CN115312131A - Crosslinked polyurethane modeling method based on molecular dynamics - Google Patents

Crosslinked polyurethane modeling method based on molecular dynamics Download PDF

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CN115312131A
CN115312131A CN202210842801.7A CN202210842801A CN115312131A CN 115312131 A CN115312131 A CN 115312131A CN 202210842801 A CN202210842801 A CN 202210842801A CN 115312131 A CN115312131 A CN 115312131A
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王翠霞
张超
袁灵修
武永深
万京
魏宁
杜明瑞
赵鹏
王磊
石明生
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Jiangnan University
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Abstract

The invention discloses a cross-linked polyurethane modeling method based on molecular dynamics, which relates to the technical field of molecular simulation methods and comprises the following steps: step 1: respectively constructing molecular structure models of reaction monomer isocyanate and polyol, and establishing a mixture model of the reaction monomer, wherein the molecular numbers of the isocyanate and the polyol in the mixture model are respectively n 1 And n 2 (ii) a Step 2: setting force field parameters of the mixture model; and step 3: performing energy minimization and molecular dynamics balance on the mixture model through Lammps software; and 4, step 4: defining the mixture as a reaction atom pair, and crosslinking the mixture model by utilizing a Python program to obtain a first crosslinked polyurethane model; and 5: will be provided withAnd carrying out molecular dynamics balance on the first cross-linked polyurethane model to obtain the target cross-linked polyurethane model. The invention obtains the cross-linked polyurethane model and provides a foundation for researching the relation between the molecular structure and the macroscopic performance of the cross-linked polyurethane.

Description

Crosslinked polyurethane modeling method based on molecular dynamics
Technical Field
The invention relates to the technical field of molecular simulation methods, in particular to a cross-linked polyurethane modeling method based on molecular dynamics.
Background
The polyurethane grouting material is a cross-linked network structure composed of polyol, polyisocyanate and other raw materials, is a multiphase block copolymer, and is widely applied to non-excavation repair of foundation engineering, underground pipe networks and other infrastructure due to the characteristics of good impermeability, environmental protection, excellent durability and the like; at present, the macrostructure and the performance of the polyurethane grouting material are widely researched; however, none of these studies can show the continuous dynamic change of microscopic particles during the polyurethane synthesis and deformation. The properties and functions of the material are determined by the microstructure of the material, the macroscopic response and the failure are both derived from the change of the microstructure, the deformation mechanism of the material is important to be revealed from the microscopic scale, and the existing experimental technology and instruments are difficult to realize the understanding of the molecular level of the material.
The molecular dynamics simulation technology can study the microscopic molecular structure from the atomic scale and reveal the properties of the material, which makes up the defects of the current experimental technology; molecular dynamics is a molecular simulation method, which simulates the motion of atoms in a system according to Newton's second law, calculates the configuration integral of the system by extracting samples from configurations in different states, and further calculates the thermodynamics and other properties of the system based on the result of the configuration integral; at present, polyurethane is researched by a molecular dynamics method, and the main research object is uncrosslinked chain polyurethane; the polyurethane grouting material used in engineering is a cross-linked network structure, isocyanate and polyol which participate in the reaction have a plurality of reaction sites, the research on the polyurethane cross-linking modeling process is less at present, and the influence of the cross-linking reaction degree on the microstructure and the thermodynamic performance of the polyurethane grouting material is not clear.
Disclosure of Invention
Therefore, in order to solve the above technical problems, it is necessary to provide a cross-linked polyurethane modeling method based on molecular dynamics, so as to solve the problems that the research on the polyurethane cross-linking modeling process is less, and the influence of the polyurethane cross-linking reaction degree on the microstructure and the thermodynamic performance is unclear at present.
The invention provides a cross-linked polyurethane modeling method based on molecular dynamics, which comprises the following steps:
step 1: respectively constructing molecular structure models of reaction monomer isocyanate and polyol, and establishing a mixture model of the reaction monomer by Moltemplate software, wherein the molecular numbers of the isocyanate and the polyol in the established mixture model are respectively n 1 And n 2 ；
Step 2: setting the parameters of a force field of the mixture model, wherein the adopted force field is an OPLS-AA force field;
and step 3: performing energy minimization and molecular dynamics balance on the mixture model through Lammps software;
and 4, step 4: defining carbon atoms on isocyanic acid radicals in the isocyanate and oxygen atoms on hydroxyl groups of the polyol as reaction atom pairs, and crosslinking the mixture model by using a Python program to obtain a first crosslinked polyurethane model;
and 5: and carrying out molecular dynamics balance on the first crosslinked polyurethane model to obtain a target crosslinked polyurethane model.
