CORRELATION BETWEEN KINETIC CONSTANTS AND PARAMETERS OF DIFFERENTIAL THERMOGRAYIMETRY,
IN THE DECOMPOSITION OF CALCIUM CARBONATE
Bv
Z. ADONYI
Department of Chemical Technology, Poly technical University. Budapest (Received April 18, 1967)
Presented by Prof. Dr. L. Y.-\JTA
It is known that in thermoanalytic measurements the quantity of the sample, the rate of heating, the shape of the crucible: generally, the conditions of measurement considerably affect the form of the thermogravimetric (TG) curve, and the temperature at the peaks of differential thermoanalytic (DTA) or differential thermograyimetric (DTG) curves.
According to the studies of PAULIK, PAULIK and ERDEY [1], carried to a high degree of precision and based on substantial experience, the following phenomena are manifest:
1. In measurements carried out on samples placed in the crucible of the apparatus.
a) if the sample is augmented from 40 mg up to 800 mg, the temperature at DTG-peak rises from 800 cC to
no
cC;b) if the heating rate is increased from 1 °C . min-I to 10 cC . min-I , th" temperature at DTG-peak rises fro111 750 cC to 920 cC;
c) if in a mixture of calcium carbonate and an inert substance the ratio of the latter is reduced from 96 per cent to nil. the temperature at the peak rises from 780 cC to 920°C.
2. In measurements carried out on samples placed on the polyplate sample-holder proposed by PAULIK, PA ULIK and ERDEY [1]. they have stated that.
a) if the sample is augmented from 10 mg up to 200, mg the temperature at DTG-peak rises from 660 cC to 730 cC;
b) if the heating rate is increased from 1 cC . min -1 to 10 cC . min -1,
the temperature at DTG-peak rises from 660 cC to 730 cC;
c) if the ratio of the inert substance is reduced from 96 per cent to nil. the temperature at DTG-peak rises from 670 cC to 730 cC.
The authors cited have found that the variation of the temperature at DTG-peak (derivative of the TG-curve) is a function of partial pressure of carbon dioxide, itself a function of the conditions of measurement, and that by the use of the polyplate sample-holder results close to those ob- tainable in measurement;;; iu vacuo can be arrived at. PAULIK, PAULTK and
326 Z. ADO,,"YI
ERDEY [1] tried to counterbalance the effect exerted by the conditions of measurement by an increase of the number of data obtainable simultaneously i.e. by measurement, at the same time, of DTA, DTG and dilatometric data, apart from the standardization of the method. In connexion with the study of the hydration products of cemeuts, PETZOLD and GOHLERT [2] hav(' broached the subject of such a standardization. In general it may be said that without the kno'wledge of the exact circumstances of measurement thermal decomposition is not accurately defined by the temperatures at DTA or DTG peaks, respectively. The question might be raised whether kinetic constants are suitable for the definition of thermal processes, respectively, how variations of the conditions of measurement affect the kinetic constants of a thermal decomposition.
Several authors have made attempts at some calculations from data furnished by thermoanalyses of kinetic constants viz. of the order of reaction and of activation energies, using calcium carbonate as the model substance.
Data, as collected and shown in Table 1, demonstrate that though the experiments themselves were carried out under quite varied circumstances the kinetic data calculated by the several authors were around certain values.
This seems to suggest that kinetic constants are more suitable for the charac- terization of thermal processes than are temperature values that appertain to peaks. On the other hand, the discrepancies seem to suggest that the constants obtained by calculation are sensitive to circumstances that prevailed at measurement. Unfortunately, the data given are incomplete in many cases, therefore no unequivocal correlation bct'ween dh-ergence of kinetic constants
Heferenee
Hl:TTIG KAPPAL [31
VALLE'L RICHTER U]
FREE3v,.X, CARROLL [5 J
BRITTOX. GREGG. WI"SOR [6]
id.
BISCHOFF [7]
SLO"m [8]
SPLICIIEL, SKRA)!OY~KY. GOLL [IOJ
KISSI"GER [9]
id.
