CN113742977B - Design method, device and terminal of organic polymer-inorganic interface - Google Patents
Design method, device and terminal of organic polymer-inorganic interface Download PDFInfo
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Abstract
The application provides a design method of an organic polymer-inorganic interface, which comprises the steps of constructing an organic polymer dynamic model and an inorganic polymer dynamic model; according to a molecular dynamics model, an organic polymer-inorganic initial system is obtained, an organic polymer-inorganic interface is generated after the organic polymer-inorganic initial system is balanced, the organic polymer-inorganic system is formed, the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacted with the inorganic layer, and the organic polymer layer comprises an organic polymer chain; the spatial distribution information of organic polymer chains in an organic polymer-inorganic system is counted; carrying out mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to a mechanical simulation test result, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface; and designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
Description
Technical Field
The application belongs to the field of molecular simulation calculation, and particularly relates to a method, a device and a terminal for designing an organic polymer-inorganic interface.
Background
With the continuous development of electronic devices, users have higher and higher requirements on the performance and appearance of the electronic devices, and in the production process of the electronic devices, the cooperation of an organic layer and an inorganic layer is increasingly adopted to realize excellent performance and rich appearance effects. However, the difference in properties between the organic material and the inorganic material may cause undesirable phenomena such as cracking and falling off between the organic layer and the inorganic layer, which is disadvantageous for the use of the electronic device.
Disclosure of Invention
In view of the above, the application provides a design method, a device, a terminal and a computer readable storage medium of an organic polymer-inorganic interface based on molecular dynamics simulation, which provide guidance for screening organic polymers and inorganic materials and designing an organic polymer layer-inorganic layer laminated structure with high stability and high reliability.
In a first aspect, the present application provides a method for designing an organic polymer-inorganic interface, including:
Constructing an organic polymer molecular dynamics model and an inorganic molecular dynamics model;
According to the organic polymer dynamics model and the inorganic polymer dynamics model, an organic polymer-inorganic initial system is obtained, an organic polymer-inorganic interface is generated after the organic polymer-inorganic initial system is balanced, and an organic polymer-inorganic system is formed, wherein the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacted with the inorganic layer, and the organic polymer layer comprises an organic polymer chain;
counting the space distribution information of the organic polymer chains in the organic polymer-inorganic system;
Performing a mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to the result of the mechanical simulation test, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface;
and designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
In a second aspect, the present application provides an organic polymer-inorganic interface design device, comprising:
The building module is used for building an organic polymer system model and an inorganic layer model;
The balance module is used for obtaining an organic polymer-inorganic initial system according to the organic polymer system model and the inorganic layer model, wherein the organic polymer-inorganic initial system generates an organic polymer-inorganic interface after being balanced to form an organic polymer-inorganic system, the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacted with the inorganic layer, and the organic polymer layer comprises an organic polymer;
the statistics module is used for counting the space distribution information of the organic polymer chains in the organic polymer-inorganic system;
The simulation module is used for carrying out mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to the results of the mechanical simulation test, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface;
and the design module is used for designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
In a third aspect, the present application provides a terminal comprising a processor and a memory storing at least one instruction for execution by the processor to implement the design method of the first aspect.
In a fourth aspect, the present application provides a computer-readable storage medium storing at least one instruction for execution by a processor to implement the design method of the first aspect.
The application provides a design method, a device, a terminal and a computer readable storage medium of an organic polymer-inorganic interface based on molecular dynamics simulation, wherein the method comprises the steps of obtaining the spatial distribution information of an organic polymer chain in a system by constructing an organic polymer-inorganic system, obtaining parameters of a cohesive force model through molecular dynamics simulation, obtaining a finite element model and an interface stress distribution condition, and playing a reference role in selecting materials of an organic polymer layer and an inorganic layer according to the spatial distribution information and the stress distribution condition of the organic polymer chain so as to provide a reference for the design of the organic polymer-inorganic interface; meanwhile, the method provided by the application avoids a large number of experiments, saves cost and time, realizes the simulation from microscopic molecular simulation to macroscopic finite element model, realizes the cross-scale simulation calculation, can better select the materials of the organic polymer layer and the inorganic layer, and plays a guiding role in designing the organic polymer layer-inorganic layer laminated structure with high stability and high reliability.
Drawings
In order to more clearly explain the technical solutions in the embodiments of the present application, the drawings that are used in the embodiments of the present application will be described below.
Fig. 1 is a schematic structural view of a housing provided in the prior art.
Fig. 2 is a detection diagram of the housing shown in fig. 1 after the water boiling test, wherein (a) in fig. 2 is an optical interference diagram, and (b) in fig. 2 is an electron microscope diagram.
FIG. 3 is a flow chart of a method for designing an organic polymer-inorganic interface according to an embodiment of the present application.
Fig. 4 is a schematic flow chart of S101 in fig. 3.
Fig. 5 is a schematic diagram of an initial polymethyl methacrylate model according to an embodiment of the present application.
Fig. 6 is a schematic diagram of an equilibrium system of an initial polymethyl methacrylate model according to an embodiment of the present application.
Fig. 7 is a schematic view of an atomic structure of an inorganic layer according to an embodiment of the present application.
Fig. 8 is a schematic diagram of an organic polymer-inorganic initial system according to an embodiment of the present application.
Fig. 9 is a schematic diagram of spatial distribution of an organic polymer chain according to an embodiment of the present application, wherein (a) in fig. 9 is a chain type schematic diagram, (b) in fig. 9 is a tail type schematic diagram, and (c) in fig. 9 is a ring type schematic diagram.
FIG. 10 is a mass density distribution curve of an organic polymer chain according to an embodiment of the present application.
Fig. 11 is a diagram showing spatial distribution information of organic polymer chains in an organic polymer molecular dynamics model according to an embodiment of the present application.
Fig. 12 is a block diagram showing spatial distribution information of organic polymer chains in an organic polymer-inorganic system according to an embodiment of the present application.
Fig. 13 is a block diagram showing spatial distribution information of organic polymer chains in an organic polymer-inorganic system corresponding to different interface types according to an embodiment of the present application.
