JP2008069242A - Method for storing thermosetting resin - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To enable the storage of a thermosetting resin in a more optimal state by setting the storage temperature of the thermosetting resin for meeting with a state for using, etc. <P>SOLUTION: This curing rate P of the thermosetting resin is obtained from the following formulae (1), (2), (3) by using K (K>0) curing rate constant and t storage period. P=1-expä-(K×t)<SP>1/N</SP>}-----(1). K=α<SB>0</SB>expä-Q<SB>K</SB>/(kT)}-----(2). N=β<SB>0</SB>expä-Q<SB>N</SB>/(kT)}-----(3). Wherein, Q<SB>K</SB>is a constant showing an activation energy for curing the thermosetting resin; Q<SB>N</SB>is a constant corresponding to the activation energy in the formula (3); T is absolute temperature of added heat; k is the Boltzmann constant: α<SB>0</SB>is a frequency factor showing the probability of collision of the thermosetting resin molecules with each other, effective for the curing of the thermosetting resin; and β<SB>0</SB>is a constant corresponding to the frequency factor in the formula (3). <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for storing a thermosetting resin used for adhesives, paints, and the like.

  In mounting electronic parts such as semiconductors and manufacturing printed wiring boards, thermosetting resins represented by epoxy resins are often used. For example, in flip chip mounting, a thermosetting resin called underfill is used between a wiring board and a semiconductor chip mounted thereon. A thermosetting resin is a plastic that is cured by heating, and a cross-linking reaction in which a side chain that branches out from an elongated polymer like a chain binds to a side chain of another polymer proceeds by heating, This is a resin in which the polymers are three-dimensionally bonded and cured. Thermosetting resins such as epoxy resins have a three-dimensional cross-linked structure, and therefore have superior physical properties such as heat resistance and chemical resistance compared to thermoplastic resins (see Non-Patent Documents 1 and 2).

Hiroshi Mori, “Coating film analysis by measuring viscoelasticity”, Toyota Central R & D Review, Vol. 29, no. 2, pp 56-62, 1994 Epoxy Resin Technology Association, “Review Epoxy Resin”, Applications II, pp. 6-9, 2003

  By the way, since the thermosetting resin is a resin that is cured by heat, it is generally stored at a low temperature of 10 ° C. or lower. However, it is costly to maintain a low temperature state. For example, when storing for a long time, store it at a lower temperature, and when storing it for a short time, store it at a certain high temperature. If the temperature can be optimized, the cost for storage can be reduced.

  The present invention was made to solve the above problems, and the thermosetting resin is stored in a more optimal state, such as setting the storage temperature of the thermosetting resin according to the state of use. The purpose is to be able to.

The storage method of the thermosetting resin according to the present invention is such that the curing rate P after the storage period t when the desired thermosetting resin is stored at a predetermined storage temperature for a predetermined period is expressed as P = 1−exp {−. (K · t) ^{1 / N} }, and the first constant Q _K , the second constant α ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k Using the second formula consisting of K = α ₀ exp {−Q _K / (kT)} to be defined, the third constant Q _N , the fourth constant β ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k The storage condition including the storage temperature and the storage period is set by predicting with the third expression of N = β ₀ exp {−Q _N / (kT)} that defines N of the first expression. It is a thing.

In addition, another thermosetting resin storage method according to the present invention predicts the curing rate when a desired thermosetting resin is stored for a predetermined period at a predetermined storage temperature. In the thermosetting resin storage method for setting the storage conditions including the first curing rate P after the first storage period t from the start of storage at the first temperature, P = 1−exp {− (K · t) ^{1 / N} }, the first constant Q _K , the second constant α ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k are used to define K of the first expression K = α ₀ exp {−Q _K / (kT)}, the third constant Q _N , the fourth constant β ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k A first step for predicting with a third equation consisting of N = β ₀ exp {−Q _N / (kT)} defining N, and a second temperature The storage period t ′ at which the first curing rate P is obtained by the storage temperature is determined from the first, second, and third expressions, and is determined from the storage period t ′ by storage at the second temperature. The change ΔP in the curing rate during the unit period Δt is expressed by the second equation, the third equation, and ΔP = 1 / N · K ^{1 / N} · t ^{1 / N−1} · exp [− (Kt) ^{1 / N} ] · Δt, and a third step for obtaining a second curing rate P + ΔP obtained by adding a change ΔP in the curing rate to the first curing rate P. (2) The curing rate after storage at the first temperature for the first storage period and then at the second temperature for the unit storage period is predicted.

  In the thermosetting resin storage method, a fourth step for obtaining a change ΔP ′ in the curing rate during Δt from the time point t ′ + Δt under the condition of the second temperature from the fourth equation; And a fifth step of obtaining a third curing rate P + ΔP + ΔP ′ obtained by adding a change ΔP ′ of the curing rate to the curing rate P + ΔP, and storing the first period at the first temperature by the third curing rate, You may make it estimate the hardening rate after storing unit period (DELTA) t as temperature, and also storing unit period (DELTA) t as 2nd temperature.

  Further, in the method for storing the thermosetting resin, a period t ″ during which the second curing rate P + ΔP is reached by heating at the third temperature is obtained from the first expression, the second expression, and the third expression, A fourth step for obtaining a change ΔP ′ in the curing rate between the period t ″ due to heating and the predetermined unit period Δt from the second expression, the third expression, and the fourth expression; And a fifth step of obtaining a third curing rate P + ΔP + ΔP ″ obtained by adding a change ΔP ′ in the curing rate to the curing rate P + ΔP, and storing the first temperature at the first temperature for the first period according to the third curing rate. As a unit period Δt, and in addition, the curing rate after storing the unit period Δt as the third temperature may be predicted.

As described above, according to the present invention, ^{N in} the first equation consisting of P = 1−exp {− (K · t) ^{1 / N} } is expressed as the third constant Q _N , the fourth constant β ₀ , Since the absolute temperature T and the Boltzmann constant k are used to define from N = β ₀ exp {−Q _N / (kT)}, the storage conditions of the thermosetting resin by a combination of an appropriate storage temperature and storage period Can be set, and an excellent effect is obtained that the thermosetting resin can be stored in a more optimal state.

Hereinafter, embodiments of the present invention will be described with reference to the drawings.
[Embodiment 1]
First, Embodiment 1 of the present invention will be described. In the first embodiment, the change in the curing rate P during a predetermined storage period when the thermosetting resin is stored at a predetermined storage temperature is described below using the curing rate constant K (K> 0) and the storage period t. The storage deadline when stored at the above storage temperature is set on the basis of the change in the curing rate P obtained by the expressions (1), (2), and (3). .

