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Initial reaction rates from DTA
J. Inorg. Nucl, Chem., 1960, Vol, 12, pp. 252 to 254. Pergamon Press Ltd. Printed in Northern Ireland
INITIAL
REACTION
RATES
FROM
DTA
H. J. BORCHARDT General Engineering Laboratory, General Electric Company, Schenectady, New York
(Received23 February; infinal form 15 May 1959) is shown that initial reaction rates can be determined in a very simple manner from differential thermal analysis measurements.
Abstract--It
IN previous communications (1,~ the utility of obtaining initial reaction rates f r o m D T A was demonstrated. The manner in which this rate can be calculated is described below. The method is based on the kinetic analysis of D T A curves described by DANIELS and this writer, cz~ The equation which relates the reaction rate to quantities obtained from the D T A trace is as follows (equation (7), ref. 3):
dn n° [ d AT T1 at -- KA C~---d~ @ K A dAT
It was found experimentally that C~ T
is small compared to K AT;
(1) therefore
dropping the smaller term and cancelling gives
an/no AT -dt A
- -
(2)
where - - dn/n° is the rate of reaction (in fraction converted per unit time) at the time (temperature) where the height of the D T A peak is AT. A is the total peak area. I f it is assumed that the D T A peak can be approximated by a triangle of height ATrnax and base % then A = ½~- ATmax and
dn/no 2 AT -- - (3) dt -r ATmax By using equation (3) at temperatures where AT/ATm~ x is a small fraction, initial reaction rates can be calculated. In order to determine the extent to which equation (3) is applicable, MgCOa, CaCO 3 (calcite) and kaolinite were subject to differential thermal analysis and initial reaction rates calculated. F o r comparison, the initial rate of decomposition of these materials was measured by means of conventional weight loss methods. EXPERIMENTAL A. Apparatus The DTA apparatus is a commercial unit manufactured by the Robert L. Stone Company, Austin, Texas. Weight loss measurements were performed on a Chevenard recording thermobalance. The average particle size of the materials was measured on a Fisher sub-sieve sizer. txl H. J. BORCHARDT,J. Inorg. Nucl. Chem. 12, 133 (1959). ts~ H. J. BORCHARDT,d. Amer. Chem. Soc. 81, 1529 (1959). ~s~H. J. BORCHARDTand F. DANIELS,d. Amer. Chem. Soc. 78, 41 (1957). 252
Initial reaction rates from DTA
253
B. Materials MgCOs, "California Magnesite" from Wards Natural Science Establishment, particle size 2'5 #; CaCOs, Fisher reagent grade, 6.3/~; kaolinite, Southern Clays, Incorporated, 1'6 F. C. Procedures The DTA measurements in each case were performed in static air with temperature rising at the rate of 12°C/rain. The samples were contained in a cylindrical well, open at the top, ~ in. diameter and ~ in. deep. The samples were loosely packed, the packing densities being 33-6, 8.27 and 23.7 per cent of theoretical density respectively for MgCO3, CaCOs, and kaolinite. Weight loss measurements were performed under conditions resembling as close as possible those in the DTA measurements. A small Inconel cylinder was constructed having the same internal dimensions as the DTA sample well. The samples were packed in this cylinder to the same densities as for DTA. The cylinder containing the sample was then inserted into the furnace for the weight-loss measurement. RESULTS~ A N D
DISCUSSION
T h e D T A p a t t e r n s are shown in Fig. 1. The t e m p e r a t u r e s at which AT]ATmax is 0"1 (a small fraction) were d e t e r m i n e d f r o m the D T A trace a n d the initial r e a c t i o n
MgC%
CoC%
KAOLINITE
400
500
600 700 TEMPERATURE- *C
800
900
FI~. 1.--DTA patterns of magnesite, calcite, kaolinite. The marker on the curve indicates the point where AT = 0"lATraax. rates at these t e m p e r a t u r e s were calculated f r o m e q u a t i o n (3). These d a t a are listed in T a b l e 1, u n d e r the h e a d i n g " ' D T A t e m p e r a t u r e " a n d " C a l c u l a t e d r a t e " , respectively. The weight loss m e a s u r e m e n t s were m a d e at n e a r l y the same t e m p e r a t u r e s as those at which the rate is c a l c u l a t e d f r o m D T A (actual t e m p e r a t u r e given in parentheses). TABLE I