Further, in the step 1, the isocyanate is polyphenyl methane polyisocyanate, and the polyol is sucrose polyether polyol;
periodic boundary conditions are adopted in all three directions of the mixture model, the number of molecules of isocyanate in the mixture model is n1, the number of molecules of polyol is n2, and the ratio of n1 to n2 is the real charge ratio.
Further, in step 2, the action potential of the force field includes bond energy, bond angle energy, dihedral angle energy and non-bond energy, and the formula is as follows:
E total ＝E bond +E angle +E dihedrals +E nonbonded
Figure BDA0003751767560000021
Figure BDA0003751767560000022
Figure BDA0003751767560000023
Figure BDA0003751767560000024
wherein E is total 、E bond 、E angle 、E dihedrals 、E nonbonded Respectively representing the total energy, bond angle energy, dihedral angle energy and non-bond energy of the system; k r Denotes the rigidity of the bond, K θ Representing angular stiffness, V i (i =1,2,3,4) represents dihedral stiffness; r and r ij Denotes the bond length between two atoms, r 0 Represents the equilibrium bond length; theta denotes the angle of the bond between three atoms, theta 0 Represents the equilibrium key angle;
Figure BDA0003751767560000025
is dihedral angle value; c is an energy conversion constant, q i And q is j Represents the charge amounts, σ, of the atoms i and j ij Denotes the equilibrium distance between two particles in the L-J potential and ε denotes the energy well depth between two particles in the L-J potential.
Further, in the step 3, energy minimization operation is performed through a conjugate gradient method, and geometric optimization is completed to obtain a structure with smaller energy; in the geometric optimization and molecular dynamics balance operation processes, periodic boundary conditions in three directions are adopted, a speed-verlet integral algorithm is adopted as a data integral algorithm, a Nose-Hoove isothermal control method is adopted as a temperature control method, and an Andersen isobaric control method is adopted as a pressure control method; the initial mixture model was equilibrated at 600k temperature for 250ps with both time steps of 0.5fs for NVT and NPT ensembles, respectively.
Further, in the step 4, the cross-linking the mixture model by using a Python program to obtain a first cross-linked polyurethane model includes:
step 401, identifying a reaction atom pair in a Python program, wherein the reaction atom pair is a carbon atom in isocyanate groups of isocyanate molecules and an oxygen atom in hydroxyl groups of polyol molecules, the carbon atom is marked as A1, and the oxygen atom is marked as A2;
step 402, setting the crosslinking reaction temperature to 600K, setting a minimum reaction cut-off radius Rmin and a maximum cut-off radius Rmax, and setting a target crosslinking degree to S0;
step 403, under the condition that there are atom pairs capable of forming bonds in the reaction radius and the surrounding topological structure is correct, crosslinking all atom pairs capable of forming bonds, and calculating the distance D between each reaction atom pair A1 and A2; if Rmin is less than or equal to D and less than or equal to Rmax, a cross-linking bond is formed between the atoms A1 and A2; if a plurality of A2 atoms capable of generating a crosslink are provided around the A1 atom, the A1 atom reacts with A2 atom located closest to it;
step 404, balancing the new structure for 40ps at NVT ensemble and 600K temperature to relax the internal stress generated by generating new bonds and reach a new balance state;
step 405, calculating a system crosslinking degree S, wherein the system crosslinking degree S is defined as the ratio of the number of isocyanate groups which have participated in the reaction to the total number of isocyanate groups which can participate in the reaction in the system;
step 406, if S is less than S0, repeating the steps 403, 404 and 405 until the target crosslinking degree is reached, and marking the obtained crosslinked polyurethane model as a first crosslinked polyurethane model; and if no atom pair capable of reacting exists in the reaction radius, gradually increasing the reaction radius from Rmin to Rmax, repeating the steps 403, 404 and 405 until the target crosslinking degree is reached, and marking the obtained crosslinked polyurethane model as a first crosslinked polyurethane model.
