CN105868563A - Modeling and simulating method for degradation process of degradable high polymer material - Google Patents

Abstract

The invention provides a modeling and simulating method for the degradation process of a degradable polymer material. Modeling methods for coupling at three different scales including the microcosmic scale, the mesoscopic scale and the macroscopic scale are established for simulating the degradation process of the degradable polymer material. The method comprises the steps that firstly, the macroscopic polymer material is dispersed into mesoscopic cells, wherein each cell comprises at least one polymer chain; secondly, a microcosmic polymer chain degradation reaction is simulated on the cells to make the polymer chains in the cells broken and crystallized, and polymer chain breaking and crystallizing results are coupled to the corresponding cells to change the states and chain numbers of the corresponding cells; thirdly, diffusion of low polymers in the corresponding cells and dissolving of small molecules in the corresponding cells are simulated on the macroscopic scale, and the chain numbers and the molecular weights of the corresponding cells are updated; fourthly, the second step is carried out again to enter a next round of iteration to continue to simulate microcosmic polymer chain degradation reactions until preset ending conditions are met. The modeling and simulating method is suitable for the technical field of degradable polymer materials.

Description

A kind of modeling and simulation method of degradable high polymer material degradation process

Technical field

The present invention relates to degradable high polymer material technical field, particularly medical slow-released system, organizational project prop up The modeling and simulation method of the degradable high polymer material degradation process that the fields such as frame use.

Background technology

In recent years, Biodegradable high-molecular polymer, such as, polylactic acid (polylactic acid, PLA), PVOH Acid (PGA, Polyglycolic acido) etc. and copolymer thereof, due to its fix at bioabsorbable suture material, orthopaedics, Remarkable advantage in drug sustained release system and tissue engineering bracket and enjoy extensive concern.By degradable high polymer material (by height The material that Molecularly Imprinted Polymer is made, described degradable high polymer material hereinafter referred macromolecular material) screw (the described screw that does It is made up of macromolecular material, belongs to macromolecule device) fixing for fracture operation, after bone heals well, nail can be certainly Row degraded, eliminates patient's re-treatm ent and takes out the secondary misery of nail；The support being made up of degradable high polymer for Cell grows into autologous tissue, is the significant innovation of future medicine, and these application success are used in clinic, at very great Cheng Depend on degree that can the degradation rate of high molecular polymer with medicament slow release speed, osteogenesis speed or the growth of cell tissue Speed is consistent, i.e. can the degradation rate of degradable high polymer be controlled.

The degradation process of high molecular polymer (being called for short, high polymer) is commonly considered as experiencing two processes: be first at water Under the attack of molecule, high polymer long chain hydrolytic cleavage becomes short chain, degrades further, ultimately generate nothing under the effect of enzyme The water of evil and carbon dioxide.Wherein first stage hydrolysis will directly affect shape and the Strength Changes of high polymer, thus high The control of polymers degradation rate depends primarily on first stage i.e. hydrolysis stage.The degradation process week of the technique study high polymer of experiment Phase is oversize, and the self-catalyzed reaction in hydrolytic process makes various sizes of polymer degradation speed the most different, thus increases A lot of workloads are with uncertain.The method of microcomputer modelling can make cycle time, and can provide more rich degraded Process data causes the concern of a lot of researcher.

In prior art, the modeling method of degradable high polymer material degradation process is also from traditional single diffusion, change Learning the Macro Mechanism model that the phenomenons such as reaction, quality transmission are set out, Monte Carlo model (MC), cellular that micro-(or Jie) is seen are automatic Machine model (CA) etc. develops into macroscopical and micro-(or Jie) and sees the model combining or combining with quality transmission at random.But on, State modeling method typically from single yardstick, degradable high polymer material degradation process to be modeled, it is impossible to reflection degradable high score The real degradation process of sub-material.

Summary of the invention

The technical problem to be solved in the present invention is to provide the modeling and simulation of a kind of degradable high polymer material degradation process Method, it is possible to from microcosmic, be situated between and see and the degradation process of three scale simulation degradable high polymer materials of macroscopic view.

For solve above-mentioned technical problem, the embodiment of the present invention provide a kind of degraded macromolecular material degradation process modeling with Emulation mode, including:

S1, by discrete for the macromolecular material macroscopically cellular for the sight that is situated between, wherein, each unit intracellular includes that at least one is high Strand；

S2, simulates microcosmic macromolecular chain degradation reaction on described cellular and the macromolecular chain in cellular is ruptured, crystallizes, And the fracture of described macromolecular chain, crystalline results are coupled on the cellular of correspondence, change state and the chain number of corresponding cellular；

S3, in macroscopically simulating described corresponding cellular, the diffusion of oligomer and described corresponding cellular small molecular is molten Solve, and update chain number and the molecular weight of described corresponding cellular；

S4, returns S2, enters next round iteration and continues simulation microcosmic macromolecular chain degradation reaction until meeting the end preset Only condition.

Further, described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular Fracture, and described macromolecular chain fracture result is coupled on the cellular of correspondence, before changing state and the chain number of corresponding cellular, Including:

Use monte carlo method, by random number r₁And r₂Random acquisition next described microcosmic macromolecular chain degraded is anti- The moment △ t answered and the macromolecular chain μ participating in described next microcosmic macromolecular chain degradation reaction:

$\mathrm{\Δ}t=\frac{1}{\underset{v=1}{\overset{M}{\Σ}}{\mathrm{\α}}_v}ln\left(\frac{1}{r_1}\right)$

$\underset{v=1}{\overset{\mathrm{\&mu;}-1}{\&Sigma;}}{\mathrm{\&alpha;}}_v<r_2\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v\&le;\underset{v=1}{\overset{\mathrm{\&mu;}}{\&Sigma;}}{\mathrm{\&alpha;}}_v$