Fig. 14 is a block diagram showing spatial distribution information of organic polymer chains in an organic polymer-inorganic system corresponding to different crosslinking densities according to an embodiment of the present application.
Fig. 15 is a mechanical simulation test chart of an organic polymer-inorganic system according to an embodiment of the present application.
Fig. 16 shows a mechanical simulation test result of an organic polymer-inorganic system according to an embodiment of the present application, wherein (a) in fig. 16 shows a pulling strength result, (b) in fig. 16 shows a maximum pulling work result, and (c) in fig. 16 shows a shear strength result.
Fig. 17 is a schematic diagram of a finite element model according to an embodiment of the present application.
FIG. 18 is a graph showing the stress distribution of an organic polymer-inorganic interface according to an embodiment of the present application.
Fig. 19 is a schematic block diagram of an apparatus for designing an organic polymer-inorganic interface according to an embodiment of the present application.
Fig. 20 is a block diagram of a terminal according to an embodiment of the present application.
Detailed Description
The following are preferred embodiments of the present application, and it should be noted that modifications and variations can be made by those skilled in the art without departing from the principle of the present application, and these modifications and variations are also considered as the protection scope of the present application.
The present application has been made based on the findings and knowledge of the inventors regarding the following facts and problems:
The inventor has found that, in the present case 10 (such as a middle frame, a front cover, a battery cover, etc.) of an electronic device, materials such as plastic, glass, metal, ceramic, etc. are often used as the substrate 11, and the performance and appearance of the substrate 11 itself have small changes, and it is necessary to prepare multiple film layers on the substrate 11 to improve the performance and appearance of the electronic device. For example, the texture layer 12 prepared by molding ultraviolet curing glue on the surface of the substrate 11, and the physical vapor deposition on the surface of the texture layer 12 are used to prepare a multi-layer inorganic layer with color or optical variation, wherein the material of the inorganic layer comprises at least one of silicon oxide, niobium oxide, indium antimonide, zirconium oxide and the like. In the related test of stability and reliability of the electronic device, as the texture layer 12 is made of an organic material and the inorganic layer is made of an inorganic material, the performance of the texture layer and the inorganic layer are obviously different, and adverse phenomena such as cracking and falling off can occur between the texture layer and the inorganic layer in the test process. Referring to fig. 1, a schematic structural diagram of a shell provided in the prior art is shown, wherein a shell 10 includes a substrate 11, a texture layer 12, a coating layer 13 and an ink layer 14, which are stacked, and the coating layer 13 includes a plurality of inorganic layers; referring to fig. 2, a detection diagram of the shell shown in fig. 1 after the water boiling test is shown, wherein (a) in fig. 2 is an optical interference diagram, and (b) in fig. 2 is an electron microscope diagram, the water boiling test includes treating in water at 80 ℃ for 30min, then performing optical interference detection and electron microscope detection on the texture layer 12 and the coating layer 13, deformation of the stripes in fig. 2 (a) indicates that cracks are generated, the dark color part in fig. 2 (b) is the texture layer 12, and the light color part is the multi-layer inorganic layer, and it can be seen that cracks are generated in the coating layer 13 after the water boiling test. The difference of the performances of the organic material and the inorganic material can diffuse into the organic polymer layer and even react in the deposition process of the inorganic layer, so that the whole brittleness is improved, the fracture strain is reduced, and the interface stability and reliability between the organic polymer layer and the inorganic layer are poor, thereby influencing the use of electronic equipment. In the related technology, the interface performance is often tested through a large number of performance detection experiments, so that proper organic materials and inorganic materials are selected, but the whole test period is long, the experiment cost is high, and the data is not rich enough. Therefore, the inventor provides a design method based on molecular dynamics simulation and finite element analysis, which realizes the cross-scale simulation calculation from microscopic molecular simulation to macroscopic finite element model, avoids the implementation of a large number of experiments, and saves cost and time.
Referring to fig. 3, a flow chart of a method for designing an organic polymer-inorganic interface according to an embodiment of the application includes:
s101: and constructing an organic polymer molecular dynamics model and an inorganic molecular dynamics model.
S102: according to the organic polymer dynamics model and the inorganic polymer dynamics model, an organic polymer-inorganic initial system is obtained, an organic polymer-inorganic interface is generated after the organic polymer-inorganic initial system is balanced, the organic polymer-inorganic system is formed, the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacted with the inorganic layer, and the organic polymer layer comprises an organic polymer chain.
S103: and (3) counting the spatial distribution information of the organic polymer chains in the organic polymer-inorganic system.
S104: and (3) carrying out mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to the result of the mechanical simulation test, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface.
S105: and designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
In the application, firstly, the spatial distribution information of an organic polymer chain in an organic polymer-inorganic system and a mechanical simulation test result are obtained through molecular dynamics simulation, namely a molecular simulation result with a microscopic size is obtained; the mechanical simulation test result is applied to the finite element model, so that the calculation simulation on the macroscopic size is realized, the real result is more accordant, the calculation simulation is performed, the multiple experiments are avoided, and the time and the cost are saved; compared with the pure molecular dynamics simulation, the design method provided by the application realizes the trans-scale analysis, and the result is more in line with the real situation; the simple finite element analysis requires a large number of experiments to determine the constitutive relation, and the parameters obtained by the method provided by the application through molecular dynamics simulation are applied to the finite element analysis, so that the implementation of a large number of experiments is avoided. The design method provided by the application provides guidance and reference for the selection of organic materials and inorganic materials, and provides theoretical basis for obtaining the organic-inorganic structure with high stability and high reliability.
In S101, an organic polymer molecular dynamics model and an inorganic molecular dynamics model are constructed, and preparation is made for subsequent molecular dynamics simulation.
Please refer to fig. 4, which is a flowchart of S101 in fig. 3, comprising:
s1011: and generating an organic polymer initial model through modeling, applying a molecular force field to the organic polymer initial model, and carrying out systematic balance to obtain the organic polymer dynamic model.
S1012: and generating an inorganic layer initial model through modeling, and applying a molecular force field to the inorganic layer initial model to obtain the inorganic molecular dynamics model.
