208 (1964) 68. J. M. Criado and J. Moraks, Xkrmockk. Ada, 19 (1977) 305. ubu%tdoaadRGarcia-Rojas,uIlpub~data_ J. Ii. Sharp. G. W. BrindIq and N. N. Achar, J. Am. C-. Sbc., 47 (1966) 379.