DTAtemperature (°C)
MgCO3 CaCOs Kaolinite
579 762 506
Calculated rate (~/min)
Observed rate (~/min)
1"67
1.90 (580) 2.78 (759) 1-28 (506)
2-11 1.29
254
H . J . BORCI-IARDT
The initial reaction rate is determined from the initial slope of the weight-loss curve. These data are tabulated under "Observed rate". The rates are in units of per cent conversion per minute. The data indicate that use of equation (3) yields results which are reliable within approximately 20 per cent. In order to determine the temperature at which the initial reaction rate is 1 per
dn/no
cent conversion per minute, this value is substituted for -- 7
and the temperature
at which the equality, 0.0057 = A T / A T ~ x is satisfied, is determined from the DTA trace. Per cent conversion per minute as a unit of rate is an extensive quantity and is dependent upon the total effective surface area. For reactions where each powder particle is reacting independently (in contrast to the situation where the powder assemblage is behaving as one large particle ~4)) per cent conversion per minute can be translated into a unit which is independent of surface area or particle size as follows: Consider one of the reactant powders to be composed of spheres of initial volume Vo. After some reaction occurs, the volume has been reduced to V and the fraction of original reactant present is V/V o. Since V = ~zrr3 dV[ Vo 3rz dr dt = roa dt
(4)
By restricting equation (4) to initial reaction rates, r ~ to, and dV/Vo .
.
dt
.
3 dr .
rodt
(5)
If differences in density between reactant and product are neglected, dr/dt may be considered to be the initial rate of growth of the product layer. The unit of rate, dr/dr is independent of particle size. For particles 6/~ in diameter, a rate of 1% per minute is seen to correspond to dr/dt = 10-6 cm/min. The various restricting assumptions in the above are rather obvious, and clearly indicate that the figure of 10--6 crn/min should be considered to be no more than an order of magnitude guide. ~4~ For example H. T. S. BlU'rror~, S. J. GREGG and G. W, WINsoR, Trans. Faraday Sac. 48, 63 (1952).
INITIAL
REACTION
RATES
FROM
DTA
H. J. BORCHARDT General Engineering Laboratory, General Electric Company, Schenectady, New York
(Received23 February; infinal form 15 May 1959) is shown that initial reaction rates can be determined in a very simple manner from differential thermal analysis measurements.
Abstract--It
IN previous communications (1,~ the utility of obtaining initial reaction rates f r o m D T A was demonstrated. The manner in which this rate can be calculated is described below. The method is based on the kinetic analysis of D T A curves described by DANIELS and this writer, cz~ The equation which relates the reaction rate to quantities obtained from the D T A trace is as follows (equation (7), ref. 3):
dn n° [ d AT T1 at -- KA C~---d~ @ K A dAT
It was found experimentally that C~ T
is small compared to K AT;
(1) therefore
dropping the smaller term and cancelling gives
an/no AT -dt A
- -
(2)
where - - dn/n° is the rate of reaction (in fraction converted per unit time) at the time (temperature) where the height of the D T A peak is AT. A is the total peak area. I f it is assumed that the D T A peak can be approximated by a triangle of height ATrnax and base % then A = ½~- ATmax and
dn/no 2 AT -- - (3) dt -r ATmax By using equation (3) at temperatures where AT/ATm~ x is a small fraction, initial reaction rates can be calculated. In order to determine the extent to which equation (3) is applicable, MgCOa, CaCO 3 (calcite) and kaolinite were subject to differential thermal analysis and initial reaction rates calculated. F o r comparison, the initial rate of decomposition of these materials was measured by means of conventional weight loss methods. EXPERIMENTAL A. Apparatus The DTA apparatus is a commercial unit manufactured by the Robert L. Stone Company, Austin, Texas. Weight loss measurements were performed on a Chevenard recording thermobalance. The average particle size of the materials was measured on a Fisher sub-sieve sizer. txl H. J. BORCHARDT,J. Inorg. Nucl. Chem. 12, 133 (1959). ts~ H. J. BORCHARDT,d. Amer. Chem. Soc. 81, 1529 (1959). ~s~H. J. BORCHARDTand F. DANIELS,d. Amer. Chem. Soc. 78, 41 (1957). 252