In S1011, constructing the organic polymer molecular dynamics model includes: and generating an organic polymer initial model through modeling, applying a molecular force field to the organic polymer initial model, and carrying out systematic balance to obtain an organic polymer dynamic model.
In one embodiment of the application, modeling is performed by modeling software. That is, an organic polymer initial model is constructed by modeling software. In particular, the modeling software includes at least one of MATERIALS STUDIO, moltemplate, VMDTopoTools, avogadro, packmol, OCAT, and Enhanced Monte Carlo.
In one embodiment of the present application, the organic polymer initial model includes a box and organic polymer chains dispersed in the box. It will be appreciated that the shape of the box may be, but is not limited to, rectangular, square, cylindrical, etc., and is selected as desired, the box being for accommodating the organic polymer chains. Further, the length of the box isThe height isThickness is/>Not only can ensure the distribution of organic polymer chains, but also can not excessively increase calculation. In one embodiment of the present application, the number of organic polymer chains in the box is 20 or more, and the number of repeating units in each organic polymer chain is 10 or more. In this way, the molecular dynamics simulation is guaranteed. Further, the number of organic polymer chains in the box is 20-100, and the number of repeating units in each organic polymer chain is 10-80. Thus, abundant calculation results can be obtained, and the calculation time is not excessively increased. Specifically, the number of organic polymer chains in the box may be, but not limited to, 20, 30, 40, 50, 65, 70, 80, 90 or 100, etc., and the number of repeating units in each organic polymer chain is 10, 20, 35, 40, 50, 65, 70 or 80, etc. In the present application, the number of repeating units in the plurality of organic polymer chains in the cassette is the same. By controlling the number of organic polymer chains in the box and the number of repeating units in the organic polymer chains, the influence of different numbers of organic polymer chains in the box and/or different numbers of repeating units in the organic polymer chains on the organic-inorganic interface performance can be studied, so that guidance can be provided for the selection of the addition amount, molecular weight and polymerization degree of the organic polymer. Specifically, a three-dimensional coordinate system (x, y, z) is constructed in modeling software, and an organic polymer initial model is constructed by taking (0, 0) as a starting point.
In one embodiment, a rectangular simulated box is constructed by Moltemplate, the box being sized20 Polymethyl methacrylate (PMMA) chains, each having 40 methyl methacrylate repeating units, were placed in a box, the PMMA chains were arranged in a regular manner, and a space was reserved for the PMMA chains to freely move during the equilibration process, and an initial model of polymethyl methacrylate was obtained, and the results are shown in FIG. 5.
In the embodiment of the application, a molecular force field is applied to the constructed organic polymer initial model. The molecular force field can calculate the interaction between atoms, so that the initial model of the organic polymer can be more in line with the actual situation. In one embodiment of the application, the molecular force field comprises at least one of CVFF, reaxFF and COMPASS. CVFF is a uniform valence force field, reaxFF is a reaction force field, and COMPASS is a molecular force field for the optimization of the aggregation state in atomic level simulation research. It can be understood that the construction of the initial model of the organic polymer and the application of the molecular force field can be completed in modeling software; after the application of the molecular force field, the model is exported as a readable file of molecular dynamics simulation software, so as to prepare for the subsequent molecular dynamics simulation.
In an embodiment of the present application, the system balance of the organic polymer initial model includes: and setting boundary conditions for the organic polymer initial model, and then sequentially adopting a regular ensemble and an isothermal and isobaric ensemble to carry out system balance.
In one embodiment of the present application, setting boundary conditions on the organic polymer initial model includes: introducing an organic polymer initial model into molecular dynamics simulation software, and establishing a three-dimensional coordinate system (x, y, z) in the molecular dynamics simulation software; periodic boundaries are arranged in the x and y directions of the initial model of the organic polymer, and impermeable constraints are arranged in the z direction. By arranging periodic boundaries in the x and y directions, mass conservation in the x and y directions is ensured, and impenetrable constraint is arranged in the z direction, so that only one organic-inorganic interface exists in the organic polymer-inorganic system. Further, the impenetrable constraint satisfies an LJ-93 function, an LJ-126 function, an LJ-1043 function, a Morse function, or a function represented by formula (I),
E＝∈(r-rc)2 (I)。
In the application, the function shown in the formula (I) represents a linear spring type wall, when the movement of an organic polymer chain spans the wall surface, the position of the organic polymer chain is updated to a specular reflection position, which is equivalent to the elastic collision of the organic polymer chain to the wall surface, so that the mass conservation in the z direction is ensured; wherein E represents the energy of the atom near the boundary, r is the distance between the wall and the atom, E is the energy constant, E represents the intensity of the constraint, and r c is the cutoff distance. In one embodiment of the application, E isR c is 0.5nm to 1.5nm. LJ-93 function represents the sum of the actions of atoms in the semi-infinite region outside the boundary on one atom in the boundary, representing the action of the wall on the organic polymer chain, LJ-93 function is
In an embodiment of the application, the organic polymer initial model with set boundary conditions is subjected to system balance under a regular ensemble (NVT ensemble) and an isothermal and isobaric ensemble (NPT ensemble). The NVT ensemble keeps the system atomic number, volume and temperature unchanged, and the NPT ensemble keeps the system atomic number, pressure and temperature unchanged. The NVT ensemble can realize high Wen Chi relaxation, provide a larger space for the activity of the organic polymer chains, enable the organic polymer chains to be fully and uniformly mixed, and eliminate the influence of an initial configuration; the adoption of NPT ensemble can make the organic polymer chain implement sufficient balance. In one embodiment, NVT ensemble comprises 1ns-10ns balanced at 500K-700K. By achieving a sufficiently uniform mixing of the organic polymer chains at a relatively high temperature. Further, the time step is 1fs. Specifically, the temperature in NVT ensemble is 500K, 550K, 600K, 650K, 700K, etc., and the equilibration time is 1ns, 2ns, 3ns, 6ns, 8ns, 9ns, 10ns, etc. In a specific embodiment, the NVT ensemble comprises 10ns balanced at 600K at a time step of 1fs. In one embodiment, the balance is 10ns or more at the NPT ensemble to achieve sufficient balance of the organic polymer chains. Further, the balancing time is 10ns-100ns, such as 10ns, 20ns, 25ns, 30ns, 40ns, 50ns, 55ns, 60ns, 70ns, 80ns, 90ns or 100ns, etc. Specifically, the temperature and pressure in the NPT ensemble may be selected according to the temperature and pressure required for molecular dynamics simulation, for example, the NPT ensemble may be equilibrated at 300K, 1atm for more than 10ns. Further, the NPT ensemble balancing time is 10ns-100ns. In the NPT ensemble, the temperature control can be a Langevin method, berendsen or a Nose-Hoover method, and the pressure control can be a Berendsen method or a Nose-Hoover method; wherein Tdamp is a parameter for controlling temperature, which represents the intensity of temperature relaxation at the time of controlling temperature, pdamp is a parameter for controlling pressure, which represents the intensity of pressure relaxation at the time of controlling pressure. Specifically, tdamp may be, but is not limited to, 10 4, pdamp may be, but is not limited to, 10 5.