In formula, r₁、r₂Belong to (0,1],Middle α_v=π_vX_vX_W, π_vRepresent and participate in the v microcosmic macromolecular chain degraded instead The speed constant answered, X_vRepresent the molecular number of the high molecular polymer participating in the v microcosmic macromolecular chain degradation reaction, X_WRepresent The water yield, M represents the maximum number of macromolecular chain in macromolecular material；

The described macromolecular chain participating in next described microcosmic macromolecular chain degradation reaction obtained is mapped to correspondence Cellular；

Wherein, described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular break Split, and described macromolecular chain fracture result is coupled on the cellular of correspondence, before changing state and the chain number of corresponding cellular, also Including:

Judge whether the cellular of described correspondence and neighbours' cellular thereof exist oligomer；

If there is not oligomer, then the fracture mode of the macromolecular chain μ participating in described microcosmic macromolecular chain degradation reaction is Tip breakages；

If there is oligomer, then participate in described microcosmic macromolecular chain degradation reaction macromolecular chain μ fracture mode for Machine ruptures；

Wherein, described oligomer is the short chain that the degree of polymerization that macromolecular chain fracture produces is less than the first predetermined threshold.

Further, the state of described cellular includes: unformed state, chain interruption state, hole state or crystalline state；

Described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and will Described macromolecular chain fracture result is coupled on the cellular of correspondence, changes state and the chain number of corresponding cellular, including:

High score during simulation microcosmic macromolecular chain degradation reaction makes the cellular of described correspondence on the cellular of described correspondence Subchain μ ruptures, and records the chain number change in the described corresponding cellular that described microcosmic macromolecular chain degradation reaction produces, and by institute The information stating the change of chain number is coupled to be situated between on the cellular seen, and updates state and the chain number of cellular, and wherein, described chain number includes: high The number of strand and the number of crystallization chain.

Further, the described crystallization chain recorded in the described corresponding cellular that described microcosmic macromolecular chain degradation reaction produces Number, including:

Obtain the number of the macromolecular chain of described corresponding element intracellular fracture；

By probability multiplication total Yu predetermined for the macromolecular chain of the described corresponding element intracellular fracture obtained, obtain unit's intracellular knot The number of brilliant chain.

Further, described in obtain unit intracellular concretion chain chain number after, including:

If the number of described corresponding element intracellular concretion chain is more than with the ratio of the number of described corresponding element intracellular macromolecular chain Second predetermined threshold, the state of the most described corresponding cellular is crystalline state.

Further, the described diffusion of oligomer in macroscopically simulating described corresponding cellular, including:

The diffusion equation seeing macroscopic view oligomer according to being situated between obtains the diffusing capacity of oligomer in described corresponding cellular；Wherein, Described diffusion equation is expressed as:

$\frac{{\mathrm{dc}}_{ol}}{dt}=\frac{{\mathrm{dR}}_{ol}}{dt}+div\&lsqb;Dgrad\left(c_{ol}\right)\&rsqb;$

In formula, R_olRepresent the number of the oligomer of microcosmic macromolecular chain degradation reaction generation, c_olRepresent oligomer concentration, D Represent diffusion coefficient；

Wherein, given an account of the diffusion equation employing calculus of differences seeing macroscopic view oligomer, used than cellular big some multiples Coarse grid calculate to keep seriality, and use time step more than monte carlo method employing time step.

Further, described diffusion coefficient D is expressed as:

D=D_P+(1.3ε²-0.3ε³)×(D_ε-D_P)；

Wherein, D_P=D₀(1-X_C), D_PRepresent oligomer diffusion coefficient in polymeric matrix, D₀Represent high molecular polymerization The diffusion coefficient of thing substrate amorphous regions, X_CRepresent degree of crystallinity；D_εRepresenting oligomer diffusion coefficient in hole, ε represents hole Gap rate.

Further, porosity ε (t) of t is expressed as:

$\mathrm{\&epsiv;}\left(t\right)=\frac{Z\left(t\right)}{n\&times;n}$

$Z\left(t\right)=\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}\mathrm{\&psi;}(i,j,t)$

Wherein, (i, j, (i, j) state is hole to the cellular of t)=1 expression t to ψ, and (i, j, t)=0 represents t to ψ (i, j) state is not hole to cellular；Z (t) represents the cellular number that t state is hole, and n represents every string or every a line net Lattice/cellular number.

Further, described medium and small according to diffusing capacity and the described corresponding cellular of oligomer in the described corresponding cellular obtained The meltage of molecule, feeds back to be situated between and sees cellular, after updating chain number and the molecular weight of cellular, including:

Calculate mean molecule quantity by all cellulars, obtain the molecular weight of macromolecular material

${\stackrel{\&OverBar;}{M}}_n\left(t\right)=\frac{1}{M_{n0}\&CenterDot;n^2}\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}{M}_n(i,j,t)$

Wherein, M_n0It is the initial molecular weight of macromolecular material, M_n(i, j t) represent t cellular (i, molecular weight j).

Having the beneficial effect that of the technique scheme of the present invention:

In such scheme, by by discrete for the degradable high polymer material macroscopically cellular for the sight that is situated between；Then, described Simulating microcosmic macromolecular chain degradation reaction on cellular makes the macromolecular chain in cellular rupture, and by described macromolecular chain fracture knot Fruit is coupled on the cellular of correspondence, changes state and the chain number of corresponding cellular；Also needing realizes being situated between further sees the coupling of macroscopic view, The diffusion of oligomer and the dissolving of described corresponding cellular small molecular in macroscopically simulating described corresponding cellular, and update described The chain number of corresponding cellular and molecular weight；Finally, it may be judged whether meet the end condition preset, if being unsatisfactory for the termination bar preset Part, then enter next round iteration and continue simulation microcosmic macromolecular chain degradation reaction until meeting the end condition preset.Thus real The modeling that existing microcosmic, the sight that is situated between, three different scales of macroscopic view are coupled, thus emulate degradable high polymer material and degraded really Journey, for degradable high polymer material application provide support.