Further, in the step 4, the maximum cutoff radius Rmax and the target crosslinking degree are changed to S0, so as to obtain the first crosslinked polyurethane model with different crosslinking degrees.
Further, in the step 5, 250ps dynamic balance is carried out under NPT ensemble, 600K temperature and 1atm, and the step length is 0.5fs; and if the first cross-linked polyurethane model reaches an equilibrium state and the total energy of the system is relatively stable, stopping the molecular dynamics balance to obtain the target cross-linked polyurethane model.
Further, in the step 1, molecular structure models of the reaction monomer isocyanate and the polyol are respectively constructed by using the ligaragen website.
The invention has the beneficial effects that:
the invention relates to a cross-linked polyurethane modeling method based on molecular dynamics, which identifies reaction atom pairs through a cross-linking program, generates covalent bonds between the reaction atom pairs to realize dynamic cross-linking of isocyanate and polyol.
Since the crosslinking procedure only involves isocyanate groups N = C = O and hydroxyl groups OH-, the invention has the characteristic of wide applicability and can be used for any crosslinking structure formed by the crosslinking reaction of the isocyanate groups and the hydroxyl groups.
The computing platform used in the invention comprises: ligpargen official network, moltemplate open source software, lammps open source software and Python program. The invention can be carried out in both Windows system and Linux system, the hardware can be ordinary PC, or server or cluster, and it has the characteristic of flexible computing environment.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described 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 inventive exercise.
FIG. 1 is a flow chart of a method for modeling crosslinked polyurethane based on molecular dynamics provided by the present invention;
FIG. 2 is a flow chart of a method for constructing a cross-linked polyurethane model according to the present invention;
FIG. 3 is a structural formula of polyphenyl methane polyisocyanate provided by the present invention;
FIG. 4 is a structural formula of a sucrose polyether polyol provided by the present invention;
FIG. 5 is a schematic representation of a model mixture provided by the present invention comprising 104 polyphenylmethane polyisocyanate and 104 sucrose polyether polyol molecules;
FIG. 6 is a schematic diagram of the cross-linking reaction of polyphenyl methane polyisocyanate and sucrose polyether polyol provided by the present invention;
FIG. 7 is a graph of a cross-linking model of 0% cross-linking provided by the present invention;
FIG. 8 is a graph of a cross-linking model of 40% cross-linking provided by the present invention;
FIG. 9 is a graph of a cross-linking model of 80% cross-linking provided by the present invention;
FIG. 10 is a plot of degree of crosslinking versus time during the crosslinking process provided by the present invention;
FIG. 11 is a cross-linking degree-density curve in the cross-linking process provided by the present invention.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system structures, techniques, etc. in order to provide a thorough understanding of the embodiments of the invention. In order to explain the technical means of the present invention, the following description will be given by way of specific examples.
Referring to fig. 1, which is a flowchart of a modeling method of a cross-linked polyurethane based on molecular dynamics according to this embodiment, the modeling method of a cross-linked polyurethane based on molecular dynamics may include the following steps:
step 1: respectively constructing molecular structure models of reaction monomer isocyanate and polyol, and establishing a mixture model of the reaction monomer by Moltemplate software, wherein the molecular numbers of the isocyanate and the polyol in the established mixture model are respectively n 1 And n 2 。
In this example, molecular structure models of the reaction monomers isocyanate and polyol were constructed using the ligapgen website, respectively.
Wherein, the isocyanate adopts polyphenyl methane polyisocyanate, and the polyalcohol adopts sucrose polyether polyalcohol. Periodic boundary conditions are adopted in all three directions of the initial mixture model, and the ratio of the molecular numbers n1 and n2 of the isocyanate and the polyol in the mixture model is a real charging ratio.
Step 2: and setting the parameters of the force field of the mixture model, wherein the adopted force field is an OPLS-AA force field.
In this embodiment, the force field used by the model is an OPLS-AA force field, the action potentials of the force field include bond energy, bond angle energy, dihedral angle energy, and non-bond energy, and as shown in formulas 1 to 5, the first-pass parameters are obtained from the ligargen website.
