CN113450879A - Simulation and strength calculation method for polymer degradation process - Google Patents

Abstract

The invention discloses a method for simulating a polymer degradation process and calculating strength, which comprises the following steps: identifying two structural modes of a blocking amorphous phase and a blocking pore phase in a state phase diagram, and calculating a blocking ratio; based on the structural mode characteristics, realizing the diffusion simulation of the polymer degradation process; identifying three intensity modes of an amorphous island, a crystalline island and an intensity cavity in an intensity phase diagram, and respectively calculating a surrounding ratio, an area and an intensity degree; calculating intensity values corresponding to the cells in different intensity states based on the intensity mode characteristics; the total strength of the polymer material was calculated. The method provides a numerical basis for the optimized design of the high-molecular degradable polymer precision medical clinical equipment in the aspect of mechanical property, and is suitable for different application fields of degradable high-molecular equipment.

Description

Simulation and strength calculation method for polymer degradation process

Technical Field

The invention relates to the technical field of degradation process analysis of degradable high molecular materials, in particular to a method for simulating a polymer degradation process and calculating strength.

Background

Biodegradable materials are gradually paid attention by researchers today with medical maturity due to their unique degradation characteristics, and typical biodegradable materials are PLA (polylactic acid), PGA (polyglycolic acid), PLLA (levorotatory polylactic acid), and applications include tissue engineering scaffolds, drug delivery systems, coronary stents, and the like. The ideal degradable polymer degradation product can be matched with tissue growth to help the tissue to recover the cardiovascular and cerebrovascular vessels. This makes the discovery of degradation mechanisms and the quantitative tracking of degradation processes important. Some studies on the degradation mechanism show that as water penetrates into the device, hydrolysis reactions occur, leading to the breaking of long chains into short chains and oligomers, the short chains having additional mobility in the device, the alcohol and acid produced by the breaking giving rise to a local acidic environment that accelerates the reaction rate, leading to autocatalytic degradation, while the polymer recrystallizes during the breaking process. If there are pathways that fill the high mobility short chains, the oligomers can diffuse out of the polymer. Thus, the degradation of these bioabsorbable polymers is a complex process involving polymer chain scission, chain scission induced crystallization, oligomer diffusion, autocatalytic hydrolysis reactions, and cavity formation.

In order to simulate the degradation process, various polymer degradation models have been proposed. Monte Carlo randomness was proposed by Siepmann et al. The cellular automata method was proposed by Zyourakis et al to simulate the release of oligomers. Pan et al propose a reaction-diffusion model for biodegradable polymers. In addition, Han and Pan propose a two-scale model, the monte carlo method is used to model short-chain scission, and oligomer diffusion is modeled by the macroscopic diffusion equation. Zhang et al proposed a multi-scale MS-CMCA model, based on which a strength model of polyester degradation process was proposed, and a strength phase image feature recognition NNBE (near Neighbor Boundary expanded method) algorithm, which discusses the influence of amorphous phases, crystalline phases and empty phase regions of different sizes and distributions on strength. The above method considers the process of diffusion of the oligomer in the material to be uniform, but actually the diffusion coefficient changes according to the change of the internal structural mode, when the oligomer is crystallized around, the diffusion of the oligomer is inhibited, and when the oligomer is wrapped by the crystal, the diffusion disappears. In the process of calculating the strength, when strength empty phases around a crystalline or amorphous phase are contacted, the strength is reduced, and when the strength empty phases surround the crystalline or amorphous phase, the strength disappears, so that the prior art cannot accurately analyze the degradation process, and therefore, focusing on various characteristic modes in the degradable material can be used for helping to deeply understand the degradation process, and the research on the degradation has great significance on the regulation and control of the material.

Disclosure of Invention

The invention provides a method for simulating a polymer degradation process and calculating strength, which aims to solve the technical problem that the simulation analysis of the degradation process of a degradable high polymer material in the prior art is not objective and accurate enough.

In order to solve the technical problems, the invention provides the following technical scheme:

in one aspect, the invention provides a method for simulating a polymer degradation process and calculating strength, comprising the following steps:

dividing a polymer material to be simulated and calculated into a plurality of cells by using a cellular automaton;

acquiring state phase diagrams at different moments, judging the state of each cell, identifying two structural modes, namely a blocking amorphous phase and a blocking hole phase, in the state phase diagrams based on the state of each cell, and respectively calculating the respective corresponding blocking ratios of the identified blocking amorphous phase and the blocking hole phase;

performing a diffusion process of each cell to surrounding cells based on the recognition result of the structural pattern and the recognized blocking ratio of each structural pattern to realize diffusion simulation of the polymer degradation process;

acquiring intensity phase diagrams at different moments, judging the intensity state of each cell, identifying three intensity modes of an amorphous island, a crystalline island and an intensity cavity in the intensity phase diagrams based on the intensity state of each cell, and respectively calculating the surrounding ratio, the area and the density degree corresponding to the identified amorphous island and crystalline island, and the area and the density degree corresponding to the identified intensity cavity;

calculating intensity values corresponding to the cells in different intensity states based on the identification result of the intensity mode and the surrounding ratio, the area and the density degree corresponding to each structure mode;

and calculating the total strength of the polymer material based on the strength values of the cells in different strength states.

Further, the occluded amorphous phase refers to a region of amorphous phase surrounded by crystals;

the blocking pore phase refers to a pore phase region surrounded by crystals.

Further, the blocking ratio R of the blocking amorphous phase_aCalculated by the following formula:

wherein N is_caIs the length of contact between the crystalline phase and the amorphous phase, N_aIs the perimeter of the amorphous phase.

