Method for adjusting process parameters in an atom transfer radical polymerization process

Abstract

The application discloses a method for adjusting process parameters in an atom transfer radical polymerization process. The method is based on an orthogonal configuration method, divides an infinite chain length into finite elements and orthogonal configuration points, reconstructs a micro quality index of the process, directly solves the micro quality, and then adjusts parameters based on a micro quality model to provide effective guidance for experiments and production. The method includes a chain length discretization method, a micro quality reconstruction algorithm, an adaptive initialization algorithm and a parameter adjustment algorithm. Compared with a traditional parameter adjustment method, the method can directly solve the micro quality index, thereby guiding the parameter adjustment, and is beneficial to simulation, optimization and operation design of polymer production.

Description

Technical Field

[0001] This invention relates to the field of process simulation optimization and parameter adjustment in chemical polymerization processes. In particular, it relates to a method for adjusting process parameters in atom transfer radical polymerization. Background Technology

[0002] Polymers are composed of repeating structural units, and their microscopic quality indicators (such as molecular weight distribution) determine the intrinsic properties of the material. However, in actual production, complex polymerization processes are often guided by macroscopic quality indicators (such as average molecular weight), which lacks description of chain structure information and is difficult to meet the needs of high-end polymer products. Simulation of the polymerization process is a key means of obtaining macroscopic and microscopic quality indicators, playing a crucial role, especially in product design and operational optimization in large-scale industrial production. However, polymerization reaction models oriented towards microscopic chain structures are typically large-scale, nonlinear, and strongly coupled. Existing research mainly focuses on relatively simple polymerization processes, lacking effective microscopic quality modeling and parameter tuning methods for systems involving complex reactions. Therefore, developing more efficient and universal methods for microscopic quality parameter tuning is crucial to solving this problem. Summary of the Invention

[0003] To guide experiments and production, this invention proposes a method for adjusting process parameters during atom transfer radical polymerization. This method reconstructs the microscopic quality indices of the process using an orthogonal configuration method, achieving parameter adjustment based on microscopic quality. The method includes a chain length discretization method, a microscopic quality reconstruction algorithm, an adaptive initialization algorithm, and a parameter adjustment algorithm.

[0004] The present invention is achieved through the following technical solution.

[0005] On the one hand, this invention proposes a method for adjusting process parameters during atom transfer radical polymerization, including:

[0006] S1: Using the orthogonal configuration method, the target polymer chain length is discretized into several finite elements, and several configuration points are selected for each finite element.

[0007] S2: Construct the material conservation equation for the atom transfer radical polymerization process, and solve the material conservation equation at each configuration point to obtain the molecular weight distribution expressions of active polymers, dead polymers and dormant chains;

[0008] S3: The coefficient matrix method is used to matrix-process the chain length dependent kinetic equation in the material conservation equation to obtain a simplified material conservation equation.

[0009] S4: Combine the placement point and material concentration to reconstruct the molecular weight distribution expression of the polymer;

[0010] S5: Based on the simplified material conservation equation and the reconstructed molecular weight distribution expression, the optimal process parameters are adaptively solved.

[0011] On the other hand, the present invention also proposes a system for adjusting process parameters during atom transfer radical polymerization to achieve the above-mentioned adjustment method.

[0012] The beneficial effects of this invention are:

[0013] (1) The atom transfer radical polymerization parameter adjustment method of the present invention can directly reconstruct the microscopic quality index of the polymer, thereby describing the performance of the polymer product in essence. Compared with the simulation of macroscopic quality index based on the moment method, the characterization is more comprehensive and more conducive to parameter adjustment.

[0014] (2) The atom transfer radical polymerization parameter adjustment method of the present invention has good portability and strong versatility, and can be applied to the simulation and parameter adjustment of various polymerization reaction processes.