1L .... SKILL, TUR"EH [11]
ZA,YADSKI, BHETSZ"AJDER [12]
Table 1
Activation O~~der of reaction energy.
Keal . ;lole- 1
o ...
1 ·~90.2 ... 0.53
0.'1 39
O.H a.6
0.3 35 ... ~2
J7
1 n ... 1.4
0.3 37 ... 39
0.32 -13.7
0.22 42.9
1 95
48
Supplementary informatiou
Isothermal Isothermal DTG (TG) DTA (vacuum.
grain size 1 nnn) air
DTA
DTA J,,;othermai
I([SETIC CO;\"STASTS A.YD PAR:DfETERS OF DIFFERENTIAL THERMOGRAVIMETRY 327
and conditions of measurement could be established on the basis of data published in the literature.
Records published by PAULIK, PAULIK and ERDEY [1] too are deficient in some data needed for calculation, therefore we tried to repeat the thermal measurements in order to study the connexion between kinetic constants and conditions of measurement, and chose calcium carbonate as the model substance. It is knov,'n that DTA curves are suitable bases for kinetic cal- culations, however, in order to arrive at a greater accuracy, in this study only an analysis of results of thermogravimetric measurements is carried out.
KREVELEN et al. [13] were the first to utilize thermogravimetric curves in a calculation of kinetic data. Among the methods of calculation that of FREE:'tIA:\ and CARROLL [5] may be pointed out, with the comment that all the demonstrations known today to be suitable for kinetic calculations are reducible to, or can start with, the derivation that follows, i.e. that these demonstrations are of about the same' value.
where
-
dx
= k(a - x)' dtdx i" the rate of thc change of weight, ((1 - x) is the mass of sub- dt
stance not decomposed, J' is the order of reaction, h is the Arrhenius con~tant,
In a calculation, the thermogravimctric (TG) curve is differentiated according to a given method, e.g. graphically. The special advantage of thl' derivatograph [14] used by us consists therein that it carries out differen- tiation automatically and in 1'. way suitable for calculations. Thus, for thermal decomposition reactions involving a weight change the differential equation mentioned can be applied directly.
I. Effect of sample mass
In our experiments P. A. grade, precipitated calcium carbonate of 10 to 11 micron particle size 'was used. Results of measurements as a function of sample mass in the range between 40 mg and 2000 mg are shown in Fig. 1.
Depcnding on sample mass, the temperature at the peak of a DTG curve may be shifted even by 155 cC. Noteworthy is the phenomenon that with a greater sample mass (greater than 1000 mg) the DTG peak appears as a composite pcak. When the order of reaction is determined according to the method proposed by FREE:IIA:\ and CARROLL [5] (Fig. 2), the log k and
T
1 function is that shown in Figs 3, 4, 5, 6 and 7. Independently of sample maS8, order of reaction is 0.25. The function log k and 1 is linear.T
328 Z. ADOSYI
5 20
60
20 1---,--.---1- 80
100
o
!2C
"" 20
~
·0 I1"
"
'-' '" C0\~,cv I
~
80i
Sample Rate of r:!JSS mg ":eating °C/T.r
"DJ.
12,6ZOO ,.
500 :,~
'QOO '2,6
2000 ~C.5
'on
L _____ -"' __
~""""''''='''=__'''''_ _ _ 'OD!J]gffDTGr 10
r-
Mgla-x) - 9 - -8
- 7 - 6 - 5 -
eoo
900 ICOO TFig. 1
cG DTG sensi:tv.ty 20 ,'10
"CO 1/10 500 1/3 500 1/5
'000 Y5
Sample mass mg Rote or' (le:::', ;; 'C/-:::n
3 2
40.1 12,6
200 11,7
800 11,4
1000 12.6
2000 10.5
<l 1.., T 103
0.2 0.4 0.6 0.8 W 1.2 tJlg(a-x)
Fig. :2
TempetCl lure a:
Ihepmk 792 820 920 93C 9~
III a good approximation, for the entire domain of decomposition. The slope of the log k and -1 line changes a little with the change of the mass of the
T
!:ample, thereby also the calculat"d values of activation energy change.
