A method for fitting polymer resin curing kinetics based on a segmented model

Abstract

This invention relates to a method for modeling the curing kinetics of polymer resins, specifically providing a method for fitting the curing kinetics of polymer resins based on a segmented model. The method employs a three-stage segmented kinetic model. In the first stage, an external catalytic model is introduced to quantify the inductive acceleration effect of the co-catalyst in the early stages of the reaction. In the second stage, the Kamal-Sourour model is used to ensure the fitting accuracy of the chemical control region. In the third stage, a diffusion correction term based on thermodynamic evolution is introduced to quantify the diffusion resistance caused by entering the glassy state in the later stages, significantly improving the fitting accuracy at the end of curing. More importantly, this invention creatively proposes a method based on the activation energy minimum point. α tr and dynamic glass transition point α vit The segmentation points effectively couple the external catalytic model, the Kamal-Sourour model, and the dynamic diffusion model, effectively solving the problem of inaccurate fitting of the full-cycle kinetics, improving the fitting accuracy, and providing data support for the fine-tuning of the curing process.

Description

Technical Field

[0001] This invention relates to a method for modeling the curing kinetics of polymer resins, specifically a method for fitting the curing kinetics of polymer resins based on a segmented model, applicable to the curing process of polymer materials such as epoxy resins, phenolic resins, and polyurethane resins that have chemically controlled and diffusion-controlled stages. Background Technology

[0002] Polymer resins (such as epoxy resins) are the core substrates in the industrial field. Their curing process is initiated by a curing agent to trigger a cross-linking reaction, which macroscopically manifests as an evolution from low molecular fluid to a three-dimensional network structure. In flexible modified systems containing external accelerators (such as alcohol catalysts), the curing process is highly complex, typically divided into an external catalytic induction stage (in the early stage of the reaction, the reaction is dominated by the interaction of accelerators and functional groups), a chemical autocatalytic control stage (in the middle stage, the formation of bulk chemical bonds is dominant), and a diffusion control stage (in the later stage, as the cross-linking density increases, the movement of molecular chains is hindered, resulting in a decrease in the rate).

[0003] Curing kinetics modeling is crucial for quantifying the curing process and guiding processing techniques. However, while the commonly used Kamal-Sourour model has high fitting accuracy in the chemical control stage, it neglects the induction effect in the early stage of the reaction and the glass transition phenomenon in the later stage, resulting in significant deviations in the fitting of the entire process. In addition, existing diffusion correction models are mostly based on empirically set fixed transition points and cannot be dynamically adjusted according to the physical state of different components, making it difficult to meet the requirements of accurate modeling. Therefore, this invention provides a method for fitting the curing kinetics of polymer resins based on a segmented model. Summary of the Invention

[0004] The purpose of this invention is to provide a method for fitting the curing kinetics of polymer resins based on a segmented model, in order to solve the problem of inaccurate full-cycle kinetic fitting in the existing technology.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for fitting the curing kinetics of polymer resins based on a piecewise model, characterized by comprising the following steps:

[0007] Step 1: Perform dynamic mechanical property testing (DMA) on the epoxy system to be fitted before curing to obtain the uncured glass transition temperature. ;

[0008] Step 2: Set several heating rates Differential scanning calorimetry (DSC) was used to obtain the heat flow curves of the epoxy system to be fitted during non-isothermal curing at each heating rate. The epoxy system to be fitted includes: epoxy resin, curing agent and catalyst.

[0009] Step 3: Based on all the obtained heat flow curves, use the Friedman conversion method to obtain the evolution curve of the activation energy of the curing reaction with the degree of curing, and record the minimum point of the evolution curve as the activation energy minimum point. ;

[0010] Step 4: Perform dynamic mechanical property testing (DMA) on the cured epoxy system to be fitted, and obtain the complete glass transition temperature after curing. ;

[0011] Step 5: Based on the uncured complete glass transition temperature With the complete glass transition temperature of curing The dynamic glass transition point is obtained by dynamic calculation based on the DiBenedetto equation. ;

[0012] Step 6: Set the activation energy minimum point With dynamic glass transition point The three-segment model is constructed by taking the segmentation points in sequence, including the external catalysis model, the Kamal-Sourour model and the dynamic diffusion model, thereby forming a full-cycle segmented kinetic model.

[0013] Step 7, based on the heating rate The heat flow curve at the minimum value is substituted into the full-cycle piecewise dynamic model, and all model parameters are obtained by fitting.

[0014] Furthermore, in step 5, the dynamic glass transition point Specifically:

[0015] ,

[0016] in, Absolute temperature The connection coefficient is denoted as .