P = 1−exp {− (K · t) ^{1 / N} } (1)
K = α ₀ exp {−Q _K / (kT)} (2)
N = β ₀ exp {−Q _N / (kT)} (3)

Here, the constant N (N> 0) is the reciprocal of the form factor m in the Weibull model (or the Abrami constant m in the KJMA model), and is approximately a value corresponding to the reaction order (approximately 0.5 ≦ N ≦ 1.2). Further, assuming that the curing rate constant K and the constant N in the formula (1) have Arrhenius type temperature dependence, the formula (2) and the formula (3) are used. Here, Q _K is a constant indicating activation energy for curing the thermosetting resin (first constant), and Q _N is a constant corresponding to the activation energy in the formula (3) (third constant). , T is the absolute temperature of the applied heat, and k is the Boltzmann constant. Α ₀ is a frequency factor (second constant) indicating the probability of collision between thermosetting resin molecules effective for curing the thermosetting resin, and β ₀ is the frequency in the equation (3). It is a constant (fourth constant) corresponding to a factor. The curing rate constant K and the frequency factor α ₀ have a dimension of [time ⁻¹ ], and the constant N and the constant β ₀ are dimensionless. In general, Q _K > 0, but the constant Q _N mainly indicates a positive or negative value close to zero.

For example, 99% is cured by heating at 150 ° C. for 30 minutes, the constant N at this curing temperature (150 ° C.) is 0.80, the activation energy Q _K is 0.80 eV, and the constant Q _N is 0.30 eV. When the relationship between the heating time and the curing rate is obtained from the formula (1) for the thermosetting resin, a curing rate curve (change in the curing rate P) as shown in FIG. 1 is obtained. By expressing in this way, the difference between the chemical reaction rate and the mechanical curing rate can be collectively expressed by the difference of the constant N. In the case of storage in the present embodiment, the heating temperature may be the storage temperature, and the heating time may be the storage period. In addition, compared to the n-th power model, the smaller the constant N, the more information about the reaction order, such as the number of crosslinking points (reactive groups) in the molecule, and the smaller the constant N, the more the cured product is three-dimensional. Geometric information about solid phase growth in the curing process, such as growth, can be obtained. The chemical reaction rate, the nth power model, and the KJMA model will be described in detail later.

  Here, the determination of each constant will be described. When the logarithm of both sides of the above equation (1) is taken twice and arranged, the following equation (4) is obtained.

  Formula (4) indicates that a straight line having a slope of 1 / N is obtained by plotting ln [-ln (1-P)] on the vertical axis and lnt on the horizontal axis. Therefore, using the experimental value P of the curing rate P for each elapsed time t at each reaction temperature for each of the various reaction temperatures in which the experiment was performed, the values obtained from the equation (4) are the vertical axis and horizontal axis defined above. Is plotted in a graph using, an approximate straight line is obtained by the least square method, and the value of the constant N (experimental value) at each reaction temperature can be obtained from the slope of the obtained approximate straight line.

For example, the target thermosetting resin is heated at a predetermined temperature to be in a completely cured state, the shear strength in this state is measured with a shear strength tester, and the measured shear strength S _{0 is set} to a cure rate of 99%. Next, for example, an experiment when the reaction temperature of 100 ° C. is added for the time t1 by dividing the shear strength S ₁ when the reaction temperature of 100 ° C. is added for the time t1 by the shear strength S ₀ , for example. The value P ₁ can be determined. Similarly, the experimental value P ₂ when the reaction temperature of 100 ° C. is added for the time t2, the experimental value P ₃ when the reaction temperature of 100 ° C. is added for the time t3, and the experimental values P ₁ , P ₂ , P ₃ ,..., The left side of equation (4) is plotted against the logarithm of time t to obtain an approximate straight line, and the experimental value of index N at a reaction temperature of 100 ° C. is obtained from this slope. it can. These are performed for each reaction temperature, such as a reaction temperature of 110 ° C., a reaction temperature of 120 ° C., a reaction temperature of 130 ° C., and so on.

  In the above description, the measured value of the curing rate is obtained by the shear strength. However, the tensile strength obtained by the tensile strength tester, the viscoelasticity obtained by the viscoelasticity measuring device, the calorie obtained by the differential thermal scanning calorimeter. The measured value of the curing rate may be obtained from the peak state (reduction) of the reactive group measured by a Fourier transform infrared spectrophotometer.

  Next, taking the logarithm of both sides of Equation (3), the following Equation (5) is obtained.

Formula (5) is a graph with the logarithm lnN of the constant N determined for each temperature on the vertical axis and the inverse 1 / T of the absolute temperature of each reaction temperature on the horizontal axis. The intercept is lnβ ₀ and the slope −Q It shows that it becomes a straight line of _N / k. Therefore, using the experimental value of the constant N at each reaction temperature, the value obtained from the equation (5) is plotted on the graph using the vertical axis and horizontal axis of the above definition, and an approximate straight line is obtained by the least square method. The constant Q _N and the constant β ₀ can be obtained from the slope and intercept of the approximate straight line. Further, using the constant Q _N and the constant β ₀ obtained here, an approximate value of the constant N for each reaction temperature is obtained from the above equation (5).

  Next, using the formula (1) again and taking the logarithm of both sides, the following formula (6) is obtained.

Equation (6) indicates that a straight line having a slope K ^{1 / N} is obtained by plotting the graph with −ln (1-P) on the vertical axis and t ^{1 / N} on the horizontal axis. Therefore, for each reaction temperature at which the experiment was performed, the experimental value of the curing rate P was used for each elapsed time t at each reaction temperature, and the values obtained from the equation (6) were expressed on the vertical axis and the horizontal axis defined above. It plots on the used graph, calculates | requires an approximate line with the least squares method, and can obtain | require the hardening rate constant K from the inclination of the calculated approximate line. The curing rate constant K determined by these is a primary approximate value determined from the approximate value of the experimental value P and the constant N. In addition, in the stage which calculated | required the constant N from the said Formula (5), the hardening rate constant K can be similarly calculated | required also from an intercept, However, Since the constant N of this stage is a value before calculating | requiring an approximate value, It becomes a numerical value with many variations by affecting the value of the curing rate constant K. For this reason, first, an approximate value of the constant N in consideration of the temperature dependency including the data of other reaction temperatures is obtained, and a more probable value is obtained by calculating the curing rate constant K using this value. Can do.

