Modeling Methods for Dissipative Particle Dynamics Studies of Ternary Entangled Polymer Mixtures of Homopolymer-Homopolymer-Diblock Copolymer

Abstract

This invention discloses a method for constructing ternary entangled polymer mixtures of homopolymer-homogene-diblock copolymers using dissipative particle dynamics. The steps are as follows: obtaining the characteristic ratios and equilibrium bond lengths of the simulation system, and generating a series of homopolymers and diblock copolymers with bond lengths as step sizes; placing the obtained series of randomly walking homopolymers and copolymers into a simulation box according to the chain length, chain number, and number density of the simulation system; introducing interaction potentials between particles, using a harmonic spring potential to introduce bonding interaction potentials and a bending potential function to introduce bond angle interaction potentials; gradually increasing the repulsion parameter, ensuring that the difference in repulsion parameter between each stage remains equal or approximately equal; setting the repulsion parameter as the final value; and detecting whether the chain conformation is in equilibrium. The ternary entangled polymer mixture constructed by this invention can accurately describe the dynamics and rheological properties of entangled polymer blends and can be used to study the structure and rheological properties of entangled polymer interfaces.

Description

Technical Field

[0001] This invention relates to a model construction method for studying ternary entangled polymer mixtures of homopolymer-homogene-diblock copolymers using dissipative particle dynamics, and belongs to the field of computer simulation. Background Technology

[0002] Blending polymers with different chemical properties is an effective method for manufacturing new materials. However, the incompatibility between different polymers can cause phase separation in the blend, leading to the formation of polymer-polymer interfaces with weak adhesion and mechanical properties within the material. The rheological and molecular chain dynamics of incompatible blends become highly complex due to the presence of interfaces, especially when entanglement topological constraints exist at the interface. Therefore, entangled polymer-polymer interfaces have become a hot topic for materials scientists. To enhance the strength of the interface, additives such as block copolymers are often added. Block copolymers exceeding the entanglement length not only reduce interfacial tension and increase interfacial viscosity but also further improve the entanglement network at the interface, suppressing the generation of interfacial velocity slip. Therefore, ternary polymer blends have significant industrial application value, and their interfacial properties are complex.

[0003] Despite abundant experimental findings on the rheological behavior of polymer-polymer interfaces in ternary polymer blends over the past decade, molecular-level explanations remain scarce. Furthermore, obtaining equilibrium homopolymer-homogene-block copolymer ternary entangled polymer mixtures with planar interfaces through phase separation kinetics is extremely difficult and time-consuming. Recently, Nikunen et al. improved upon traditional dissipative particle dynamics by increasing the conservative force from 25 to 200 to induce entanglement. Moreover, researchers have demonstrated that this method achieves shorter entanglement lengths compared to the Kremer-Grest model, thus enabling the simulation of polymers with higher entanglement numbers for the same chain length. Therefore, this invention aims to provide a modeling method for studying homopolymer-homogene-diblock copolymer ternary entangled polymer blend systems using dissipative particle dynamics, to investigate the properties and rheological behavior of the entangled polymer-polymer interfaces within these systems. Summary of the Invention

[0004] The purpose of this invention is to provide a method for studying the construction of ternary entangled polymer mixtures of homopolymer-homogene-diblock copolymers using dissipative particle dynamics.

[0005] The present invention provides a method for constructing ternary entangled polymer mixtures of homopolymer-homogene-diblock copolymers using dissipative particle dynamics, comprising the following steps:

[0006] S1. Obtain the characteristic ratio and equilibrium bond length of the simulation system. Based on the equilibrium bond length and the characteristic ratio, generate a series of homopolymers and diblock copolymers with bond length as the step size, so that the generated chains have the correct end distance on a large scale.

[0007] S2. Based on the chain length, chain number, and number density of the simulation system, place the series of random walk homopolymers and copolymers obtained in step S1 into the simulation box;

[0008] S3. Use dissipative particle dynamics to introduce interaction potentials between particles, use simple harmonic spring potentials to introduce bonding interaction potentials, and use bending potential functions to introduce bond angle interaction potentials.

[0009] S4. Gradually increase the repulsion parameter. The difference in repulsion parameter between each stage should be equal or approximately equal, and the increase in repulsion parameter for different particles should be equal.

[0010] S5. Set the rejection parameter to the final usage value and run for 1-2 Rouse times;

[0011] S6. Check if the conformation of the chain is in equilibrium. If the mean square intrachain distance of each component no longer changes with time, the system has reached equilibrium. Otherwise, the system has not reached equilibrium. Repeat step S5 to obtain an equilibrium system.

[0012] In the above construction method, in step S1, if the characteristic ratio is known, it can be used directly; if the characteristic ratio of the simulated polymer is unknown, the equilibrium bond length can be obtained by directly simulating short-chain polymers, and the bond angle cosine value can be obtained according to the bond vector correlation function. Then, the theoretical value of the characteristic ratio can be obtained according to the theoretical prediction of the free-rotating chain. Here, the characteristic ratio and chain length used to generate the initial state of the diblock copolymer are the same as those of the homopolymer.