Further, the plugging hole has a plugging ratio R_hCalculated by the following formula:

wherein N is_chIs the length of the crystal phase in contact with the pore, N_hIs the perimeter of the pore phase.

Further, based on the recognition result of the structural pattern and the recognized blockage ratio of each structural pattern, performing a diffusion process of each unit cell to the surrounding unit cells, and realizing a diffusion simulation of the polymer degradation process, wherein the diffusion simulation comprises the following steps:

calculating the diffusion coefficient of the corresponding cell in the corresponding structural mode by using the updated diffusion coefficient according to the identification result of the structural mode and the identified blocking ratio of each structural mode; wherein for a plugged pore that is in contact with the edge of the phase diagram, all of the cellular diffusion coefficients therein are set to 0;

and executing the diffusion process of each unit cell to the surrounding unit cells according to the diffusion coefficient of the corresponding unit cell.

Further, the calculating the diffusion coefficient of the corresponding cell in the corresponding structure mode by using the updated diffusion coefficient includes:

according to the identified blocking amorphous phase and the blocking pore, updating diffusion coefficients of cells belonging to the two structural modes in a certain area, wherein the updating formula is as follows:

D＝R_a·D_p+R_h·D_ε

wherein D is the updated diffusion coefficient; d_pAs initial diffusion coefficient in amorphous phase, D_εIs the initial diffusion coefficient, R, in the pore phase_aIs the blockage ratio of blocking the amorphous phase, and Rh is the blockage ratio of blocking the pore phase;

the formula for calculating the diffusion of short chains is:

wherein, C_olLow short chain concentration in a certain area; r_olThe number of oligomers in a cellular region; t represents time, div () is divergence, D is diffusion coefficient, and grad () is gradient.

Further, the amorphous island refers to a region surrounded by a crystalline phase and an intensity empty phase;

the crystallization island refers to a crystallization area surrounded by strength empty phase;

the strength void refers to a region composed of a whole block of strength voids which are interconnected.

Further, the amorphous island has a rounding ratio R_saCalculated by the following formula:

wherein N is_sacAnd N_sahThe lengths of the sides of the crystalline phase and the intensity empty phase, respectively, in contact with the current amorphous phase region, N_saThe perimeter of the current amorphous phase region.

Further, the surrounding ratio R of the crystalline islands_scCalculated by the following formula:

wherein N is_schLength of the edge of the strong void phase in contact with the region of the currently crystalline phase, N_scThe perimeter of the current crystalline phase region.

Further, the calculating intensity values corresponding to the cells in different intensity states based on the recognition result of the intensity pattern and the surrounding ratio, the area and the density degree corresponding to each structure pattern includes:

the strength pattern of the cells comprises amorphous phases, crystalline phases and strength voids;

when the intensity pattern of the unit cell is an amorphous phase, the intensity σ thereof_aExpressed as:

σ_a＝σ_anp+σ_ap

wherein σ_apIs the strength, σ, of the amorphous islands_anpIs the strength of the conventional amorphous phase, alpha_aiIs the number of amorphous islands, S_aiIs the density of amorphous islands, alpha_ahIs the area of the conventional amorphous phase, S_ahIs the density of the conventional amorphous phase, r_aIs the amorphous island wrap ratio threshold; gamma, eta, gamma₂、η₂Is a parameter related to the properties of the polymer material, the value of which is defined byCalculating and fitting to determine, wherein L multiplied by L is the number of the cells;

when the intensity pattern of the unit cell is a crystalline phase, the intensity σ thereof_cExpressed as:

σ_c＝σ_cnp+σ_cp

wherein σ_cpIs the strength of the crystalline islands, σ_cnpIs the strength of the conventional crystalline phase, alpha_ciIs the number of crystalline islands, S_ciIs the density of crystalline islands, alpha_zcIs the area of the conventional crystalline phase, S_zcIs the density of the conventional crystalline phase, r_cIs the threshold of the crystal island surrounding ratio, phi,

φ₂、

Is a parameter related to the properties of the polymer material;

when the intensity pattern of the unit cell is an intensity hole, the intensity σ thereof_eExpressed as:

wherein alpha is_eiIs the number of strength voids, S_eiIs the density of the strength cavity, mu and v are parameters related to the polymer material property, the numerical value is determined by calculation fitting, L multiplied by L is the number of cells;

the total strength of the polymer material is calculated based on the strength values of the cells in different strength states, and the expression is as follows:

wherein,

for the total strength value of the polymer material to be calculated, X_a(t)、X_c(t)、X_e(t) is the ratio of the number of unit cells in the amorphous islands, the crystalline islands and the strength voids to the total unit cells, respectively.

In another aspect, the present invention also provides an electronic device comprising a processor and a memory; wherein the memory has stored therein at least one instruction that is loaded and executed by the processor to implement the above-described method.

In yet another aspect, the present invention also provides a computer-readable storage medium having at least one instruction stored therein, the instruction being loaded and executed by a processor to implement the above method.

The technical scheme provided by the invention has the beneficial effects that at least:

according to the polymer degradation process simulation and strength calculation method provided by the invention, the concepts of a structure mode and a strength mode in a degradation process are provided according to the structure evolution in the degradation process, the structure mode and the strength mode are identified in an image processing mode, a structure mode identification algorithm and a strength mode identification algorithm are provided, some special conditions of the structure mode are considered, a flow algorithm is provided, so that two structure mode characteristics of a blocking hole and a blocking amorphous phase in a state diagram and three strength mode characteristics of an amorphous island, a crystalline island and a strength cavity in the strength diagram are identified, and the diffusion simulation of the degradation process is performed according to the blocking hole and the blocking amorphous phase characteristics; and establishing and calculating a strength model according to the characteristics of the amorphous island, the crystalline island and the strength cavity. Model calculation is compared with experimental data, the simulation value of the model is well matched with the experimental value, and the extraction of the structural mode characteristics and the strength mode characteristics is feasible for the degradation simulation. The invention provides a numerical basis for the optimized design of the high-molecular degradable polymer precision medical clinical equipment in the aspect of mechanical property, and is suitable for different application fields of degradable high-molecular equipment.

