JPH1123442A - Method for analyzing thermal decomposition reaction of solid - Google Patents

Abstract

PROBLEM TO BE SOLVED: To enable the calculation of the activation energy E of a thermal decomposition reaction by performing a CDRC(constant decomposition rate control) method at different reaction rates and analyzing measured results in a specific analytical technique. SOLUTION: For example, sample temperature Ta and Tb at the point of reaching three reaction rates αx, αy, and αz are each found, and from them three types of activation energy Ex, Ey, and Ez are calculated. Then it is possible to find final activation energy E from the average value of the three. The activation energy E is compared with n-pieces of activation energy Ei. Then an Ei that is the closest to the activation energy 5 is selected, and a reaction model expression f (α) corresponding to the Ei becomes the most reliable reaction model expression f (α) of the measured thermal decomposition reaction. Once the expression f (α) is decided, a previous exponential factor A is obtained from the intercept of the straight line of the expression of (α). By this, the previous exponential factor A and the function form of the activation energy E and the reaction model expression f (α) are all obtained, and the thermal decomposition reaction is elucidated.

Description

DETAILED DESCRIPTION OF THE INVENTION

[0001]

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method for analyzing the kinetics of a thermal decomposition reaction of a solid, and more particularly to a method for controlling the temperature of a sample so that the rate of weight loss of the thermal decomposition reaction is constant. The present invention relates to an analysis method characterized by analyzing a thermal decomposition reaction based on a thermogravimetric curve.

[0002]

2. Description of the Related Art In general, the rate of a thermal decomposition reaction of a solid changes according to the progress of the reaction. The progress of the reaction is represented by a reaction rate α, which is defined by the following equation (4).

Α = (Wi−W) / (Wi−Wf) (4) where α: reaction rate Wi: sample weight at the beginning of thermal decomposition reaction Wf: sample weight at the end of thermal decomposition reaction W: Sample weight at any point in the pyrolysis reaction

The rate of change of the reaction rate α with time is the reaction rate (dα / dt), and this reaction rate is expressed by the following equation (1) as a general reaction rate equation for a thermal decomposition reaction of a solid. be able to.

Dα / dt = A · exp (−E / RT) · f (α) (1) where α: reaction rate t: time A: pre-exponential factor E: activation energy of thermal decomposition reaction R: gas constant T: sample temperature f (α): reaction model formula as a function of α

[0004] The reaction model equation f in the above equation (1)
(α) expresses how the reaction rate changes according to the reaction rate α, and is a function of only α. When trying to analyze a specific thermal decomposition reaction, the activation energy E, the function form of the reaction model equation f (α), and the pre-exponential factor A in the equation (1) are generally unknown. If these can be clarified, the sample temperature T
It can be understood how the reaction rate changes according to the reaction rate α and the reaction rate α.

[0005] The above equation (1) is based on Thermochimica Acta,
157 (1990) 171-179, and this paper also introduces many functional forms of the reaction model formula f (α).

[0006]

In order to observe a change in weight of a sample in a thermal decomposition reaction, a thermogravimetric method is used. In order to observe the thermal decomposition reaction of a solid, a method of observing a change in weight while keeping the sample temperature constant (isothermal method) and a method of observing the change in weight of the sample by heating the sample at a constant speed (non-isothermal method The uniform heating method is well known. Although the isothermal method has high accuracy, it has a problem that it takes time. The isothermal heating method is often used because it is simpler than the isothermal method.However, the measurement accuracy is inferior because the temperature distribution, pressure distribution, and particle size distribution in the sample are measured in a non-uniform state. There's a problem.

In order to solve such a problem, a thermogravimetric measuring method has been developed in which the rate of temperature rise of the sample is changed in accordance with the rate of weight loss of the sample (JP-A-7-2606).
No. 62). As described above, the thermal analysis method of changing the heating rate is referred to as CRTA (Controlled-Rate Thermal Analysis,
The method is called the "rate control thermal analysis" method.

An object of the present invention is to provide a new method for obtaining the activation energy E of the thermal decomposition reaction and the reaction model equation f (α) using the above-mentioned reaction rate equation (1) and the CRTA method. It is to provide a method.

[0009]

In the above equation (1), the change over time (dα / dt) of the reaction rate α is determined by the reaction rate C
Which is equal to the absolute value of the weight loss rate (dW / dt) that can be determined by thermogravimetry. This reaction rate C
Considering the case where the sample temperature T is controlled so as to be constant, the left side of the above equation (1) becomes C, which can be modified as in the following equation (3).