[0013] In the above construction method, in step S2, the simulated box is divided into an upper part and a lower part, and homopolymer A is... N B N The elements are randomly placed into the upper and lower parts of the simulated box, thus forming A at the middle, upper boundary, and lower boundary of the simulated box, respectively. N -B N Interface, randomly place the diblock copolymer into A N -B N The interface maintains equal areal densities of the block copolymers at both interfaces, with the junction of the two blocks located at A. N -B N The interface is determined to be a diblock copolymer.

[0014] In the above construction method, in step S3, in the dissipative particle dynamics method, in order to better separate particles from each other, the repulsion parameter of the conservative force between like particles or between particles with affinity is 25, i.e., a. AA =a BB =a CC =a DD =a AC =a BD =25, the repulsion parameter between different copolymer particles is a AB =55, the repulsion parameter between the incompatible block copolymer and the homopolymer particles is a. BC =a AD =40~55; in addition, the bonding potential coefficient is always twice the repulsion parameter between the same type of particles.

[0015] In the above construction method, in step S3, the simulation time in the dissipative particle dynamics method is 1 to 2 Rouse times, where the Rouse time is the Rouse relaxation time of the homopolymer of the same chain length corresponding to the polymer with the longest chain length in the system.

[0016] In the above construction method, the running time in step S4 is 1 to 2 Rouse times.

[0017] In the above construction method, in step S5, the repulsion parameter is 200, i.e., a AA =a BB =a CC =a DD =a AC =a BD =200, a AB =230, a BC =a AD =215~230.

[0018] The ternary entangled polymer mixture melt with equilibrium conformation obtained through the above steps can qualitatively describe the structure, kinetics, and rheological properties of the polymer mixture, especially the structure and rheological properties of the interface. This allows for a molecular-level explanation of experimental phenomena and the establishment of more accurate related theories.

[0019] The equilibrium system obtained by constructing the model using the above method also falls within the protection scope of this invention.

[0020] The present invention has the following beneficial effects:

[0021] The present invention constructs a ternary entangled polymer mixture with an entangled interface and a near-equilibrium conformation. By placing homopolymer and copolymer molecules into a pre-defined phase region and adjusting the corresponding repulsion parameters, the equilibrium conformation of the entangled polymer mixture can be obtained quickly. Compared with the method of directly obtaining phase-separated entangled polymer mixtures through phase separation kinetics, the present invention uses a shorter equilibrium time, saving a significant amount of time and computational resources. It provides an effective way to efficiently and accurately study the structure and property relationships of entangled polymer mixtures and their entangled interfaces. Attached Figure Description

[0022] Figure 1 This invention illustrates the homopolymer (A) used in this invention. N B N ), diblock copolymer (C N D N )Model.

[0023] Figure 2 This paper presents a dissipative particle dynamics model of the homopolymer-homogeneous-diblock copolymer ternary entangled polymer mixture system constructed according to the present invention.

[0024] Figure 3 The changes in total particle number and entanglement point number density along the interface normal direction are shown.

[0025] Figure 4 The displacement of the interfacial block copolymer along the flow velocity direction and velocity gradient direction under shear flow is shown as a function of time.

[0026] Figure 5 A cross-sectional view of the particle velocity along the interface normal direction under shear flow is shown. Detailed Implementation

[0027] Unless otherwise specified, the experimental methods used in the following examples are conventional methods.

[0028] Unless otherwise specified, all materials and reagents used in the following examples are commercially available.

[0029] Homopolymer A 125 -Homopolymer B 125 -Diblock copolymer C 125 D 125 Taking the equilibrium of a ternary entangled polymer mixture as an example, the specific implementation steps of the equilibrium method of the present invention will be illustrated:

[0030] 1) For a homopolymer system with a chain length of 10, a chain number of 10, and a number density of 1, the equilibrium bond length was directly simulated using the entangled dissipative particle dynamics method, yielding a value of 0.964. Based on the potential function in the form of the bending potential cosine, the value of the bond angle cosine when the bending potential coefficient is 2 was obtained. Substituting this value into the intra-chain distance formula of the free-rotating chain FRC model, the eigenvalue ratio was found to be 3.32. Setting the equilibrium bond length of the initial conformation to 0.95, and based on the relationship between the end-to-end distance of the free-rotating chain and the eigenvalue ratio, a series of homopolymers and diblock copolymers with approximately correct end-to-end distances on a large scale were generated through random walks.

