A self-catalytic reaction intensity grading method based on isothermal induction period characteristics

Abstract

The application provides a self-catalytic reaction intensity grading method based on isothermal induction period characteristics. The method is based on the shape difference of the reaction curve, and first divides the self-catalytic reaction into four intensity grades according to the isothermal induction period characteristics. In the experiment, the sensitivity of the induction period characteristics of the curve to the temperature change is analyzed by carrying out isothermal tests at two or more different temperatures, so that the intensity grade of the self-catalytic reaction can be determined. In the theoretical aspect, the self-catalytic intensity grades of three classical models in different orders are determined through theoretical derivation, and for the self-catalytic reaction of a known reaction function, the corresponding self-catalytic reaction intensity grade can be quickly determined. The method can directly determine the self-catalytic intensity through the experimental curve characteristics, and can also grade from the model parameter angle, which is simple to operate, directly related to the induction period factor in risk analysis, and provides an important basis for quickly evaluating the reaction risk.

Description

Technical Field

[0001] This invention belongs to the field of thermal analysis kinetics, and in particular, it is a method for classifying the intensity of autocatalytic reactions based on the characteristics of the isothermal induction period. Background Technology

[0002] Thermal analysis is one of the reliable methods for detecting and characterizing isothermal reactions. Reaction rate curves can be obtained through thermal analysis, where autocatalytic reactions exhibit characteristic peaks, accelerated reactions show a monotonically increasing trend, and decelerated reactions show a monotonically decreasing trend.

[0003] In the study of autocatalytic reaction intensity, the Swiss Institute for Safety Research proposed a qualitative analysis method based on the induction period. This method classifies autocatalytic reactions with an induction period as strong autocatalytic reactions, whose initial exothermic rates are difficult to detect with DSC; while weak autocatalytic reactions have detectable initial exothermic rates. From an emergency response perspective, systems with longer induction periods have lower initial reaction rates, and once acceleration begins, the reaction rate rapidly reaches its maximum value and releases a large amount of heat, making them more prone to runaway reactions; therefore, they are classified as strong autocatalytic reactions.

[0004] In quantitative research, Reference 1 (A study of classifying autocatalytic strength with adiabatic conditions) first introduced the autocatalytic factor Z from the Benito-Perez model for strength classification. This method, based on standardized curves, divides autocatalytic strength into five levels and has been successfully applied to the classification assessment of specific substances. Reference 2 (Quantitative classification of autocatalytic strength for material decomposition based on the ratio of heat release) proposes a quantitative classification method based on DSC dynamic experiments from a kinetic and thermodynamic perspective, using the "3σ principle" to divide autocatalytic strength into five intervals. Reference 3 (Reaction model screening and autocatalytic decomposition thermal behavior study based on isothermal methods) establishes a model based on (dα / dt) by comparing the exothermic behavior characteristics of three autocatalytic models under isothermal conditions. max -TMRO's matrix hierarchical method.

[0005] However, existing methods all have certain limitations: the method from the Swiss Institute for Safety Research only relies on the induction period, ignoring other kinetic parameters; the methods in References 1 and 2 are only applicable to specific reaction conditions and a single model; while the method in Reference 3 covers multiple reaction models, it requires extensive testing and calculation. Considering that autocatalytic behavior involves multiple decomposition models, there is an urgent need to develop a simpler and more widely applicable hierarchical method to accurately determine the strength of various autocatalytic exothermic decomposition reactions. Summary of the Invention

[0006] To address the problem of the criteria for classifying autocatalytic intensity, the present invention aims to provide a simple and rapid method for classifying autocatalytic reaction intensity based on the characteristics of the isothermal induction period.

[0007] The technical solution to achieve this invention is:

[0008] A method for classifying the intensity of autocatalytic reactions based on isothermal induction period characteristics includes the following steps:

[0009] (1) Based on the characteristics of the reaction rate versus time curve in the reaction curve under a single isothermal temperature, the autocatalytic intensity is divided according to the induction period characteristics of the mechanism function model. The autocatalytic intensity is divided into four levels from weak to strong: I, II, III, IV, and an autocatalytic intensity classification table is determined.