[0015] (3) The method for adjusting the atomic transfer radical polymerization parameters of the present invention is simple to implement and has good accuracy. Attached Figure Description

[0016] The following description of embodiments of the present invention, in conjunction with the accompanying drawings and tables, demonstrates its effects and provides further insight into the purpose, features, and advantages of the present invention.

[0017] Figure 1 This is a schematic diagram of the orthogonal collocation method and the coefficient matrix method;

[0018] Figure 2 A schematic diagram of the adaptive solution algorithm;

[0019] Figure 3 Comparison of molecular weight distribution examples for grade 1;

[0020] Figure 4 Comparison of molecular weight distribution examples for grade 2;

[0021] Figure 5 Comparison of molecular weight distribution examples for grade 3. Detailed Implementation

[0022] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application can be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods are omitted so as not to obscure the description of this application with unnecessary details. The invention will now be further described in conjunction with the accompanying drawings and specific embodiments.

[0023] Example 1

[0024] This embodiment provides a method for adjusting process parameters during atom transfer radical polymerization, specifically including the following steps:

[0025] S1: Using the orthogonal configuration method, the chain length of the polymer is discretized into several finite elements, and several configuration points are selected for each finite element;

[0026] S2: Construct the material conservation equation for the atom transfer radical polymerization process, and solve the material conservation equation at each configuration point to obtain the molecular weight distribution of active polymers, dead polymers and dormant chains;

[0027] S3: The coefficient matrix method is used to matrix-process the chain length-dependent kinetic equations, thereby simplifying the material conservation equations;

[0028] S4: Using orthogonal alignment point data, combined with concentration data of living polymerized chains and dead chains, the molecular weight distribution of the three chains in the polymerization process is reconstructed;

[0029] S5: Based on the simplified material conservation equation and molecular weight distribution, a genetic algorithm is used to solve the microscopic quality indicators, and a homotopy algorithm is used for backtracking. The process parameters are then optimized based on the solution results.

[0030] The present invention will now be described in more detail with reference to the accompanying drawings and tables, so as to illustrate the specific implementation process of the invention to those skilled in the art.

[0031] In this embodiment, the atom transfer radical polymerization chemical device for continuous production is CSTR. The reactor is a homogeneous reactor, and after all materials enter the reactor, they react to generate polymers.

[0032] (1) Configure the computing environment

[0033] Configure a high-performance computing environment that supports large-scale matrix operations and high-order interpolation algorithms. It is recommended to use MATLAB, Python (including NumPy and SciPy libraries), or other engineering software that supports matrix computations.

[0034] When setting up the environment, pre-configure a polynomial solving module, a matrix dimensionality reduction module, and an algorithm for calculating the roots of orthogonal polynomials to ensure the calculation accuracy of each sub-module throughout the simulation process.

[0035] (2) Simulation of the polymerization process

[0036] The free radical polymerization process includes the following changes:

[0037] Chain trigger:

[0038] Chain growth:

[0039] Chain activation:

[0040] Chain deactivation:

[0041] Termination of coupling:

[0042] Disproportionation termination:

[0043] This invention first employs an orthogonal configuration method to discretize the polymer chain length and construct a material conservation equation to model the atom transfer radical polymerization reaction. Subsequently, solving the material conservation equation at the discretized configuration points yields microscopic quality indicators, including the molecular weight distribution of the materials. The specific process is as follows:

[0044] Orthogonal polynomial selection: Based on the distribution characteristics of the aggregated chain length of the object, the Legendre orthogonal polynomial is selected as the basis function for the chain length discretization process.

[0045] Finite element partitioning: The polymer chain length interval is divided into several finite elements. The partitioning rules are adaptively adjusted according to the density changes of the chain length distribution to ensure that different chain segments have appropriate resolution in the simulation. The selected finite elements are shown in Table 1. There are ten finite elements in total, with each row being a finite element and the first point being the starting point.