  Next, taking the logarithm of both sides of equation (2), the following equation (7) is obtained.

Formula (7) is a graph with the logarithm lnK of the curing rate constant K determined for each temperature on the vertical axis and the reciprocal 1 / T of the absolute temperature on the horizontal axis, and the intercept is lnα ₀ and the slope −Q _K / It shows that it becomes a straight line of k. Therefore, using the cure rate constant K at each reaction temperature obtained from the above equation (6), the graph is plotted on the graph using the vertical axis and horizontal axis defined above, an approximate straight line is obtained by the least square method, and the obtained approximation is obtained. The activation energy Q _K and the frequency factor α ₀ can be obtained from the slope and intercept of the straight line. The cure rate constant K obtained from the equation (7) using the activation energy Q _K and the frequency factor α ₀ obtained here is the final approximate value at each temperature.

A statistical approximation of each constant (Q _K , Q _N , α ₀ , β ₀ ) is obtained by the procedure using the above-described formulas (4) to (7), and these are used for arbitrary storage temperature (reaction temperature). The curing rate constant K, constant N, and curing rate P (change in curing rate P) can be determined (predicted). Moreover, what is necessary is just to set the storage time limit in arbitrary storage temperature by the change of the calculated | required hardening rate P. FIG. For example, the storage time limit may be a range where the predicted curing rate P does not exceed 5% at a desired storage temperature. Further, among the obtained changes in the curing rate P, the storage temperature may be a temperature at which the curing rate P does not exceed 5% during a desired storage period. Thus, according to the first embodiment, since the storage conditions including the storage temperature and storage period of the thermosetting resin can be set according to the state of use, the thermosetting resin can be stored in a more optimal state. become able to.

式（９）は、式（１）を時間で微分して得られた式（８）をもとにしたものであり、式（９）により、式（１）で定義される硬化率ＰのΔｔ時間内の変化分を求めることができる。 [Embodiment 2]
Next, a second embodiment of the present invention will be described. In this second embodiment,
The change in the curing rate P of the thermosetting resin during a predetermined storage period when the storage temperature changes is expressed by the above-described formula (1), formula (2), formula (3), and formula (9) shown below. The storage deadline is set based on the obtained change in the curing rate P.

Formula (9) is based on Formula (8) obtained by differentiating Formula (1) with respect to time. From Formula (9), the curing rate P defined by Formula (1) is calculated. The amount of change within the time Δt can be obtained.

Hereinafter, the storage method of the thermosetting resin according to the second embodiment will be described with reference to FIG. In the following, the storage temperature is initially stored as the first storage temperature T1 for the first storage period t1, and then the curing rate after storage for the second storage period t2 is predicted as the second storage temperature T2. Will be described. First, as shown in FIG. 2 (S1), the curing rate P ₀ at the time after the first storage period t1 in the initial stage at the first storage temperature T1 in the initial stage of storage is expressed by the formulas (1) and (2). ) And equation (3).

Next, as shown in FIG. 2 (S2), the virtual storage period t ′ at which the curing rate P ₀ is obtained under the condition of the second storage temperature T2 from the beginning is expressed by the equations (1), (2), and (3 )
Next, as shown in (S3) of FIG. 2, the change ΔP in the curing rate after being stored at the set second storage temperature T2 during the unit period Δt after the virtual storage period t ′ is stored. ₁ is obtained from Equation (2), Equation (3), and Equation (9). The virtual storage period t ′ is calculated as t in the equation (9).
Next, as shown in FIG. 2 (S4), the obtained change ΔP ₁ is added to the curing rate P ₀ of the first storage period t1 at the first storage temperature T1, and the resulting curing is obtained. Let the rate P _{0 + 1 be} the curing rate after the first storage period t1 + unit period Δt hours.

Thereafter, the change ΔP ₂ of the curing rate when stored at the second storage temperature T2 set between Δt from the virtual storage period t ′ + Δt is obtained from the equation (9), and the obtained change ΔP _{2 is} obtained. Is added to the curing rate P _{0 + 1} already obtained by addition, and the curing rate P _{0 + 1 + 2} obtained by this addition is calculated as the curing rate after the first storage period t1 + Δt time + Δt time. To do. By repeating this, a change in the curing rate can be obtained.

  Further, by changing the storage temperature for each unit period and taking the sum of the change in the curing rate at the changed temperature, the cumulative change in the curing rate when the temperature is changed can be obtained. In this case, by setting the unit period Δt to a very short period, it is possible to obtain a change in the curing rate when the storage temperature is changed pseudo and continuously.

For example, when the third storage temperature is set from the time point of the first storage period t1 + Δt, first, the virtual storage period t ″ at which the curing rate P _{0 + 1} is obtained under the condition of the third storage temperature from the beginning is expressed by the equation (1). , (2) and (3) (additional step 1).
Next, under the condition of the third storage temperature, the change ΔP ₂ ′ in the curing rate during the unit period Δt from the time when the virtual storage period t ″ has elapsed is expressed by (2), (3), and Equation (9). (Additional step 2).
Next, variation [Delta] P ₂ obtained the 'a is added to the hardening rate P _{0 + 1,} the addition and hardening rate obtained by P _{0 + 1 + 2',} the first storage period t1 + unit period Delta] t + unit period The curing rate after the period of Δt has elapsed (additional step 3).

  By repeating the additional step 1, the additional step 2, and the additional step 3 every time the storage temperature is changed, it can be applied when the storage temperature changes for each unit period Δt.

  In the above formula (9), the mechanical property value that is changed by curing in the process of storage of the thermosetting resin is defined as a ratio (curing rate) P to a certain property value in a completely cured state, and a unit period. The increment ΔP of the ratio P per Δt is expressed by using a curing rate constant K and a constant N. Further, the curing rate constant K and constant N in the equation (9) are represented by a curing model having temperature dependency represented by the equations (2) and (3). Predicting changes in the curing rate due to storage of the thermosetting resin when the storage temperature is changed, based on the cumulative value of the change obtained from these expressions (9), (2), and (3). Therefore, the storage deadline may be set. For example, the storage time limit may be a range where the predicted curing rate P does not exceed 5% under the set storage temperature condition. Further, a range (allowable range) of change in storage temperature may be set based on a desired storage period. As described above, according to the second embodiment, since the storage conditions including the storage temperature and storage period of the thermosetting resin can be set according to the state of use, the thermosetting resin is stored in a more optimal state. become able to.