E total ＝E bond +E angle +E dihedrals +E nonbonded (1)
Figure BDA0003751767560000051
Figure BDA0003751767560000052
Figure BDA0003751767560000053
Figure BDA0003751767560000054
Wherein E is total 、E bond 、E angle 、E dihedrals 、E nonbonded Respectively representing the total energy, bond angle energy, dihedral angle energy and non-bond energy of the system; k r Denotes the rigidity of the bond, K θ Representing angular stiffness, V i (i =1,2,3,4) represents dihedral stiffness; r and r ij Denotes the bond length between two atoms, r 0 Represents the equilibrium bond length; theta denotes the angle of the bond between three atoms, theta 0 Represents the equilibrium key angle;
Figure BDA0003751767560000055
is dihedral angle value; c is an energy conversion constant, q i And q is j Represents the charge amounts, σ, of the atoms i and j ij Denotes the equilibrium distance between two particles in the L-J potential and ε denotes the energy well depth between two particles in the L-J potential.
And step 3: the mixture model was energy minimized and molecular dynamics balanced by Lammps software.
In this example, both energy minimization and molecular dynamics balancing were performed in Lammps software. And performing energy minimization operation by a conjugate gradient method to complete geometric optimization so as to obtain a structure with smaller energy. In the geometric optimization and molecular dynamics balance operation processes, periodic boundary conditions in three directions are adopted, a speed-verlet integral algorithm is adopted in a data integral algorithm, a Nose-Hoove isothermal control method is adopted in a temperature control method, and an Andersen isobaric control method is adopted in a pressure control method.
In order to obtain a model of isocyanate and polyol reaction monomer mixture with reasonable density, the initial model is balanced at 600K for 250ps under NVT and NPT ensemble respectively, and the time step is 0.5fs; meanwhile, the distance between the active atom pairs is closer, and the crosslinking reaction is easier to occur.
And 4, step 4: and defining a carbon atom on isocyanic acid radical in the isocyanate and an oxygen atom on hydroxyl of the polyol as a reaction atom pair, and crosslinking the mixture model by utilizing a Python program to obtain a first crosslinked polyurethane model.
In this embodiment, a Python program is used to crosslink the mixture model to obtain a first crosslinked polyurethane model, which specifically includes the following steps:
step 401: the cross-linking reaction is realized by a Python program, which specifically comprises the following steps: identifying a reaction atom pair in a Python program, wherein the reaction atom pair is a carbon atom in isocyanate groups of isocyanate molecules and an oxygen atom in hydroxyl groups of polyol molecules, the carbon atom in the isocyanate groups of the isocyanate molecules is marked as A1, and the oxygen atom in the hydroxyl groups of the polyol molecules is marked as A2.
Step 402: in order to accelerate the crosslinking reaction process, the crosslinking reaction temperature is set to be 600K; setting a minimum reaction cut-off radius Rmin and a maximum cut-off radius Rmax; the target degree of crosslinking was set to S0.
Step 403: and under the conditions that the bonding atom pairs exist in the reaction radius and the surrounding topological structure is correct, all the bonding atom pairs are crosslinked, and the distance D between each reaction atom pair A1 and A2 is calculated.
If Rmin is less than or equal to D and less than or equal to Rmax, a cross-linking bond is formed between the atoms A1 and A2.
If a plurality of A2 atoms capable of generating a cross-linking bond are present around the A1 atom, the A1 atom reacts with the A2 atom located closest thereto.
Step 404: the new structure is balanced for 40ps at NVT ensemble and 600K temperature to relax the internal stress generated by generating new bonds, and simultaneously, a new balance state is achieved, so that the distance between other active atom pairs is closer.
Step 405: the degree of crosslinking S of the system, defined as the ratio of the number of isocyanate groups already reacted to the total number of isocyanate groups available for reaction in the system, is calculated.
Step 406: if S is less than S0, repeating the steps 403, 404 and 405 until the target crosslinking degree is reached, and marking the obtained crosslinked polyurethane model as a first crosslinked polyurethane model; and if no atom pair capable of reacting exists in the reaction radius, gradually increasing the reaction radius from Rmin to Rmax, repeating the steps 403, 404 and 405 until the target crosslinking degree is reached, and marking the obtained crosslinked polyurethane model as a first crosslinked polyurethane model.