[0017] Furthermore, in step 6, the first stage: The corresponding external catalytic model is expressed as:

[0018] ,

[0019] ,

[0020] in, The degree of polymerization is represented by t, which indicates the reaction time. Indicates the reaction rate; For activation energy, Indicates pre-exponential factor, This represents the reaction order in the first stage. For universal gas constants, This refers to absolute temperature.

[0021] Furthermore, in step 6, the second stage: The corresponding Kamal-Sourour model is expressed as follows:

[0022] ,

[0023] ,

[0024] in, The degree of polymerization is represented by t, which indicates the reaction time. Indicates the reaction rate. , This refers to the reaction order in the second stage. For activation energy, Indicates pre-exponential factor, For universal gas constants, This refers to absolute temperature.

[0025] Furthermore, in step 6, the third stage: The corresponding dynamic diffusion model is expressed as:

[0026] ,

[0027] ,

[0028] in, The degree of polymerization is represented by t, which indicates the reaction time. Indicates the reaction rate. , This refers to the reaction order in the second stage. For activation energy, Indicates pre-exponential factor, For universal gas constants, Absolute temperature is the diffusion factor.

[0029] Based on the above technical solution, the beneficial effects of the present invention are as follows:

[0030] The purpose of this invention is to provide a method for fitting the curing kinetics of polymer resins based on a segmented model. This method employs a three-stage segmented kinetic model. The first stage introduces an external catalytic model to quantify the inductive acceleration effect of the co-catalyst in the early stages of the reaction. The second stage utilizes the Kamal-Sourour model to ensure the fitting accuracy of the chemical control region. The third stage introduces a diffusion correction term based on thermodynamic evolution to quantify the diffusion resistance caused by entering the glassy state in the later stages, significantly improving the fitting accuracy at the end of curing. More importantly, this invention creatively proposes a method based on the activation energy minimum point α. tr and dynamic glass transition point α vit The segmentation points effectively couple the external catalytic model, the Kamal-Sourour model, and the dynamic diffusion model, effectively solving the problem of inaccurate fitting of the full-cycle kinetics, improving the fitting accuracy, and providing data support for the fine-tuning of the curing process. Attached Figure Description

[0031] Figure 1 This is a heat flow curve of the epoxy system to be fitted in Embodiment 1 of the present invention.

[0032] Figure 2 This is a heat flow curve of the epoxy system to be fitted in Embodiment 2 of the present invention.

[0033] Figure 3 This is a fitting curve of the activation energy of the curing reaction of the epoxy system to be fitted as a function of the degree of curing in Examples 1 and 2 of the present invention.

[0034] Figure 4 For the curing kinetics fitting of the epoxy system to be fitted in Example 1 of this invention ( ) Result figure.

[0035] Figure 5 For the curing kinetics fitting of the epoxy system to be fitted in Example 2 of this invention ( ) Result figure.

[0036] Figure 6 This is a comparison chart of the curing kinetics fitting results of the epoxy systems to be fitted in Examples 1 and 2 of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and beneficial effects of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0038] This invention provides a method for fitting the curing kinetics of polymer resins based on a segmented model, characterized by comprising the following steps:

[0039] Step 1: Perform dynamic mechanical property testing (DMA) on the epoxy system to be fitted before curing to obtain the uncured glass transition temperature. ;

[0040] Step 2: Set several heating rates Differential scanning calorimetry (DSC) was used to obtain the heat flow curves of the epoxy system to be fitted during non-isothermal curing at each heating rate. The epoxy system to be fitted includes: epoxy resin, curing agent and catalyst.

[0041] Step 3: Based on all the obtained heat flow curves, use the Friedman conversion method to obtain the evolution curve of the activation energy of the curing reaction with the degree of curing, and record the minimum point of the evolution curve as the activation energy minimum point. ;

[0042] Step 4: Perform dynamic mechanical property testing (DMA) on the cured epoxy system to be fitted, and obtain the complete glass transition temperature after curing. ;

[0043] Step 5: Based on the uncured complete glass transition temperature With the complete glass transition temperature of curing The dynamic glass transition point is obtained by dynamic calculation based on the DiBenedetto equation. Specifically:

[0044] ,

[0045] in, Absolute temperature The connection coefficient;

[0046] Step 6: Set the activation energy minimum point With dynamic glass transition point Using these points as segmentation points, the rapid curing kinetic model of epoxy resin is modeled in three segments to obtain a full-cycle segmented kinetic model.

