Solid State Reaction Kinetics Differential Scanning Calorimetric Determination of the Solid State Decomposition Kinetics and Activation Parameters of N-Aryl-N’-Tosyloxydi-ImideN-Oxides Ernest A. Dorko, Richard S . Hughes, and Clelland R. Downs Department of Mechanical Engineering, Air Force Institute of Technology, Wright-Patterson Air Force Base, Ohio 45433 The isothermal decompositions of N-aryl N‘-tosyloxydiimide N-oxides were accomplished in a differential scanning calorimeter. Using a new method of reducing the data contained in the isothermal thermograms, the decomposition histories could be obtained without prior consideration of a kinetic mechanism. Kinetic and activation parameters were calculated and the decompositions were shown to be autocatalytic. A simple model was proposed to account for the observed decomposition pattern. I n addition a comparison of parameters calculated from the isothermal studies was made with parameters calculated from constant heating rate data.
THE INSTRUMENTATION USefUl for the analysis Of solid phase reactions has developed to the point that precise determinations of the kinetic and activation parameters can be performed. We wish to report the novel application of one such instrument, the differential scanning calorimeter, to the analysis of the solid state decomposition of pure, crystalline N-phenyl-N’-tosyloxydi-imideN-oxide (Ia) and of its N44chloro) and N-(4-methyl) derivatives (Ib, and IC) (I). The parent compound is known by the trivial name of cupferron tosylate. Subsequently it will be referred to by this name.
0 a. R = H, b. R =C1,
C.
R=CH,
I Each compound in the series was decomposed in the calorimeter under both isothermal and constant heating conditions. Data obtained from the thermograms produced were used to construct curves showing the decomposition as a function of time. Linear slopes obtained by plotting the curves in logarithmic form were used to determine the decomposition rate constants which in turn were used to determine Arrhenius activation energies and frequency factors. Finally a simple model was proposed to account for the observed decomposition pattern. EXPERIMENTAL
Preparation of Samples. Samples of the cupferron tosylates were obtained from the Rohm & Haas Company. The purity of the compounds was determined by the calorimeter melting point technique (2) to be greater than 99.9%. A standard weight (1.100 f .003 mg) was used for each decomposition sample. Weighings were performed on the Cahn electrobalance. After weighing, each sample holder was (1) T. E. Stevens, J. Org. Chem., 29, 311 (1964). (2) E. F. Westrum, Jr., in “Analytical Calorimetry,” R. S . Porter and J. F. Johnson, Eds., Plenum Press, New York, 1968, p 231.
capped and sealed and the cap was pin pricked to allow gas evolving during decomposition to escape. Decomposition. Decomposition was accomplished in a Perkin-Elmer Differential Scanning Calorimeter (Model DSC-1B). Aluminum sample holder covers were utilized to minimize emissivity effects (3). Preliminary experiments established the temperature maximum above which the recorder would not return to the base line prior to the onset of reaction. Kinetic experiments were performed below this temperature. Isothermal heating produced thermograms which are a plot of mcal/sec us. time, and constant heating rate produced thermograms which are a plot of mcal/sec cs. absolute temperature. Typical isothermal and constant heating rate thermograms are shown in Figures 1 and 2, respectively. Data Reduction. The area under each isothermal thermogram was integrated with a planimeter for time increments measured from the time of complete reaction to time t. Dividing the area of each time increment by the total area under the curve gave the reactant fraction a, at the time. The decomposition history as obtained from a plot of a us. time is shown in Figure 3. Reaction rate constants for decomposition were determined in two different ways. With the assumption of an autocatalytic mechanism (see below) the rate constants were determined from plots of the common logarithm of the reactant fraction (a) multiplied by 100 us. time. With the assumption of the Prout-Tompkins nucleation model (4), the rate constants were determined from plots of the common logarithm of 100(l/a - 1) us. time. Figure 4 shows a typical plot obtained by both methods of data reduction. Arrhenius activation energies (E*) and frequency factors (A*) were determined from a plot of the common logarithm of the rate constant us. the reciprocal of the absolute temperature. For comparison, the activation energies were obtained by the method of Rogers and Morris from constant heating rate data (5) and also from plots of the common logarithm of the maximum deflection during isothermal heating us. the reciprocal of the absolute temperature. RESULTS