Ln (1 / f (α)) = ln (A / C) − (E / RT) (3)

This equation (3) is obtained by calculating ln (1 / f (α)) and (1 /
T) has a linear relationship. That is,
The relationship between the reaction rate α and the sample temperature T is plotted, where ln (1 / f (α)) is plotted on the vertical axis and the reciprocal (1 / T) of the sample temperature T on the horizontal axis. become. Then, the slope of the straight line becomes (−E / R), and the intercept becomes ln (A / C).

However, in reality, for the thermal decomposition reaction to be analyzed, ln (1 / f (α)) cannot be obtained because the functional form of the reaction model formula f (α) is unknown. Therefore, assuming n kinds of reaction model equations f (α), n kinds of linear relationships can be obtained. FIG.
Is a graph schematically showing the n types of linear relationships. The vertical axis is ln (1 / f (α)), and the horizontal axis is (1 / T). Since the slopes of the straight lines are equal to (−E / R), the assumed values Ei (i = 1 to n) of n types of activation energies can be obtained by actually measuring the slopes of the respective straight lines. In FIG. 1, five types of reaction model equations are assumed.

In such a situation, it is not possible to determine which reaction model formula f (α) is the closest to the actual pyrolysis reaction for the measured pyrolysis reaction, and It is not possible to determine what the activation energy E of the reaction is.

Therefore, it is considered that thermogravimetric curves are measured at the two kinds of reaction rates Ca and Cb for the same thermal decomposition reaction. That is, first, the thermogravimetric curve is measured by controlling the sample temperature so that the reaction rate has a constant value Ca (first measurement step). Next, the sample temperature is controlled so that the reaction rate has a constant value Cb. Control and measure the thermogravimetric curve (second measuring step). Corresponding to this, by transforming the above equation (3),
The following equations (5) and (6) are obtained. When these are arranged, the equation (2) is obtained.

Ln (1 / f (α)) = ln (A / Ca) − (E / RTa) (5) ln (1 / f (α)) = ln (A / Cb) − (E / RTb) (6) ln (Cb / Ca) = (E / R) {(1 / Ta)-(1 / Tb)} (2)

Here, Ta means the sample temperature in the first measurement stage, and Tb means the sample temperature in the second measurement stage.

Since the above equation (2) does not include the reaction model equation f (α), the activation energy E can be obtained even if the reaction model equation f (α) is unknown. in this way,
The present inventor has performed a thermogravimetric measurement method using a plurality of different reaction rates so that the reaction rate is constant, so that the activity of the thermal decomposition reaction can be determined even when the reaction model formula f (α) is unknown. The present inventors have found a method for obtaining the activation energy E.

In the above equation (2), Ca, Cb and R are known. Further, the sample temperatures Ta and Tb at the time when the specific reaction rate α is reached can be obtained from the thermogravimetric curves of the first measurement stage and the second measurement stage. By substituting these values into the equation (2), the activation energy E can be calculated.

Further, a plurality of values of the activation energy E can be calculated based on a plurality of reaction rates α. For example, the sample temperatures Ta and Tb at the time when the three types of αx, αy and αz are reached are obtained, and the three types of activation energies Ex, Ey and Ez can be calculated from these.
Then, as shown in FIG. 2, the final activation energy E can be obtained by taking the average value of them. Thereby, the reliability of the numerical value of the obtained activation energy E is improved. If the activation energy E is calculated for each of a large number of reaction rates α and the average value is calculated, the reliability is further improved.

Next, the activation energy E thus obtained is compared with n activation energies Ei obtained from the slope of the straight line in FIG. Then, Ei closest to the activation energy E is selected. The reaction model formula f (α) corresponding to the selected Ei becomes the most probable reaction model formula f (α) of the measured pyrolysis reaction. Therefore, when assuming as many types of possible reaction model formulas f (α) as possible and estimating many Ei as shown in FIG. The probability of (α) is improved.

Once the reaction model equation f (α) is determined, the pre-exponential factor A can be obtained from the intercept of the straight line of the reaction model equation f (α) in FIG. Thus, the activation energy E, the function form of the reaction model equation f (α), and the pre-exponential factor A have all been determined, and the thermal decomposition reaction has been elucidated.

In the above description, the two reaction rates Ca, Cb
However, when three or more reaction rates are used, the calculation accuracy of the activation energy E is improved. For example, when three types of thermogravimetry are performed using three reaction rates Ca, Cb, and Cc, the above equation (2) is obtained by combining Ca and Cb, and the combination of Cb and Cc and the combination of Cc and Cc The following equations (7) and (8) are obtained by combining Ca.