Drawings

In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the description of the embodiments will be briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.

FIG. 1 is a flow chart of a polymer degradation process simulation and strength calculation method provided by an embodiment of the present invention;

FIG. 2 is a flow chart of degradation simulation based on structural pattern recognition provided by an embodiment of the present invention;

FIG. 3 is a flow chart for computing intensity based on intensity pattern recognition provided by an embodiment of the present invention;

FIG. 4 is another flow chart of degradation simulation based on structural pattern recognition provided by embodiments of the present invention;

FIG. 5 is another flow chart for computing intensity based on intensity pattern recognition provided by embodiments of the present invention;

FIG. 6 is a schematic diagram of an edge wrapping algorithm provided by an embodiment of the present invention;

FIG. 7 is a schematic diagram of a state phase diagram provided by an embodiment of the present invention; wherein, the light gray is amorphous phase, the white is holes, and the black is crystalline phase; (a) schematic of blocking amorphous phase; (b) is a schematic view of a blocked hole; (c) the implementation diagram of the pipeline algorithm provided by the embodiment of the invention is shown;

FIG. 8 is a schematic diagram of an intensity phase diagram provided by an embodiment of the present invention; wherein, gray is amorphous phase, black is crystalline phase, and white is intensity empty phase; (a) is a schematic view of a crystalline island; (b) schematic representation of amorphous islands; (c) is a schematic representation of a strength void;

FIG. 9 is a plot of intensity of PLLA with an initial degree of crystallinity of 30% as a function of time; wherein, (a) is an amorphous island identification map (amorphous islands marked dark gray); (b) a crystal island identification pattern (marked with dark gray is a crystal island), (c) an intensity void identification pattern (marked with black is an intensity void);

FIG. 10 is a plot of PLLA with an initial crystallinity of 30% comparing the molecular weight, crystallinity and intensity over time for both the simulated and experimental data, where the solid line represents the model prediction results and the scatter points represent the experimental data;

FIG. 11 is a plot of PLLA with an initial crystallinity of 45% comparing the molecular weight, crystallinity and intensity over time of the simulated and experimental data; wherein the solid line represents the model prediction result, and the scattered points represent experimental data;

FIG. 12 is a plot of PLLA with an initial crystallinity of 54% comparing the molecular weight, crystallinity and intensity over time of the simulated and experimental data; wherein the solid line represents the model prediction results and the scatter points represent experimental data.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be described in detail with reference to the accompanying drawings.

First embodiment

Because of good degradation characteristics and strength performance, the medical degradable high polymer material is widely applied in medicine, and how to accurately simulate the change of the internal structure and the mode of interaction between the structures has important significance for researching the evolution of the whole degradation process. In the degradation process, the internal structures of the material are unevenly distributed along with time and space, certain interaction can be generated among different structures, the diffusion and strength calculation of the degradation process can be greatly influenced by the interaction, the key of deep understanding of the degradation process is also realized, and the investigation finds that no relevant report is provided so far for researching the influence of the interaction of the internal structures in the degradation process on the degradation process. In view of this, the present embodiment provides a method for simulating and predicting a diffusion property change and a strength property change of a degradable polymer material in a degradation process, where the method is implemented by an electronic device, and the electronic device may be a terminal or a server. The execution flow of the polymer degradation process simulation and intensity calculation method is shown in fig. 1, and comprises the following steps:

s1, dividing the polymer material to be simulated and calculated into a plurality of cells by using a cellular automaton;

s2, acquiring state phase diagrams at different moments, judging the state of each cell, identifying two structural modes of a blocking amorphous phase and a blocking hole phase in the state phase diagrams based on the state of each cell, and respectively calculating the blocking ratios corresponding to the identified blocking amorphous phase and the blocking hole phase;

s3, based on the identification result of the structural mode and the identified blockage ratio of each structural mode, executing the diffusion process of each unit cell to the surrounding unit cells so as to realize the diffusion simulation of the polymer degradation process;

s4, obtaining intensity phase diagrams at different moments, judging the intensity state of each cell, identifying three intensity modes of an amorphous island, a crystalline island and an intensity cavity in the intensity phase diagrams based on the intensity state of each cell, and respectively calculating the surrounding ratio, the area and the density degree corresponding to the identified amorphous island and crystalline island, and the area and the density degree corresponding to the identified intensity cavity;

s5, calculating intensity values corresponding to the cells in different intensity states based on the identification result of the intensity mode and the surrounding ratio, the area and the density degree corresponding to each structure mode;

s6, calculating the total strength of the polymer material based on the strength values of the unit cells in different strength states.

It should be noted that, in step S1, the high polymer material is divided into N × N small grids by using a cellular automaton, and each small grid is called a cell, and the function of each small grid is to realize the discretization of the high polymer into the cells.

The state phase diagram in S2 is composed of LxL pixel points, each pixel is represented as a cell, each cell is initially set to include a long molecular chain, the pixel values of the pixel points represent cell states, and the specified cell states are divided into three types: amorphous phase, crystalline phase, pore phase; the amorphous phase is divided into a state that the initial long molecular chain of the cellular is not broken and a state that the chain is broken but the chain average molecular weight is larger than a threshold value, the crystalline phase represents a state that the chain is broken and the recrystallization is generated, and the pore phase represents a state that the chain is broken and the chain average molecular weight is smaller than the threshold value. The state threshold is determined by a computational fit.