[0047] From the perspective of kinetic model thermal analysis principles: the DSC method for studying the kinetics of epoxy resin ring-opening reactions is based on two fundamental assumptions: 1) the heat generated by the curing reaction is proportional to the amount of reactants already reacted; 2) the change in heat flow is proportional to the change in the degree of polymerization. Therefore, the degree of polymerization can be expressed as:

[0048] ,

[0049] Where t represents the reaction time (min), The heat of reaction (J·g) at which the curing reaction proceeds to t. -1 ), Indicates the total heat of reaction;

[0050] The epoxy resin curing reaction rate equation can then be expressed as:

[0051] ,

[0052] in, Absolute temperature Indicates the reaction rate. For dynamic model functions, The temperature is The reaction rate constant at that time, As the apparent pre-exponential factor, As the apparent activation energy, It is a universal gas constant;

[0053] Based on this, from the perspective of the curing reaction mechanism, the catalyst has a significant impact on the curing system in the early stages of the reaction, while in the later stages, the curing reaction restricts chain segment movement, causing the activation energy to rise rapidly. During these two stages, the existing Kamal-Sourour model performs poorly in fitting the equation. Therefore, this invention proposes a method based on the activation energy minimum point... With dynamic glass transition point The three-segment segmentation model is as follows:

[0054] Phase 1: External Catalysis Model , is represented as:

[0055] ,

[0056] in, For activation energy, Indicates pre-exponential factor, This represents the reaction order in the first stage.

[0057] This stage is used to capture the initial reaction burst induced by the co-catalyst;

[0058] Phase Two: The Kamal-Sourour model is used to describe the chemical control phase:

[0059] ,

[0060] in, The constant of the catalytic reaction of the reactants. The catalytic constant of the reaction product is given. , The first term on the right is the n-order reaction model, and the second term is the autocatalytic reaction model. The n-order reaction model is characterized by the highest reaction rate in the initial stage of the reaction, and then the reaction rate decreases with time. The autocatalytic reaction model is characterized by the existence of an induction period in the reaction, and the maximum solidification reaction rate occurs after the reaction has gone through a certain period of time.

[0061] Phase 3: Dynamic Diffusion Model :

[0062] ,

[0063] in, The diffusion factor;

[0064] By coupling the three-stage criteria with the model, a full-cycle piecewise dynamic model is constructed as follows:

[0065] ,

[0066] Step 7, based on the heating rate The heat flow curve of the epoxy system to be fitted during non-isothermal curing, obtained by DSC at the minimum value, is substituted into the full-cycle piecewise kinetic model to obtain all model parameters, including: , , , , .

[0067] Based on the above steps, the present invention uses a first transformation node. (Activation energy evolution characteristic point) and the second transition node The dynamic glass transition criterion enables a smooth switching between different evolution mechanisms. Compared with the traditional single model, the full-cycle segmented kinetic model proposed in this invention can simultaneously accommodate the initial catalytic effect and the later diffusion control effect of the catalyst-containing epoxy system, significantly reducing the fitting residual of the entire process and providing a unified mathematical benchmark for the precise control of the curing process of complex systems.

[0068] The beneficial effects of the present invention will be further described in detail below with reference to the embodiments.

[0069] Example 1

[0070] Dissolve 5g of epoxy resin in 0.9g of acetone solution and stir thoroughly. Then add 5g of diamine polymer (curing agent) and mix. After stirring evenly, ultrasonically disperse at 25°C for 20 minutes until completely dissolved. Mark as EP.

[0071] The heating rate was 2.5 °C / min using DSC (Dynamic Differential Scanning Calorimetry). -1 5 °C·min -1 10°C·min -1 15 °C·min -1 Non-isothermal DSC testing was conducted to measure the heat flow curves of the epoxy resin system under heating conditions, such as... Figure 1As shown; the sample volume for DSC testing is 3-5 mg, and the nitrogen flow rate introduced into the DSC sample cell is 50 mL / min. -1 .

[0072] Example 2

[0073] Dissolve 5g of epoxy resin in 0.9g of acetone solution and stir thoroughly. Add 10pr of ethylene glycol (0.5g) as a catalyst, then add 5g of diamine polymer (curing agent) and mix. After stirring evenly, ultrasonically disperse at 25°C for 20min until completely dissolved. Label as EP / EG.

[0074] The heating rate was 2.5 °C / min using DSC (Dynamic Differential Scanning Calorimetry). -1 5 °C·min -1 10°C·min -1 15 °C·min -1 Non-isothermal DSC testing was conducted to measure the heat flow curves of the epoxy resin system under heating conditions, such as... Figure 2 As shown; the sample volume for DSC testing is 3-5 mg, and the nitrogen flow rate introduced into the DSC sample cell is 50 mL / min. -1 .

[0075] The DSC parameters obtained from tests in Example 1 and Example 2 are shown in Table 1:

[0076] Table 1

[0077]

[0078] In Table 1, T i T is the initial temperature of the curing reaction. p The reaction is exothermic, T f ΔT is the reaction termination temperature, and ΔT is the peak width.