A characteristic effect in connexion with the kinetic influence exerted by the mass of the sample can be obsf>rvec1 on Fig. 4 (200 mg) where the function
KEYETIC CONSTASTS ASD PARA.1fETERS OF DIFFERESTIAL THER-'IOGIUJDfETRY 329
6
!gk+7
5
0.8 0,9
6
I
5
~.
I
DJ
igr:f7
6
Fig. 3
1,0 Fig.
Fig . .5
Sample .77055 frO mg Rate or heating ~2.5 cC/mm
1,1
Sample mass 200 mg Role of ,"eating i1,7 °C/min
1,1
Sample mass 800 mg Pale of healing 1 ({, 'C/mm
i.2
330
6
5 I - - - i - - - . - l -
!gk+7
0,8 0,9
z. ADONYI
Fig:. 6
10
Sample mass 1000 mg Role of healing 12,6 "C/min
Sample mass 2000 mg Rate of heating 1Q5 cClmin
log k and 1 l~ composed of two linear sections. That ascribed to low tem- T
p<"ratures shows some correspondence to the 40 mg curve, that to higher temperatures shows correspondence to greater sample mass.
R('sults are collected in Table 2. It iE' to be seen that the mass of the sample affects kinetic constants to a lesser degree than it does at the temperatures In Fig. 1 that pertain to DTG-peaks. On Fig. 8, which contains all the data concerning the mass of samples, an av('rage log k and 1 function can be determined. This was the basis for the
T
h:INETIC COSSTASTS .ISD PARAJfETER.' OF DIFFERESTIAL THER.\fOGRArIMETRY 331
Jgx+7
Fig. 8
calculation of the average actiYation energy shown in Table 2. Further study of the asymmetric deyiations observahle in Fig. 8 will perhaps help us towards a more thorough interpretation of the effect exerted hy the mass of the sample.
Cnl{'ibIe
Small . . . . . . . . Small . . . :UcdiUI1l Jfedium
Large ...
Sample.
mg
-to 200 8UO 1000 2000
Hatf'.
cC'min-1
1:!.6 11.7 llA 12.6 lOA
Table 2
Activation
Kc<:f~~ie-l
38.14 15.9
·t6A .51.6
Temp. rang~
of validity. \.:c
737 ... 872 700 ... 980 680 ... 94-.) 742 ... 92:3 Average, independent of sample
lnas~ -15.23 666 ... 9,17
2. Effect of the rate of heating
Acti .... ation energ\;.
Keal . n;~le-!
46.7
·1,6.6
Temp. rang!' of validity,
'c . 620 ... 790 6Ti .. . 1'37
Fig. 9 shows derivatogramE recorded for rates of heating of 3.7, 8.2, and 11.7 cC . min -1, respectiyely. A shift by ahout 45 QC of the temperatures at DTG peaks is obseryahle. Following the kinetic evaluation of the deriyato- grams carried out as hefore, it could he stated that the rate of heating does not affect the order of reaction within the inten-al studied: this value is 0.25
332 Z. ADO.'TI
1
III all three instanccs. The log k and function IS shown III Fig. 10, yalues T
of activation energies are collected in Table 3.
Hate of heating, CC'min- 1
11.7 8.2 3.7
Temp. at transition point, cC
7.J.7 735 696
700
1
Tahle 3
Acti-.-ation
energy. , Temp. rang". "C Kenl . xllole-1
800 55.5 56.3 56.8
677 ... 735 655 ... 693
Sampie Role moss mg ti£cifr.g
200 '7,7
200 8,2
200 3.7
1)00 tOOD
cc
Fig. 9
Acti..-ation
Temp. range. ::c
4·0.5 .J.3.3
TG DIG
sensl/rvi/!::t'
!DD
!DO iOG
1/10 1/10
74-7 ... 867 735 ... 74-7 693 ... 827
Temperotun:
cl the peak 870 855 825
On the log k and diagram the temperature at transition point changes T
with a change of the rate of heating. \Vhen this rate is increased the activation energy decreases in the range of the higher temperatures, it does not changc in the range of the lower temperatures, therefore the temperature at transition point is higher.