[0046] Configuration point selection: Within each finite element, several configuration points are determined according to the roots of the orthogonal polynomial to achieve polymer chain length discretization. These configuration points are key nodes for achieving accurate solutions to chain length-dependent microscopic quality indices. The selected configuration points are shown in Table 1. Each finite element contains a starting point and three other configuration points.

[0047] Table 1: Orthogonal collocation points for finite element analysis

[0048]

[0049] Chain length interpolation: This method maps discrete chain length points to Lagrange fundamental polynomials, thereby constructing a polynomial approximation of the chain length distribution, which improves the accuracy and flexibility of the simulation.

[0050] Material conservation equations are written as follows: Based on the results of chain length discretization, material conservation equations are written for each material in the polymerization reaction (including initiator, active chain, dormant chain, dead chain, activator, and deactivator). The written material conservation equations are shown below.

[0051]

[0052]

[0053] Where t r [I] represents the residence time in the reactor, [Mt] represents the initiator concentration, and [Mt] represents the initiator concentration. n X / L] and [Mt] n-1 [L] represents the concentrations of the inactivating agent and the activating agent, [M] represents the monomer concentration, [P0] represents the concentration of vacant active sites, and [P...] represents the concentration of... r ]、[P s [P] represents the concentration of activated polymers with chain lengths r and s. r [X] represents the concentration of dormant chains of length r, [D] r [] represents the concentration of dead polymer with chain length r, k d k p k a k d k tc and k td The reaction kinetic parameters characterize chain initiation, chain growth, chain activation, chain deactivation, coupling termination, and disproportionation termination, respectively.

[0054] Application of the orthogonal collocation method: At each collocation point, a material conservation equation is established and solved to directly obtain microscopic quality indices (such as chain length distribution, molecular weight distribution, etc.). By using the orthogonal collocation method to handle differential terms, the residuals at the collocation points are ensured to be zero, thus improving the accuracy of the model solution.

[0055] Polynomial fitting of micro-quality indices: Using the Lagrange interpolation method, based on the micro-quality data at the configuration points, a polynomial describing function of the micro-quality indices of the polymerization reaction is constructed, providing a data foundation for the reconstruction of molecular weight distribution.

[0056] The specific details regarding the discretization of the polymer chain length mentioned above are as follows.

[0057] The chain length of a polymer is a variable in free radical polymerization. This invention discretizes the chain length using an orthogonal configuration method, in which:

[0058]

[0059] <R(s),w k (s)>=∑ s∈S R(s)w k (s)=0

[0060] w k (s)=δ(ss k )

[0061] Where <.,.> denotes the discrete inner product, s is the polymer chain length variable, and Φ k (s) represents the selected basis functions, and b represents the basis function coefficients. This is a set of polynomials used to estimate a portion of the functions in the system. Let p(s) be the estimated system, p(s) be the original system, R(s) be the residual, and w be the value of the original system. k (s) The impulse function is chosen as the weighting function, δ(ss) k ) is the impulse function, and s k If we consider a location point, then:

[0062] <R(s),w k (s)>=∑ s∈S R(s)δ(ss k )=0 (2.27)

[0063] At this point, the residual R(s) is present at all configuration points s. k The value on Φ is 0, which ensures the accuracy of the orthogonal collocation method. Regarding the selection of polynomial basis functions and collocation points, Φ... k (s) is generally a Lagrange fundamental polynomial, and Φ k (s k )=1,Φ i (s k )=0,i≠k. The most accurate method for determining the placement points is using the roots of the orthogonal polynomial. First, define an nth-order P... n (x) are orthogonal polynomials and satisfy:

[0064]

[0065] Where w(x) is the chosen weight function, which determines the type of orthogonal polynomial. When w(x) = 1, P n (x) is a Legendre polynomial; and At that time, P n (x) is a Chebyshev polynomial. Furthermore, any n-order polynomial p n (x) can be obtained by linear weighted summation of orthogonal polynomials of any class, i.e.