Referring to fig. 6, a schematic diagram of an equilibrium system of an initial polymethyl methacrylate model according to an embodiment of the present application is shown, specifically, the initial polymethyl methacrylate model shown in fig. 5 is introduced into LAMMPS to perform molecular dynamics simulation, periodic boundaries are adopted in x and y directions, and an impenetrable constraint is applied in z direction; then adopting NVT ensemble balance to balance 1ns at 600K and time step of 1 fs; and then the temperature is reduced to 300K, the pressure is controlled to be 1atm, wherein the temperature is controlled to be 10 4 by adopting a Langevin method, the control parameter Tdamp is controlled to be 10 5379 by adopting a Berendsen method, the control parameter Pdamp is controlled to be 10 5, and the balance is more than 10ns, so that the polymethyl methacrylate molecular dynamics model is obtained.
In S1012, constructing an inorganic molecular dynamics model includes: and generating an inorganic layer initial model through modeling, and applying a molecular force field to the inorganic layer initial model to obtain an inorganic molecular dynamics model.
In one embodiment of the application, modeling is performed by modeling software. That is, an inorganic layer initial model is constructed by modeling software. Specifically, the modeling software includes at least one of LAMMPS, MATERIALS STUDIO, moltemplate, VMDTopoTools, avogadro, packmol, OCAT, and Enhanced Monte Carlo. It can be understood that the thickness of the inorganic layer model generated by modeling is larger than 1nm, so that the subsequent molecular dynamics simulation analysis can be performed. In one embodiment, si unit cells are selected in the MATERIALS STUDIO structure database; super cell construction was performed on the Si cells using supercell and the silicon layer was expanded. In one embodiment of the application, a molecular force field is applied to the inorganic layer initial model, the molecular force field comprising at least one of CVFF, reaxFF and COMPASS. It can be understood that the charge distribution condition of the inorganic layer surface is obtained by adding a molecular force field; in the structure of the lamination arrangement of the actual organic polymer layer and the inorganic layer, the morphology of the organic polymer chain near the organic-inorganic interface is different from the morphology of the organic polymer chain at other positions of the organic polymer layer due to the adsorption effect and charge transfer of the surface of the inorganic layer, so that the interface performance is also affected to a certain extent; therefore, by adding a molecular force field, the influence of the charged inorganic layer and the uncharged inorganic layer on the interface performance can be studied. Referring to fig. 7, a schematic view of an atomic structure of an inorganic layer according to an embodiment of the present application is shown, wherein Si {100} surfaces are not charged; the surface of SiO 2 is charged, O is-0.3 e, si is 0.6e, the light circle represents silicon atom, and the dark circle represents oxygen atom; the ZrO 2 surface was charged, O was-0.505 e, zr was 1.010e, the light circles represent zirconium atoms, and the dark circles represent oxygen atoms. It can be understood that the construction of the initial model of the inorganic layer and the application of the molecular force field can be completed in the modeling; if the model is not modeled in the molecular dynamics simulation software, after the molecular force field is applied, the model is exported as a readable file of the molecular dynamics simulation software, so that preparation is made for subsequent molecular dynamics simulation.
In S102, an organic polymer-inorganic system is formed based on the organic polymer kinetic model and the inorganic molecular kinetic model.
In the application, the organic polymer molecular dynamics model and the inorganic molecular dynamics model can be imported into molecular dynamics simulation software, and the organic polymer-inorganic system can be obtained through balancing. In one embodiment of the present application, after the organic polymer molecular dynamics model and the inorganic molecular dynamics model are introduced into the molecular dynamics simulation software, the organic polymer molecular dynamics model and the inorganic molecular dynamics model are contacted to generate an organic polymer-inorganic interface. In the present application, it is also possible to consider whether or not bonding occurs between the organic polymer layer and the inorganic layer, chemical bonds or the like may be introduced between interfaces; specifically, for example, when a CVFF molecular force field is adopted, whether bonding occurs between an actual organic polymer layer and an inorganic layer needs to be judged, so that the bonding is added according to the actual situation; when ReaxFF molecular force fields are adopted, the preparation can be directly generated without adding. In one embodiment of the application, periodic boundaries are arranged in the x and y directions of the initial model of the organic polymer, and impenetrable constraints are arranged in the z direction, so that the interface between the inorganic layer and the organic polymer layer is perpendicular to the z direction, thereby ensuring that only one interface exists in the system. Referring to fig. 8, a schematic diagram of an organic polymer-inorganic initial system according to an embodiment of the application is shown, wherein the organic polymer is PMMA and the inorganic layer is a silicon layer.
In one embodiment of the application, the organic polymer-inorganic initial system is balanced under the NPT ensemble. In one embodiment of the application, the organic polymer-inorganic initial system generates an organic polymer-inorganic interface after being balanced to form an organic polymer-inorganic system, wherein the organic polymer-inorganic initial system is balanced for more than 10ns under the NPT system, so as to obtain the organic polymer-inorganic system. Further, the balancing time is 10ns-100ns, such as 10ns, 20ns, 25ns, 30ns, 40ns, 50ns, 55ns, 60ns, 70ns, 80ns, 90ns or 100ns, etc. Specifically, the temperature and pressure of the NPT ensemble are selected according to the requirements of molecular dynamics simulation. In one embodiment, the organic polymer-inorganic initial system is balanced at 300K and 1atm, so that the organic polymer-inorganic initial system and the organic polymer-inorganic initial system can be fully contacted to form a stable interface, and the subsequent study of interface performance is facilitated.