Ln (Cb / Ca) = (E / R) {(1 / Ta) − (1 / Tb)} (2) ln (Cc / Cb) = (E / R) {(1 / Tb) ) − (1 / Tc)} (7) ln (Ca / Cc) = (E / R) {(1 / Tc) − (1 / Ta)} (8)

Since the activation energies E can be calculated from each of the equations (2), (7) and (8), the reliability of the numerical values of E can be improved by calculating the average value.

The present invention employs, among the CRTA methods, a special method of controlling the sample temperature so that the rate of weight loss is constant. This control method is referred to as CDRC (Cons
tantDecomposition Rate Control, equal decomposition rate control)
Let's call it the law.

[0023]

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS Although the present invention can be implemented in principle using any thermobalance, the following shows an example of the configuration of a thermobalance. FIG. 3 is a front sectional view showing a schematic configuration of an example of a thermal balance for carrying out the present invention. The thermobalance includes a measurement sample container 12 inside a protection tube 10 made of quartz.
And a standard sample container 14, which are supported by a sample holder 16. Around the two containers 12 and 14, a soaking cylinder (not shown) made of Pt or Ni is arranged. Around the protective tube 10, there are a total of four infrared lamps 20.
It is arranged at the position of two focal points. The temperature of the sample was measured by the differential thermocouple 1 bonded to the heat-sensitive plate supporting the containers 12 and 14.
8 can be measured.

The lower end of the sample holder 16 is supported by the tip of the balance beam 24. A balance weight 28 is provided at the other end of the balance beam 24, and a screen 30 is fixed ahead of the balance weight 28. Light from the light source lamp 32 passes through the screen 30 and is incident on the photoelectric element 34. A change in the weight of the sample holder 16 appears as a change in the output of the photoelectric element 34. on the other hand,
A magnet 26 and a weight 36 are fixed to the lower end of the sample holder 16. The output of the photoelectric element 34 is input to a balance control circuit 38, and the balance control circuit 38 supplies a current to the control coil 40 according to the weight of the sample holder 16. That is, the weight of the sample holder 16 is fed back to the control coil 40. Then, the magnet 2 is controlled according to the current of the control coil 40.
Force is applied to 6. As a result, the position of the sample holder 16 is maintained.

The sample temperature measured by the differential thermocouple 18 is input to a program automatic temperature controller 42. Further, the differential heat temperature measured by the differential thermocouple 18 is the same as that of the DC amplifier 44.
And is recorded by the recorder 46. The output of the balance control circuit 38, that is, the weight of the sample holder 16 is also recorded by the recorder 46.

The program automatic temperature control device 42 includes the sample temperature data from the differential thermocouple 18 and the balance control circuit 3
8 is input. The program automatic temperature controller 42 controls the temperature of the sample by supplying a current to the infrared lamp 20 so that the weight change rate of the sample is constant.

The infrared heating furnace shown in FIG. 3 has smaller thermal inertia than the resistance heating furnace, and has excellent temperature control response.

Next, a method for controlling the temperature of the sample will be described. In order to observe the thermal decomposition reaction of a solid, basically, a temporal change in the weight of a sample is measured while heating the sample. In the present invention, the CDRC method for controlling the rate of temperature rise of the sample so that the rate of weight loss of the sample becomes constant is adopted.
Therefore, as the thermal decomposition reaction becomes active, the heating rate decreases. When the thermal decomposition reaction becomes intense, the temperature may be shifted from a rise in temperature to a fall in temperature in order to maintain the desired rate of weight loss.

FIG. 4 is a graph of a thermogravimetric curve comparing the conventional constant temperature heating method and the CDRC method. Samples used is a powder of CaSO ₄ · 2H ₂ O. The vertical axis represents the weight loss rate of the sample (the reduction from the initial weight Wi is expressed in percentage), and the horizontal axis represents the absolute temperature T (unit: K). In the conventional constant temperature heating method (heating rate of 5 ° C. per minute), the amount of the sample decreases as the temperature T increases. In contrast, CDR
In the method C, it can be seen that the temperature T2 at the time when the thermal decomposition reaction has progressed is lower than the temperature T1 at the time when the thermal decomposition reaction starts. This is because temperature control is performed in order to keep the rate of weight loss of the sample constant.

By the way, since the weight loss of the sample does not occur until the thermal decomposition reaction starts, if the temperature control is performed without any limitation so that the weight reduction rate is constant, the temperature increase rate will increase infinitely. To avoid this, in reality,
The maximum value of the heating rate is set so that the heating rate does not become higher.