  In addition, the prediction of the curing rate by storage in the thermosetting resin storage method according to the present embodiment described above is, for example, the procedure of each step described with reference to FIG. 2 in the case where the storage temperature changes. Can be implemented as a program by a computer. For example, as illustrated in FIG. 3, a computer including an arithmetic processing unit 301, a main storage unit 302, an external storage unit 303, an input unit 304, a display unit 305, and a printer 306 may be used.

In this computer, for example, in the external storage unit 303 that is a magnetic recording device, the first curing rate P ₀ after the first storage period t1 from the start of storage at the first storage temperature T1 is expressed by the equations (1) and (2). ), And the first step predicted from the equation (3), and the virtual storage period t ′ at which the first curing rate P ₀ is obtained by the storage at the second storage temperature T2, the equations (1), (2), and The second step obtained from the equation (3) and the change ΔP ₁ in the curing rate during the predetermined unit period Δt from the virtual storage period t ′ by the storage at the second storage temperature T2 are expressed by the equations (2) and ( 3), and obtains a third step of obtaining the equation (9) to the virtual storage period was t, the second cure rate P _{0 + 1} plus the variation [Delta] P ₁ of cure rate in the first cure rate P ₀ A program including at least the fourth step is stored.

The program stored in the external storage unit 303 in this manner is expanded and executed in the main storage unit 302 by the arithmetic processing unit 301 and the execution result is displayed on the display unit 305 in real time. Is printed out. Further, the processing result is stored in the external storage unit 303. In addition, information (data) such as constants necessary for arithmetic processing is input from the input unit 304 by the operation of the operator, temporarily stored in the main storage unit 302, and stored in the external storage unit 303. The arithmetic processing unit 301 uses the data such as the stored constants and executes the program developed in the main storage unit 302, so that the curing rate P ₀ , P _{0 + 1} , P _{0 + 1 + 2} , P _{0 + 1 + 2 + 3} ,... Are calculated. Further, by performing only the first step, it is possible to obtain a change in the curing rate P when the storage temperature is constant.

  In the above-described embodiment, the storage temperature of the thermosetting resin is predicted by predicting the curing rate using the chemical curing rate obtained by calorimetric analysis or the like and the mechanical curing rate obtained from shear strength measurement as an index. The storage conditions including the storage period are set, but the present invention is not limited to this. For storage materials other than thermosetting resins, such as foods and medicines, the freshness and efficacy of the storage material decrease over time, and the rate of decrease in freshness and efficacy changes due to temperature changes. When the deterioration state of freshness and efficacy can be expressed by the equations (1), (2), and (3), the curing rate can be predicted by replacing the deterioration rate with deterioration as an index.

  By the way, the prediction of the curing rate by the formula (1), the formula (2), and the formula (3) is performed in order to grasp the curing behavior of the thermosetting resin by using the mechanical curing rate such as adhesive strength as an index. As a result of studying a kinetic cure model that can be expressed as a function of temperature and time. In this study, the inventor is based on the KJMA model similar to the Weibull cumulative distribution function, and determines the curing rate of the thermosetting resin by a new model that takes into account the temperature dependence of the shape factor and the scale factor. We found that it can be predicted approximately.

  This will be described in more detail below. First, the reaction mechanism of the thermosetting resin will be described. The thermosetting resin such as an epoxy resin is a first stage (A Stage) in which only the molecular chain growth of molecules having an epoxy group is performed and the reaction rate is 30% or less. Through the second stage (B Stage) with a reaction rate of 50 to 60% where the crosslinking reaction by the ether side chain of the grown linear polymer begins to occur, the three-dimensional crosslinking reaction occurs actively due to the strong network binding. It is said that it will be in the 3rd stage (C Stage) which hardens | cures (refer nonpatent literature 2).

  In this case, the adhesive strength and elastic modulus hardly increase at the first stage, gradually develop after the second stage, and predetermined cured physical properties are obtained at the third stage. Therefore, as shown in FIG. 4, the chemical reaction rate measured with a differential scanning calorie meter (hereinafter referred to as “DSC”) and the mechanical strength obtained by a die shear test are used as indicators. A curing curve different from the curing rate is drawn. This curve becomes an S-shaped curve called a sigmoid curve when the horizontal axis represents the logarithm of time and the vertical axis represents the reaction rate or the curing rate, and this curve can be arbitrarily expressed by formulating (specifying the function). It becomes possible to determine the reaction rate or curing rate at the temperature and time. Furthermore, by extracting the coefficient (factor) of the function obtained by formulating the curve, the curing characteristics of the resin can be replaced with several kinds of numerical data and can be described very simply.

  In the following, formulating the above curve will be described based on the similarity between chemical reaction kinetics and reliability engineering such as probability density function, and isothermal crystallization theory considering geometric nucleus growth.

[1.0] Approach from chemical reaction kinetics [1.1] First order reaction model and exponential distribution Before discussing the reaction model of complex thermosetting resin, first of all, basic of reaction rate in simple chemical reaction Explain the basic idea. For example, as shown in FIG. 5, from a state of 10 unreacted (circle) and 3 reacted (square) at a certain moment, 2 newly reacted (hexagonal) within a unit time, and 8 Assuming that the number of new reactions (hexagons) follows the rule that “the number of new reactions (hexagons) is determined by the number of unreacted (circles)” To do.

  Next, assuming that this rule is “a certain percentage of the number of unreacted reacts (multiply by proportional constant K)”, this reaction is two (= 10 × K), so K = 0. 2 Since K is always constant, similarly, in the next unit time, (10−2) × K (= 0.2) = 1.6, and in the next unit time, (10−2−1.6) × 0.2 = 1.28 ... The number of units that react per unit time decreases. However, the amount of reaction has increased to 3 + 2 + 1.6 + 1.28 ... although the momentum has declined.

The above can be expressed more generally as follows.
“When substance B is produced from substance A by some reaction, if the initial concentration of substance A is a and the cumulative reaction amount (the amount of B produced) after t time is x, the reaction amount dx per unit time / Dt is proportional to the unreacted amount C _A at this dt, and this proportional constant (reaction rate constant) is K ”.
Since this model is expressed by a linear function of an unreacted amount, it is called a primary reaction model. The reaction rate constant K has a dimension of [time- ¹ ].

dx / dt = K · C _A (10)

Furthermore, since the unreacted amount C _A is obtained by subtracting the accumulated reaction amount x from the initial concentration a to the time t, it becomes “dx / dt = K · C _A = K (ax)”. Therefore, in order to express the cumulative reaction amount x as a function of time t, it is only necessary to separate the variables and solve the differential equation.

dx / dt = K (ax) (11)
dx / (ax) = Kdt
∫dx / (ax) = ∫Kdt
−ln (ax) = K · t + const.