In S103, guidance is provided for selection of molecular weight, polymerization degree, and the like of the organic material by counting spatial distribution information of the organic polymer chains in the organic polymer-inorganic system. The influence of different organic molecular weights, polymerization degrees and the like on the spatial distribution information of the organic polymer chains is calculated and simulated, so that a theoretical basis is provided for the selection of organic materials and the design of an organic polymer-inorganic interface.
In the embodiment of the application, the statistical information of the spatial distribution of the organic polymer chains in the organic polymer-inorganic system comprises statistics of the chain, tail and ring distribution duty ratio of the organic polymer chains in a preset area, wherein the preset area is an area of the organic polymer layer with the distance between the preset area and the surface of the inorganic layer within a preset value range. By counting the space distribution information of the organic polymer chains in the preset area, the organic-inorganic interface performance can be analyzed, and the calculated amount is not excessively increased; in the application, the space distribution information is the distribution ratio of chain, tail and ring of the organic polymer chains in a preset area, wherein the organic polymer chains are all positioned in the preset area and defined as chain; one end of the organic polymer chain is positioned in a preset area, and the other end of the organic polymer chain is positioned outside the preset area, and is defined as a tail type; the two ends of the organic polymer chain are both positioned in a preset area, and the middle part is positioned outside the preset area and is defined as a ring type. In one embodiment, the coordinates of all atoms in the organic polymer chains in the preset area in the equilibrium state are output through molecular dynamics software, so that the spatial distribution condition of the organic polymer chains is obtained, and the spatial distribution information of all the organic polymer chains in the preset area is obtained. Referring to fig. 9, a schematic spatial distribution diagram of an organic polymer chain according to an embodiment of the present application is shown in fig. 9, wherein (a) is a chain type schematic diagram, fig. 9 (b) is a tail type schematic diagram, fig. 9 (c) is a ring type schematic diagram, and a PMMA chain is taken as an example for illustration, and a range of a dashed frame is an organic polymer layer region within a preset value range from the surface of an inorganic layer, as shown in fig. 9 (a), and two PMMA chains are all located within the preset region, and are chain type; as shown in fig. 9 (b), one end of the three PMMA chains is located in a preset area, and the other end is located outside the preset area, and then the three PMMA chains are tail-shaped; as shown in fig. 9 (c), two ends of the three PMMA chains are located in a preset region, and the middle part is located outside the preset region, and is ring-shaped.
In an embodiment of the present application, the preset value is determined according to the mass density of the organic polymer chain. In an embodiment of the present application, according to a curve of a distance from the inorganic layer and a mass density of the organic polymer chain in a region where the distance is located, a distance after the mass density of the organic polymer chain reaches an equilibrium is selected from the curve as a preset distance. Referring to fig. 10, a mass density distribution curve of an organic polymer chain according to an embodiment of the present application is shown, wherein after the organic polymer-inorganic initial system shown in fig. 8 is balanced for 10ns at 300K and 1atm, a PMMA-Si system is obtained, the mass density distribution of the organic polymer chain in a region distant from the surface of the inorganic layer is counted, different curves represent the cross-linking density between the inorganic layer and the organic polymer layer, the unit of the cross-linking density is 1/nm 2, the number of covalent bonds between PMMA and Si in the contact surface range of the cross-linking density is 1nm 2, and a molecular force field is CVFF during modeling, so that covalent bonds are added between PMMA and Si in the organic polymer-inorganic initial system; it can be seen that when the distance from the surface of the inorganic layer is close to 2nm, the mass density of the organic polymer chain is stable, so that 2nm can be selected as a preset value, namely, the spatial distribution information of the organic polymer chain within the range of 2nm from the surface of the inorganic layer is counted. The inventor of the present application has found that chain conformation is unfavorable for load transmission through molecular chain, and the conformation at interface shows weaker mechanical performance, so that reference is provided for the selection of organic material and inorganic material based on the spatial distribution information of organic polymer chain in preset area. Referring to fig. 11 and fig. 12, fig. 11 is spatial distribution information of an organic polymer chain in an organic polymer molecular dynamics model provided by an embodiment of the present application, fig. 12 is spatial distribution information of an organic polymer chain in an organic polymer-inorganic system provided by an embodiment of the present application, wherein the organic polymer molecular dynamics model is a PMMA molecular dynamics model provided by the above embodiment, a statistical region is within a thickness range of 2nm from a surface of a PMMA layer, the organic polymer-inorganic system is a PMMA-Si system provided by the above embodiment, the statistical region is a PMMA layer within a thickness range of 2nm from a surface of a silicon layer, and meanwhile, influences of organic polymer chains with different molecular weights on the spatial distribution information are compared to provide a reference for selection of an organic polymer molecular weight; it can be seen that in the system formed by the organic polymer chains with high molecular weight, the chain duty ratio of the organic polymer chains is reduced, which is favorable for forming an entangled network structure and improving the interfacial mechanical properties of the inorganic layer and the organic polymer layer. Referring to fig. 13, in the spatial distribution information of organic polymer chains in an organic polymer-inorganic system corresponding to different interface types provided in an embodiment of the present application, a PMMA molecular dynamics model is used as a reference, and the spatial distribution information of organic polymer chains in a range of 2nm away from the surface of the inorganic layer in a PMMA-Si system and a PMMA-SiO 2 system are compared, so that it can be seen that the chain ratio in a PMMA-Si system and a PMMA-SiO 2 system is improved, and the chain ratio in a PMMA-Si system is lower than that in a PMMA-SiO 2 system. Referring to fig. 14, in the spatial distribution information of organic polymer chains in an organic polymer-inorganic system corresponding to different crosslinking densities provided in an embodiment of the present application, the statistics of the situation of the organic polymer chains in the PMMA-Si system within 2nm from the surface of the silicon layer shows that proper control of the crosslinking density in the system helps to reduce the chain duty ratio. In the application, the spatial distribution condition of the organic polymer chain is obtained by controlling different parameters such as the material quality of the organic material, the molecular weight, the polymerization degree and the like of the organic material and utilizing molecular dynamics simulation, and the selection of the organic material can be guided according to the spatial distribution condition, thereby being beneficial to obtaining a more stable and reliable organic-inorganic laminated structure.