Accompanying drawing explanation

The stream of the modeling and simulation method of the degradable high polymer material degradation process that Fig. 1 provides for the embodiment of the present invention one Cheng Tu；

The signal of the modeling and simulation method of the degradable high polymer material degradation process that Fig. 2 provides for the embodiment of the present invention Figure；

The enforcement of the modeling and simulation method of the degradable high polymer material degradation process that Fig. 3 provides for the embodiment of the present invention Flow chart；

Fig. 4 (a) is that the embodiment of the present invention two simulates degradation process at cellular initial configuration schematic diagram；

Fig. 4 (b) is that the embodiment of the present invention two simulates degradation process cellular form schematic diagram when 5 weeks；

Fig. 4 (c) is that the embodiment of the present invention two simulates degradation process cellular form schematic diagram when 10 weeks；

Fig. 4 (d) is that the embodiment of the present invention two simulates degradation process cellular form schematic diagram when 15 weeks；

Fig. 4 (e) is that the embodiment of the present invention two simulates degradation process cellular form schematic diagram when 20 weeks；

Fig. 4 (f) is that the embodiment of the present invention two simulates degradation process cellular form schematic diagram when 25 weeks；

Fig. 4 (g) is that the embodiment of the present invention two simulates degradation process cellular form schematic diagram when 30 weeks；

Fig. 5 is that the embodiment of the present invention two is simulated degradation process molecular weight and schemed over time；

Fig. 6 (a) is that the embodiment of the present invention three simulates degradation process at cellular initial configuration schematic diagram；

Fig. 6 (b) is that the embodiment of the present invention three simulates degradation process cellular form schematic diagram when 30 days；

Fig. 6 (c) is that the embodiment of the present invention three simulates degradation process cellular form schematic diagram when 60 days；

Fig. 6 (d) is that the embodiment of the present invention three simulates degradation process cellular form schematic diagram when 120 days；

Fig. 6 (e) is that the embodiment of the present invention three simulates degradation process cellular form schematic diagram when 210 days；

Fig. 6 (f) is that the embodiment of the present invention three simulates degradation process cellular form schematic diagram when 240 days；

Fig. 6 (g) is that the embodiment of the present invention three simulates degradation process cellular form schematic diagram when 270 days；

Fig. 7 (a) is that the embodiment of the present invention three is simulated degradation process molecular weight and changed over schematic diagram；

Fig. 7 (b) is that the embodiment of the present invention three is simulated degradation process degree of crystallinity and changed over schematic diagram；

Fig. 8 (a-1) is that the embodiment of the present invention three simulates the degradation process molecular weight original distribution schematic diagram at cellular；

Fig. 8 (a-2) is that the embodiment of the present invention three simulates degradation process molecular weight original distribution density schematic diagram；

Fig. 8 (b-1) be the embodiment of the present invention three simulate degradation process when 120 days molecular weight at the distribution schematic diagram of cellular；

Fig. 8 (b-2) is that the embodiment of the present invention three simulates degradation process molecular weight distribution density schematic diagram when 120 days；

Fig. 8 (c-1) be the embodiment of the present invention three simulate degradation process when 210 days molecular weight at the distribution schematic diagram of cellular；

Fig. 8 (c-2) is that the embodiment of the present invention three simulates degradation process molecular weight distribution density schematic diagram when 210 days；

Fig. 8 (d-1) be the embodiment of the present invention three simulate degradation process when 300 days molecular weight at the distribution schematic diagram of cellular；

Fig. 8 (d-2) is that the embodiment of the present invention three simulates degradation process molecular weight distribution density schematic diagram when 300 days.

Detailed description of the invention

For making the technical problem to be solved in the present invention, technical scheme and advantage clearer, below in conjunction with accompanying drawing and tool Body embodiment is described in detail.

Embodiment one

Referring to shown in Fig. 1, the modeling of a kind of degradable high polymer material degradation process that the embodiment of the present invention provides is with imitative True method, including:

S1, by discrete for the macromolecular material macroscopically cellular for the sight that is situated between, wherein, each unit intracellular includes that at least one is high Strand；

In the embodiment of the present invention, for example, it is possible to by macroscopic view macromolecular material with cellular automation method discrete as n × n Individual cellular/the grid seen that is situated between, as in figure 2 it is shown, set up the mesoscopic model of macromolecular material, each unit intracellular includes that at least one is high Strand, wherein, n represents every string or the lattice number of every a line, and each grid represents a cellular, is positioned at the i-th row jth row Cellular can be expressed as that (i, j), stress and strain model the thinnest, yardstick is the least, and amount of calculation is the biggest.Ready-portioned cellular passes through Physics, chemical mechanism that cellular contains and constitute dynamically/iteration Evolution System, wherein, described dynamic evolution system has as follows Several key elements:

(1) cellular

Cellular is the elementary cell of this dynamic evolution system, and each cellular has the state of oneself, and all cellulars may The collection that the state occurred is constituted is collectively referred to as cellular state space.Physics that each cellular contains, chemical quantity constitute the attribute of cellular, It is linear that what cellular was discrete be distributed in, in plane or Spatial Dimension, according to the state of neighbours' cellular and predetermined transformation rule from State change is carried out in the time gap dissipated.