[0010]

[0011] (2) For reactions with unknown mechanism functions, perform isothermal DSC tests to obtain reaction curves at two or more isothermal temperatures. Compare the curve characteristics of the four autocatalytic intensity levels in the autocatalytic intensity grading table to directly obtain the grading corresponding to the autocatalytic intensity.

[0012] (3) For reactants with known mechanism functions, consult the autocatalytic strength classification table and classify the autocatalytic strength according to the corresponding mechanism function model and model parameters.

[0013] Furthermore, the autocatalytic intensity grading table includes induction period characteristics, curve characteristics, and the model parameter range of the mechanism function model.

[0014] Furthermore, based on the characteristics of the reaction rate versus time curves in the autocatalytic reaction curves under a single isothermal temperature, the induction period characteristics (TMR) of the autocatalytic reaction curves are analyzed. iso =t sd +TMR o The induction period characteristics are divided into two parts, t sd TMR refers to the subtle induction period, the time from the start of the reaction until a significant exothermic signal is detected. oIt refers to the induction period characteristics from the point where a significant exothermic signal is detected to the point where the maximum reaction rate is reached.

[0015] Furthermore, based on the induction period characteristics of the mechanistic function model, the autocatalytic intensity is divided into four levels from weak to strong. The specific steps are as follows:

[0016] The induction period characteristics correspond to the curve characteristics. The induction period characteristics are determined based on the curve characteristics, and the model parameter range of the mechanism function model under the induction period characteristics is obtained through mathematical derivation.

[0017] Furthermore, the mathematical derivation employs the following equations and mechanistic function model:

[0018] Differential dynamic equations:

[0019]

[0020] Where A refers to the pre-exponential factor, in units of s. -1 E refers to activation energy, in kJ / mol; f(α) refers to the kinetic mechanism function of the reaction; T refers to temperature, in °C; R is the ideal gas constant, R = 8.314 J / (mol·K);

[0021] extended-Prout-Tompkins model:

[0022] f(α)=α m (1-α) n (2)

[0023] Avrami-Erofeev model:

[0024]

[0025] Jander model:

[0026] 4(1-α) 1 / 2 [1-(1-α) 1 / 2 ] 1 / 2 (4)

[0027] 6(1-α) 2 / 3 [1-(1-α) 1 / 3 ] 1 / 2 (5)

[0028] Where α is the reaction conversion rate, n is the reaction order, and m is a parameter related to the "growth" dimension of the reaction.

[0029] Furthermore, in step (2), a dynamic non-isothermal DSC test is first performed. The first isothermal temperature T1 is selected, the second isothermal temperature T2 = T1 - 5℃ is selected, the third isothermal temperature T3 = T2 - 5℃ is selected, and so on, to determine the isothermal DSC test temperature. The isothermal curves of a substance at two or more temperatures are measured. By comparing the curve characteristics of the four self-catalytic intensity levels in the self-catalytic intensity grading table, the grading corresponding to the self-catalytic intensity is directly obtained.

[0030] Furthermore, T1 is the initial decomposition temperature -(5~10)℃.

[0031] Compared with existing technologies, the positive effects of this invention are:

[0032] (1) Not limited to known models, the method is applicable not only to the most commonly used extended-Prout-Tompkins model, Avrami-Erofeev model and Jander model, but also to the response of unknown mechanism function models.

[0033] (2) From an experimental perspective, autocatalytic intensity can be graded directly based on the characteristics of the isothermal induction period, which is a fast and simple method.

[0034] (3) From a theoretical perspective, for reactions with known kinetic models, the corresponding isothermal reaction curve characteristics can be directly derived mathematically to obtain the parameter ranges of four autocatalytic intensities. The method is highly reliable and also simple and easy to understand. Attached Figure Description

[0035] Figure 1 This is a flowchart of the autocatalytic reaction intensity classification method based on the isothermal induction period characteristics in this invention.