In the application, the material, molecular weight, polymerization degree and the like of the organic polymer affect the spatial distribution information of the organic polymer chain, and the spatial distribution information also affects the result of the subsequent mechanical simulation test, thereby affecting the finite element model and the stress distribution, so that the selection of the organic polymer can be guided to a certain extent by counting the spatial distribution information of the organic polymer chain, thereby being beneficial to the design of the subsequent organic polymer-inorganic interface.
In S104, the interfacial properties in the organic polymer-inorganic system are obtained through mechanical simulation, the parameters of the cohesion model (Cohesive Zone Model, CZM) can be obtained according to the structure of the mechanical simulation, the parameters of the cohesion model obtained through microscopic simulation can be applied to the finite element model of the macroscopic structure, and the simulation calculation from microscopic nano level to macroscopic centimeter level is realized, so that the calculation simulation data which is closer to the real situation is obtained, and a solid foundation is provided for obtaining the stable and reliable organic-inorganic structure.
In an embodiment of the application, the mechanical simulation test includes a pull simulation and a shear simulation. The drawing strength, the maximum drawing work and the shearing strength are obtained through the curve of the interaction force between the organic polymer layer and the inorganic layer corresponding to the displacement in the drawing simulation and the shearing simulation, so that the parameters of the cohesive force model can be obtained. In one embodiment of the present application, the pulling simulation includes keeping the inorganic layer stationary, moving the organic polymer layer at a constant speed in a direction perpendicular to a contact surface of the organic polymer layer and the inorganic layer; the shearing simulation comprises the step of keeping the inorganic layer stationary and moving the organic polymer layer at a constant speed along a direction parallel to the contact surface of the organic polymer layer and the inorganic layer. In the traction simulation and the shearing simulation processes, constant-speed simulation is required to be kept, and the whole system is in a constant-temperature environment, so that the reliability of a test result is ensured. In one embodiment, the pulling simulation includes holding the inorganic layer stationary along the interface normal toThe upper end of the high polymer block is moved at a constant speed, the thickness of the upper end is taken to be 2nm, and meanwhile, the temperature of the system is kept at 300K; the shear simulation includes holding the inorganic layer stationary along a direction parallel to the interfaceThe upper end of the polymer block is uniformly moved, the thickness of the upper end is 2nm, and meanwhile, the temperature of the system is kept at 300K. Specifically, the moving speed, the grabbing thickness and the temperature can be selected according to the requirements. In one embodiment of the application, the displacement in the moving process and the interaction force between the corresponding organic polymer layer and the inorganic layer are counted through molecular dynamics simulation software, so that a displacement-force curve is obtained, and further, the parameters of the cohesive force model can be obtained. Referring to fig. 15, a mechanical simulation test chart of an organic polymer-inorganic system according to an embodiment of the present application is shown, wherein the PMMA-Si system according to the above embodiment is used for pulling simulation and shearing simulation; referring to fig. 16, the mechanical simulation test results of the organic polymer-inorganic system provided by an embodiment of the present application are shown in fig. 16, where (a) is a pulling strength result, and (b) is a maximum pulling work result, and (c) is a shear strength result, and the influence of the inorganic materials and the different crosslinking densities on the mechanical simulation test results is studied, and it can be seen that the test results are the highest when the inorganic materials are ZrO 2, siO 2 times, si is the lowest, and the test results are unchanged after the increase of the crosslinking density, which indicates that the appropriate change of the crosslinking density is also helpful to improve the pulling strength, the maximum pulling work and the shear strength. Through molecular dynamics simulation, the structure evolution and mechanical response of the organic high molecular structure under external load can be obtained; the interfacial mechanical properties of different types of organic polymer-inorganic interfaces are compared, so that the organic polymer-inorganic combination with the optimal interfacial properties can be selected.
In an embodiment of the present application, the cohesion model includes at least one of a bilinear type, a parabolic type, a normal type, and an exponential type. The cohesive force model parameters can be obtained according to the mechanical simulation test. Taking bilinear type as an example, fitting the cohesion model requires simulation results of the pulling strength and the maximum pulling work. In the application, the cohesive force model is used as a bridge for inputting a molecular simulation result into the macroscopic model, and can be the same as the bridge for describing the interfacial mechanical property in the macroscopic model, thereby realizing the calculation simulation analysis of the cross scale. In an embodiment of the present application, parameters of a cohesive force model are obtained according to a result of a mechanical simulation test, so as to construct a cohesive force model, and a finite element model can be constructed according to the cohesive force model.