(2) cellular state

Generally, in real calculating simulation is applied, cellular state is defined as the discrete of an integer form Collection { k₁, k₂..., k_v-1, k_v, wherein v is all status numbers being likely to occur.Each k_vThere is a mapped reality Meaning.Such as, in the embodiment of the present invention, there are 4 states in cellular evolutionary process, and such as, state " 1 " can represent macromolecule material Undegradable amorphous regions in material, state " 0 " can represent in cellular and there occurs that chain interruption is reacted, and state "-1 " can represent The diffusion of short chain in macromolecular material and define hole, state "-2 " can represent the crystal region in macromolecular material, with x generation List cell born of the same parents (i, j) in the state of t, can be expressed as:

(3) cellular space and cellular neighbours

Cellular space refers to be arranged in linearly by cellular with the form of site, institute on plane or three-dimensional Euclidean space The set formed.The surrounding of self cellular is referred to as cellular neighbours, common, such as 4 neighbours' structures, 8 neighbours' structures etc., it is preferable that The embodiment of the present invention uses 4 neighbours' structures to carry out evolution iteration.

(4) cellular attribute

Physics in the dynamic evolution system of cellular, the evolution of chemical process are the cores of whole modeling and simulation method. The embodiment of the present invention introduces physics that cellular had, chemical attribute to participate in cellular on the basis of cellular automation method Dynamic Evolution, react the physics in true degradation process, chemical change with this so that simulation result is the most reliable； Physics contained by cellular, chemical parameters are referred to as cellular attribute by the embodiment of the present invention.Described cellular attribute includes: Mei Geyuan The molecular weight M that born of the same parents have_n(i, j, t), chain number N (i, j, t), all cellular crystalline states statistics crystallinity X_c(t), wherein, cellular The chain number in each moment can count cellular molecular weight and the distribution thereof in degradation process each moment.

(5) transformational rule

Transformational rule refers to that the evolution condition according to current time self cellular and neighbours' cellular thereof calculates subsequent time The rule of cellular evolutionary process；Transformational rule is to combine physics in cellular evolutionary process to make with the change of chemical attribute herein Fixed, wherein, it is intended that transformation rule can be:

A) state of the initial amorphous regions of cellular is set to " 1 ", and the state of crystal region is set to "-2 "；

B) unit's intracellular has chain interruption chemical reaction to occur, and this cellular state changes " 0 " into；

If c) degree of first intracellular link crystalline substance is more than 90%, then this cellular state is changed into crystalline state "-2 "；

If d) the weight loss of this cellular is to the 40% of not enough original weight, it is believed that this cellular be changed into hole state "- 1”。

S2, simulates microcosmic macromolecular chain degradation reaction on described cellular and the macromolecular chain in cellular is ruptured, and will Described macromolecular chain fracture result is coupled on the cellular of correspondence, changes state and the chain number of corresponding cellular；

S3, the diffusion of oligomer and the dissolving of described corresponding cellular small molecular in macroscopically simulating described corresponding cellular The weight loss produced, and update chain number and the molecular weight of described corresponding cellular；

In the embodiment of the present invention, being shown by research, in degradation process, the weight loss of macromolecular material is not only due to In cellular, the diffusion of oligomer causes, it is also possible to the little molecular melting broken to form by macromolecular chain causes；Wherein, described Little molecule refers to that the degree of polymerization that macromolecular chain breaks to form is less than the short chain of the marginal value preset.

S4, returns S2, enters next round iteration and continues simulation microcosmic macromolecular chain degradation reaction until meeting the end preset Only condition.

The modeling and simulation method of the degradable high polymer material degradation process described in the embodiment of the present invention, by by macroscopic view On degradable high polymer material discrete for be situated between see cellular；Then, described cellular is simulated the degraded of microcosmic macromolecular chain anti- The macromolecular chain in cellular should be made to rupture, and described macromolecular chain fracture result be coupled on the cellular of correspondence, it is right to change Answer state and the chain number of cellular；Also needing realizes being situated between further sees the coupling of macroscopic view, in macroscopically simulating described corresponding cellular The diffusion of oligomer and the weight produced of dissolving of described corresponding cellular small molecular are lost, and update the chain of described corresponding cellular Number and molecular weight；Finally, it may be judged whether meeting the end condition preset, if being unsatisfactory for the end condition preset, then entering next Wheel iteration continues simulation microcosmic macromolecular chain degradation reaction until meeting the end condition preset.Be achieved in microcosmic, be situated between see, grand See the modeling that is coupled of three different scales, thus emulate the real degradation process of degradable high polymer material, high for degradable The application of molecular material provides to be supported.

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and by described Macromolecular chain fracture result is coupled on the cellular of correspondence, before changing state and the chain number of corresponding cellular, including:

Use monte carlo method, by random number r₁And r₂Random acquisition next described microcosmic macromolecular chain degraded is anti- The moment △ t answered and the macromolecular chain participating in described next microcosmic macromolecular chain degradation reaction:

$\mathrm{\&Delta;}t=\frac{1}{\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v}ln\left(\frac{1}{r_1}\right)$

$\underset{v=1}{\overset{\mathrm{\&mu;}-1}{\&Sigma;}}{\mathrm{\&alpha;}}_v<r_2\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v\&le;\underset{v=1}{\overset{\mathrm{\&mu;}}{\&Sigma;}}{\mathrm{\&alpha;}}_v$

In formula, r₁、r₂Belong to (0,1],Middle α_v=π_vX_vX_W, π_vRepresent and participate in the v microcosmic macromolecular chain degraded instead The speed constant answered, X_vRepresent the molecular number of the high molecular polymer participating in the v microcosmic macromolecular chain degradation reaction, X_WRepresent The water yield, M represents the maximum number of macromolecular chain in macromolecular material；

The described macromolecular chain participating in next described microcosmic macromolecular chain degradation reaction obtained is mapped to correspondence Cellular.

In the embodiment of the present invention, in each unit intracellular of meso-scale, it is assumed that have one or more macromolecular chain, macromolecule The degradation reaction of chain can be as a example by hydrolysis, and hydrolysis is secondary response, i.e. water molecules attack macromolecular chain so that high Molecule long-chain is fractured into shorter short chain, and the modeling of micro-scale occurs to belong in the simulation of chain yardstick；Wherein, macromolecular chain water The reaction equation solving reaction can be expressed as:

P₂+W→2P₁

P₃+W→P₁+P₂

…

P_N+W→P_N-r+P_r(r=1,2 ..., N-1)

In formula, W represents hydrone, P₂,P₃,…,P_NRepresenting the degree of polymerization is 2,3 ..., the high molecular polymer of N.