  Here, since t = 0 and x = 0, const. = − Lna. Further, since the reaction rate P (t) expressed as a function of time t is a ratio (= x / a) between the cumulative reaction amount x and the initial concentration a, the reaction rate P (t) after t time is a reaction rate constant. (Curing rate constant) It is expressed as follows using K.

−ln (a−x) = K · t−lna
−ln {(ax) / a} = K · t
−ln {1-P (t)} = K · t (12)
P (t) = 1−exp (−K · t) (13)

That is, assuming that the reaction amount per unit time is proportional to the unreacted amount (expressed as a linear function), the equation (13) is obtained.
This reaction rate curve is represented by the following equation which takes the logarithm of both sides of Equation (13), Equation (12), and Equation (12), taking as an example the case where P (t) = 0.99 is reached at t = 1000. From (14), it becomes as shown in FIG.

ln {-ln (1-P (t))} = lnt + lnK (14)

  On the other hand, in terms of reliability engineering, the reaction from A to B is “A fails and becomes B”. In other words, the amount of reaction per unit time is the number of failures per unit time, and the reaction rate is the cumulative failure distribution. It is equivalent to a function. The correlation between reaction kinetics and reliability engineering can be explained as follows.

  Assuming that the number of failures per unit time dx / dt is the product of the number of non-failures (= ax) and the proportional constant λ as the cumulative number of failures x up to time t as the parameter a, the following is shown. it can.

dx / dt = λ (ax) (15)
dx / (ax) = λdt
∫dx / (ax) = ∫λdt
−ln (ax) = λ · t + const.

Here, since t = 0 and x = 0, const. = − Lna, and the cumulative failure distribution function (
Since cumulative distribution function F (t) is the ratio (= x / a) of cumulative failure number x and parameter a, the following exponential distribution function (exponential distribution function) is obtained.

−ln (ax) = λ · t−lna
−ln {(ax) / a} = λ · t
−ln {1-F (t)} = λ · t (16)
F (t) = 1−exp (−λ · t) (17)

  The equation (17) is differentiated and expressed as a failure probability density function (Probability density function) f (t) as follows.

dF (t) / dt = f (t) = λexp (−λ · t) (18)

  The failure rate function (hazard rate function) λ (t) is the ratio of the number of failures per unit time out of the remaining number n (t) after t hours.

λ (t) = {− dn (t) / dt} / n (t) (19)

  In other words, the failure rate λ (t) is the ratio n (t) / a (= reliability R) of the remaining amount with respect to the parameter a after t hours. (T)) shows the probability of failure in the next unit time-(dn (t) / a) / dt (= failure probability density function f (t)), and is given by the following equation: .

λ (t) = f (t) / R (t) = {dF (t) / dt} / R (t) = {− dR (t) / dt} / R (t) (20)

  When this is integrated and R (t) = 1 when t = 0, the result is as follows.

λ (t) dt = −dR (t) / R (t) (21)

  Further, when the cumulative hazard H (t) that is an integral amount of the failure rate function λ (t) is used, it is expressed as follows.

  Therefore, the basic form of the cumulative failure distribution function “F (t) is exponential, and the form of the function varies depending on the form of λ (t).

  That is, the assumption of equation (18) in the exponential distribution indicates that λ (t) = λ, and the exponent part of equation (24) is integrated from t = 0 to t as shown in the following equation. Thus, the equation (20) is obtained.

  The expressions (11) and (19) have the same essential meaning. In Expression (11), both sides are divided by a and compared with Expression (20). Is the reaction rate constant K, and the failure rate function λ (t).

Left side: (dx / a) / dt Change in reaction rate per unit time → probability density function f (t) and equivalent right side: (a−x) / a Ratio of unreacted amount (residual amount) → Reliability function R ( equivalent to t)

  Therefore, the fact that a certain function is related by a ratio with its differential function is the reason why it becomes exponential. In other words, when the “quantity that changes per unit time” is expressed as a ratio to the “quantity that remains unchanged”, the cumulative change of this ratio becomes an exponential increase function, and in particular the above ratio A so-called “random phenomenon in which no dependency is recognized for each component” expressed by “a constant constant regardless of time” indicates an exponential distribution.

  As described above, the most basic primary reaction in a chemical reaction is a model based on essentially the same assumption as the exponential distribution, and the primary reaction rate curve is expressed by a cumulative distribution function of the exponential distribution.

The primary reactions described with reference to FIG. 5 described model and Weibull distributions described above n-th power of [1.2] n order reaction is a reaction between the substance A alone, in this case, considering only unreacted amount C _A, reaction The product of the velocity constant K is the instantaneous reaction amount. As shown in Fig. 7, this means that "Many people are blindfolded in the ground and move freely, appearing and disappearing at every moment. If you are playing a game that says “You have to leave the ground when shoes enter the“ water pool ”,” the amount of reaction per unit time that shoes enter the “water pool” and exit the ground at a certain moment. It can be considered that it corresponds to.

  The number of people left in the ground gradually decreases, but at a certain moment, the more people who remain in the ground, the more people enter the “water pool”, and the fewer people remain in the ground. The number of people entering the “water pool” will also decrease. In addition, if the number (probability) of the “water pool” itself is large, many people enter the “water pool”. The person who is in the ground is the amount or concentration of the molecule present in the reaction system, and the probability of “water pool” indicates the reaction rate constant. Speaking of these in terms of reliability engineering, the concentration is the residual rate (= reliability), and the reaction rate constant is the failure rate.

Next, when substance A and B react to produce substance C, if the same idea is applied, “the person in the ground consists of men and women, and the man and the woman are in the“ water pool ”at the same time. Think of it as a game rule that when you enter, you both get out of the ground. The probability of two people to enter the water reservoir is the product of each of the probability, when the two substances are reacted are the product of the concentration C _B of the concentration C _A and unreacted B unreacted A. Strictly speaking, in this illustration, the reaction rate constant K is squared, but if treated as one constant, it is expressed as the product of the respective unreacted component concentrations and the reaction rate constant.