[0066] p n (x)=∑β i P i (x)

[0067] For general engineering problems, the time and space scale is large and the model is complex. High-order interpolation can lead to large estimation errors outside the interpolation points. Therefore, low-order piecewise interpolation, i.e., the finite element orthogonal collocation method, is often used. First, the chain length is discretized into several finite elements i = 1, ..., N. fe Then, for each finite element method, configuration points k = 1, ..., N are selected. cp The selection rule remains the same: the roots of orthogonal polynomials, as described below:

[0068]

[0069] R(s ik ) = 0

[0070] Among them l ik (s) is a piecewise Lagrange polynomial, b ik To estimate the function, we first divide the finite element into sub-element ...

[0071] The specific details regarding the formulation of the material conservation equation are as follows:

[0072] Write the material conservation equations for all substances, including initiators, activated polymers, dormant chains, dead polymers, activators, and deactivators. The polymer chains in the equations do not need to be written using the average moment; the moment is defined as follows:

[0073]

[0074] Among them, Y i For the i-th order live moment, Q i For the i-th order dead moment, P r For an active polymer with chain length r, D r Let r be a dead polymer. For active polymers, dead polymers, and dormant chains, the material conservation equations are written at the orthogonal configuration points selected above. First, based on the orthogonal configuration method, the concentrations of active polymers, dead polymers, and dormant chains with chain length n can be approximated by polynomials.

[0075]

[0076] Where n ik For the selected orthogonal placement points of the chain length, n il l is the configuration point used for iteration. ik (s) is the Lagrange interpolation polynomial, [P] n [This represents the concentration of the activated polymer.] For orthogonal collocation points n ik The concentration of activated polymer, [P] n X] represents the concentration of the dormant chain. For orthogonal collocation points n ik The concentration of the dormant chain, [D n [This represents the concentration of dead polymers.] For orthogonal collocation points n ik The concentration of the euthanasia polymer; s represents the chain length, i (=1,2,…,N) fe ) represents the finite element index, k(=1,2,…,N) cp ) represents the configuration point index, N cp Let be the number of orthogonal configuration points. At this point, the material conservation equations for each chain are expressed as:

[0077]

[0078] Where V is the volume of the mixture in the reactor. The rate of change over time, and Each is a configuration point n ik The formation rates of activated polymers, dormant chains, and dead polymers.

[0079] Using the above method, the material conservation equation is established and solved at each configuration point, and the microscopic quality indicators (such as chain length distribution, molecular weight distribution, etc.) are directly solved.

[0080] (3) Dimensionality reduction using the coefficient matrix method

[0081] Figure 1 The document demonstrates the basic framework for chain length discretization using the orthogonal configuration method and model simplification using the coefficient matrix method. The process of the coefficient matrix method is as follows:

[0082] Matrix construction: For the moment operation terms in the model, the infinite-dimensional differential algebraic equation is reduced to a finite-dimensional algebraic system.

[0083] Convolution and Higher-Order Coefficient Matrix Method: To handle complex convolution terms and infinite summation terms in polymerization reactions, the higher-order coefficient matrix method is introduced to achieve efficient numerical computation.

[0084] Weighted matrix solution: The dynamic parameters dependent on the length of the aggregate chain are calculated by weighted solution, thereby significantly reducing the computational complexity while ensuring the accuracy of the solution.

[0085] The coefficient matrix method in this invention is as follows. This invention achieves dimensional reduction by introducing a two-dimensional orthogonal configuration method. The moment method is used to handle basic operations, but it is difficult to close the equations under chain-length-dependent reaction rates. The orthogonal configuration method can transform infinite-dimensional differential-algebraic equations into finite-dimensional algebraic systems, but complex operations (such as infinite summation terms in the polymer's material conservation equation) make the model difficult to solve. This invention reconstructs complex operations through the coefficient matrix method, enabling the orthogonal configuration method to enhance versatility and computational efficiency while retaining accuracy. It can handle chain-length-dependent kinetic parameters and achieve more reliable solutions.