In the embodiment of the present invention, as a example by hydrolysis, when macromolecular chain ruptures and which bar macromolecular chain can be by water Molecule is attacked and ruptured is a stochastic problems, and this stochastic problems can use monte carlo method obtain the next one The moment △ t of hydrolysis and participate in the macromolecular chain μ of described next hydrolysis, and the participation next one water just obtained The described macromolecular chain solving reaction is mapped to the cellular of correspondence, and wherein, △ t and μ meets:

$\mathrm{\&Delta;}t=\frac{1}{\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v}ln\left(\frac{1}{r_1}\right)$

$\underset{v=1}{\overset{\mathrm{\&mu;}-1}{\&Sigma;}}{\mathrm{\&alpha;}}_v<r_2\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v\&le;\underset{v=1}{\overset{\mathrm{\&mu;}}{\&Sigma;}}{\mathrm{\&alpha;}}_v$

In formula, r₁、r₂Belong to (0,1] random number,Middle α_v=π_vX_vX_W, π_vRepresent and participate in v hydrolysis Speed constant, X_vRepresent the molecular number of the high molecular polymer participating in v hydrolysis, X_WRepresent the water yield, it is assumed that the water yield is to fill Foot, M represents the maximum number of macromolecular chain in macromolecular material；

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and by described Macromolecular chain fracture result is coupled on the cellular of correspondence, before changing state and the chain number of corresponding cellular, also includes:

Judge whether the cellular of described correspondence and neighbours' cellular thereof exist oligomer；

If there is not oligomer, then the fracture mode of the macromolecular chain μ participating in described microcosmic macromolecular chain degradation reaction is Tip breakages；

If there is oligomer, then participate in described microcosmic macromolecular chain degradation reaction macromolecular chain μ fracture mode for Machine ruptures；

Wherein, described oligomer is the short chain that the degree of polymerization that macromolecular chain fracture produces is less than the first predetermined threshold.

In the embodiment of the present invention, at micro-scale, monte carlo method can be used, obtain next described microcosmic high score Moment of subchain degradation reaction and participate in the macromolecular chain of described next microcosmic macromolecular chain degradation reaction, but not can determine that Macromolecular chain fracture mode (such as, the fracture mode of described macromolecular chain includes: random fracture or tip breakages), does not namely have There is the self-catalyzed reaction considering degradation process.And the fracture mode of actually macromolecular chain be the key determining degradation rate because of Element, the short chain gathering produced in the fracture of degradation process macromolecular chain can cause microenvironment acid, and sour environment can promote hydrolysis Further reaction, thus the self-catalyzed reaction of degradation process occur, this is also that the device that size is big is degraded fast reason on the contrary.

In the embodiment of the present invention, and new chain that the macromolecular chain of each cellular and fracture produce (include oligomer, wherein, institute Stating oligomer is the short chain that the degree of polymerization that macromolecular chain fracture produces is less than the first predetermined threshold, and described first predetermined threshold is permissible It is 8) can carry out storing record by the variable data array that cellular is corresponding, each macromolecular chain fracture both corresponds to each unit Born of the same parents, thus realize coupling of meso-scale and micro-scale.According to coupling of described meso-scale and micro-scale, it is also possible to sentence Determining the fracture mode of macromolecular chain, concrete, each cellular have recorded the chain number being continually changing along with degradation reaction process, example As, the oligomer produced during record degradation reaction, this is equal to have recorded be situated between sees the microenvironment of structure, can be according to described The microenvironment that the sight that is situated between constructs decides whether self-catalyzed reaction.Concrete, will drop when certain macromolecular chain is selected When solving reaction, whether self cellular corresponding using this macromolecular chain and neighbours' cellular thereof have oligomer as whether occurring from urging Changing the basis for estimation of reaction, if there being oligomer, then explanation does not has self-catalyzed reaction, this macromolecular chain generation random fracture；If not yet Have oligomer, then explanation has self-catalyzed reaction, this macromolecular chain generation tip breakages.

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and by described Macromolecular chain fracture result is coupled on the cellular of correspondence, changes state and the chain number of corresponding cellular, including:

The cellular of described correspondence is simulated the Micro-fracture of macromolecular chain μ in the cellular of described correspondence, and records institute State the chain number change in the described corresponding cellular that microcosmic macromolecular chain degradation reaction produces, and the information coupling changed by described chain number Closing to and be situated between on the cellular seen, state and chain number to described corresponding cellular are updated, and wherein, described chain number includes: macromolecule The number of chain and the number of crystallization chain.

Further, the described crystallization chain recorded in the described corresponding cellular that described microcosmic macromolecular chain degradation reaction produces Number, including: obtain the number of macromolecular chain of described corresponding element intracellular fracture；The described corresponding element intracellular fracture that will obtain Total Yu the predetermined probability multiplication of macromolecular chain, obtain the number of unit's intracellular concretion chain.

In the embodiment of the present invention, along with macromolecular chain ruptures, result in some and ruptured by macromolecular chain and the crystallization that causes, A predetermined Probability p can be used to obtain the chain number of crystallization, such as, the macromolecular chain chain sum of described corresponding element intracellular fracture For R_S, the number of described corresponding element intracellular concretion chain is N_c, then R_SAnd N_cMeet: N_c=pR_S。

In the embodiment of the present invention, record the chain number that each unit intracellular is continually changing with degradation reaction on a microscopic scale (described chain number includes: macromolecular chain number, crystallization chain number), and calculate according to the chain number of micro-scale, mesoscopic model can obtain The cellular attributes such as the molecular weight of each cellular, degree of crystallinity, and deduce out the state change of cellular, thus realize meso-scale and microcosmic The coupling of yardstick.