  Expressing the above in terms of mathematical expressions, the initial concentration of unreacted A is a, and the initial concentration of unreacted B is b.

dx / dt = K · C _A · C _B = K (ax) (bx)
dx / {(ax) (bx)} = Kdt
∫dx / {(ax) (bx)} = ∫Kdt (25)

This is generalized and substances A, B, C, D.I. When the reaction amount (generated amount) per unit time is proportional to the product of the power of each substance in the reaction of a plurality of substances, the sum of these powers is called the reaction order. When this is expressed as an equation, “dx / dt = K (C _A ^a · C _B ^b · C _C ^c · C _D ^d ...) N-order reaction is n = a + b + c + d +.

  Reactions in nature are those in which multiple substances react in a complex manner, but it is only necessary to consider reactions that are rate-limiting (slow) in terms of reaction rate, and are well known even in the case of epoxy resins. In many cases, it can be approximated by several types of products such as the following formulas (26), (27), and (28) (Kamar's formula, α is the reaction rate).

dx / dt = K (1−x) (1 / r−x) (b + x) (26)
dx / dt = K (a ₀ −x) ² (b ₀ + x) (27)
dα / dt = (K ₁ + K ₂ α ^m ) (1−α) ⁿ (28)

  If the reaction amount per unit time is proportional to the nth power of the substance A concentration (nth power model) as the simplest approximation among these, the following equation is obtained with a as the initial concentration. As is obvious, a> 0, x> 0, t> 0, n> 0.

  This is integrated as described in [1.1] as follows.

  This reaction rate curve is obtained from the following formulas (31) and (32) as in the case of formula (14) and FIG. 6, taking the case of reaching P (t) = 0.99 at t = 1000. As shown in FIG. FIG. 8 shows the shape of the nth-order reaction rate curve (n = 0.8).

Up to this point, as shown in FIG. 7, the n-th order reaction due to the reaction of a plurality of substances has been considered, but when there are a plurality of (i) functional groups in one molecule like a thermosetting organic molecule, The reaction of one molecule is finished only when all the functional groups in one molecule react.
In this case, the probability that one functional group reacts is p, and the probability of simultaneous occurrence of i functional groups is p to the power of i. Therefore, when the probability p of one molecule is taken, it is equivalent to the concentration becoming the 1 / i power. That is, the reaction rate equation is as follows.

dx / dt = K (ax) ^{1 / i} (33)

  In addition, since the definition of the reaction order is the sum of the exponent parts of the concentration, in such a case, the reaction order n is 1 or less when expressed by the equation (29).

  On the other hand, in section [1.1], it was described that the reaction rate in the first order reaction corresponds to the cumulative distribution function in the exponential distribution, but by introducing a shape parameter m (m> 0) into the exponential distribution. It is expected that the expanded weibull distribution corresponds to the reaction rate in the nth order reaction.

Pw (t) = 1−exp {− (Kt) ^m } (34)

  Assuming that a reaction rate curve is estimated for a reaction whose reaction end point is known, such as reaching P (t) = 0.99 at t = 1000, the Weibull cumulative distribution function (hereinafter, Comparing the reaction rate curves of the n-th power model of Equation (30) with the “Weibull model”), the reaction order n and the reciprocal number of the form factor m have the same magnitude relationship with each other. In a range of 5 to 1.2 and a reaction rate P of 40% or more, there is a relationship of n≈1 / m.

  When calculating the reaction rate of a thermosetting resin, the reaction amount is not measured as the concentration of unreacted molecules, but the DSC (Differential Thermal Scanning Calorimeter) uses the ratio of the calorific value in the overall chemical reaction, Fourier transform. Infrared spectrophotometer (Fourier Transform Infarred Spectroscopy, hereinafter referred to as “FT-IR”) calculates the ratio of absorption wavelength intensity based on a specific functional group, so the number of molecules and functional groups involved in the reaction can be accurately determined. The reaction rate formula is not reflected. Furthermore, considering a model in which the three-dimensional network structure developed by the crosslinking reaction develops and cures after the molecules are in close proximity, the functional groups are paired with each other rather than moving around freely and meeting the partner to be reacted. Considering the state, it is better to consider the reaction rate as an abundance (concentration) as a pair. Therefore, it is considered that the chemical reaction rate of the thermosetting resin by the crosslinking reaction often shows a reaction order close to the first-order reaction rate equation that is an exponential distribution, regardless of the type of the functional group.

  In other words, considering these, Equation (34) and Equation (30) are completely different from each other, but in the range where the actual curing reaction expected to have a reaction order n of around 1 is experimentally examined, the Weibull model Based on the above, the analysis of experimental data can be applied, and the approximate reaction order can be predicted from the reciprocal of the form factor.

  Further, when the analysis result using the Kamal model represented by the equation (28) is compared between both the primary reaction model (m = 1.0) and the Weibull model (m = 1.2), it is particularly noted. It can be seen that the Weibull model has a well-matched curve in the region of high cure rate to be achieved.

Note that the Weibull model in reliability engineering is expressed as in Expression (35a) and Expression (35b) using a scale parameter η. Therefore, K in Equation (34) corresponds to the reciprocal of η. Incidentally, if t = η in the equation (35a), Pw (η) = 1−exp (− (1) ^m ) = 0.632, and the cumulative failure rate reaches 63.2% regardless of the value of the shape factor m. Time corresponds to η. For this reason, η is sometimes referred to as a characteristic life.

  Further, since the accumulated hazard H (t) is expressed by the following expression (36) from the expression (24), the failure rate λ (t) that is the differential is expressed by the expression (37).

  In the case of an exponential distribution (m = 1) which is a first order reaction, λ (t) is a constant λ regardless of time, meaning a random reaction on the time axis, but a reaction according to the Weibull model In the case where m> 1 (reaction order n is smaller than 1), the reaction increases with time, and the reaction rate increases with time. The curve rises rapidly. That is, when the reaction order at which a molecule having a large number of functional groups reacts in one molecule is 1 or less, it is expected that the shape factor m represented by the Weibull model takes a value of 1 or more.

[1.3] Temperature dependence of reaction rate constant The reaction rate constant K (that is, the reciprocal of the scale factor η) in the model represented by the n-th order reaction including the first order reaction and the Weibull cumulative failure rate function is the Arrhenius type. Assuming that it has the temperature dependence, it can be expressed as Here, Q is the activation energy, T is the absolute temperature, k is the Boltzmann constant, and α ₀ is the frequency factor.