Further, by changing the maximum cutoff radius Rmax to a target crosslinking degree S0, a first crosslinked polyurethane model with a different crosslinking degree can be obtained. For example, the maximum cutoff radius Rmax may be set to 20%, 40%, 60%, 80% of the target degree of crosslinking, respectively
Figure BDA0003751767560000061
And 5: and carrying out molecular dynamics balance on the first crosslinked polyurethane model to obtain a target crosslinked polyurethane model.
In this embodiment, after the system reaches the expected crosslinking degree, the obtained first crosslinking model is subjected to molecular dynamics balance to obtain a target crosslinked polyurethane model; 250ps kinetic equilibrium was carried out at NPT ensemble, 600K temperature, 1atm, step size 0.5fs. This is to make the first crosslinking model reach an equilibrium state, and stop the molecular dynamics equilibrium if the total energy of the system is relatively stable, and to record the final crosslinking network structure as the target crosslinking polyurethane model.
By way of example, in the case of crosslinking a polyphenylmethane polyisocyanate with a sucrose polyether polyol, the mechanism of the crosslinking reaction of the polyphenylmethane polyisocyanate with the sucrose polyether polyol is as follows:
when the crosslinking reaction occurs, as shown in formula (6), the double bond between the N atom and the C atom is changed to a single bond in the case where the isocyanate group N = C = O in the polyphenyl methane polyisocyanate. The C atom of the isocyanate group N = C = O is then linked to the O atom of the hydroxyl group OH "to form a cross-link. And finally, H atom saturation is carried out according to the atom coordination condition.
Figure BDA0003751767560000071
In this embodiment, the reaction process is refined and programmed by a Python algorithm, and the modeling flow is shown in fig. 2.
FIG. 3 is a molecular structural formula of polyphenyl methane polyisocyanate, FIG. 4 is a molecular structural formula of sucrose polyether polyol, and monomer molecular models of polyphenyl methane polyisocyanate and sucrose polyether polyol are established through the Ligpargen official network. And a mixture model is established through Moltemplate software, wherein the mixture model comprises 104 polyphenyl methane polyisocyanate molecules and 104 sucrose polyether polyol molecules.
Energy minimization and molecular dynamics balancing were performed on the blending model by Lammps software. And the energy minimization adopts a conjugate gradient method to calculate so as to complete geometric optimization and obtain a structure with smaller energy. In the geometric optimization and molecular dynamics balance operation processes, periodic boundary conditions in three directions are adopted. In order to obtain a reasonable density model of the isocyanate and polyol reaction monomer mixture, the initial model was equilibrated at 250ps for NVT and NPT ensembles, 600K, respectively, with a time step of 0.5fs. Meanwhile, the distance between the active atom pairs is closer, and the crosslinking reaction is easier to occur. Fig. 5 is a relaxation-completed blending model.
The reaction of crosslinking the polyphenylmethane polyisocyanate and the sucrose polyether polyol is initiated. (1) Firstly, identifying a reactive atom pair in a Python program, wherein the reactive atom pair is a C atom in isocyanate group N = C = O and an O atom in hydroxyl group OH-of a polyol molecule, and is respectively marked as A 1 And A 2 . (2) next, the setting of reaction parameters is started: the reaction temperature is 600K, and the minimum reaction cut-off half is setDiameter R min And maximum cutoff radius R max Are respectively 0 and
Figure BDA0003751767560000072
setting a target degree of crosslinking S 0 20%, 40%, 60%, 80%, respectively. (3) All the atom pairs capable of forming bonds are crosslinked under the condition that the atom pairs capable of forming bonds exist in the reaction radius and the surrounding topological structure is correct, and FIG. 6 is a schematic diagram of the crosslinking reaction process of two monomer molecules. (4) And balancing the cross-linked structure for 40ps under NVT ensemble and 600K to relax the internal stress generated by generating a new bond and achieve a new balance state, so that the distance between other active atom pairs is closer. (5) The degree of crosslinking S of the system, defined as the ratio of the number of isocyanate groups already reacted to the total number of isocyanate groups available for reaction in the system, is calculated. If S is less than S 0 And (5) repeating the step (3) and the step (4) until the target crosslinking degree is reached. (6) If there are no atom pairs available to react within the reaction radius, the reaction radius is increased from R min Gradually increase to R max . Repeating the steps until the target crosslinking degree is reached.