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, described in obtain unit intracellular concretion chain chain number after, including:

If the number of described corresponding element intracellular concretion chain is more than with the ratio of the number of described corresponding element intracellular macromolecular chain Second predetermined threshold, the state of the most described corresponding cellular is crystalline state.

In the embodiment of the present invention, crystallinity X can be calculated according to the number being in crystalline state cellular_C。

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, the described diffusion of oligomer in macroscopically simulating described corresponding cellular, including:

The diffusion equation seeing macroscopic view oligomer according to being situated between obtains the diffusing capacity of oligomer in described corresponding cellular；Wherein, Described diffusion equation is expressed as:

$\frac{{\mathrm{dc}}_{ol}}{dt}=\frac{{\mathrm{dR}}_{ol}}{dt}+div\&lsqb;Dgrad\left(c_{ol}\right)\&rsqb;$

In formula, R_olRepresent the number of the oligomer of microcosmic macromolecular chain degradation reaction generation, c_olRepresent oligomer concentration, D Represent diffusion coefficient；

Wherein, given an account of the diffusion equation employing calculus of differences seeing macroscopic view oligomer, and the time step used is more than The time step that monte carlo method uses.

In the embodiment of the present invention, along with oligomer gathering formed concentration difference, oligomer can according to Fick second law to Macromolecular material external diffusion, wherein, the diffusion equation of described Fick second law sees the diffused sheet of macroscopic view oligomer as being situated between Journey, can be expressed as:

$\frac{{\mathrm{dc}}_{ol}}{dt}=\frac{{\mathrm{dR}}_{ol}}{dt}+div\&lsqb;Dgrad\left(c_{ol}\right)\&rsqb;$

$R_{ol}\left(t\right)=\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}\underset{k=1}{\overset{m}{\&Sigma;}}{N}_k(i,j,t)$

In formula, N_kT () is at t cellular (i, degree of polymerization j) the recorded oligomer (such as, m=8) less than m；R_olTable Show the number of the oligomer that microcosmic macromolecular chain degradation reaction generates, c_olRepresenting oligomer concentration, D represents diffusion coefficient.

In the embodiment of the present invention, the oligomer in diffusion macromolecular material later can be calculated according to described diffusion equation Number, the calculating of described diffusion equation uses calculus of differences, some cellulars can be merged into one group, by original stress and strain model Thicker, prevent continuous diffusion equation from discontinuous problem occurring in solving with coarse grid, such as, unit's intracellular occurs that hole causes Discontinuous problem.

In the embodiment of the present invention, the calculating of diffusion equation uses asynchronous method to carry out with calculating of monte carlo method, Concrete, the time step of described diffusion equation is greater than the time step of monte carlo method, in such manner, it is possible to ensureing calculating In the case of precision, reduce amount of calculation.

In the embodiment of the present invention, remaining low in causing macromolecular material by the oligomer of diffusion with the little molecule of dissolving Aggressiveness number is designated as R_ol(t+1), by this new R_ol(t+1) each cellular is fed back to so that chain number N (i, j, t+1) of each cellular Any updated with weight loss, in order to carry out subsequent time △ t and select bar macromolecular chain to carry out microcosmic macromolecular chain degradation reaction. So far, macroscopic view, the sight that is situated between, the reaction of three yardsticks of microcosmic intercouple, the common mechanism disclosing Degradation of Polymer Materials process.

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, described diffusion coefficient D is expressed as:

D=D_P+(1.3ε²-0.3ε³)×(D_ε-D_P)；

Wherein, D_P=D₀(1-X_C), D_PRepresent oligomer diffusion coefficient in polymeric matrix, D₀Represent high molecular polymerization The diffusion coefficient of thing substrate amorphous regions, X_CRepresent degree of crystallinity；D_εRepresenting oligomer diffusion coefficient in hole, ε represents hole Gap rate.

In the embodiment of the present invention, crystallinity X can be calculated according to the number being in crystalline state cellular_C；

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, porosity ε (t) of t is expressed as:

$\mathrm{\&epsiv;}\left(t\right)=\frac{Z\left(t\right)}{n\&times;n}$

$Z\left(t\right)=\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}\mathrm{\&psi;}(i,j,t)$

Wherein, (i, j, (i, j) state is hole to the cellular of t)=1 expression t to ψ, and (i, j, t)=0 represents t to ψ (i, j) state is not hole to cellular；Z (t) represents the cellular number that t state is hole, and n represents every string or every a line net Lattice/cellular number.

In the detailed description of the invention of the modeling and simulation method of aforementioned degradable high polymer material degradation process, further Ground, described according to the diffusing capacity of oligomer in the described corresponding cellular obtained and the meltage of described corresponding cellular small molecular, After updating chain number and the molecular weight of cellular, microcosmic chain disconnected reaction, crystallization next time etc. can be carried out and calculate, to simulate macromolecule The degradation process of material, including:

The molecular weight M of each cellular is obtained according to mesoscopic model_n(i, j, t), calculate mean molecule quantity by all cellulars, Molecular weight to macromolecular material

${\stackrel{\&OverBar;}{M}}_n\left(t\right)=\frac{1}{M_{n0}\&CenterDot;n^2}\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}{M}_n(i,j,t)$

Wherein, M_n0It is the initial molecular weight of macromolecular material, M_n(i, j t) represent t cellular (i, molecular weight j).