Further, when taking the logarithm of both sides of the equation (38) and arranging it, it can be seen that 1 / T and 1 nK have a linear relationship as shown in the following equation (39). Therefore, the activation energy Q and the frequency factor α ₀ can be obtained from the fact that the slope of the straight line is −Q / k and the intercept is lnα ₀ .

In this regard, in the fatigue life test of the solder material, an analysis based on a life prediction formula called “Coffin-Manson correction formula” shown in the following formula (40) is performed. It defines the number of cycles N _f repeated stress reaches the cumulative percent defective in the fatigue life, which is assumed to have a temperature dependence of the Arrhenius type dependence of the environmental conditions, such as the activation energy and the strain amount and temperature Thus, N _f in the actual use state is predicted.

  When the cumulative defect rate P follows the Weibull model with the number of stress repetitions Nc as a variable, the time t in the equation (35a) is replaced with Nc to become the equation (41), and when arranged by Nc, the equation (42) is obtained.

Therefore, when the standard of the cumulative defect rate P is set, Nc corresponding to this is obtained. For example, if P = 0.632 as described above, Nc = η. Therefore, if the defect rate P _f defined as the lifetime and Nc at that time are N _f , the following expression (43) is obtained from the expression (38), which is the same expression as the expression (40).

  That is, it can be seen that the “Coffin-Manson correction formula” in the formulas (38) and (40) has a completely equivalent meaning in the portion showing the temperature dependence. Therefore, if it is assumed that the other constant part has no temperature dependency and the life test result such as the temperature cycle test follows the Weibull model, the life prediction can be performed using only the equation (43). Further, when temperature dependence is recognized in the phenomenon expressed by the Weibull model even in cases other than the fatigue life, the activation energy is obtained by applying the reciprocal (= K) of the scale factor η to the equation (38). In addition, phenomena in unknown temperature zones can be predicted.

[2.0] Approach from geometric isothermal crystallization theory In section [1.0], chemical reactions were considered centering on individual molecules. However, in the case of actual thermosetting resins, solid reaction from the liquid phase is considered. It resembles the phenomenon of crystallization or phase transition that changes to a phase. Therefore, the KJMA model, which is known as an isothermal crystallization theory considering geometric nucleus growth and often used in thermal analysis such as DSC, is as follows.

  In this model, first, after the initial nucleation as shown in FIG. 9 (a), the nuclei (domains) generated as shown in FIG. 9 (b) grow straight without contact and overlap. Assuming that, the rate of minute change per unit time of the solid phase volume (crystallinity or degree of phase change) is equal to the rate of minute change to the solid phase per unit time in the liquid phase volume It is.

As is well known, the ratio f of the solid phase volume V to the _total volume V _total , the rate of change df of the rate f, and the rate of change df _ex that changes to the solid phase in the liquid phase are as follows. It is expressed as

This is rewritten in terms of reliability engineering terms as compared with the equation (20) described in the section [1.0]. F is a cumulative distribution function F (t), (1-f) is a reliability R (t), df is a probability density function f (t) which is a derivative of the cumulative distribution function, df _ex corresponds to the failure rate λ (t), and f _ex corresponds to the cumulative hazard H (t).

  Thus, the equation (44) can be replaced as the following equation (45), and is as follows similarly to the equations (21) to (23).

  Therefore, when equation (44) is solved, equation (46) shown below is obtained.

f = 1−exp (−f _ex ) (46)

  Next, when the solid phase in which the nucleus is generated is isotropically grown as a sphere having a radius r three-dimensionally, the volume v of the grown spherical fine particles is proportional to the cube of the radius r, and the radius r becomes the time t. Assuming that the growth is proportional, the proportional constant D can be expressed as follows.

Further, f _ex is the ratio of the cumulative solid phase increase amount V in the liquid phase, and this is the sum total of the number N of individual nuclei growing particles.

  Therefore, substituting equation (48) into equation (46) yields the following equation (49).

  Moreover, if the constants of the exponent part of Formula (49) are collectively expressed as Z, the following Formula (50) is finally obtained.

  That is, by assuming that the volume grows in proportion to the cube of time in Equation (47), the exponent part in Equation (50) is also proportional to the cube of time. Similarly, if the nucleus growth is one-dimensional dendritic growth, the volume is proportional to the first power of time, and if it is two-dimensional flaky growth, the volume is proportional to the second power of time. Furthermore, when changing from the liquid phase to the solid phase, it is expected that the nucleus growth radius is proportional to the first power of time if the interface reaction is rate-controlled, and is proportional to 1/2 power if the mass transfer rate is determined by diffusion.

In the actual phenomenon, there is a possibility that these are complicatedly combined. Therefore, the general formula of the KJMA model is expressed as the following formula (51).
f = 1−exp (−Zt ^m ) (51)

  The index m (m> 0) in the formula (51) is particularly called the Avrami constant, and is related to the geometric growth as described above and takes the values shown in Table 6 below. Has been. According to this, information such as one-dimensional and diffusion-controlled solid phase growth is obtained as the Abram constant m is smaller, and conversely, as the Abram constant m is larger, information is obtained such as three-dimensional and interface reaction-limited solid-phase growth. .

The constant Z expressed in this way has a dimension of [time- ^{1 / m 2} ]. Originally, the KJMA model is often used in isothermal crystallization, and does not take into account that the index (Abramy constant) m changes. Assuming that the index m is always constant, there is no particular problem in data analysis. However, it varies depending on the temperature, and it is not preferable that the constant dimension changes when describing the curing rate including this.

Therefore, the expression (51) may be rewritten and expressed as the following expression (52) using a constant K such that K = Z ^{1 / m} . Note that this equation (52) matches the Weibull model expressed by equations (34) and (35a), (35b).
f = 1−exp {− (Kt) ^m } (52)

  In other words, by analogy with the KJMA model, the failure according to the Weibull model in reliability engineering is that the cumulative hazard is the m-th power of time as shown in Equation (36), which is an elementary reaction expressed as a function of time. It is expected that the phenomenon spreads by the power of this elementary reaction and corresponds to the mechanism leading to the final failure. Considering the correlation with the reaction order, the reaction satisfying m> 1 means that it corresponds to a low-order reaction of n <1 in which the number of functional groups is large and the reaction proceeds exponentially. Matches the typical image.

Similarly to the temperature dependence of the reaction rate constant shown in Expression (38), if the constant K is assumed to have Arrhenius type temperature dependence in the KJMA model, it can be expressed as Expression (53) below. Can do. Here, Q _k is a constant corresponding to the activation energy, T is an absolute temperature, k is a Boltzmann constant, and α ₀ is a frequency factor.