FIG. 7 is a graph showing a crosslinking pattern at a crosslinking degree of 0%, FIG. 8 is a graph showing a crosslinking pattern at a crosslinking degree of 40%, and FIG. 9 is a graph showing a crosslinking pattern at a crosslinking degree of 80%. From the three figures, it is understood that as the degree of crosslinking increases, the more crosslinking reaction occurs in the system, the more crosslinking bonds are generated.
Referring to FIG. 10, a graph of the degree of crosslinking versus time during the crosslinking process of this example is shown. As can be seen from the graph, the degree of crosslinking significantly increased with the increase in the crosslinking reaction time. The crosslinking speed is initially fast and decreases until it levels off with increasing crosslinking time.
Referring to fig. 11, a graph of the cross-linking degree and the density in the cross-linking process of this example is shown. As can be seen from the graph, the density of the crosslinked polyurethane increases as the degree of crosslinking increases. The smaller and tighter the intermolecular spacing.
In the method for modeling crosslinked polyurethane based on molecular dynamics of this embodiment, the reaction atom pair is identified by Python program, and a covalent bond is generated between the reaction atom pair, so as to realize dynamic crosslinking of isocyanate and polyol. The method has the characteristic of controllable reactivity, and can obtain cross-linked polyurethane models with different cross-linking degrees by controlling parameters in the cross-linking process, such as reaction cut-off radius, target cross-linking degree and the like, thereby providing a foundation for researching the relationship between the molecular structure and the macroscopic property of the cross-linked polyurethane.
The above-mentioned embodiments are only used to illustrate the technical solution of the present invention, and not to limit the same; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; such modifications and substitutions do not substantially depart from the spirit and scope of the embodiments of the present invention, and are intended to be included within the scope of the present invention.

Claims (8)

1. A method for modeling crosslinked polyurethane based on molecular dynamics, comprising:
step 1: respectively constructing molecular structure models of reaction monomer isocyanate and polyol, and establishing a mixture model of the reaction monomer by Moltemplate software, wherein the molecular numbers of the isocyanate and the polyol in the established mixture model are respectively n 1 And n 2 ；
Step 2: setting the parameters of a force field of the mixture model, wherein the adopted force field is an OPLS-AA force field;
and step 3: performing energy minimization and molecular dynamics balance on the mixture model through Lammps software;
and 4, step 4: defining carbon atoms on isocyanic acid radicals in the isocyanate and oxygen atoms on hydroxyl groups of the polyol as reaction atom pairs, and crosslinking the mixture model by using a Python program to obtain a first crosslinked polyurethane model;
and 5: and carrying out molecular dynamics balance on the first crosslinked polyurethane model to obtain a target crosslinked polyurethane model.
2. The method for modeling crosslinked polyurethane based on molecular dynamics as claimed in claim 1, wherein in the step 1, the isocyanate is polyphenylmethane polyisocyanate and the polyol is sucrose polyether polyol;
periodic boundary conditions are adopted in all three directions of the mixture model, the number of molecules of isocyanate in the mixture model is n1, the number of molecules of polyol is n2, and the ratio of n1 to n2 is the real charge ratio.
3. The method for modeling crosslinked polyurethane based on molecular dynamics as claimed in claim 1, wherein in step 2, the action potential of the force field comprises bond energy, bond angle energy, dihedral angle energy and non-bond energy, and the formula is as follows:
E total ＝E bond +E angle +E dihedrals +E nonbonded
Figure FDA0003751767550000011
Figure FDA0003751767550000012
Figure FDA0003751767550000013
Figure FDA0003751767550000014
wherein E is total 、E bond 、E angle 、E dihedrals 、E nonbonded Respectively representing the total energy, bond angle energy, dihedral angle energy and non-bond energy of the system; k r Denotes the rigidity of the bond, K θ Representing angular stiffness, V i (i =1,2,3,4) represents dihedral stiffness(ii) a r and r ij Denotes the bond length between two atoms, r 0 Represents the equilibrium bond length; theta denotes the angle of the bond between three atoms, theta 0 Represents the equilibrium key angle;
Figure FDA0003751767550000015
is dihedral angle value; c is an energy conversion constant, q i And q is j Represents the charge amounts of the atoms i and j, σ ij Denotes the equilibrium distance between two particles in the L-J potential and ε denotes the energy well depth between two particles in the L-J potential.