Embodiment two

In the embodiment of the present invention, the 2mm dish that degradable high polymer polylactic acid (PDLLA) is made is placed in phosphate In sustained-release liquid (pH 7.4,37 DEG C), utilize the modeling of the degradable high polymer material degradation process that the embodiment of the present invention provides with The degradation process of described dish is emulated by emulation mode；Wherein, the initial number average molecular weight (M of described dish_n0) be 2.883 × 105g/mol, participates in the speed constant of the 1st microcosmic macromolecular chain degradation reactionD₀=2 × 10-9m2/week, D_ε=1000 × D₀, every string or every a line grid/cellular number n=1000.Perform the stream shown in Fig. 3 In Cheng Tu, Fig. 3, t_sThe time step used for monte carlo method, Δ t_dThe time step used for diffusion equation, this implements In example, crystalline polamer is inconspicuous, ignores crystallization, and performing step can be reduced to:

1) initialize: initializing chain number and the molecular weight (by normal distribution) of each cellular, each cellular represents one Individually macromolecular chain, cellular state is all set to unformed state, and (x (i, j)=1), makes t=0, and arranges the total time of reaction T_total；

2) determine the moment Δ t of next microcosmic macromolecular chain degradation reaction and participate in described next microcosmic macromolecular chain The macromolecular chain μ of degradation reaction；

3) the macromolecular chain μ participating in described next microcosmic macromolecular chain degradation reaction is mapped to cellular (i, j)；

4) (, j) there is macromolecular chain fracture in i to cellular, calculates cellular (i, j) chain number, and update cellular (i, j) state

5) calculate the diffusing capacity of oligomer, the meltage of little molecule in cellular, and update cellular chain number and molecular weight；

6) time t=t+ Δ t is updated_dIf, t < T_total, return step 2, otherwise terminate.

In the embodiment of the present invention, Fig. 4 (a)-Fig. 4 (g) is that in mimic panel degradation process, cellular state is time dependent to be shown Being intended to, Fig. 5 is the time dependent schematic diagram of cellular molecular weight in mimic panel degradation process, according to analog result and true experiment Value comparison understands, the modeling and simulation method mimic panel of the degradable high polymer material degradation process that the embodiment of the present invention provides Degradation process is the most feasible.

Embodiment three

In the embodiment of the present invention, to degradable high polymer PLLA in phosphate buffer (pH 7.4,37 DEG C) Degradation experiment as a example by, utilize the modeling and simulation method of the degradable high polymer material degradation process that the embodiment of the present invention provides The degradation process of described polylactic acid is emulated.Wherein, primary data and calculating parameter are: monomer molecule amount M₀=72g/ Mol, M_n0=2.003 × 104g/mol, initial crystallinity X_c0=0.448, participate in the 1st microcosmic macromolecular chain degradation reaction Speed constantWeek, the first predetermined threshold m=8, every string or every a line grid/cellular number n= 1000, predetermined Probability p=0.01.

In the embodiment of the present invention, performing the flow process of Fig. 3, Fig. 6 (a)-Fig. 6 (g) is cellular in simulation polylactic acid degradation process The time dependent schematic diagram of state；Fig. 7 (a)-Fig. 7 (b) for simulation polylactic acid degradation process middle-molecular-weihydroxyethyl and degree of crystallinity at any time Between change schematic diagram, Fig. 8 (a-1)-Fig. 8 (d-2) be simulate polylactic acid degradation process middle-molecular-weihydroxyethyl distribution schematic diagram.At figure In 6 (a)-Fig. 6 (g), 1000 × 1000 so many cellulars are difficult to show concrete evolution, regional area can be used to put Big way shows.And use the different conditions occurred in different characterization cellular degradation processes, wherein, at the beginning of green expression The unformed state (x (i, j, 0)=1) begun, the blue chain representing cellular has chain interruption state (x (i, j, t)=0), black table Show that cellular occurs that (x (i, j, t)=-1), pink colour represents that crystalline state (x (i, j, t)=-2) occurs in cellular to hole state.Perform Molecular weight and degree of crystallinity that the flow process of Fig. 3 obtains are shown in Fig. 7 (a)-Fig. 7 (b), Fig. 7 (a)-Fig. 7 (b) with true experiment value comparison diagram Showing that analog simulation result matches with true experiment value, accuracy in computation is high.The degradable provided by the embodiment of the present invention is high The modeling and simulation method of molecular material degradation process can obtain the molecular weight distribution in any moment (such as Fig. 8 (a-1)-Fig. 8 (d-2)) and cloud born of the same parents' state change (such as Fig. 6 (a)-Fig. 6 (g)), this is true to test unapproachable experimental amount.

The above is the preferred embodiment of the present invention, it is noted that for those skilled in the art For, on the premise of without departing from principle of the present invention, it is also possible to make some improvements and modifications, these improvements and modifications are also Should be regarded as protection scope of the present invention.

Claims (9)

1. the modeling and simulation method of a degradable high polymer material degradation process, it is characterised in that including:

S1, by discrete for the macromolecular material macroscopically cellular for the sight that is situated between, wherein, each unit intracellular includes at least one macromolecule Chain；

S2, simulates microcosmic macromolecular chain degradation reaction on described cellular and the macromolecular chain in cellular is ruptured, crystallizes, and will The fracture of described macromolecular chain, crystalline results are coupled on the cellular of correspondence, change state and the chain number of corresponding cellular；

S3, the diffusion of oligomer and the dissolving of described corresponding cellular small molecular in macroscopically simulating described corresponding cellular, and Update chain number and the molecular weight of described corresponding cellular；

S4, returns S2, enters next round iteration and continues simulation microcosmic macromolecular chain degradation reaction until meeting the termination bar preset Part.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 1, it is characterised in that Described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and by described high score Subchain fracture result is coupled on the cellular of correspondence, before changing state and the chain number of corresponding cellular, including:

Use monte carlo method, by random number r₁And r₂The next described microcosmic macromolecular chain degradation reaction of random acquisition Moment △ t and participate in the macromolecular chain μ of described next microcosmic macromolecular chain degradation reaction:

$\mathrm{\&Delta;}t=\frac{1}{\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v}ln\left(\frac{1}{r_1}\right)$