[0079] Based on the above DSC parameters and heat flow curves, the evolution curve of the activation energy of the curing reaction as a function of the degree of curing was obtained using the Friedman conversion method, as shown in the figure. Figure 3 As shown, the activation energy minimum point is thus obtained. .

[0080] The DSC parameters and heat flux curves mentioned above are then fitted using the nonlinear least squares method based on the Kamal-Sourour model and the full-cycle piecewise dynamic model of this invention, respectively. The results are as follows: Figure 4 , Figure 5 As shown;

[0081] Finally, all parameters of the full-cycle piecewise dynamic model in Embodiments 1 and 2 of this invention are shown in Table 2:

[0082] Table 2

[0083]

[0084] The full-cycle piecewise dynamic model in Example 1 is as follows:

[0085]

[0086] The full-cycle piecewise dynamic model in Example 2 is as follows:

[0087]

[0088] As shown in Table 2, the goodness of fit (Rfit) of the three-segment piecewise model constructed in this invention is [data missing]. 2 The correlation coefficients were extremely close to 1, and the full-cycle fitting correlation coefficients reached 0.9997 (Example 1) and 0.9978 (Example 2), respectively, indicating that the model had extremely high accuracy in fitting the non-isothermal curing reaction of the epoxy system.

[0089] Furthermore, using the traditional Kamal-Sourour model as a comparative example, the Kamal-Sourour model is compared with the full-cycle piecewise dynamics model in this embodiment. The results are as follows: Figure 6 As shown in the figure, the full-cycle segmented kinetic model in this invention has a higher goodness of fit, especially in the initial and final stages of the reaction.

[0090] The above description is merely a specific embodiment of the present invention. Any feature disclosed in this specification may be replaced by other equivalent or similar features unless otherwise specified. All disclosed features, or steps in all methods or processes, may be combined in any way except for mutually exclusive features and / or steps.

Claims

1. A method for fitting the curing kinetics of polymer resins based on a piecewise model, characterized in that, Includes the following steps: Step 1: Perform dynamic mechanical property testing (DMA) on the epoxy system to be fitted before curing to obtain the uncured glass transition temperature. ; Step 2: Set several heating rates Differential scanning calorimetry (DSC) was used to obtain the heat flow curves of the epoxy system to be fitted during non-isothermal curing at each heating rate. The epoxy system to be fitted includes: epoxy resin, curing agent and catalyst. Step 3: Based on all the obtained heat flow curves, use the Friedman conversion method to obtain the evolution curve of the activation energy of the curing reaction with the degree of curing, and record the minimum point of the evolution curve as the activation energy minimum point. ; Step 4: Perform dynamic mechanical property testing (DMA) on the cured epoxy system to be fitted, and obtain the complete glass transition temperature after curing. ; Step 5: Based on the uncured complete glass transition temperature With the complete glass transition temperature of curing The dynamic glass transition point is obtained by dynamic calculation based on the DiBenedetto equation. ; Step 6: Set the activation energy minimum point With dynamic glass transition point The three-segment model is constructed by taking the segmentation points in sequence, including the external catalysis model, the Kamal-Sourour model and the dynamic diffusion model, thereby forming a full-cycle segmented kinetic model. Step 7, based on the heating rate The heat flow curve at the minimum value is substituted into the full-cycle piecewise dynamic model, and all model parameters are obtained by fitting.

2. The method for fitting the rapid curing kinetics of epoxy resin based on a segmented model according to claim 1, characterized in that, In step 5, the dynamic glass transition point Specifically: ， in, Absolute temperature The connection coefficient is denoted as .

3. The method for fitting the rapid curing kinetics of epoxy resin based on a piecewise model according to claim 1, characterized in that, In step 6, the first stage: The corresponding external catalytic model is expressed as: ， ， in, The degree of polymerization is represented by t, which indicates the reaction time. Indicates the reaction rate; For activation energy, Indicates pre-exponential factor, This represents the reaction order in the first stage. For universal gas constants, This refers to absolute temperature.

4. The method for fitting the rapid curing kinetics of epoxy resin based on a segmented model according to claim 1, characterized in that, Step 6, the second stage: The corresponding Kamal-Sourour model is expressed as follows: ， ， in, The degree of polymerization is represented by t, which indicates the reaction time. Indicates the reaction rate. , This refers to the reaction order in the second stage. For activation energy, Indicates pre-exponential factor, For universal gas constants, This refers to absolute temperature.

5. The method for fitting the rapid curing kinetics of epoxy resin based on a segmented model according to claim 1, characterized in that, Step 6, the third stage: The corresponding dynamic diffusion model is expressed as: , ， in, The degree of polymerization is represented by t, which indicates the reaction time. Indicates the reaction rate. , This refers to the reaction order in the second stage. For activation energy, Indicates pre-exponential factor, For universal gas constants, Absolute temperature is the diffusion factor.

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