JPH04309852A - Measurement of activation energy and device thereof - Google Patents

Abstract

PURPOSE:To obtain the new method and device for determining the activation energy by collecting the data through the thermal analysis method and processing the collected data. CONSTITUTION:As for a variety of temperature rise speed, the point where the variation speed dC/dt of the physical property C becomes max. in the case that the temperature rise at a constant temperature rise speed becomes max. is detected, and the gradient of the straight line is calculated through the least square method from the relation between the logarithm of dC/dt at the point and the inverse number of the absolute temperature, and the activation energy is calculated from the gradient.

Description

[Detailed description of the invention]

0001

BACKGROUND OF THE INVENTION 1. Field of the Invention The present invention relates to a method and apparatus for collecting data using thermal analysis techniques and processing the collected data to determine the activation energy of changes occurring in a sample. The thermal analysis method generally refers to a method of measuring the physical properties of a sample or the physical properties of decomposition products produced by a reaction or the like while changing the temperature of the sample according to a predetermined program. These physical properties include mass, temperature,
enthalpy, dimensions, mechanical properties, acoustic properties, optical properties,
Includes electrical properties, magnetic properties, etc. In addition, the measured activation energy is used as an index to evaluate the instability of unstable substances such as explosives, and is used to predict temporal changes in the physical properties of materials such as electrical materials in various environments. There are various usage forms such as , etc.

0002

[Prior Art] Conventionally, activation energy has been determined by observing changes at a constant temperature to obtain a reaction rate constant, and by observing that the logarithm of the reaction rate constant has a linear relationship with the reciprocal of the absolute temperature (Ahrenius' law). ) was used to find it from its slope. However, in recent years, thermal analysis methods that observe changes while increasing the temperature at a constant rate have developed and become popular, and many methods have been proposed to determine activation energy using the results of thermal analysis. has been done. [J. Fly
nn and L. A. Wall, J. Res
．． Natl. Bur. Standard. , 7
0A (1966) 487; edited by Hirotaro Kobe, Thermal Analysis (Kodansha, 1975)] Among them, a method previously proposed by one of the inventors [T. Ozawa, J. Th
Ermal Anal. , 2 (1970) 301
] has a wide range of application and high reliability, so AST
M (American Society for Te
Sting Materials) has been adopted as a testing standard and is widely used. In this method, the activation energy ΔE is determined by utilizing the fact that the common logarithm of the temperature increase rate and the reciprocal of the absolute temperature at the point where the rate of change is maximum have a linear relationship, and the slope is 0.4567ΔE/R. are doing. (Here, R is a gas constant.) Furthermore, this method is incorporated into the thermal analysis device as software for a data processing computer attached to the device.

0003

[Problems to be Solved by the Invention] The present invention provides a method for determining activation energy independently of this, and by using it in a complementary manner with the above method, the reliability of activation energy determination can be improved. It is an object of the present invention to provide an activation energy measuring method and a measuring device that can further increase the activation energy and reduce the error.

0004

[Means for Solving the Problems] The activation energy measuring method of the present invention which achieves the above-mentioned object includes: i) heating a sample at a predetermined heating rate; ii) the sample and its changed substances during heating; successively measuring the rate of change and temperature of a predetermined physical property of at least a portion of the
iii) Repeat steps i) and ii) for the same type of sample at multiple different heating rates, iv) For each heating rate, find the point where the rate of change is maximum, and v) For each heating rate. The present invention is characterized by comprising steps of calculating the activation energy of a change occurring in the sample from the relationship between the rate of change and temperature at the maximum point of the rate of change.

FIG. 1 is a block diagram showing the basic structure of the activation energy measuring device of the present invention. In the figure, the activation energy measurement device of the present invention includes a heating means 10 for heating a sample 50 at a plurality of different heating rates.
, a change rate measuring means 12 that sequentially measures the rate of change of a predetermined physical property of at least a part of the sample 50 and its changed material during heating; and a temperature measuring means 14 that sequentially measures the temperature during heating. , a maximum point extracting means 18 for finding the point at which the rate of change measured by the change rate measuring means 12 is maximum for each temperature increase rate; The present invention is characterized by comprising an activation energy calculating means 20 for calculating the activation energy of a change occurring in the sample 50 from the relationship between the rate of change and the temperature.

[0006]

[Operation] First, the following two conditions must be satisfied by a system to which the present invention can be applied. 1. When C is a parameter representing an observable physical property, and x is a parameter representing a physical or chemical property that causes this physical property to be expressed,
C=f(x)

(1) holds true, that is, C is uniquely defined by x. Note that C may be x itself.

2. x is uniquely determined by θ (referred to as conversion time) defined by equation (2);
θ=∫exp(-ΔE/R
T)dt (2)
That is, x is x=G(θ)

(3). However, Δ
E is the desired activation energy, and R, T, and t are the gas constant, absolute temperature, and elapsed time, respectively.