[0036] Figure 2 This is a classification diagram of the autocatalytic intensity corresponding to the reaction curves based on the extended-Prout-Tompkins model at the same isothermal temperature, where a: autocatalysis I, b: autocatalysis II, c: autocatalysis III, and d: autocatalysis IV.

[0037] Figure 3 This shows the effect of different isothermal temperatures on the induction period characteristics of four types of autocatalytic reaction curves, where a: isothermal temperature T1 = 78.09℃, b: isothermal temperature T2 = 73.09℃, c: isothermal temperature T3 = 68.09℃, and d: T3 = 63.09℃.

[0038] Figure 4 These are the reaction rate curves of substance 1 obtained by simulation at four isothermal temperatures.

[0039] Figure 5 These are the reaction rate curves of substance 2 obtained by simulation at four isothermal temperatures. Detailed Implementation

[0040] The implementation of the present invention will now be described in detail with reference to the accompanying drawings, so that the advantages and features of the present invention can be more easily understood by those skilled in the art, thereby making a clearer and more explicit definition of the scope of protection of the present invention.

[0041] like Figure 1 As shown, the autocatalytic reaction intensity classification method based on isothermal induction period characteristics described in this invention includes the following steps:

[0042] (1) Based on the characteristics of the reaction rate versus time curve in the reaction curve at a single isothermal temperature, the autocatalytic intensity is classified according to the induction period characteristics of the mechanistic function model. The autocatalytic intensity is divided into four levels from weak to strong: I, II, III, and IV, as follows. Figure 2 As shown, a self-catalytic intensity grading table was determined;

[0043]

[0044] The autocatalytic intensity grading table includes induction period characteristics, curve characteristics, and model parameter ranges for the mechanistic function model. The induction period characteristics in the table are derived from the reaction rate versus time curves of the autocatalytic reaction curve under a single isothermal temperature, analyzing the induction period characteristics (TMR) of the autocatalytic reaction curve. iso =t sd +TMR o The induction period characteristics are divided into two parts, t sd TMR refers to the subtle induction period, the time from the start of the reaction until a significant exothermic signal is detected. o It refers to the induction period characteristics from the point where a significant exothermic signal is detected to the point where the maximum reaction rate is reached.

[0045] The autocatalytic intensity is classified based on the induction period characteristics using a mechanistic function model, and is divided into four levels from weak to strong. The specific steps are as follows:

[0046] The induction period characteristics correspond to the curve characteristics. The induction period characteristics are determined based on the curve characteristics, and the model parameter range of the mechanism function model under the induction period characteristics is obtained through mathematical derivation.

[0047] The mathematical derivation uses the following equations and mechanistic function model:

[0048] Differential dynamic equations:

[0049]

[0050] Where A refers to the pre-exponential factor, in units of s. -1E refers to activation energy, in kJ / mol; f(α) refers to the kinetic mechanism function of the reaction; T refers to temperature, in °C; R is the ideal gas constant, R = 8.314 J / (mol·K);

[0051] extended-Prout-Tompkins model:

[0052] f(α)=α m (1-α) n (2)

[0053] Avrami-Erofeev model:

[0054]

[0055] Jander model:

[0056] 4(1-α) 1 / 2 [1-(1-α) 1 / 2 ] 1 / 2 (4)

[0057] 6(1-α) 2 / 3 [1-(1-α) 1 / 3 ] 1 / 2 (5)

[0058] Where α is the reaction conversion rate, n is the reaction order, and m is a parameter related to the "growth" dimension of the reaction.