In the application, the construction of the finite element model can be performed in finite element software, such as Abaqus and the like; in addition to the cohesive layer constructed by cohesive model parameters, the construction of finite element models also requires modulus, density, thermal expansion coefficient, etc. of inorganic materials, organic materials to construct inorganic layers and organic polymer layers. That is, the finite element model comprises an inorganic layer and an organic polymer layer, wherein the mechanical property at the interface of the inorganic layer and the organic polymer layer is represented by a CZM layer; parameters used by the CZM layer are parameters obtained through molecular dynamics simulation, and the CZM layer can simulate fracture, failure and the like of an interface. In the application, the influence of the fluctuation morphology of the interface on the stress distribution on the interface can be considered, and the CZM layers with different morphologies can be constructed. The molecular dynamics simulation provides mechanical information of an interface, and the simulation size of the molecular dynamics simulation is in the nanometer level; through the finite element model, a numerical model with the same size and the same structure as the real structure can be established, and stress distribution conditions, such as thermal stress mismatch, stress concentration and other problems, are analyzed, so that the selection of inorganic materials and organic materials can be guided. In the application, stress analysis is performed in finite element software, and stress in different dimensions, such as stress distribution under thermal mismatch, shear stress, stress along a certain axis direction, point stress and the like, can be specifically selected according to requirements. Referring to fig. 17, a schematic diagram of a finite element model is provided according to an embodiment of the present application, in which parameters of a cohesion model are obtained by a mechanical simulation experiment of a PMMA-Si system in the above embodiment, and a CZM layer is configured according to the parameters of the cohesion model, and meanwhile, a PMMA layer and a Si layer are configured according to properties of PMMA and Si, wherein the CZM layer is disposed between the PMMA layer and the Si layer, and the CZM layer may have a structure shown in pattern 1, pattern 2 and pattern 3. It will be appreciated that the CZM layer may be distributed in other patterns, and may be specifically selected as desired. Referring to fig. 18, an organic polymer-inorganic interface stress distribution diagram provided by an embodiment of the present application is shown, in which a CZM layer and a finite element model are constructed according to mechanical simulation results obtained by a PMMA-Si system and a PMMA-SiO 2 system, and Von mises stress (Von MISES STRESS) σ v distribution is obtained by thermal mismatch simulation, so that stress distribution in pattern 1 is uniform, stress values at corner portions in the CZM layer in pattern 2 and pattern 3 are large, and thus, in a thermal mismatch condition, PMMA-SiO 2 interface performance is more stable than PMMA-SiO 2, which has more stress concentration positions in PMMA-Si.
In the application, the selection of the organic polymer is screened through the spatial distribution information of the organic polymer chain, and the selection of the inorganic material is further guided through stress analysis in the finite element model, so that the design of the subsequent organic polymer-inorganic interface is facilitated.
S105: and designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface. According to the spatial distribution information of the organic polymer chain and the stress distribution condition in the finite element model, guidance is provided for the selection of the organic polymer and the inorganic material, so that an organic-inorganic interface with high stability and high reliability can be designed according to the guidance, and guidance is provided for obtaining a stable and reliable organic polymer layer-inorganic layer laminated structure.
The design method provided by the application can analyze the spatial distribution information of the organic polymer chain in a molecular dynamics simulation stage, and finally obtain a finite element model according to a mechanical simulation test result to obtain stress distribution conditions, so as to guide the design of an organic-inorganic interface; the method provided by the application realizes the trans-scale simulation, is closer to the real size, guides the selection of inorganic materials and organic materials through the spatial distribution information and the stress distribution condition, and performs rapid screening, thereby saving cost and time. The method provided by the application can be used for providing references for improving the ultraviolet curing adhesive formula, selecting the material of the inorganic layer and the like.
Referring to fig. 19, a schematic block diagram of an organic polymer-inorganic interface design apparatus according to an embodiment of the present application is shown, where the design apparatus 20 includes a building block 21, a balancing block 22, a statistics block 23, a simulation block 24, and a design block 25, and the building block 21 is used for building an organic polymer dynamic model and an inorganic polymer dynamic model; the balancing module 22 is configured to obtain an organic polymer-inorganic initial system according to an organic polymer dynamics model and an inorganic polymer dynamics model, wherein the organic polymer-inorganic initial system generates an organic polymer-inorganic interface after being balanced to form an organic polymer-inorganic system, the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacting with the inorganic layer, and the organic polymer layer comprises an organic polymer chain; the statistics module 23 is used for counting the spatial distribution information of the organic polymer chains in the organic polymer-inorganic system; the simulation module 24 is used for performing mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to the results of the mechanical simulation test, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface; the design module 25 is configured to design the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
In the embodiment of the present application, the building block 21 includes a first building unit for building an organic polymer molecular dynamics model and a second building unit for building an inorganic molecular dynamics model.
In the embodiment of the present application, the balancing module 22 includes an acquisition unit for obtaining an organic polymer-inorganic initial system according to an organic polymer dynamic model and an inorganic molecular dynamic model, and a balancing unit for balancing the organic polymer-inorganic initial system to obtain the organic polymer-inorganic system.
In the embodiment of the present application, the simulation module 24 includes a mechanical simulation unit, a cohesive force unit, a finite element unit and an analysis unit, where the mechanical simulation unit is used for performing a mechanical simulation test on the organic polymer-inorganic system, the cohesive force unit is used for obtaining parameters of a cohesive force model according to a mechanical simulation test result, the finite element unit is used for obtaining a finite element model according to the parameters of the cohesive force model, and the analysis unit is used for analyzing stress distribution conditions of an organic polymer-inorganic interface according to the finite element model.
The specific details of each module in the design apparatus 20 are described in detail in the corresponding design method, so that the details are not repeated here. It should be noted that although in the above detailed description several modules or units of a device for action execution are mentioned, such a division is not mandatory. Indeed, the features and functions of two or more modules or units described above may be embodied in one module or unit in accordance with embodiments of the application. Conversely, the features and functions of one module or unit described above may be further divided into a plurality of modules or units to be embodied.
Referring to fig. 20, a block diagram of a terminal according to an embodiment of the present application is provided, where the terminal 100 includes a processor 1001 and a memory 1002, and the memory 1002 stores at least one instruction for being executed by the processor 1001 to implement the design method according to any of the above embodiments of the present application. The processor 1001 may include one or more processing cores. The processor 1001 connects various parts within the overall terminal 100 using various interfaces and lines, performs various functions of the terminal 100 and processes data by executing or executing instructions, programs, code sets, or instruction sets stored in the memory 1002, and calling data stored in the memory 1002. Alternatively, the processor 1001 may be implemented in at least one hardware form of digital signal processing, field programmable gate array, and programmable logic array. The processor 1001 may integrate one or a combination of several of a central processor, an image processor, a modem, and the like. The CPU mainly processes an operating system, a user interface, an application program and the like; the GPU is used for being responsible for rendering and drawing of display content; the modem is used to handle wireless communications. It will be appreciated that the modem may not be integrated into the processor 1001 and may be implemented solely by a single communication chip. Memory 1002 may include random access memory or read only memory. Memory 1002 may be used to store instructions, programs, code, sets of codes, or instruction sets. The memory 1002 may include a stored program area and a stored data area, wherein the stored program area may store instructions for implementing an operating system, instructions for implementing at least one function (e.g., a touch function, a sound playing function, etc.), instructions for implementing various method embodiments described below, and the like. The storage data area may also store data created by the terminal 100 in use, etc.