The above-mentioned S2 to S3 are degradation simulations based on structure pattern recognition, where it should be noted that, in this embodiment, a dynamic interaction model based on different cellular state phases in the degradation process is designed, specifically: the molecular chain is broken and crystallized in the polymer degradation process, the cellular with the average molecular weight smaller than the threshold value after the breaking is defined as a hole, the molecules in the hole are called small molecules, the small molecules have higher diffusion effect, the crystallization is considered to have higher strength and can not be further degraded, when the crystallization is arranged around the hole, the diffusion of the small molecules in the hole can be blocked by the crystallization, so that the diffusion of the small molecules in the hole is weakened, the small molecules can form local acidity, so that the acidity around the blocked hole is enhanced, the acidity can promote the degradation of the surrounding cellular, so that continuous circulation can cause more holes and more crystallization to be formed around the original blocked hole, according to the crystallization amount, the blocked hole is proposed, and similarly, the non-crystallized cellular which is not broken and has the average molecular weight smaller than the threshold value in the broken cellular also has the diffusion effect, crystallization also has a blocking effect on it, so it is proposed to block the amorphous phase. And introducing a blockage ratio to express the blockage degree, and designing a diffusion coefficient according to the blockage ratio.

Specifically, in this embodiment, the simulation implementation process is as shown in fig. 2 and fig. 4, and includes the following steps:

step 1, reading state phase diagrams at different moments;

step 2, traversing from the origin of the state phase diagram coordinates, and judging the state of the cells on each pixel point;

step 3, identifying two structural modes (blocking amorphous phases and blocking holes) formed by pixel points in the same state in the state phase diagram according to an edge bounding algorithm, and obtaining the blocking ratio of the two structural modes;

step 4, updating the diffusion coefficient according to the two structure modes identified in the set of the step 3 and the corresponding blocking ratio, calculating the diffusion coefficient of the corresponding cell in the corresponding mode by using the updated diffusion coefficient, and if the blocking hole is contacted with the edge of the phase diagram, using a pipelining algorithm for the blocking hole;

and 5, executing the diffusion process of each cell to the surrounding cells according to the diffusion coefficient of the corresponding cell.

Further, the identification process for the blocked hole in step 3 is as follows:

s301, reading the state phase diagrams in sequence according to different time

S302, traversing from the origin of the coordinate of the cell,

s303, when the cell is a hole, pressing the cell to record the cell;

s304, when the stack is not empty, popping the hole cells in the stack, traversing according to the sequence of four neighborhoods of the upper right, the lower left and the right of the popped cell, respectively and cumulatively recording the number of crystalline phases and the number of non-hole phases in the four neighborhoods, and when holes exist in the four neighborhoods, sequentially pressing the holes into the same stack and recording the stack-pressing cells; when the stack is empty or the number of the recorded hole cells is greater than K (K is determined by experimental fitting), performing step S305, otherwise, continuing to perform step S304;

s305, marking all the recorded pore cells in S303 and S304 as a blocked pore phase, recording the perimeter of the blocked pore (the value of the perimeter is the number of the neighborhood non-pore phases recorded in the S304), recording the side length of the crystal contact (the value of the side length is the number of the neighborhood crystalline phases recorded in the S304), calculating the blocking ratio of the blocked pore, and adding the blocked pore into a set;

s306, when the cells are not traversed, clearing the stack of the S304, and executing S303 for next cell jump, otherwise, finishing the identification of all the blocking holes.

It should be noted that the above method is also a method for identifying a blocked amorphous phase, and only needs to replace hole traversal with amorphous phase traversal, and other operations remain unchanged.

Wherein the blocked amorphous phase refers to a region of amorphous phase surrounded by crystals, and as shown in fig. 7 (a), the blocking ratio of the blocked amorphous phase is defined as:

wherein N is_caIs the length of contact between the crystalline phase and the amorphous phase, N_aIs the perimeter of the amorphous phase.

The blocking pore phase refers to a region of the pore phase surrounded by crystals, and as shown in fig. 7 (b), the blocking ratio of the blocking pore phase is defined as:

wherein N is_chIs the length of the crystal phase in contact with the pore, N_hIs the perimeter of the pore phase.

The diffusion coefficient in step 4 is calculated as follows:

according to the identified blocking amorphous phase and blocking hole, updating the diffusion coefficients of the cells belonging to the two structural modes in a certain area, wherein the updating formula is as follows:

D＝R_a·D_p+R_h·D_ε

wherein D is the diffusion coefficient; d_pInitial diffusion coefficient in the amorphous phase, D_εIs the initial diffusion coefficient in the pore phase.

The diffusion formula for calculating the diffusion coefficient of short chains (the number of units on the polymer chain is less than 8) is as follows:

wherein, C_olIs a certain area is lowShort chain concentration; r_olThe number of oligomers in a cellular region; t represents time, div () is divergence, D is diffusion coefficient, and grad () is gradient.

With respect to a blocking hole, the running water algorithm means that when the blocking hole is in contact with the edge of the phase diagram, all the cellular diffusion coefficients in the blocking hole are set to 0, as shown in fig. 7 (c), indicating that it does not diffuse inside the polymer, but flows directly out of the polymer.

The intensity phase diagram in S4 is composed of LxL pixel points, the pixel values of the pixel points represent the cell intensity states, and the specified cell intensity states are divided into three types: an amorphous phase, a crystalline phase, and an unstressed phase, wherein the amorphous state is divided into a state in which the initial long molecular chain of the cell is not broken and a state in which the chain is broken but the chain average molecular weight is greater than the strength threshold, the crystalline state indicates a state in which the chain is broken and recrystallization occurs, and the pore state indicates a state in which the chain is broken and the chain average molecular weight is less than the strength threshold. The intensity threshold is determined by a computational fit.