[0008] General chemical reactions satisfy the above conditions. That is, in a general chemical reaction, if x is the concentration of a substance and A is a constant, then dx/dt=Aexp(-Δ
E/RT)g(x) (4) holds, so from this equation, ∫dx/g(x)=A∫ex
p(-ΔE/RT)dt
=Aθ
(5)
is obtained, and this equation means the same as equation (3). Note that g(x) is 1-x in the case of a first-order reaction, where x is the concentration of the reaction product. If we measure a parameter uniquely determined by x, for example the total mass, this system will satisfy conditions 1 and 2 above.

Crystallization and solid-state reactions that proceed due to growth from pre-existing nuclei are also expressed as -ln(1-x)=Aθm

There is the relationship (6) (m is the order of growth) [
T. Ozawa, Bull. Chem. Soc.
．． Jpn. , 57 (1984) 639], and it has been shown that equation (3) holds similarly in the case of diffusion [T. Ozawa, J. Thermal An
al. 5 (1973) 56].

Therefore, the present invention can be applied to at least the above-mentioned system. When heating at a constant rate,
The following equation holds true at the point where the rate of change dC/dt of parameter C becomes maximum. d2C/dt2=0

(7) According to the conditions of equations (1) and (3), (
7) The formula is {(dθ/dt)2/(d2θ/dt2)
}d2C/dθ2 +dC/dθ=0 (8). Under a constant temperature increase rate φ, from equation (2) (dθ/dt)2/(d2θ/dt2)=(RT2
/ΔEφ)exp(-ΔE/RT) (9), and under a constant temperature increase rate, θ=(RT2 /ΔEφ)e
Since it can be approximated as xp(-ΔE/RT) (10), equation (8) becomes
θd2 C(θ)/dθ2 +dC(θ)/dθ
It can be written as =0 (11). However, C(θ) represents C as a function of θ.

What Equation (11) means is that if the above preconditions hold, at the maximum point of the rate of change dC/dt when the physical property C is measured by increasing the temperature at a constant temperature increase rate, , θ always takes a certain value regardless of the temperature increase rate, and therefore x and C always take a certain value from equations (3) and (1). Therefore, the differential coefficients dC/dx and dx/dθ with respect to minute time changes dt also take specific values, so dC/dt=(dC/dx)
(dx/dθ) (dθ/dt)
= (constant) (dθ/dt)
(12), and from equation (2) dC/dt=(constant)exp
(-ΔE/RT) (13) holds true. Therefore, the logarithm ln(
dC/dt) and the reciprocal of the absolute temperature 1/T, the slope is equal to -ΔE/R, and the activation energy ΔE can be calculated.

Note that the following approximation also holds true for θ. [C.
D. Doyle, Nature, 207 (19
65) 290] log θ
=log (ΔE/φR)+2.315 -0.456
7ΔE/RT Therefore, since θ is constant, the following equation is obtained. log φ + 0.4567ΔE/RT = constant Therefore, if we plot the reciprocal of the absolute temperature against the logarithm of the temperature increase rate at the point where the rate of change is maximum, we will obtain a straight line whose slope is equal to -0.4567ΔE/R Become. Activation energy can also be determined using this relationship. This is the method specified by the ASTM mentioned above. As aforementioned,
By using these two methods in a complementary manner,
Activation energy can be determined with high reliability and accuracy.

[0013]

Embodiment FIG. 2 is a diagram showing an activation energy measuring system according to an embodiment of the present invention. A sample 500 is placed in an electric furnace 102, and a thermocouple 140 detects its temperature. A temperature control device 100 controls the power of an electric furnace 102 while feeding back the temperature detected by a thermocouple 140, thereby controlling the sample according to a set heating rate.
Control is performed to increase the temperature of 500 at a constant rate. A measuring device 120 sequentially measures the physical properties of a sample 500 during heating, and detects the physical properties of the sample 500 with a thermocouple 140.
The temperature is recorded on the recorder 122, and the data is sent to the data processing device 200. The data processing device 200 performs processing on the data as described later to calculate the value of activation energy.

The physical properties measured by the measurement device 120 include mass, temperature, enthalpy, dimensions, mechanical properties, acoustic properties, optical properties, electrical properties, and magnetic properties, each of which is measured by the techniques shown in Table 1. Ru.

[0015]

[Table 1]

[0016] Details of each technique are well known to those skilled in the art, and therefore will not be described in detail. Note that these are merely examples, and it goes without saying that the present invention can be applied to any system that satisfies the above conditions. The temperature control device 100 raises the temperature of the sample 500 at a plurality of predetermined heating rates, and the measuring device 120 sequentially measures parameters representing physical properties and temperature values during that time, and sends the results to a recorder 122. It is recorded and supplied to the data processing device 200.