The sigmoid shape of the curves of reaction histories indicates that the reaction mechanism is autocatalytic (6). The curves are described as consisting of two distinct periods: the acceleratory or first half, and the decay or last half. Each of the logarithmic plots used for reaction rate determination (3) R. N. Rogers and E. D. Morris, Jr., ANAL.CHEM., 38, 410 (1966). (4) E. G. Prout and F. C. Tompkins, Trans. Faraday SOC.,40, 488 (1944). ( 5 ) R. N. Rogers and E. D. Morris, Jr., ANAL.CHEM., 38, 412 (1966). (6) P. W. M. Jacobs and F. C . Tornpkins, in “Chemistry of the Solid State,” W. E. Garner, Ed., Academic Press, Inc., New York, p 184.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
253
b Figure 1. Isothermal thermogram of cupferron tosylate obtained at 114°C. Point A is point of maximum deflection
Y
y 2 0 4 8
16
20
24
28
32
36
U
R
40 0
360
440 TEMPERATURE
480
( O K )
Figure 2. Constant heating rate thermogram of cupferron tosylate showing ( A ) the initial reaction exotherm, ( B ) the melting endotherm, and (0 the main reaction exotherm
0
1.0
-
.E
z+ a
0.4
U V t
a
0.8
1.0
1.2
1.4
(see R I O - ~ )
-
1)
0.6
LL
d w
0.6
Figure 4. Plots of ( A ) log lOOa and ( B ) log 100 (l/a us. time for cupferron tosylate at 118 "C
0.8
(L
!-
0.4
Time
z
0
0.2
0.2 I
0.0 0
I
I 2
I
1
3
4
I 5
6
7
T i m e (sec x
Figure 3. Decomposition history of cupferron tosylate at 103 "C shows two straight line segments from which the reported rate constants for the acceleratory and decay periods were determined. The rate constants are given in Table I. Table II lists the values of activation energies obtained by the various data reduction methods described. The values were determined from a least squares fit of the experimental data. The common logarithms of the frequency factors are presented in Table 111.
(7). The system decomposes exothermally in solution to yield phenyl tosylate plus gaseous products. In the present study, infrared analysis of the solid products remaining after decomposition showed them to be the appropriately substituted pheny! tosylates. The decomposition histories, as obtained by the method of this report, could be determined without a prior reference to the kinetics of the reaction. The method therefore is quite general for any type of reaction which will occur under thermolytic conditions. From the sigmoid shape of the histories, it is reasonable to postulate an autocatalytic decomposition mechanism for the system (6). The differential rate expression for the disappearance of reactant is given by Equation I
where a and b refer to reactant and condensed product fraction, respectively, This analysis is mathematically similar to the one presented by Bawn (8) for a system undergoing decomposition with partial liquefaction. In the current report the authors have chosen to retain the concept of reactant and
DISCUSSION
Kinetics. The cupferron tosylate system was chosen for analysis because its decomposition has been studied previously 254
(7) E. A. Dorko and T. E. Stevens, Chem. Comm., 871 (1966). (8) C. E.H.Bawn, in "Chemistry of the Solid State," W. E. Garner, Ed., Academic Press, Inc., New York, 1955, p 254.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
In the last stages of reaction the term kna becomes small compared to (kl kz)so that Equation 2 reduces to Equation 3
+
Table I. Reaction Rate Constants (sec-’ X lo2). Temperature T , “C
Autocatalytic model ka
kD
ka
ci
(3)
- (ki
+ kz)a = kza2
(4)
which is recognizable as the Bernoulli differential equation (9). The general solution of this equation is shown in Equation 5
On re-writing, and niaking the approximation that =
(a - )
(1
product fraction in order to demonstrate a correlation of results on this basis. At the start of reaction, b is zero, and a = a, = 1. In the early stages the reaction can be analyzed as a simple first order reaction. To analyze the subsequent stages of reaction the equality, b = a, - a, is substituted into Equation 1 and the expression is integrated to produce Equation 2
(2)
kn -
ki
1, it becomes Equation 6
In -
Table 111. Log Arrhenius Frequency Factora Frep-Chloro- p-Methylquency Cupferron cupferron cupferron Method factor tosylate tosylate tosylate Isothermal A: 12.44 9.29 12.54 autocatalytic Ai 13.40 10.87 13.47 model Isothermal A: 20.80 24.87 25.72 Prout-Tompkins A: 14.44 11.18 16.70 model A:, acceleratory period; A: decay period
+ kz)t - In (kl + kz - kza) + constant
+ kz)t + constant
+
0
(kl
(kl
+
Table 11. Activation Energies (kcal/mole)a Cup- p-Chloro- p-MethylActivation ferron cupferron cupferron Method energy tosylate tosylate tosylate Isothermal E,* 29.3 24.4 29.8 autocatalytic E: 28.5 24.0 28.8 model Isothermal E;: 41.7 50.3 50.4 Prout-Tompkins E: 30.3 24.6 34.5 model Constant heating Run 1 E* 37.7 35.3 45.7 Run2E* 40.0 37.7 39.7 Maximum reaction E,*., 39.4 35.2 42.2 E,* acceleratory period; E:, decay period.