Since there is a relationship of K = Z ^{1 / m} between Z represented by equation (51) and K represented by equation (52), the logarithm of both sides is taken and organized in the same manner as equation (39). Then, since it has the relationship shown in the following formula (54), the value obtained by dividing the activation energy Q _z represented by the formula (51) by the Abram constant (form factor) m corresponds to the activation energy Q _K. There is a relationship.

[3.0] Construction of thermosetting resin curing model (introduction of a new model according to the present invention)
In the schematic diagram of the curing reaction of the thermosetting resin shown in FIG. 4, the chemical reaction is the primary reaction shown in the formula (11) described in the section [1.1] or the formula (26) in the section [1.2]. The reaction rate formula obtained from the concentration of the reactive species shown in (28) is considered to be the most correct, but these formulas can be applied only when the reaction system can be predicted and applied to unknown resin materials. There is no guarantee that it can be applied widely. Furthermore, the curing rate based on mechanical strength cannot be expressed.

  Therefore, it is considered that the development of mechanical strength occurs as a result of polymerization due to a crosslinking reaction or a phase change from a liquid phase to a solid phase, and the correlation between the n-power model and the Weibull model shown in [1.2] and the result The KJMA model shown in the section [2.0] obtained as a function exactly the same as the Weibull model is used for the thermosetting resin as shown in the above formulas (1), (2), and (3). It was decided to represent the cure rate.

It is explanatory drawing which shows the example of the hardening rate curve calculated | required using Formula (1), Formula (2), and Formula (3) in embodiment of this invention. It is explanatory drawing for demonstrating the storage method of the thermosetting resin which concerns on embodiment of this invention. It is a block diagram which shows the structural example of the computer which implements prediction of the hardening rate by storage in the storage method of the thermosetting resin which concerns on embodiment of this invention. It is explanatory drawing which shows a comparison with the ascending curve which shows the chemical reaction rate measured with the differential thermal scanning calorimeter etc., and the ascending curve which shows the hardening rate which uses as a parameter | index the mechanical strength obtained by a die shear test etc. . It is explanatory drawing explaining the basic view of the reaction rate in a simple chemical reaction. It is explanatory drawing explaining the reaction rate curve when it is assumed that the reaction amount per unit time is proportional to the unreacted amount (expressed as a linear function). Explanatory diagram for explaining the reaction when the primary reaction is a reaction of the substance A alone, considering only the unreacted amount C _A and assuming that the product with the reaction rate constant K is an instantaneous reaction amount. It is. It is explanatory drawing which shows an example of a reaction rate curve when the reaction amount per unit time is proportional to the nth power of the substance A concentration (nth power model). It is explanatory drawing for demonstrating the reaction in a KJMA model.

Explanation of symbols

  DESCRIPTION OF SYMBOLS 301 ... Arithmetic processing part 302 ... Main memory | storage part 303 ... External memory | storage part 304 ... Input part 305 ... Display part 306 ... Printer.

Claims (4)

In the thermosetting resin storage method of setting storage conditions including storage temperature and storage period by predicting the curing rate when the desired thermosetting resin is stored for a predetermined period at a predetermined storage temperature,
The curing rate P after the storage period t is
A first expression consisting of P = 1−exp {− (K · t) ^{1 / N} };
K = α ₀ exp {−Q _K / (kT)} that defines K in the first equation using the first constant Q _K , the second constant α ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k. A second equation comprising:
N = β ₀ exp {−Q _N / (kT)} that defines N in the first equation using the third constant Q _N , the fourth constant β ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k A method for storing a thermosetting resin, characterized in that the prediction is based on the third formula. In the thermosetting resin storage method of setting storage conditions including storage temperature and storage period by predicting the curing rate when the desired thermosetting resin is stored for a predetermined period at a predetermined storage temperature,
The first curing rate P after the first storage period t from the start of storage at the first temperature,
A first expression consisting of P = 1−exp {− (K · t) ^{1 / N} };
K = α ₀ exp {−Q _K / (kT)} that defines K in the first equation using the first constant Q _K , the second constant α ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k. A second equation comprising:
N = β ₀ exp {−Q _N / (kT)} that defines N in the first equation using the third constant Q _N , the fourth constant β ₀ , the absolute temperature T of the storage temperature, and the Boltzmann constant k A first step of predicting with a third equation comprising:
The storage period t ′ at which the first curing rate P is reached by the storage temperature set to the second temperature is obtained from the first formula, the second formula, and the third formula, and stored at the second temperature. The change ΔP in the curing rate between the storage period t ′ and the predetermined unit period Δt by the second expression, the third expression, and ΔP = 1 / N · K ^{1 / N} · t ^{1 A} second step obtained from the fourth expression consisting of ^{/ N−1} · exp [− (Kt) ^{1 / N} ] · Δt;
And a third step of obtaining a second curing rate P + ΔP obtained by adding a change ΔP in the curing rate to the first curing rate P, and
Storage of the thermosetting resin characterized by predicting the curing rate after storing for the first storage period at the first temperature and then storing for the second storage temperature as the second temperature based on the second curing rate. Method. In the storage method of the thermosetting resin of Claim 2,
A fourth step of obtaining a change ΔP ′ in the curing rate during Δt from the time point of the period t ′ + Δt under the condition of the second temperature from the fourth equation;
And a fifth step of obtaining a third curing rate P + ΔP + ΔP ′ obtained by adding the change ΔP ′ of the curing rate to the second curing rate P + ΔP,
According to the third curing rate, the curing rate after storing the first period at the first temperature, storing the unit period Δt as the second temperature, and additionally storing the unit period Δt as the second temperature. A method of storing a thermosetting resin characterized by predicting. In the storage method of the thermosetting resin of Claim 2,
The period t ″ when the second curing rate P + ΔP is reached by heating at the third temperature is obtained from the first expression, the second expression, and the third expression, and the period by heating at the third temperature is obtained. a fourth step of obtaining a change ΔP ′ in the curing rate between t ″ and a predetermined unit period Δt from the second equation, the third equation, and the fourth equation;
And a fifth step of obtaining a third curing rate P + ΔP + ΔP ″ obtained by adding the variation ΔP ′ of the curing rate to the second curing rate P + ΔP,
Based on the third curing rate, the curing rate after storing the first period at the first temperature, storing the unit period Δt as the second temperature, and additionally storing the unit period Δt as the third temperature is predicted. A method of storing a thermosetting resin, characterized by:

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