[0086] For general moment operations and formulas caused by chain growth, chain inactivation, chain activation, and dissimilarity termination. The coefficient matrix method proposed in this invention is as follows:

[0087]

[0088] Where s is the chain length, l is the order of the moment, [P s[ ] represents the concentration of the active polymer with chain length s, and x and y represent the finite element method and placement points used for iterative calculation. For orthogonal collocation points n xy The concentration of activated polymers, Let I be the l-th order reduction coefficient matrix, I be the finite element set, and K be the set of placement points.

[0089] For convolution operations and expressions caused by coupling termination The higher-order coefficient matrix method proposed in this invention is as follows:

[0090]

[0091] in, Let n be the chain length. ik -s concentration of activated polymers, n ik Let x1, y1, x2, y2 be the orthogonal collocation points, representing the finite element and collocation point combination used for convolution operations, and thus characterizing the convolution operation pair. and Characterizes the configuration point and The concentration of active polymers on the surface, The higher-order coefficient matrix representing the convolution operation caused by coupling termination.

[0092] Based on the coefficient matrix method, in the material conservation equation as well as The operations are reduced to coefficient matrix expressions, which significantly reduces the complexity of the model and makes it easier to solve.

[0093] (4) Calculation and plotting of molecular weight distribution

[0094] Distribution calculation based on orthogonal collocation points: Using orthogonal collocation point data, combined with the concentration data of living polymer chains and dead chains, the molecular weight distribution of the polymer is reconstructed.

[0095] This invention utilizes the orthogonal collocation method and the coefficient matrix method to determine the concentration of dead polymers [D]. nik Furthermore, the value of ] can be used to calculate the precise molecular weight distribution curve, which can be derived on a logarithmic scale as follows:

[0096]

[0097] Among them mwd ik P For activated polymers with chain length n ik molecular weight, mwd ik PX For a dormant chain of length n ik molecular weight, mwd ik For dead polymers with chain length n ikThe molecular weight (i.e. conventional) is ln(10), which is the logarithm of 10.

[0098] This invention proposes a backtracking method based on the homotopy algorithm for adaptive solving of atom transfer radical polymerization. This method is based on the generalized homotopy description H(x,s)=sF(x)+(1-s)F0(X), where G(X,0)=0 is the known solution and H(x,1)=0 is the original problem, satisfying the two conditions of the homotopy algorithm: known solution and problem continuity. Assuming the initial model has solutions F(Z0,U0,Y0)=0 and G(Z0,U0,Y0)=0 under nominal operating conditions, the proposed solution steps include: 1) attempting to solve the target steady-state model with a virtual solution; 2) if unsuccessful, decreasing the parameter s and resolving; 3) increasing s until convergence; 4) if convergence fails, backtracking to the last solution and continuing. In this invention, the set of various kinetic parameters is selected as parameter s. This method utilizes known solutions to accelerate convergence.

[0099] (5) Adaptive parameter tuning and solution based on genetic algorithm

[0100] This invention improves the solution efficiency of atom transfer radical polymerization by combining a genetic algorithm with an adaptive solution strategy. The solution method is as follows: Figure 2 As shown. The main flow of this process is as follows:

[0101] Encoding and Initialization: First, the process parameters are converted into genetic codes, and an initial population is generated, with each individual representing a different set of parameter combinations. A genetic algorithm is used to select a fitness function to evaluate the impact of different parameter combinations on the polymerization reaction results, particularly the optimization of molecular weight distribution.

[0102] Fitness function: Define a fitness function that evaluates the performance of each combination of parameters in the reaction and compares it with the target molecular weight distribution.

[0103] Adaptive genetic operations: Through selection, crossover, and mutation operations in genetic algorithms, a new population is generated, and the crossover and mutation probabilities are dynamically adjusted based on the fitness of the current population in each generation iteration. This operation ensures that parameters can be effectively optimized under varying reaction conditions, gradually approaching the optimal solution.