The present application also provides a computer-readable storage medium storing at least one instruction for execution by a processor to implement the design method of any one of the above embodiments of the present application. The computer readable storage medium may be an electronic memory such as a flash memory, an electrically erasable programmable read-only memory, a hard disk, or a read-only memory. Optionally, the computer readable storage medium comprises a non-volatile computer readable medium. The computer readable storage medium has storage space for instructions to perform the method steps in any of the embodiments described above. The instructions may be read from or written to one or more computer program products.
The foregoing has outlined rather broadly the more detailed description of embodiments of the application in order that the principles and embodiments of the application may be better understood, and in order that the present application may be better understood; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present application, the present description should not be construed as limiting the present application in view of the above.
Claims (13)
1. The design method of the organic polymer-inorganic interface is characterized by comprising the following steps:
Constructing an organic polymer molecular dynamics model and an inorganic molecular dynamics model;
According to the organic polymer dynamics model and the inorganic polymer dynamics model, an organic polymer-inorganic initial system is obtained, an organic polymer-inorganic interface is generated after the organic polymer-inorganic initial system is balanced, and an organic polymer-inorganic system is formed, wherein the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacted with the inorganic layer, and the organic polymer layer comprises an organic polymer chain;
counting the space distribution information of the organic polymer chains in the organic polymer-inorganic system;
Performing a mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to the result of the mechanical simulation test, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface;
and designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
2. The method according to claim 1, wherein the statistics of the spatial distribution information of the organic polymer chain in the organic polymer-inorganic system includes:
counting the chain type, tail type and ring type distribution duty ratio of the organic polymer chains in a preset area, wherein the preset area is the area of the organic polymer layer with the distance between the preset area and the surface of the inorganic layer within a preset value range.
3. The method according to claim 2, wherein the preset value is determined based on a mass density of the organic polymer chain.
4. The method of designing according to claim 1, wherein constructing the organic polymer molecular dynamics model includes: generating an organic polymer initial model through modeling, applying a molecular force field to the organic polymer initial model, and carrying out system balance to obtain an organic polymer dynamics model;
The constructing of the inorganic molecular dynamics model comprises: and generating an inorganic layer initial model through modeling, and applying a molecular force field to the inorganic layer initial model to obtain the inorganic molecular dynamics model.
5. The design method of claim 4, wherein the molecular force field comprises at least one of CVFF, reaxFF, and COMPASS.
6. The method of designing according to claim 4, wherein the system balancing includes setting a boundary condition to the initial model of the organic polymer, and then sequentially performing the system balancing using a canonical ensemble and an isothermal and isobaric ensemble.
7. The method of designing according to claim 6, wherein the setting of the boundary condition on the initial model of the organic polymer includes:
The organic polymer initial model is imported into molecular dynamics simulation software, and a three-dimensional coordinate system (x, y, z) is established in the molecular dynamics simulation software;
setting periodic boundaries in x and y directions of the organic polymer initial model, setting an impenetrable constraint in z direction, wherein the impenetrable constraint meets LJ-93 function, LJ-126 function, LJ-1043 function, morse function or a function shown in formula (I),
E＝∈(r-rc)2 (I)，
Wherein E isR c is 0.5nm-1.5nm, E represents the energy of the atom near the boundary, and r is the distance between the wall and the atom;
The system balance is carried out by adopting a regular ensemble and an isothermal and isobaric ensemble in sequence, wherein the system balance comprises balancing for 1ns to 10ns under 500K to 700K, and then balancing for more than 10ns under the isothermal and isobaric ensemble.
8. The method of designing according to claim 1, wherein the organic polymer-inorganic initial system is equilibrated to create an organic polymer-inorganic interface, forming an organic polymer-inorganic system comprising:
The organic polymer-inorganic initial system is balanced for more than 10ns under the isothermal and isobaric ensemble, so that the organic polymer-inorganic system is obtained.
9. The design method of claim 1, wherein the mechanical simulation test comprises a pull simulation and a shear simulation;
the traction simulation comprises the steps of keeping the inorganic layer fixed, and moving the organic polymer layer at a constant speed along the direction perpendicular to the contact surface of the organic polymer layer and the inorganic layer;
the shear simulation comprises the step of keeping the inorganic layer stationary and moving the organic polymer layer at a constant speed along a direction parallel to the contact surface of the organic polymer layer and the inorganic layer.
10. The design method of claim 1, wherein the cohesion model comprises at least one of a bilinear type, a parabolic type, a normal type, and an exponential type.
11. An organic polymer-inorganic interface design device, comprising:
the building module is used for building an organic polymer molecular dynamics model and an inorganic molecular dynamics model;
The balance module is used for obtaining an organic polymer-inorganic initial system according to the organic polymer dynamics model and the inorganic polymer dynamics model, wherein the organic polymer-inorganic initial system generates an organic polymer-inorganic interface after being balanced to form an organic polymer-inorganic system, the organic polymer-inorganic system comprises an inorganic layer and an organic polymer layer contacted with the inorganic layer, and the organic polymer layer comprises an organic polymer chain;
the statistics module is used for counting the space distribution information of the organic polymer chains in the organic polymer-inorganic system;
the simulation module is used for carrying out mechanical simulation test on the organic polymer-inorganic system, obtaining parameters of a cohesive force model according to the results of the mechanical simulation test, and constructing a finite element model according to the parameters of the cohesive force model to obtain the stress distribution condition of an organic polymer-inorganic interface;
and the design module is used for designing the organic polymer-inorganic interface according to the stress distribution condition of the organic polymer-inorganic interface.
12. A terminal comprising a processor and a memory, the memory storing at least one instruction for execution by the processor to implement the design method of any one of claims 1-10.
13. A computer-readable storage medium storing at least one instruction for execution by a processor to implement the design method of any one of claims 1-10.
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