3. Effect of the shape of the crucible
After the study of the effect of sample mass and rate of heating, re- spectively, we inyestigated the effect of some less definite factors the influence
KI'\"ETlC CO.\"STA,"\7::; A'\"D PARAJIETERS OF DIFFERE'\"TlAL THERJIOGRAIDIETllY 333
of which might bc expected upon diffusion processes. }Ieasurements are grouped as follows.
1. 40 mg samples, 12 cC min -1 heating rate. in a small crucible, and
ll1 a large crucible:
:2. :200 mg samples, 8 cC . min-1 heating rat('. 111 an open crncibl(,. and In a C'oYf'red crncihle:
,
'0--:-- - '. '.-
~- -
, .
Fig. 10
Sample mass 20D iT;g Paie of hearing 11.7 CC/mm 0
8,2 3)
3. 190 mg samples, 1.:3 cC . min -] heating rate, on a polyplate sample- holtlr-r proposed by PArLIK, PArLIK and ERDEY [1]*. Fig. 11 shows the dcri,-- atogram;;;. The maximum deyiation of the temperatures at DTG-peaks i"
212 cC undf'l' the conditions chosen. Applying the eyaluation method preYiously dp;;cribecL an order of reaction of 0.25 was found independently of crucible shap(>. A differ('nt yalue. Yiz. zero order of reaction was found in the case of the ('oyercd crucible. The log k and T 1 function is plotted in Fig. 12. aetiYa-
tion pnprgIPs an' listed in Ta.~,le .1.
Small . . .
.
~O()SmalL l'oyprpd :200 Polyplate holc!.:r 190 Small ...
-to
]_ar~e . . . -J.O
ll.~
7.5 1.3 12.6 11.6
Tahle -1
Activation ('ner!!:Y.
Ken! l;;Olr--:
·t6.6 -17.0
~0.8
-16.7 46.9
674 ... 870 698 ... 898 595 ... 692 621 ... 792 665 ... 710
Acti\-atiPH ('nerg ...
Kl'aJ . ;;01('-!
3fUl
Temp. rangt'o :.c
76~ ... BOO
" These authors Kere so kind as to oblige Kith their records of this experiment. we
"'ish to thank them for this co-operation.
:334 Z. ADOSYI
As is to be seen, the shape of the crucible is generally of small effect
OIl activation energy. The difference that originates with the crucible being covered with a lid is negligible, but the same k rate constant is reached at a temperature higher by about 60 cC. It is noteworthy that if a polyplate sample-holder is used the rate constant that pertains to a given temperature is about ten times as high as the rate constant measured with a sample in a conventional crucible.
"S2 , 2
'-' ·10
'" 3
~
"
5 -120
0 20
* '"
Sample Rate of iG DTG remperalure . mossmg nealing '()mtn sensitivity allhepeax. CruCible
200 ".7 100 1/10 870
g> 40
.g
"
190 1,3 100 1/5 680 poiypiDte
he",,'
200 7,5 100 1/10 892 t~
:<: 60 40 125 20 1/10 792
S2>
~ 80 40 11,6 20 ill.] 793
100
600 700 800 900 1000 'C
Fig. 11
The result of a measurement on a 4·0 mg sample in a large crucibIP allows the conclusion to be drawn that the diffusion from and into the crucible of the gas layer above the substance exposed to the effect of heat, can be of significant influence.
In spite of the decreased thickness of the laver of the substance, the activation energy of 64.9 Kcal· molc-1 in the domain between 727 and 762 cC was unusualh- high. From the log k and
.