FIG. 5 shows three types of reaction rates Ca, Cb and Cc.
Is a graph obtained by measuring a thermogravimetric curve by the CDRC method using the graph, wherein the horizontal axis represents time t and the vertical axis represents the weight loss rate. Also,
The changes in the sample temperatures Ta, Tb, and Tc at that time are also shown.

FIG. 6 shows a method for obtaining a value to be substituted into the above equation (2) from the data of the thermogravimetric curve by the CDRC method. When a thermogravimetric curve is measured for the two reaction rates Ca and Cb, first, the initial weight Wi and the final weight Wf of the pyrolysis reaction are known. Therefore, the reaction rate α can be calculated at an arbitrary weight loss rate by using the above equation (4).
Now, considering the point in time when the specific reaction rate αx is reached, the sample temperatures Ta and Tb at this time can be obtained for two thermogravimetric curves. The activation energy E can be calculated by substituting these Ta and Tb, Ca and Cb, and the gas constant R into the above equation (2).

Further, the activation energy E can be similarly calculated at another reaction rate (for example, αy, αz, etc.). When a plurality of activation energies E are obtained based on a plurality of reaction rates, as shown in FIG. 2, an average value thereof is taken as a final activation energy.

Next, in order to obtain the graph of FIG.
For each type of reaction model formula f (α), the combination of the sample temperature T and the reaction rate α at each point on the thermogravimetric curve shown in FIG. 6 is represented by ln (1 / f (α)) on the vertical axis and on the horizontal axis. May be plotted on the (1 / T) coordinate axis. At this time, as a thermogravimetric curve to be used, a curve based on the reaction rate Ca in FIG. 6 may be used, a curve based on the reaction rate Cb may be used, or a thermogravimetric curve measured separately may be used.

The functional form of the reaction model equation f (α) for the thermal decomposition reaction is described, for example, in Thermochimica Acta, 157 (1990) 1.
Many of them are described in 71-179. Among them, the relatively simple functional forms are as follows.

F (α) = 1 f (α) = (1−α) ^1/2 f (α) = (1−α) ^2/3 f (α) = (1−α) f (α) = 1 / (2α) f (α) = 1 / {− ln (1-α)}

By assuming such a reaction model formula, n types of straight lines as shown in FIG. 1 are selected, and n types of activation energies Ei are obtained from their slopes. From them, the one closest to the already determined activation energy E is selected. The reaction model equation f (α) corresponding to the activation energy Ei is the most likely reaction model equation.
By obtaining the intercept of the straight line in FIG. 1 for the reaction model equation, the pre-exponential factor A in the above equation (1) is also determined.

[0037]

According to the analysis method of the present invention, the CDRC method is performed at least at two reaction rates, and the measurement results are analyzed by a specific analysis method, whereby the reaction model equation f
Even if (α) is unknown, the activation energy E of the thermal decomposition reaction can be determined. Further, based on the activation energy E, the function form of the reaction model equation f (α) and the pre-exponential factor A of the reaction rate equation can be obtained.

[Brief description of the drawings]

FIG. 1 is a graph in which the relationship between the reaction rate α and the temperature T in the CDRC method is plotted in a specific coordinate system and represented by a linear relationship.

FIG. 2 is a graph showing that activation energy E obtained for each reaction rate α is averaged.

FIG. 3 is a front sectional view showing a schematic configuration of a thermal balance for carrying out the present invention.

FIG. 4 is a graph of a thermogravimetric curve comparing a conventional constant temperature heating method and a CDRC method.

FIG. 5 is a graph of a thermogravimetric curve and a temperature change by a CDRC method.

FIG. 6 is a graph showing a method for obtaining a value to be substituted into equation (2) from a thermogravimetric curve by the CDRC method.

[Explanation of symbols]

 Ca: first reaction rate Cb: second reaction rate α: reaction rate Wi: sample weight at the beginning of pyrolysis reaction Wf: sample weight at the end of pyrolysis reaction W: sample weight at any point in the pyrolysis reaction t: time A: pre-exponential factor E: activation energy of pyrolysis reaction R: gas constant T: sample temperature f (α): reaction model formula as a function of α

Claims (6)