Initial reaction rates from DTA
253
B. Materials MgCOs, "California Magnesite" from Wards Natural Science Establishment, particle size 2'5 #; CaCOs, Fisher reagent grade, 6.3/~; kaolinite, Southern Clays, Incorporated, 1'6 F. C. Procedures The DTA measurements in each case were performed in static air with temperature rising at the rate of 12°C/rain. The samples were contained in a cylindrical well, open at the top, ~ in. diameter and ~ in. deep. The samples were loosely packed, the packing densities being 33-6, 8.27 and 23.7 per cent of theoretical density respectively for MgCO3, CaCOs, and kaolinite. Weight loss measurements were performed under conditions resembling as close as possible those in the DTA measurements. A small Inconel cylinder was constructed having the same internal dimensions as the DTA sample well. The samples were packed in this cylinder to the same densities as for DTA. The cylinder containing the sample was then inserted into the furnace for the weight-loss measurement. RESULTS~ A N D
DISCUSSION
T h e D T A p a t t e r n s are shown in Fig. 1. The t e m p e r a t u r e s at which AT]ATmax is 0"1 (a small fraction) were d e t e r m i n e d f r o m the D T A trace a n d the initial r e a c t i o n
MgC%
CoC%
KAOLINITE
400
500
600 700 TEMPERATURE- *C
800
900
FI~. 1.--DTA patterns of magnesite, calcite, kaolinite. The marker on the curve indicates the point where AT = 0"lATraax. rates at these t e m p e r a t u r e s were calculated f r o m e q u a t i o n (3). These d a t a are listed in T a b l e 1, u n d e r the h e a d i n g " ' D T A t e m p e r a t u r e " a n d " C a l c u l a t e d r a t e " , respectively. The weight loss m e a s u r e m e n t s were m a d e at n e a r l y the same t e m p e r a t u r e s as those at which the rate is c a l c u l a t e d f r o m D T A (actual t e m p e r a t u r e given in parentheses). TABLE I
DTAtemperature (°C)
MgCO3 CaCOs Kaolinite
579 762 506
Calculated rate (~/min)
Observed rate (~/min)
1"67
1.90 (580) 2.78 (759) 1-28 (506)
2-11 1.29
254
H . J . BORCI-IARDT
The initial reaction rate is determined from the initial slope of the weight-loss curve. These data are tabulated under "Observed rate". The rates are in units of per cent conversion per minute. The data indicate that use of equation (3) yields results which are reliable within approximately 20 per cent. In order to determine the temperature at which the initial reaction rate is 1 per
dn/no
cent conversion per minute, this value is substituted for -- 7
and the temperature
at which the equality, 0.0057 = A T / A T ~ x is satisfied, is determined from the DTA trace. Per cent conversion per minute as a unit of rate is an extensive quantity and is dependent upon the total effective surface area. For reactions where each powder particle is reacting independently (in contrast to the situation where the powder assemblage is behaving as one large particle ~4)) per cent conversion per minute can be translated into a unit which is independent of surface area or particle size as follows: Consider one of the reactant powders to be composed of spheres of initial volume Vo. After some reaction occurs, the volume has been reduced to V and the fraction of original reactant present is V/V o. Since V = ~zrr3 dV[ Vo 3rz dr dt = roa dt
(4)
By restricting equation (4) to initial reaction rates, r ~ to, and dV/Vo .
.
dt
.
3 dr .
rodt
(5)
If differences in density between reactant and product are neglected, dr/dt may be considered to be the initial rate of growth of the product layer. The unit of rate, dr/dr is independent of particle size. For particles 6/~ in diameter, a rate of 1% per minute is seen to correspond to dr/dt = 10-6 cm/min. The various restricting assumptions in the above are rather obvious, and clearly indicate that the figure of 10--6 crn/min should be considered to be no more than an order of magnitude guide. ~4~ For example H. T. S. BlU'rror~, S. J. GREGG and G. W, WINsoR, Trans. Faraday Sac. 48, 63 (1952).