$\underset{v=1}{\overset{\mathrm{\&mu;}-1}{\&Sigma;}}{\mathrm{\&alpha;}}_v<r_2\underset{v=1}{\overset{M}{\&Sigma;}}{\mathrm{\&alpha;}}_v\&le;\underset{v=1}{\overset{\mathrm{\&mu;}}{\&Sigma;}}{\mathrm{\&alpha;}}_v$

In formula, r₁、r₂Belong to (0,1],Middle α_v=π_vX_vX_w, π_vRepresent and participate in the v microcosmic macromolecular chain degradation reaction Speed constant, X_vRepresent the molecular number of the high molecular polymer participating in the v microcosmic macromolecular chain degradation reaction, X_wRepresent the water yield, M represents the maximum number of macromolecular chain in macromolecular material；

The described macromolecular chain participating in next described microcosmic macromolecular chain degradation reaction obtained is mapped to the cellular of correspondence；

Wherein, described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and Described macromolecular chain fracture result is coupled on the cellular of correspondence, before changing state and the chain number of corresponding cellular, also includes:

Judge whether the cellular of described correspondence and neighbours' cellular thereof exist oligomer；

If there is not oligomer, then the fracture mode of the macromolecular chain μ participating in described microcosmic macromolecular chain degradation reaction is end Fracture；

If there is oligomer, then participate in the fracture mode of macromolecular chain μ of described microcosmic macromolecular chain degradation reaction for random disconnected Split；

Wherein, described oligomer is the short chain that the degree of polymerization that macromolecular chain fracture produces is less than the first predetermined threshold.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 2, it is characterised in that The state of described cellular includes: unformed state, chain interruption state, hole state or crystalline state；

Described microcosmic macromolecular chain degradation reaction of simulating on described cellular makes the macromolecular chain in cellular rupture, and by described Macromolecular chain fracture result is coupled on the cellular of correspondence, changes state and the chain number of corresponding cellular, including:

Macromolecular chain μ during simulation microcosmic macromolecular chain degradation reaction makes the cellular of described correspondence on the cellular of described correspondence Fracture, and record the chain number change in the described corresponding cellular that described microcosmic macromolecular chain degradation reaction produces, and by described chain The information of number change is coupled to be situated between on the cellular seen, and updates state and the chain number of cellular, and wherein, described chain number includes: macromolecule The number of chain and the number of crystallization chain.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 3, it is characterised in that The number of the described crystallization chain recorded in the described corresponding cellular that described microcosmic macromolecular chain degradation reaction produces, including:

Obtain the number of the macromolecular chain of described corresponding element intracellular fracture；

By probability multiplication total Yu predetermined for the macromolecular chain of the described corresponding element intracellular fracture obtained, obtain unit's intracellular concretion chain Number.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 4, it is characterised in that After the described chain number obtaining unit's intracellular concretion chain, including:

If the number of described corresponding element intracellular concretion chain is more than second with the ratio of the number of described corresponding element intracellular macromolecular chain Predetermined threshold, the state of the most described corresponding cellular is crystalline state.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 1, it is characterised in that The described diffusion of oligomer in macroscopically simulating described corresponding cellular, including:

The diffusion equation seeing macroscopic view oligomer according to being situated between obtains the diffusing capacity of oligomer in described corresponding cellular；Wherein, described Diffusion equation is expressed as:

$\frac{{\mathrm{dc}}_{ol}}{dt}=\frac{{\mathrm{dR}}_{ol}}{dt}+div\&lsqb;Dgrad\left(c_{ol}\right)\&rsqb;$

In formula, R_olRepresent the number of the oligomer of microcosmic macromolecular chain degradation reaction generation, c_olRepresenting oligomer concentration, D represents Diffusion coefficient；

Wherein, given an account of and see the diffusion equation of macroscopic view oligomer and use calculus of differences, used than cellular big some multiples thick Grid computing is to keep seriality, and the time step that the time step used uses more than monte carlo method.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 1, it is characterised in that Described diffusion coefficient D is expressed as:

D=D_P+(1.3ε²-0.3ε³)×(D_ε-D_P)；

Wherein, D_P=D₀(1-X_C), D_PRepresent oligomer diffusion coefficient in polymeric matrix, D₀Represent high molecular polymer base The diffusion coefficient of matter amorphous regions, X_CRepresent degree of crystallinity；D_εRepresenting oligomer diffusion coefficient in hole, ε represents hole Rate.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 1, it is characterised in that Porosity ε (t) of t is expressed as:

$\mathrm{\&epsiv;}\left(t\right)=\frac{Z\left(t\right)}{n\&times;n}$

$Z\left(t\right)=\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}\mathrm{\&psi;}(i,j,t)$

Wherein, (i, j, (i, j) state is hole to the cellular of t)=1 expression t to ψ, and (i, j, t)=0 represents the cellular of t to ψ (i, j) state is not hole；Z (t) represents that t state is the cellular number of hole, n represent every string or every a line grid/ Cellular number.

The modeling and simulation method of degradable high polymer material degradation process the most according to claim 1, it is characterised in that Described according to the diffusing capacity of oligomer in the described corresponding cellular obtained and the meltage of described corresponding cellular small molecular, feedback Cellular is seen to being situated between, after updating chain number and the molecular weight of cellular, including:

Calculate mean molecule quantity by all cellulars, obtain the molecular weight of macromolecular material

${\stackrel{\&OverBar;}{M}}_n\left(t\right)=\frac{1}{M_{n0}\&CenterDot;n^2}\underset{i=1}{\overset{n}{\&Sigma;}}\underset{j=1}{\overset{n}{\&Sigma;}}{M}_n(i,j,t)$

Wherein, M_n0It is the initial molecular weight of macromolecular material, M_n(i, j t) represent t cellular (i, molecular weight j).