=
=
which is recognizable as the integrated rate expression for a first order reaction. Graphically Equation 3 will produce a straight line with the negative of the slope equal to kl k2. Figure 4 shows that the plot of log 100 a us. time does indeed produce a curve with two straight line segments at either extreme. At first glance this would indicate that referring to the autocatalytic model the kA of Table I is equivalent to kl and kDis equivalent to kl k p . However, this simple correspondence does not seem to hold exactly throughout the entire temperature range of decomposition. To demonstrate the difficulty consider Equation 1. This equation can be expressed as Equation 4
kD
Cupferron tosylate (m.p. 139.5 “C) O.OO60 0.1403 ... 0.1279 100 0.0053 0.1518 0.1068 0.1781 103 0. 0072 0.2160 0.1173 0.2181 106 0.0127 0.3087 0.1811 0.3260 109 0.0115 0.4340 0.3797 0.4631 112 0.0201 0.6940 0.4765 0.6961 115 0.0283 0.6990 0.7797 0.7417 118 0.0435 0.8880 1.1584 ... 121 4-Chloro-cupferron tosylate (mop.149.0 “C) 0.0626 0.3615 112 0.0068 0.3670 0.4658 0.0806 115 0.0102 0.4596 0.1354 0.6481 118 0.0102 0.6507 0.7830 1.1062 0.2504 121 0.0105 1.0291 1.0153 0.3757 124 0.0185 1.1729 0.7099 127 0.0227 1.3824 1.5064 1.0011 130 0.0282 1.4243 2.0170 1,9242 1.6180 133 0.0363 CMethyl-cupferron tosylate (m.p. 134.5 “C) 0.1594 0.1698 0.0555 103 0. 0050 0.1431 0.1604 106 0.0055 0.1548 0.2324 0.2419 109 0.0070 0.2259 0.2217 0,3002 112 0.W8 0.2799 0.4227 0.4397 115 0.0125 0.4163 1.0926 0.6822 118 0.0238 0.7144 k A , acceleratory period; k D , decay period.
-In a
-In a
Prout-Tompkins model
1
= (kl
+ kz
+ kz)t + In C,
which is recognizable as the Ostwald equation (IO) adapted somewhat to the system under study. The Ostwald equation has been applied to the decomposition of high-melting, crystalline materials by Tompkins and co-workers (10) and this method of analysis has come to be called the Prout-Tompkins analysis (4). It can be seen from Equation 6 that the ProutTompkins analysis should lead to a straight line in the present system. From Figure 4 it can be seen that the plot of log
(i -
1) us. time approaches a straight line at higher tem-
peratures (ix.,at temperatures near the melting points of the reactants); however, the bend in the curve at co. a = 0.5 becomes pronounced as the temperature is lowered. This bending has been observed and discussed for the Prout-Tompkins model (4, IO). The rate constants for the Prout-Tompkins analysis in Table I1 show a convergence of ka and k D as the temperature increases. This is to be expected according to Equation 6 and a comparison of Equations 3 and 6 shows the high temperature value should equal the value for k D determined from the autocatalytic model. This is also observed on comparing the data for the two methods of analysis. The existence of autocatalysis in solid phase decompositions near the melting point is postulated by Bawn (8) to be due to the formation of an intermediate which is either liquid or which lowers the melting point of the reactant. Duswalt ( / I ) has observed that autocatalysis caused by the melting of the (9) See for example, I. S. Sokolnikoff, and R. M. Redheffer, “Mathematics of Physics and Modern Engineering,” McGrawHill Book Company, Inc., New York, 1958, p 27. (10) Cf.D. A. Young, “The InternationalEncyclopedia of Physical Chemistry and Chemical Physics, Vol. I” Pergamon Press, New York, 1966, p 49. (11) A. A. Duswalt, in “Analytical Calorimetry,” R. S. Porter and J. F. Johnson, Eds., Plenum Press, New York, 1968, p 313.