The above S4 to S6 are intensity calculations based on intensity pattern recognition, where it should be noted that the embodiment designs a dynamic interaction model based on the intensity state phases of different cells in the degradation process, specifically: in terms of strength, when the amorphous phase is in contact with the crystalline phase around the non-orientation, the crystalline phase enhances the strength of the amorphous phase, and when the amorphous phase is in contact with the crystalline phase, the non-strength phase weakens the strength of the amorphous phase. Similarly for crystalline phases, the intensity of the surrounding non-intensity phase is reduced when present, so amorphous and crystalline islands are defined to represent the interaction between the current intensity phase and the surrounding different intensity phases. The strength void is defined to indicate a strength-free phase which itself only reduces strength, and the larger the area in which the strength-free phases in contact with each other are formed, the greater the strength-reducing effect.

Specifically, in the present embodiment, the intensity calculation process is as shown in fig. 3 and 5, and includes the following steps:

step 1, reading a strength phase diagram of a polymer to be calculated;

step 2, traversing from the origin of coordinates of the intensity phase diagram, and judging the intensity state of the cells on each pixel point;

and 3, identifying three intensity modes, namely an amorphous island consisting of amorphous phases, a crystalline island consisting of crystalline phases and an intensity cavity consisting of cavity phases in the intensity phase diagram according to an edge surrounding algorithm, and acquiring the surrounding ratio, the area and the density of the three intensity modes.

Step 4, calculating the intensities of the cells in different intensity states according to the surrounding ratio, the area and the density of different intensity modes and a pre-established intensity calculation model;

and 5, calculating the total strength of the polymer according to the cellular strengths in different strength states.

Further, the process of identifying the intensity pattern in step 3 is shown in fig. 6, and includes:

s501, reading the intensity phase diagrams in sequence according to different time

S502, traversing from the origin of the cell coordinates

S503, when the cellular is in an amorphous phase, the cellular is pushed and recorded;

s504, when the stack is not empty, the amorphous phase cells in the stack are ejected, traversal is performed according to the sequence of four neighborhoods, namely the upper right, the lower left and the lower left of the ejected cells, the number of crystalline phases, the number of holes and the number of all the non-amorphous phase cells in the four neighborhoods are respectively recorded in an accumulated mode, when the amorphous phase exists in the four neighborhoods, the amorphous phase cells are sequentially pushed, and the pushing cells are recorded; when the stack is empty or the number of the recorded cells is more than K (determined by calculation and fitting), the step S505 is carried out, otherwise, the step S504 is continuously executed;

s505, marking all the amorphous phase cells recorded in S503 and S504 as an amorphous island, recording the perimeter of the amorphous island (the value is the number of neighborhood non-amorphous phases recorded cumulatively in S504), recording the side length in contact with the crystal (the value is the number of neighborhood crystalline phases recorded cumulatively in S504), recording the side length in contact with the intensity null (the value is the number of neighborhood intensity null recorded cumulatively in S504), calculating the surrounding ratio of the amorphous island, and adding the amorphous island to the set;

and S506, when the cells are not traversed, clearing the stack of the S504, and jumping to the S503 for the next cell, otherwise, finishing the identification of all the amorphous islands.

It should be noted that the above describes the algorithm by taking amorphous islands as an example. The method is also a method for identifying the crystalline island mode and the intensity void, and only amorphous phase traversal is replaced by crystalline phase traversal and intensity void traversal, and attention needs to be paid to the following steps: for the crystalline island, step S503 is to calculate the surrounding ratio of the crystalline island by recording the side length of the crystalline island and the side length of the crystalline island, and count the crystalline island into the set; for intensity holes, step S503 is to directly record the intensity holes and count the intensity holes into the collection.

Wherein the amorphous island refers to a region of an amorphous phase surrounded by a crystalline phase and an intensity vacancy, as shown in (b) of fig. 8, wherein the crystallinity enhances the intensity of the amorphous phase region and the intensity vacancy attenuates the intensity of the amorphous phase region, defining the surrounding ratio of the amorphous phase:

wherein N is_sacAnd N_sahThe length of the sides of the crystalline phase and the intensity void phase, respectively, in contact with the current amorphous phase region, N_saThe perimeter of the current amorphous phase region.

The crystalline island refers to a block of crystalline region surrounded by an intensity void, and as shown in fig. 8 (a), the attenuation effect of the intensity void on the intensity of the crystalline phase is represented by the surrounding ratio of the crystalline island:

wherein N is_schRespectively the length of the edge of the strong void phase in contact with the region of the crystalline phase present, N_scThe perimeter of the current crystalline phase region.

The strength voids refer to a region composed of a bulk of strength voids interconnected with each other, as shown in fig. 8 (c), and the strength voids weaken the strength of the entire polymer.

Further, the present embodiment derives different phase diagrams from the definition of the intensity angle, and uses the phase diagrams as the input of three intensity pattern recognition algorithms, and traverses from the origin of the cell coordinates. When the area formed by the target pixels accords with the definition of the intensity mode, marking the area; respectively stored in the sets of respective patterns. As the pixels are traversed, the area (here in number of pixels), the surround ratio, and the degree of density of each intensity pattern are recorded. Based on the calculation of the mechanical strength of each cell, the material has the coexistence of crystalline state, amorphous state and pore state at the same time, and the strength calculation of three different strength states adopts different calculation formulas.