[0031] 2) Set the system number density to 1, homopolymer A 125 B 125 Both have a chain length of 125 and a chain number of 1440, and are diblock copolymers C 125 D 125 The length of each segment is 125, the total chain length is 250, the number of chains is 160, and the simulated box size is set to 80r. c ×50r c ×100r c Divide the box into upper and lower parts along the z-direction, and place the homopolymer A produced in step (1) into the box. 125 B 125 The top and bottom parts of the box are randomly placed respectively, so that when z = 50r c and z = 0 (or 100r) c A is generated at each of the following locations: 125 -B 125 The interface, then z=50r c Eighty diblock copolymer C lines were placed on the interface at z=0. 125 D 125 That is, block C 125 and D 125 The connection point is located at z=50r c z = 0;

[0032] 3) An interparticle interaction potential is introduced using dissipative particle dynamics, where the repulsion parameter is a. AA =a BB =a CC =a DD =a AC =a BD =25, a AB =55, a BC =a AD =55, using a simple harmonic spring potential to introduce the bonding interaction potential, and using a cosine-form bending potential to introduce the bond angle potential, to simulate a Rouse time;

[0033] 4) Adjust the repulsion parameter to a every Rouse interval. AA =a BB =a CC =a DD =a AC =a BD =50, a aB =80, a BC =a AD =80, a AA =a BB =a CC =a DD =a AC =a BD =100, a AB =130, a BC =a AD =130 and a AA =a BB =a CC =a DD =a AC =a BD =150, a AB =180, a BC =a AD =180, the bonding potential coefficient is always twice the repulsion parameter between the same type of particles;

[0034] 5) Set the rejection parameter to the final usage value, i.e., the rejection parameter is a. AA =a BB =a CC =a DD =a AC =a BD =200, a AB =230, a BC =a AD =230, run for one Rouse time, characterizing A in the system respectively. 125 B 125 and C 125 D 125 Chain conformation, i.e., the distance within the chain;

[0035] 6) Repeat step (5) until the distances within the chain no longer change, resulting in an initial state with good conformational equilibrium, such as... Figure 2 As shown.

[0036] The system established above is analyzed. First, its particle density and normalized entanglement number density are statistically analyzed as a function of the interface normal direction. Figure 3The study found that the particle number density and entanglement number density at the interface decreased, indicating that the intermolecular chain interactions at the interface were weaker than those in the bulk. If a shear flow with a velocity direction parallel to the interface and a velocity gradient perpendicular to the interface is applied to the system, the displacements of the block copolymer in various directions are statistically analyzed. Figure 4 It can be observed that the displacement of the molecular chains in the direction of the velocity gradient in the flow field is almost negligible compared to that in the direction of the flow field velocity, indicating that the block copolymer is fixed at the interface and cannot move along the interface normal direction. Statistical analysis of the velocities of all particles along the shear field direction reveals a discontinuous change in velocity at the interface. Figure 5 This is the velocity slip phenomenon, which is caused by weak inter-chain interactions between molecules at the interface.

[0037] In summary, the equilibrium conformation of the ternary entangled polymer mixture melt constructed in this invention can qualitatively describe the structure, dynamics, and rheological properties of polymer mixtures, especially the structure and rheological properties of the interfaces. This allows for a molecular-level explanation of experimental phenomena and the establishment of more accurate related theories.

Claims

1. A method for constructing a ternary entangled polymer mixture of homopolymer-homogene-diblock copolymer using dissipative particle dynamics, comprising the following steps: S1. Obtain the characteristic ratio and equilibrium bond length of the simulation system. Based on the equilibrium bond length and the characteristic ratio, generate a series of homopolymers and diblock copolymers with bond length as the step size, so that the generated chains have the correct end distance on a large scale. S2. Based on the chain length, chain number, and number density of the simulation system, place the series of random walk homopolymers and copolymers obtained in step S1 into the simulation box; The simulated box was divided into an upper part and a lower part, and homopolymer A was placed... N B N The elements are randomly placed into the upper and lower parts of the simulated box, thus forming A at the middle, upper boundary, and lower boundary of the simulated box, respectively. N -B N Interface, randomly place the diblock copolymer into A N -B N The interface maintains that the areal density of the block copolymers at both interfaces is equal; S3. Use dissipative particle dynamics to introduce interaction potentials between particles, use simple harmonic spring potentials to introduce bonding interaction potentials, and use bending potential functions to introduce bond angle interaction potentials. S4. Gradually increase the repulsion parameter, and keep the difference in repulsion parameter between each stage equal, and keep the increase in repulsion parameter for different particles equal; S5. Set the rejection parameter to the final usage value and run for 1~2 Rouse times; S6. Check if the conformation of the chain is in equilibrium. If the mean square intrachain distance of each component no longer changes with time, the system has reached equilibrium. Otherwise, the system has not reached equilibrium. Repeat step S5 to obtain an equilibrium system.

2. The construction method according to claim 1, characterized in that: In step S3, in the dissipative particle dynamics method, the repulsion parameter of the conservative force between like particles or between particles with affinity is 25, that is... The repulsion parameter between different copolymer particles is The repulsion parameter between the incompatible block copolymer and the homopolymer particles is: = .

3. The construction method according to claim 2, characterized in that: In step S3, the simulation time in the dissipative particle dynamics method is 1 to 2 Rouse times.

4. The construction method according to any one of claims 1-3, characterized in that: In step S4, the running time is 1 to 2 Rouse times.

5. The construction method according to any one of claims 1-3, characterized in that: In step S5, the repulsion parameter is 200.

6. The initial equilibrium state of the coarse-grained ternary entangled polymer mixture constructed by the method of any one of claims 1-5.

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