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
255
solid into the more thermally unstable liquid can be predicted from the constant heating rate DSC thermogram where a melting endotherm appears just prior to the initial decomposition. This effect was observed with the present system. This observation, along with the demonstration that decomposition near the melting point obeys the simple autocatalytic scheme proposed, lends credence to the melting theory. It also, however, becomes obvious that as the decomposition occurs at temperatures substantially below the melting point, effects other than chemical or melting begin to play substantial roles in determining the reaction mechanism. The nature and extent of these effects on the cupferron tosylate system are currently being studied. In this regard, a Hammett pa analysis (12) of the kinetics revealed that there is no systematic substitutent effect on the decomposition behavior within the series. Another approach taken indicates when that the substrates are imbedded in potassium bromide matrix and decomposed in the sample beam of an infrared spectrophotometer the sigmoid shaped curve is distorted. Additional work is being done to delineate the cause of this distortion. The results will be reported in the future. Activation Energies. The activation energies Gbtained from the rate data were compared with activation energies -
(12) L. P. Hammett, “Physical Organic Chemistry,” McGrawHill Book Company, Inc., New York, 1940, p 184.
obtained by the method of Rogers and Morris (5). There is no correlation between the respective sets of values. However, there is a striking correlation between the energies determined from constant heating and those determined from the point of maximum reaction during isothermal heating. (The maximum reaction values obtained from the isothermal thermograms correspond to the inflection points of the decomposition histories.) The similarity of values as determined from both methods indicates that analysis of the maximum deflection distance and of the constant heating curve is a measure of maximum decomposition reaction for an autocatalytic reaction. However, these values for activation energy cannot be related back to the proposed reaction mechanism. Therefore, the authors feel that these values are of utility only for comparative studies and have little utility when dealing with kinetically defined activation energies.
ACKNOWLEDGMENT The authors thank Travis E. Stevens of the Rohm & Haas Company, Huntsville, Ala., for samples of the cupferron tosylates.
RECEIVED for review May 29, 1969. Accepted November 21, 1969. A portion of this work was presented at the 158th National Meeting, American Chemical Society, New York, September 1969.
Corrections Activation Analysis for Molybdenum in Samples Containing Large Amounts of Tungsten In this article by Barbara A. Thompson and Philip D. LaFleur [ANAL.CHEM.,41, 1888 (lS69)], the following errors in Table I should be corrected. The last item in column 2 should be 23.96 i:0,23b. Also in Table I items three, four, and five in column 3 should be
0.996’ 23.90 f 0.06‘ 23.75 i0.15‘
Activity Measurements in Concentrated Sodium Chloride-Potassium Chloride Electrolytes Using Cation-Sensitive Glass Electrodes In this article by Rima Huston and James N. Butler [ANAL. y 1 2 and 7 2 1 are mean activity coefficients of NaCl and KCI. Equation J should read:
CHEM., 41, 1695-8 (196911, note that
Equation 3 should read:
256
Theory of Curved Molar Ratio Plots and a New Linear Plotting Method In this article by Kozo Momoki et al. [ANAL.CHEM.,41, 1286 (1969)], there are several errors that should be corrected as follows: ColPage umn
1288 1288 1288 1288 1290 1293 1293 1294 1298
Line
For
changing-ligand concentration 2 5 Beers’ law 2 8 [MrnZnIi 2 22 If the 1 7 seep 1 28“ C’L Equation 27 (Cc)mx = SL . CL TablePV and P Results (title) 2 9 compleses
2
4
Read changing ligandconcentration Beer’s law [*WrnLnlt In the steep
C,’ (Cc)m,x
= SL ’ CL’
and Results complexes
1298 Equation 28
” Also in Figures 7, 8, 12, 14, 15, and 16, experimentally weighed conc&tration of ligand used should-be read as there printed or drawn. CL‘ instead of
ANALYTICAL CHEMISTRY, VOL. 42, NO. 2, FEBRUARY 1970