(1) Amorphous phase intensity model

For the amorphous phase intensity model, the intensity value includes two parts, one is the intensity of amorphous islands and the other is the intensity of conventional amorphous phase (intensity of amorphous islands removed from amorphous phase), and the intensity σ thereof is_aExpressed as:

σ_a＝σ_anp+σ_ap

wherein σ_apIs the strength, σ, of the amorphous islands_anpIs the strength of the conventional amorphous phase, alpha_aiIs the number of amorphous island patterns, S_aiIs the density of amorphous islands (expressed as the area of amorphous islands within a region), α_ahIs the area of the conventional amorphous phase, S_ahIs the density of the conventional amorphous phase (expressed asThe area of the conventional amorphous phase within a region). r is_aIs the amorphous island wrap ratio threshold. Gamma, eta, gamma₂、η₂Is a parameter related to the material property, the numerical value of which is determined by computational fitting, and L × L is the number of cells.

(2) Crystalline phase strength model

For the crystalline phase strength model, the strength value thereof includes two parts, one is the strength of the crystalline islands and the other is the strength of the conventional crystalline phase (the strength of the crystalline island portion removed in the crystalline phase), and the strength σ thereof is_cExpressed as:

σ_c＝σ_cnp+σ_cp

wherein σ_cpIs the strength of the crystalline islands, σ_cnpIs the strength of the conventional crystalline phase, alpha_ciIs the number of crystalline island patterns, S_ciIs the density of crystalline islands (expressed as the area of amorphous islands within a region), α_zcIs the area of the conventional crystalline phase, S_zcIs the density of the conventional crystalline phase (expressed as the area of amorphous phase within a region). r is_cIs the crystalline island wrap ratio threshold. Phi, phi,

φ2、

Is a parameter related to a material property. L × L represents the number of cells.

(3) Model of strength of empty phase

For the intensity model of the empty phase, its intensity σ_eExpressed as:

wherein alpha is_eiIs the number of intensity hole patterns, S_ciIs the density of the intensity voids (expressed as the number of intensity voids within a region), and μ, v are parameters related to the material properties. L × L represents the number of cells.

The final total intensity is the accumulation of intensity values in three states, the total intensity value is calculated as:

in the formula,

for the required total strength, X_a(t)、X_c(t)、X_eAnd (t) is the proportion of the unit cells in three states of amorphous, crystalline and empty phase to the total number of the unit cells. Sigma_a、σ_c、σ_eThe calculated intensities for amorphous islands, crystalline islands, and intensity voids as mentioned above.

The method for building the strength calculation model in advance in the step 4 comprises the following steps:

step 1, reading a strength phase diagram of a polymer for modeling;

step 2, traversing from the origin of coordinates of the intensity phase diagram for modeling, and judging the intensity state of the cells on each pixel point;

and 3, according to an edge surrounding algorithm, identifying the intensity pattern of the region formed by the pixel points in the same intensity state in the intensity phase diagram for modeling, and acquiring the surrounding ratio (the surrounding ratio is not required to be calculated for intensity holes), the area and the density of different intensity patterns

Step 4, calculating the intensities of the cells in different intensity states according to the intensity states of the cells and the initial value of the model;

step 5, calculating the total strength for modeling of the polymer according to the strength of the cells in different strength states;

and 6, comparing the total strength for modeling with the experimental value of the total strength of the polymer for modeling, and continuously adjusting the parameters of the model according to the comparison result to obtain the optimal model as the built model.

Further, in order to better understand the polymer degradation process simulation and strength calculation method proposed in this example, the following takes PLLA with initial crystallinity of 30%, 45% and 54% as an example to describe the polymer degradation process simulation and strength calculation method proposed in this example in detail:

example 1

Setting the initial strength at 50MPa, the initial molecular weight Mn0 at 5.143x10^5g/mol and the initial crystallinity of the material at 30%. The degradation probability p is set to 0.16, the calculation parameters in the combination of the multiple-term intensity model are subjected to model fitting, and gamma, eta and gamma are obtained₂、η₂Set to 2.4, 4.1, 1.4 and 0.5 respectively, phi,

φ₂、

Are respectively set as 8, 3.7, 2, 2.1, r_aAnd r_cSet to 0.45 and 0.6. A portion of the phase diagram is selected and observed for changes in state over different time periods, as shown in fig. 9. Selecting a part of the intensity phase diagram, observing the change of the intensity in different time periods, as shown in fig. 10, comparing the simulated values of the molecular weight, the crystallinity and the intensity with the experimental values, and obtaining a better fitting effect, as shown in fig. 11.

The method comprises the following specific steps:

(1) reading the state phase diagram according to different phase diagrams at different moments;

(2) after structural pattern recognition, the blocking ratio is calculated and diffusion is performed

(3) Reading an intensity phase diagram according to different phase diagrams at different moments;

(4) after intensity pattern recognition is carried out, the surrounding ratio and the number of patterns are calculated, and the total area of the patterns is substituted into a matched intensity calculation formula;

(5) calculating the ratio of the number of the cells of each intensity mode to the total number of the cells, and taking the product of the ratio and the intensity value as a final intensity value;

(6) adding the intensity values in the third intensity state to obtain a total intensity value of the material;

(7) and comparing the simulated intensity value with the experimental intensity value, and continuously optimizing parameters to obtain an optimal model.

Example 2

An initial strength of 49MPa, an initial molecular weight Mn0 of 5.0x10^5g/mol, and an initial material crystallinity of 45%. The degradation probability p is set to 0.16, the calculation parameters in the combination of the multiple-term intensity model are subjected to model fitting, and gamma, eta and gamma are obtained₂、η₂Set to be 3.8, 4.2, 1.1 and 0.7 respectively phi,

φ2、

Are respectively set as 8.1, 4.6, 2.4, 1.8, r_aAnd r_cSet to 0.4 and 0.62. The simulated values of molecular weight, crystallinity and strength were compared with the experimental values, and the fitting effect was better, as shown in fig. 11.