[0059] The mathematical derivation involves the following principle: the isothermal "dα / dt-t" curve of an autocatalytic reaction first increases and then decreases, and its second derivative function d... 2 α / dt 2 =0 has a solution, which is the point of maximum conversion rate, and the third derivative d 3 α / dt 3 The difference in solutions when the value equals 0, i.e., the difference in inflection points, can distinguish the curve characteristics of different autocatalytic levels in detail. Autocatalytic level I: 0 inflection points before the maximum conversion rate and 1 inflection point after the maximum conversion rate; Autocatalytic level II: 0 inflection points before the maximum conversion rate and 0 inflection points after the maximum conversion rate; Autocatalytic level III: 1 inflection point before the maximum conversion rate and 1 inflection point after the maximum conversion rate; Autocatalytic level IV: 1 inflection point before the maximum conversion rate and 0 inflection points after the maximum conversion rate. By calculating sequentially, the range of model parameters for each of the four autocatalytic intensity levels in the autocatalytic intensity classification table can be obtained.

[0060] (2) For reactions with unknown mechanism functions, perform isothermal DSC tests to obtain reaction curves at two or more isothermal temperatures. Compare the curve characteristics of the four autocatalytic intensity levels in the autocatalytic intensity grading table to directly obtain the grading corresponding to the autocatalytic intensity. First, perform dynamic non-isothermal DSC tests. Select the first isothermal temperature T1, where T1 is the initial decomposition temperature - (5~10)℃. Select the second isothermal temperature T2 = T1 - 5℃. Select the third isothermal temperature T3 = T2 - 5℃. And so on to determine the isothermal DSC test temperature. Measure the isothermal curves of a substance at two or more temperatures. Compare the curve characteristics of the four autocatalytic intensity levels in the autocatalytic intensity grading table to directly obtain the grading corresponding to the autocatalytic intensity.

[0061] (3) For reactants with known mechanism functions, consult the autocatalytic strength classification table and classify the autocatalytic strength according to the corresponding mechanism function model and model parameters.

[0062] Example

[0063] The autocatalytic reaction intensity classification method based on isothermal induction period characteristics described in this invention includes the following steps:

[0064] (1) A method for classifying the strength of autocatalysis is proposed: Based on the characteristics of the reaction rate versus time curves in isothermal DSC test data, the strength of autocatalysis is divided into four levels from weak to strong: I, II, III, and IV, as follows. Figure 2 As shown, the mechanism function model is given to classify the autocatalytic strength according to the above induction period characteristics, and the autocatalytic strength classification table is determined.

[0065] (2) For reactions with unknown mechanism functions, isothermal DSC tests are performed. The first isothermal temperature T1 (5-10℃ before the initial decomposition temperature), the second isothermal temperature T2 = T1 - 5℃, the third isothermal temperature T3 = T2 - 5℃, and the fourth isothermal temperature T4 = T3 - 5℃ are selected. The isothermal curves of a substance at these four temperatures are measured. An example is using simulation to predict the isothermal curves at these four temperatures. The simulated kinetic parameters are: pre-exponential factor lnA = 35.55ln(s). -1 The activation energy is E = 124.01 kJ / mol. T1 = 78.09 °C. See the results below. Figure 4 Compare step (1) Figure 3 The four types of curve characteristics can be used to classify the autocatalytic strength, and the substance corresponds to level I of autocatalytic strength.

[0066] (3) For reactants with known mechanism functions, directly consult the model parameter range table corresponding to the four autocatalytic strength levels given in step (1), as shown in Table 1. The kinetic model of a certain substance is the Avrami-Erofeev model, with a model parameter n of 3. The table shows that the autocatalytic strength of this substance is level III. To further demonstrate the consistency between experimental and theoretical methods, simulation methods are used for verification. Kinetic parameters: pre-exponential factor lnA = 46.1ln(s) -1 The activation energy is E = 222.2 kJ / mol. T1 = 266.85 °C. Reaction rate curves for four temperature conditions are shown below. Figure 5 The curve classification results correspond to autocatalytic intensity level III, and the two results are completely consistent.