[0104] Homotopy Algorithm Backtracking and Convergence Adjustment: To accelerate convergence and address potential convergence failures, a backtracking algorithm based on the generalized homotopy description is employed. Through adaptive solution and the backtracking mechanism of the homotopy algorithm, this invention can more efficiently optimize the key parameters of the polymerization reaction and maintain good solution performance and stability under various complex conditions.

[0105] The backtracking mechanism of the homotopy algorithm is based on the generalized homotopy description H(x,s)=sF(x)+(1-s)F0(x), where H(x,0)=0 is the known solution and H(x,1)=0 is the original problem, satisfying the two conditions of the homotopy algorithm: known solution and problem continuity. Assuming the initial model has solutions f(Z0,U0,Y0)=0 and g(Z0,U0,Y0)=0 under nominal operating conditions, the proposed solution steps include: 1) attempting to solve the target steady-state model with a virtual solution; 2) if it fails, reducing the parameter s and solving again; 3) increasing s until convergence; 4) if convergence fails, backtracking to the last solution and continuing. In this invention, the set of various dynamic parameters is selected as parameter s. This method can accelerate convergence by utilizing known solutions.

[0106] Example 2

[0107] This embodiment, completed in a Python environment, focuses on modeling and parameter estimation for the atom transfer radical polymerization (ATRP) process. Particularly in the calculation of microscopic quality indicators such as molecular weight distribution and chain length distribution, it combines the orthogonal collocation method and the coefficient matrix method to optimize model accuracy and computational efficiency for parameter tuning. The detailed steps and processing procedures of this embodiment are as follows.

[0108] 1. Chain length discretization and orthogonal configuration

[0109] First, based on the chain length range of the polymerization reaction, a suitable interval (e.g., 0 to 2500) was selected, and this interval was divided into 10 finite element methods. Within each finite element, the orthogonal placement method was used based on the characteristics of the chain length distribution, selecting placement points through the roots of orthogonal polynomials. To ensure high simulation accuracy, this embodiment used the roots of Legendre polynomials for placement point selection. This effectively reduces errors and enhances the smoothness of chain length discretization. Within each finite element, piecewise Lagrange polynomials were used for placement point selection. Each placement point represents a chain length state, and the simulation process reflects the polymer distribution of different chain lengths through these placement points. For example, the placement points selected within the interval [0,10] are: 1, 2, 3, 8. These placement points directly affect the calculation accuracy of microscopic quality indicators.

[0110] 2. Construction of the material conservation equation

[0111] After chain length discretization, the material conservation equations are listed one by one. These equations describe the changes in the concentration of various substances (such as initiators, active chains, dead chains, etc.) over time during polymerization. By using piecewise Lagrange interpolation, the concentration of all substances is expressed as a polynomial function of the chain length. The concentration calculation at each configuration point is performed using interpolation polynomials, ensuring the continuity and accuracy of concentration changes.

[0112] These equations were solved using a combination of direct and iterative methods. At each configuration point, the concentrations of active, dead, and dormant chains were approximated using a Lagrange interpolation function. For example, initial conditions were set as initial values ​​for the reaction rate constant and concentrations, and the final polymer distribution was approximated through iterative solutions. The polymer material conservation equations for this case are as follows:

[0113]

[0114] 3. Dimensionality reduction using the coefficient matrix method

[0115] To address the chain length-dependent reaction rate and its complex differential-algebraic equations, this embodiment employs the coefficient matrix method for dimensionality reduction. Traditional polymerization reaction models involve numerous high-dimensional matrix calculations. To improve computational efficiency, the coefficient matrix method simplifies the high-dimensional system into a low-dimensional system, significantly reducing computational complexity.

[0116] In practical implementation, the coefficient matrix method avoids redundant summation terms and simplifies equation calculations by matrixing the polymer chain length-dependent kinetic parameters. For example, by expanding the polynomial of the chain length distribution into matrix form, we can efficiently calculate the concentration of substances at each time step, thereby accurately simulating the kinetics of the polymerization reaction.