Example 3

An initial strength of 56MPa, an initial molecular weight Mn0 of 5.842x10^5g/mol, and an initial material crystallinity of 54% were set. Setting the degradation probability p to 0.05, fitting the calculation parameters in the combination of the multiple-term intensity model by the model, and carrying out gamma, eta and gamma₂、η₂Set to be 3.0, 4.0, 2.0 and 1.1, phi,

φ₂、

Are respectively set as 8.3, 4.5, 2.5, 1.6, r_aAnd r_cSet at 0.42 and 0734. The simulated values of molecular weight, crystallinity and strength were compared with the experimental values, and the fitting effect was better, as shown in fig. 12.

In summary, the polymer degradation process simulation and strength calculation method of this embodiment divides the polymer material into N × N small grids by using the cellular automata, each small grid is called a cell, and the polymer material is divided into: amorphous phase, crystalline phase, and void phase, wherein when the crystalline phase wraps the amorphous phase or the void phase, the diffusion of the amorphous phase or the void phase is blocked, and the surrounding acidity is increased to increase the degradation probability. In terms of intensity, it is divided into: amorphous strength phase, crystalline strength phase, strength void phase, generally, crystalline phase is the highest in strength throughout the interior of the material, but when a large amount of strength void phase is wrapped around the crystals, the crystals will loosen within the interior of the material, greatly weakening the strength of the material as a whole, as well as for the amorphous phase. Therefore, the embodiment proposes concepts of a structure mode and an intensity mode in a degradation process according to the structure evolution in the degradation process, identifies the structure mode and the intensity mode in an image processing mode, proposes a structure mode identification algorithm and an intensity mode identification algorithm, and proposes a running water algorithm by considering some special conditions of the structure mode, so as to identify two structure mode characteristics of a blocking hole and a blocking amorphous phase in a state diagram and three intensity mode characteristics of an amorphous island, a crystalline island and an intensity cavity in the intensity diagram, and perform diffusion simulation of the degradation process according to the blocking hole and the blocking amorphous phase characteristics; and establishing and calculating a strength model according to the characteristics of the amorphous island, the crystalline island and the strength cavity. Model calculation is compared with experimental data, the simulation value of the model is well matched with the experimental value, and the extraction of the structural mode characteristics and the strength mode characteristics is feasible for the degradation simulation.

Second embodiment

The present embodiment provides an electronic device, which includes a processor and a memory; wherein the memory has stored therein at least one instruction that is loaded and executed by the processor to implement the method of the first embodiment.

The electronic device may have a relatively large difference due to different configurations or performances, and may include one or more processors (CPUs) and one or more memories, where at least one instruction is stored in the memory, and the instruction is loaded by the processor and executes the method.

Third embodiment

The present embodiment provides a computer-readable storage medium, in which at least one instruction is stored, and the instruction is loaded and executed by a processor to implement the method of the first embodiment. The computer readable storage medium may be, among others, ROM, random access memory, CD-ROM, magnetic tape, floppy disk, optical data storage device, and the like. The instructions stored therein may be loaded by a processor in the terminal and perform the above-described method.

Furthermore, it should be noted that the present invention may be provided as a method, apparatus or computer program product. Accordingly, embodiments of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, embodiments of the present invention may take the form of a computer program product embodied on one or more computer-usable storage media having computer-usable program code embodied in the medium.

Embodiments of the present invention are described with reference to flowchart illustrations and/or block diagrams of methods, terminal devices (systems), and computer program products according to embodiments of the invention. It will be understood that each flow and/or block of the flow diagrams and/or block diagrams, and combinations of flows and/or blocks in the flow diagrams and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, embedded processor, or other programmable data processing terminal to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing terminal, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing terminal to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks. These computer program instructions may also be loaded onto a computer or other programmable data processing terminal to cause a series of operational steps to be performed on the computer or other programmable terminal to produce a computer implemented process such that the instructions which execute on the computer or other programmable terminal provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.

It should also be noted that, in this document, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or terminal that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or terminal. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, method, article, or terminal that comprises the element.

Finally, it should be noted that while the above describes a preferred embodiment of the invention, it will be appreciated by those skilled in the art that, once the basic inventive concepts have been learned, numerous changes and modifications may be made without departing from the principles of the invention, which shall be deemed to be within the scope of the invention. Therefore, it is intended that the appended claims be interpreted as including preferred embodiments and all such alterations and modifications as fall within the scope of the embodiments of the invention.

Claims (10)

1. A method for simulating and calculating strength of a polymer degradation process is characterized by comprising the following steps:

dividing a polymer material to be simulated and calculated into a plurality of cells by using a cellular automaton;

acquiring state phase diagrams at different moments, judging the state of each cell, identifying two structural modes, namely a blocking amorphous phase and a blocking hole phase, in the state phase diagrams based on the state of each cell, and respectively calculating the respective corresponding blocking ratios of the identified blocking amorphous phase and the blocking hole phase;

performing a diffusion process of each cell to surrounding cells based on the recognition result of the structural pattern and the recognized blocking ratio of each structural pattern to realize diffusion simulation of the polymer degradation process;

acquiring intensity phase diagrams at different moments, judging the intensity state of each cell, identifying three intensity modes of an amorphous island, a crystalline island and an intensity cavity in the intensity phase diagrams based on the intensity state of each cell, and respectively calculating the surrounding ratio, the area and the density degree corresponding to the identified amorphous island and crystalline island, and the area and the density degree corresponding to the identified intensity cavity;

calculating intensity values corresponding to the cells in different intensity states based on the identification result of the intensity mode and the surrounding ratio, the area and the density degree corresponding to each structure mode;

and calculating the total strength of the polymer material based on the strength values of the cells in different strength states.