~ ~~ T
function of measurements on ,10 mg samples in a large crucihle thc activation energy 'was 46.9 Kea! . mole-1 in the 665 to 710 cC, 64.9 Kcal . mole-1 in the 727 to 762 QC. and 38.78 Kcal . mole 1 in the 762 to 800 cC range.The deviations between this curve and the data taken from the literature in Fig. 8 can hp explained, on the one hand, that in their calculations some authors started from a not sufficiently generalized section, perhaps frnm one distinguished by special conditions of measurement, of the log hand
KLVETIC CONSTANTS AND PARA.\IETEUS OF DIFFERE,\TlAL THEIUIOGUAILHETRY 335
1 function, on the other hand, that under the influence of diffusion pro- T
cesses activation energy fluctuates between certain limits according to con- ditions of measurement. For the characterization of the thermal process, besides the calculation of the order of reaction and of actinltion energy the determination of the temperature limits within which these are valid i", advisable, or of the log k and 1 function, which is the basis of a deeper
T insif?:ht into the processes.
Igkf7
5
5 I
Q8
co
Sample mass mg 200 200 190 40
small cruCible, covered J} ; Q25 -,,- Y;O polyp!ale sample hclder small crucible
"0 large crucible 200 small crucible
Fig, 1:!
In summarlzmg the results we might state that the values of kinetic constants calculable from thermogravimetric data are much less affected by the conditions of measurement than are the shapes of the TG, or of the DTG curves, and the temperatures at the peak of the DTG cun'es. Therefore orclt'l"
of reaction, activation energ-v.' and the log
-
~ le and -T
1 function simultaneoush''
utilized seem to be adequate for the characterization of thermal process(~",.
\Vhen kinetic constants are knovin, the idt'ntification and tht' intf'rpretatioll of thermal proct','ses hecomt' eaSIer.
Summary
Data obtained in thermic measurements. the respective shapes of TG. DTG and DTA curves, the temperatures at peaks are strongly affected by the conditions of meaS'lrelllenL the mass of the sample. the rate of heating, the shape of crucibles. etc. rsing calcium carbonate as the model substance, a kinetic analysis with the aid of the conventional differential equation has shown that kinetic constan'ts. order of reaction. activation energy are affected in a lesser degree by the conditions of measurement and ar~, therefore. bett~e'r suited for a characterization of thermal processes than is a statement of e.g. the temperature at the peak of a DTG curye, A study of the correlation lwtween conditions of measurement and kinetic-
336 Z. ADOXYI
constants facilitates the interpretation of thermal processes. From this point of yiew the knowledge of the function rate constant ys. temperature offers the most information and without this the activation energy is not of full value in the characterization of a thermal process.
References
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2. PETZOLD, A .. GOHLERT. I.: TIZ-Zhl. 86, i28 (1962).
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4. Y,ULET, P .. RICHTER, A.: Compt. rend. 238, 1020 (1954).
:;. FRED!A:>;, E. S .. CARROLL. B. J.: J. Phys. Chem. 62, 394 (1958).
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i . BrscHoFF. F.: Z. Anorg. Chem. 262, 288 (1950).
B. SL07\I:'d~ C.: Z. ElektrocheIl1. 36, k139 (1930).
9. I';:ISSI:>;GEll, H. E.: Anal. Chem. 29. 1702 (1957).
10. SPLICHEL. S .. SKRA}!OVSKY, ST .. GOLL . .T.: CoIl. Czecl!osloy. Chem-C0111mun. 9, 302 (1937).
11. }IASKILL. TrR:>;EIL ",', E. S.: J. Soc. Glass Techn. 16, 80 (1932).
12. Z .. HLl.DSKI. J., BrrETsz:>;AJDEH. S.: Z. ElektrochE'!l1. 4·1, 215 (1935).
n. KIlE\TLE". D. W .. YA:>;. HEIlDE:>;.
c..
YA:>; Hr:>;TJE:>;s. F. J.: Fuel 30, 253 (1(,1.';1).H. PArLIK. F .. P .. U'LIK . .T., EIlDEY, L.: Z. A.l1a1. Chem. 160. HI (1958).
Dr. Zoltan ADO:"YI, Budape'3t XI., Budafoki lit 8. Hungary