[Claims] When the reaction rate equation of a thermal decomposition reaction of a solid is represented by the following equation (1), the activation energy E of the thermal decomposition reaction is determined by the following steps (a) to (e). The method for analyzing the thermal decomposition reaction of solids. Dα / dt = A · exp (−E / RT) · f (α) (1) where α = (Wi−W) / (Wi−Wf) α: reaction rate Wi: thermal decomposition Sample weight at the beginning of the reaction Wf: Sample weight at the end of the pyrolysis reaction W: Sample weight at any point in the pyrolysis reaction t: Time A: Pre-exponential factor E: Activation energy of the pyrolysis reaction R: Gas constant T : Sample temperature f (α): reaction model formula as a function of α (a) Absolute value of sample weight loss rate (dW / dt) (which is equal to dα / dt) is constant first reaction rate Ca
A first measurement step of measuring the weight change of the sample caused by a specific thermal decomposition reaction by changing the sample temperature T such that (B) From the thermogravimetric curve of the first measurement stage, the sample temperature T at the time when the thermal decomposition of the sample reaches a specific reaction rate α
And setting this as the first temperature Ta. (C) The absolute value of the weight loss rate (dW / dt) of the sample (which is equal to dα / dt) is a constant second reaction rate Cb
A second measurement step of measuring the weight change of the sample caused by the specific thermal decomposition reaction by changing the sample temperature T such that (D) obtaining a sample temperature T at the time when the thermal decomposition of the sample reaches the specific reaction rate α from the thermogravimetric curve in the second measurement step, and setting this as a second temperature Tb. (E) First reaction rate Ca, second reaction rate Cb, first temperature T
a, using the second temperature Tb and the gas constant R, the following (2)
From the equation, the activation energy E of the specific pyrolysis reaction is given by
Seeking stage. Ln (Cb / Ca) = (E / R) {(1 / Ta) − (1 / Tb)} (2) 2. The analysis method according to claim 1, wherein a first temperature Ta and a second temperature Tb are obtained for each of a plurality of different reaction rates α, and then the activation energy E is calculated for each of the reaction rates α. An analysis method characterized in that the average value of the obtained activation energies E is determined as the final activation energy E in the step (e). 3. The analysis method according to claim 1, wherein the reaction model formula f (α) is calculated based on the activation energy E obtained in the step (e) as follows: Analysis method determined by the stage of (F) The specific thermal decomposition is performed by changing the sample temperature T so that the absolute value of the weight loss rate (dW / dt) of the sample (which is equal to dα / dt) becomes a constant reaction rate C. A measuring step of measuring a change in weight of a sample due to a reaction. (G) For the specific thermal decomposition reaction, the reaction model formula f
Assuming n kinds of (α) (n is a natural number of 2 or more), the relationship between the reaction rate α and the sample temperature T is expressed as ln (1 / f (α)) based on the thermogravimetric curve in the step (f). ) And the reciprocal of the sample temperature T
(1 / T) is plotted on a graph having a coordinate axis consisting of (1 / T) to obtain a linear relationship. From the slope of the straight line, for each of the n types of reaction model formulas f (α), activation of the thermal decomposition reaction is performed. A step of obtaining an assumed value of energy Ei (i = 1 to n). (H) Among the n assumed values Ei, the one closest to the activation energy E obtained in the step (e) is selected, and the reaction model equation f corresponding to the selected assumed value Ei is selected.
(α) as a reaction model formula f (α) of the specific thermal decomposition reaction. 4. The analysis method according to claim 3, wherein the thermogravimetric curve in the measuring step (f) is a heat-gravity curve in the first measuring step (a) or the second measuring step (c). An analysis method characterized by using a weight curve. 5. The analysis method according to claim 3, wherein the reaction model formula f (α) obtained in the step (h) is used to
An analysis method in which the pre-exponential factor A is determined in the following steps (i) and (nu). (I) The specific thermal decomposition is performed by changing the sample temperature T so that the absolute value of the weight loss rate (dW / dt) of the sample (which is equal to dα / dt) becomes a constant reaction rate C. A measuring step of measuring a change in weight of a sample due to a reaction. (Nu) Using the reaction model formula f (α) obtained in the step (h) based on the thermogravimetric curve in the step (i),
The relationship between the reaction rate α and the sample temperature T is plotted on a graph having coordinate axes composed of ln (1 / f (α)) and the reciprocal of the sample temperature T (1 / T) to obtain a linear relationship. A step of obtaining an intercept of a straight line and obtaining a pre-exponential factor A based on the following equation (3). Ln (1 / f (α)) = ln (A / C) − (E / RT) (3) 6. The analysis method according to claim 5, wherein the thermogravimetric curve of the measuring step of (i) is used as the thermogravimetric curve of the first measuring step of (a) or the second measuring step of (c). An analysis method characterized by using a weight curve.