[0117] The coefficient matrix calculation process for this case is as follows:

[0118]

[0119] Where, N fe For the index of finite element method, l xy (s) is a Lagrange polynomial. For the sequence of convolution pairs corresponding to the x1 finite element indexed by the algorithm, is the dimension of the convolutional sequence pair.

[0120] 4. Calculation of molecular weight distribution and parameter adjustment

[0121] Based on the aforementioned microscopic quality indicators (such as chain length distribution and concentration distribution), we accurately calculated the molecular weight distribution of the polymer using the orthogonal collocation method. The chain length distribution of the polymer was obtained by establishing and solving the material conservation equation at the collocation points. Then, the molecular weight distribution was reconstructed from the results of these collocation points using Lagrange interpolation. To further optimize key process parameters (such as temperature, initiator concentration, and reaction time), we introduced a genetic algorithm parameter tuning method. Through multi-generation iterative optimization, the optimal parameter combination was obtained, thereby improving simulation accuracy and computational efficiency. The distribution curve was compared with traditional methods (such as distribution calculation based on the method of moments) to verify the accuracy of the proposed method in microscopic quality characterization. The graphical molecular weight distribution curve clearly shows the fit between the simulation results and experimental data after parameter adjustment, further confirming the effectiveness of the proposed method. The results obtained under different experimental conditions are compared, for example... Figure 3 , Figure 4 and Figure 5 As shown, the simulation results and experimental data fit almost perfectly.

[0122] Example 3

[0123] This embodiment also provides a system for adjusting process parameters during atom transfer radical polymerization, which is used to implement the above embodiments. The terms "module," "unit," etc., used below refer to combinations of software and / or hardware that perform a predetermined function. Although the system described in the following embodiments is preferably implemented in software, hardware implementation, or a combination of software and hardware, is also possible.

[0124] The process parameter adjustment system for the atom transfer radical polymerization process includes:

[0125] The discretization module is used to discretize the target polymer chain length and determine several configuration points;

[0126] A solution module is constructed to build the material conservation equation for the atom transfer radical polymerization process, and solves the material conservation equation at each configuration point to obtain the molecular weight distribution expression of each material.

[0127] The matrixing module is used to matrix-process the chain length-dependent kinetic equations to obtain simplified material conservation equations.

[0128] The index reconstruction module is used to reconstruct the molecular weight distribution expression of the polymer;

[0129] The parameter solving module is used to adaptively solve for the optimal process parameters.

[0130] For the system embodiments, since they basically correspond to the method embodiments, relevant details can be found in the descriptions of the method embodiments; the implementation methods of the remaining modules will not be repeated here. The system embodiments described above are merely illustrative. The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of the present invention according to actual needs. Those skilled in the art can understand and implement this without any creative effort.

[0131] The system embodiments of the present invention can be applied to any device with data processing capabilities, such as a computer or other similar device. The system embodiments can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution.