The data processing device 200 is a computer equipped with a CPU, a storage device, an input/output interface, etc., and may be, for example, a commercially available personal computer. FIG. 3 is a flowchart showing processing in the data processing device 200. First, the rate of change dC/dt of the parameter C representing physical properties is calculated (step a
). Next, at each temperature increase rate, find the point where this dC/dt is maximum (step b), and at this point
The value of log(dC/dt) and the reciprocal 1/T of the absolute temperature are calculated (step c). log(
The gradient is calculated by applying the least squares method to the values of dC/dt) and 1/T, and the activation energy is calculated from that value (step d).

Next, an example in which activation energy was actually determined will be explained. 80% cold stretched polycarbonate film (thickness 100μm, length 10mm, width 5m)
m) was heated under a tension of about 105 Pa, and the change in length, that is, thermal shrinkage, was measured. The results are shown in FIG. FIG. 4 shows the relationship between temperature T (° C.) and film dimensional change ΔL (%) for five temperature increase rates. In this system, the measured physical property C is the dimensional change ΔL and the parameter x is the trans/gauche ratio in the polymer backbone conformation. Note that x is difficult to measure directly. Heating reduces the transformer ratio and increases the gauche ratio, which is uniquely reflected in the dimensional change ΔL.

FIG. 5 shows the dimensional change ΔL from the results shown in FIG.
The rate of change dΔL/dt is calculated and plotted against the temperature T (°C), and from this curve, the rate of change dΔL/dt
The maximum point of L/dt is determined. FIG. 6(b) shows the logarithm of the rate of change dΔL/dt at the maximum point plotted against the reciprocal of the absolute temperature T according to the method of the present invention, and FIG. 6(a) shows the method described in ASTM. in accordance with
The logarithm of the heating rate φ is plotted against the reciprocal of the absolute temperature. The activation energies determined from the slope are 500 kJ/mol and 520 kJ/mol, respectively.
kJ/mol, and are in good agreement with each other.

The activation energy determination method described here uses the approximation shown in equation (10). Therefore, the present invention was applied to the theoretically calculated rate of change rather than the actual measurement results as described above. Figure 7 shows the calculation of the volatilization rate of volatile substances due to diffusion from the sphere when the diffusion constant follows Arrhenius' law [T
．． Ozawa, J. Thermal Anal. ，
5 (1973) 563]. (The vertical axis in the figure is dC/d
T, and by multiplying this by the temperature increase rate, dC/dt can be obtained. ) At this maximum point, the result of applying the method of the present invention is shown in FIG. In the calculation, the activation energy is 40
kcal/mol, but in the method of the present invention it was 39.
A result of 8 kcal/mol was obtained. These results revealed that the method of the present invention can be used to accurately determine activation energy. The results of plotting the logarithm of the heating rate against the reciprocal of the absolute temperature according to the method described in ASTM are also shown as white circles in accordance with FIG. The activation energy in this case is 40.6 kcal/m
It was ol.

[0021]

[Effects of the Invention] As described above, according to the present invention,
A novel method for determining activation energy is provided, which can be used complementarily with conventional ASTM standard methods to further increase the reliability of activation energy determination.

[Brief explanation of drawings]

FIG. 1 is a diagram showing the principle configuration of the present invention.

FIG. 2 is a diagram showing an example of the activation energy measuring device of the present invention.

FIG. 3 is a flowchart of data processing in the data processing device 200 of FIG. 2;

FIG. 4 is a diagram showing measurement results of dimensional changes due to heat shrinkage of a cold-stretched polycarbonate film in an example of the present invention.

FIG. 5 shows the heat shrinkage rate of cold stretched polycarbonate film.

FIG. 6 is a diagram for determining the activation energy of heat shrinkage of a cold stretched polycarbonate film.

FIG. 7 is a diagram showing a theoretical curve of the rate of diffusion and volatilization of a volatile substance from a sphere.

FIG. 8 is a diagram for determining the activation energy of the diffusion rate constant.

[Explanation of symbols]

102...Electric furnace 140...Thermocouple 500...sample

Claims (2)

[Claims] [Claim 1] i) heating the sample at a predetermined heating rate;
ii) sequentially measuring the rate of change of predetermined physical properties and temperature of at least a part of the sample and its changes during heating;
iii) Repeat steps i) and ii) for the same type of sample at multiple different heating rates, iv) For each heating rate, find the point where the rate of change is maximum, and v) For each heating rate. A method for measuring activation energy, comprising the steps of calculating the activation energy of a change occurring in a sample from the relationship between the rate of change and temperature at the maximum point of the rate of change. 2. Temperature raising means (10) for raising the temperature of the sample (50) at a plurality of different heating rates; a temperature measuring means (14) for successively measuring the temperature during heating; The maximum point extracting means (18) finds the point where the measured rate of change is maximum, and the sample ( 50) An activation energy measuring device characterized by comprising an activation energy calculation means (20) for calculating the activation energy of a change that occurs during the process.