[0067] In summary, isothermal methods can obtain essential information about the characteristics of thermal decomposition reactions. Based on this, this paper, using the characteristics of reaction curves obtained by isothermal DSC testing, first analyzes the differences in characteristics between accelerating, decelerating, and autocatalytic curves, and then further classifies autocatalytic curves into four categories according to the proportion of the induction period. From an experimental perspective, two or more isothermal temperatures are set to analyze the influence of isothermal temperature changes on the induction period characteristics. The autocatalytic intensity is divided into four levels according to the order of temperature sensitivity from weakest to strongest, and two substances are used for simulation applications. From a theoretical perspective, mathematical analysis is used to directly derive the corresponding model parameter range, and finally, substances from the literature are applied. Whether classifying autocatalytic intensity directly from the perspective of experimental curve characteristics or from the perspective of mechanistic function parameters, the method demonstrates its scientific feasibility and ease of use.

Claims

1. A method for classifying the intensity of autocatalytic reactions based on isothermal induction period characteristics, characterized in that, Includes the following steps: (1) Based on the characteristics of the reaction rate versus time curve in the reaction curve under a single isothermal temperature, the autocatalytic intensity is divided according to the induction period characteristics of the mechanism function model. The autocatalytic intensity is divided into four levels from weak to strong: I, II, III, IV, and an autocatalytic intensity classification table is determined. (2) For reactions with unknown mechanism function models, perform isothermal DSC tests to obtain reaction curves at two or more isothermal temperatures. Compare the curve characteristics of the four autocatalytic intensity levels in the autocatalytic intensity grading table to directly obtain the grading corresponding to the autocatalytic intensity. (3) For reactants with known mechanism function models, consult the autocatalytic strength classification table and classify the autocatalytic strength according to the corresponding mechanism function model and model parameters.

2. The method as described in claim 1, characterized in that, The autocatalytic intensity grading table includes induction period characteristics, curve characteristics, and the model parameter range of the mechanism function model.

3. The method as described in claim 1, characterized in that, Based on the characteristics of the reaction rate versus time curves in autocatalytic reaction curves under a single isothermal temperature, the induction period characteristics (TMR) of the autocatalytic reaction curves are analyzed. iso =t sd +TMR o The induction period characteristics are divided into two parts, t sd TMR refers to the subtle induction period, the period from the start of the reaction until a significant exothermic signal is detected. o It refers to the induction period characteristics from the point where a significant exothermic signal is detected to the point where the maximum reaction rate is reached.

4. The method as described in claim 1, characterized in that, The autocatalytic intensity is classified based on the induction period characteristics using a mechanistic function model, and is divided into four levels from weak to strong. The specific steps are as follows: The induction period characteristics correspond to the curve characteristics. The induction period characteristics are determined based on the curve characteristics, and the model parameter range of the mechanism function model is obtained through mathematical derivation.

5. The method as described in claim 4, characterized in that, The mathematical derivation uses the following equations and mechanistic function model: Differential dynamic equation: Where A refers to the pre-exponential factor, in units of s. -1 E refers to activation energy, in kJ / mol; f(α) refers to the kinetic mechanism function of the reaction; T refers to temperature, in °C; R is the ideal gas constant, R = 8.314 J / (mol·K); extended-Prout-Tompkins model: f(α)＝α m (1-α) n (2) Avrami-Erofeev model: Jander model: 4(1-α) 1 / 2 [1-(1-α) 1 / 2 ] 1 / 2 (4) 6(1-α) 2 / 3 [1-(1-α) 1 / 3 ] 1 / 2 (5) Where α is the reaction conversion rate, n is the reaction order, and m is a parameter related to the "growth" dimension of the reaction.

6. The method as described in claim 1, characterized in that, In step (2), a dynamic non-isothermal DSC test is first performed. The first isothermal temperature T1 is selected, the second isothermal temperature T2 = T1 - 5℃ is selected, the third isothermal temperature T3 = T2 - 5℃ is selected, and so on, to determine the isothermal DSC test temperature. The isothermal curves of a substance at two or more temperatures are measured. By comparing the curve characteristics of the four self-catalytic intensity levels in the self-catalytic intensity grading table, the grading corresponding to the self-catalytic intensity is directly obtained.

7. The method as described in claim 6, characterized in that, T1 is the initial decomposition temperature - (5~10)℃.

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