4. The modeling method of crosslinked polyurethane based on molecular dynamics according to claim 1, wherein in step 3, energy minimization operation is performed by conjugate gradient method to complete geometric optimization so as to obtain a structure with smaller energy; in the geometric optimization and molecular dynamics balance operation processes, periodic boundary conditions in three directions are adopted, a speed-verlet integral algorithm is adopted in a data integral algorithm, a Nose-Hoove isothermal control method is adopted in a temperature control method, and an Andersen isobaric control method is adopted in a pressure control method; the initial mixture model was equilibrated at 600k temperature for 250ps with both time steps of 0.5fs for NVT and NPT ensembles, respectively.
5. The method according to claim 4, wherein the step 4 of cross-linking the mixture model by Python program to obtain a first cross-linked polyurethane model comprises:
step 401, identifying a reaction atom pair in a Python program, wherein the reaction atom pair is a carbon atom in isocyanate groups of isocyanate molecules and an oxygen atom in hydroxyl groups of polyol molecules, the carbon atom is marked as A1, and the oxygen atom is marked as A2;
step 402, setting the crosslinking reaction temperature to 600K, setting a minimum reaction cut-off radius Rmin and a maximum cut-off radius Rmax, and setting a target crosslinking degree to S0;
step 403, under the condition that there are atom pairs capable of forming bonds in the reaction radius and the surrounding topological structure is correct, crosslinking all atom pairs capable of forming bonds, and calculating the distance D between each reaction atom pair A1 and A2; if Rmin is less than or equal to D and less than or equal to Rmax, a cross-linking bond is formed between the atoms A1 and A2; if a plurality of A2 atoms capable of generating a cross-linking bond are present around the A1 atom, then the A1 atom reacts with the A2 atom that is closest to it;
step 404, balancing the new structure for 40ps at NVT ensemble and 600K temperature to relax the internal stress generated by generating new bonds and reach a new balance state;
step 405, calculating a system crosslinking degree S, wherein the system crosslinking degree S is defined as the ratio of the number of isocyanate groups already participating in the reaction to the total number of isocyanate groups capable of participating in the reaction in the system;
step 406, if S is less than S0, repeating the steps 403, 404 and 405 until the target crosslinking degree is reached, and marking the obtained crosslinked polyurethane model as a first crosslinked polyurethane model; and if no atom pair capable of reacting exists in the reaction radius, gradually increasing the reaction radius from Rmin to Rmax, repeating the steps 403, 404 and 405 until the target crosslinking degree is reached, and marking the obtained crosslinked polyurethane model as a first crosslinked polyurethane model.
6. The method for modeling crosslinked polyurethane based on molecular dynamics as claimed in claim 5, wherein in the step 4, the first crosslinked polyurethane model with different degrees of crosslinking is obtained by changing the maximum cutoff radius Rmax and the target degree of crosslinking to S0.
7. The molecular dynamics-based modeling method of crosslinked polyurethane according to claim 1, wherein in step 5, 250ps kinetic equilibrium is performed at NPT ensemble, 600K temperature and 1atm, step size is 0.5fs; and if the first cross-linked polyurethane model reaches an equilibrium state and the total energy of the system is relatively stable, stopping the molecular dynamics balance to obtain the target cross-linked polyurethane model.
8. The method for modeling crosslinked polyurethane based on molecular dynamics as claimed in claim 1, wherein in step 1, molecular structure models of the reactive monomer isocyanate and the polyol are constructed respectively by using the ligapgregen website.
CN202210842801.7A 2022-07-18 2022-07-18 Crosslinked polyurethane modeling method based on molecular dynamics Pending CN115312131A (en)

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Publication number Priority date Publication date Assignee Title
CN115831259A (en) * 2022-12-12 2023-03-21 华东理工大学 Performance prediction method of polycyanate ester and application thereof

Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115831259A (en) * 2022-12-12 2023-03-21 华东理工大学 Performance prediction method of polycyanate ester and application thereof
CN115831259B (en) * 2022-12-12 2023-09-05 华东理工大学 Performance prediction method of polycyanate and application thereof

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