2. The method of polymer degradation process simulation and intensity calculation of claim 1, wherein the blocked amorphous phase refers to a region of amorphous phase surrounded by crystals;

the blocking pore phase refers to a pore phase region surrounded by crystals.

3. The method of polymer degradation process simulation and intensity calculation of claim 2, wherein the blocking ratio R of the blocked amorphous phase_aCalculated by the following formula:

wherein N is_caIs the length of contact between the crystalline phase and the amorphous phase, N_aIs the perimeter of the amorphous phase.

4. The method of polymer degradation process simulation and intensity calculation of claim 3, wherein the plugging pore has a plugging ratio R_hCalculated by the following formula:

wherein N is_chIs the length of the crystal phase in contact with the pore, N_hIs the perimeter of the pore phase.

5. The method for polymer degradation process simulation and intensity calculation according to claim 4, wherein the performing of the diffusion process of each cell to the surrounding cells based on the recognition result of the structural pattern and the recognized blocking ratio of each structural pattern to realize the diffusion simulation of the polymer degradation process comprises:

calculating the diffusion coefficient of the corresponding cell in the corresponding structural mode by using the updated diffusion coefficient according to the identification result of the structural mode and the identified blocking ratio of each structural mode; wherein for a plugged pore that is in contact with the edge of the phase diagram, all of the cellular diffusion coefficients therein are set to 0;

and executing the diffusion process of each unit cell to the surrounding unit cells according to the diffusion coefficient of the corresponding unit cell.

6. The method of polymer degradation process simulation and intensity calculation of claim 5, wherein the calculating the diffusion coefficient of the corresponding cell in the corresponding structural mode using the updated diffusion coefficient comprises:

according to the identified blocking amorphous phase and the blocking pore, updating diffusion coefficients of cells belonging to the two structural modes in a certain area, wherein the updating formula is as follows:

D＝R_a·D_p+R_h·D_ε

wherein D is the updated diffusion coefficient; d_pAs initial diffusion coefficient in amorphous phase, D_εIs the initial diffusion coefficient, R, in the pore phase_aTo block the blocking ratio of the amorphous phase, R_hIs the plugging ratio of the plugged hole;

the formula for calculating the diffusion of short chains is:

wherein, C_olLow short chain concentration in a certain area; r_olThe number of oligomers in a cellular region; t represents time, div () is divergence, D is diffusion coefficient, and grad () is gradient.

7. The polymer degradation process simulation and intensity calculation method of claim 1, wherein the amorphous islands refer to a region of an amorphous phase surrounded by a crystalline phase and an intensity void phase;

the crystallization island refers to a crystallization area surrounded by strength empty phase;

the strength void refers to a region composed of a whole block of strength voids which are interconnected.

8. The method of polymer degradation process simulation and intensity calculation of claim 7, wherein the amorphous islands have a rounding ratio R_saCalculated by the following formula:

wherein N is_sacAnd N_sahCrystalline phase and strong phase respectively in contact with the current amorphous phase regionLength of side of dimensional space phase, N_saThe perimeter of the current amorphous phase region.

9. The method of polymer degradation process simulation and intensity calculation of claim 8, wherein the crystalline islands have a rounding ratio R_scCalculated by the following formula:

wherein N is_schLength of the edge of the strong void phase in contact with the region of the currently crystalline phase, N_scThe perimeter of the current crystalline phase region.

10. The method for polymer degradation process simulation and intensity calculation according to any one of claims 1 to 9, wherein the calculating of the intensity values corresponding to the cells in different intensity states based on the recognition result of the intensity pattern and the surrounding ratio, the area and the density degree corresponding to each structure pattern comprises:

the strength pattern of the cells comprises amorphous phases, crystalline phases and strength voids;

when the intensity pattern of the unit cell is an amorphous phase, the intensity σ thereof_aExpressed as:

σ_a＝σ_anp+σ_ap

wherein σ_apIs the strength, σ, of the amorphous islands_anpIs the strength of the conventional amorphous phase, alpha_aiIs the number of amorphous islands, S_aiIs the density of amorphous islands, alpha_ahIs conventional withoutArea of the shape phase, S_ahIs the density of the conventional amorphous phase, r_aIs the amorphous island wrap ratio threshold; gamma, eta, gamma₂、η₂The parameters related to the polymer material properties are obtained, the numerical values of the parameters are determined by calculation fitting, and L multiplied by L is the number of the unit cells;

when the intensity pattern of the unit cell is a crystalline phase, the intensity σ thereof_cExpressed as:

σ_c＝σ_cnp+σ_cp

wherein σ_cpIs the strength of the crystalline islands, σ_cnpIs the strength of the conventional crystalline phase, alpha_ciIs the number of crystalline islands, S_ciIs the density of crystalline islands, alpha_zcIs the area of the conventional crystalline phase, S_zcIs the density of the conventional crystalline phase, r_cIs the threshold of the crystal island surrounding ratio, phi,

φ₂、

Is a parameter related to the properties of the polymer material;

when the intensity pattern of the unit cell is an intensity hole, the intensity σ thereof_eExpressed as:

wherein alpha is_eiIs the number of strength voids, S_eiIs the density of the strength voids, λ, v and the polymer material propertiesThe relevant parameters, the numerical values of which are determined by calculation fitting, and L multiplied by L is the number of the cells;

the total strength of the polymer material is calculated based on the strength values of the cells in different strength states, and the expression is as follows:

wherein,

for the total strength value of the polymer material to be calculated, X_a(t)、X_c(t)、X_e(t) is the ratio of the number of unit cells in the amorphous islands, the crystalline islands and the strength voids to the total unit cells, respectively.

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