[0132] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the present invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for adjusting process parameters during atom transfer radical polymerization, characterized in that, include: S1: Using the orthogonal configuration method, the target polymer chain length is discretized into several finite elements, and several configuration points are selected for each finite element. S2: Construct the material conservation equation for the atom transfer radical polymerization process, and solve the material conservation equation at each configuration point to obtain the molecular weight distribution expressions of active polymers, dead polymers and dormant chains; The material conservation equations for constructing the atom transfer radical polymerization process specifically include: The concentrations of active polymers, dead polymers, and dormant chains in the polymerization reaction are expressed using approximate calculation polynomials: ； ； ； ； in, For the k-th placement point in the i-th finite element, For the j-th configuration point in the i-th finite element, For the Lagrange interpolation polynomial, Let n be the concentration of the activated polymer with chain length n. For configuration points The concentration of active polymers at that location, Let n be the concentration of dormant chains of length n. For configuration points The concentration of dormant chains at that location, Let n be the concentration of the dead polymer with chain length n. For configuration points The concentration of dead polymers at the location; s represents the chain length. The number of finite elements, Configure the number of points; Differentiating the approximate calculation polynomial with respect to time yields expressions for the formation rates of active polymers, dead polymers, and dormant chains, which serve as the material conservation equation. S3: The coefficient matrix method is used to matrix-process the chain length dependent kinetic equation in the material conservation equation to obtain a simplified material conservation equation. S4: Combining the placement point and material concentration, reconstruct the molecular weight distribution expression of the polymer as follows: ； ； ； in, For active polymers with a chain length of molecular weight, For the dormant chain with a chain length of molecular weight, For dead polymers with chain length of molecular weight, For the k-th placement point in the i-th finite element, For configuration points The concentration of activated polymers, and respectively configuration points and configuration points The concentration of the dormant chain, For configuration points The concentration of the culprit, for Order reduction coefficient matrix, and For iteration variables, For finite element sets, For the set of configuration points; S5: Based on the simplified material conservation equation and the reconstructed molecular weight distribution expression, the optimal process parameters are adaptively solved.

2. The method for adjusting process parameters during atom transfer radical polymerization according to claim 1, characterized in that, Specifically, S1 involves: constructing a Lagrange orthogonal polynomial as the basis function for chain length discretization, dividing the polymer chain length into several finite elements, selecting several placement points in each finite element according to the roots of the orthogonal polynomial, and ensuring that the residual is 0 at all placement points.

3. The method for adjusting process parameters during atom transfer radical polymerization according to claim 1, characterized in that, In step S3, the matrix transformation of the chain-length-dependent kinetic equation in the material conservation equation using the coefficient matrix method is specifically as follows: For the moment operations and expressions in the material conservation equation caused by chain growth, chain deactivation, chain activation, and disproportionation termination, the coefficient matrix method simplifies them as follows: ； in, Let be the order of the moment. Chain length Concentration of activated polymers, for Order reduction coefficient matrix; For the convolution operation and expression in the material conservation equation caused by coupling termination, the coefficient matrix method simplifies it to: ； in, The chain length is The concentration of activated polymers, For the combination of finite element and placement points used in convolution operations, and respectively configuration points and The concentration of active polymers at that location, This is the higher-order coefficient matrix for the convolution operation.

4. The method for adjusting process parameters during atom transfer radical polymerization according to claim 1, characterized in that, In step S5, the adaptive solution for the optimal process parameters employs an adaptive solution method based on a genetic algorithm, specifically as follows: The process parameters are converted into genetic codes and an initial population is generated. Each individual in the population represents a set of process parameter combinations. The process parameters are iteratively optimized through a genetic algorithm. In each generation, the molecular weight distribution under the current process parameter combination is solved according to the simplified material conservation equation and molecular weight distribution expression. The crossover probability and mutation probability are dynamically adjusted according to the fitness of the current population to finally obtain the optimal solution. The fitness is the error between the calculated molecular weight distribution and the target molecular weight distribution.

5. The method for adjusting process parameters during atom transfer radical polymerization according to claim 4, characterized in that, In the adaptive solution method based on genetic algorithm, the homotopy algorithm is used for solution in each iteration.

6. A system for adjusting process parameters during atom transfer radical polymerization, used to implement the adjustment method described in claim 1, characterized in that, The system includes: The discretization module is used to discretize the target polymer chain length and determine several configuration points; A solution module is constructed to build the material conservation equation for the atom transfer radical polymerization process, and solves the material conservation equation at each configuration point to obtain the molecular weight distribution expression of each material. The matrixing module is used to matrix-process the chain length-dependent kinetic equations to obtain simplified material conservation equations. The index reconstruction module is used to reconstruct the molecular weight distribution expression of the polymer; The parameter solving module is used to adaptively solve for the optimal process parameters.

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