CN115240796B - Construction method of dielectric constant model of graphene doped piezoelectric polymer matrix composite material - Google Patents
Construction method of dielectric constant model of graphene doped piezoelectric polymer matrix composite material Download PDFInfo
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Abstract
The invention provides a method for constructing a dielectric constant model of a graphene doped piezoelectric polymer matrix composite material, which comprises the following steps: setting model parameters, calculating the number of graphene nano sheets in a piezoelectric polymer simulation space, randomly generating position distribution of the graphene nano sheets, dividing a piezoelectric polymer simulation space grid, calculating the distance from each grid point to the nearest graphene nano sheet, calculating interface region parameters of the graphene nano sheets, calculating local electric fields and local dielectric constants of each grid point in the piezoelectric polymer simulation space, calculating the interface polarization dielectric constants of the model according to an interface dielectric theory, obtaining multiple interface polarization dielectric constants, selecting an average value as the theoretical interface polarization dielectric constant of the model, and calculating the effective dielectric constant of the composite material of the graphene-doped piezoelectric polymer matrix composite material. According to the invention, through the interfacial dielectric theory, the seepage phenomenon of the graphene nano sheet can be better explained, and the dielectric property of the composite material doped with the conductive filler can be simulated.
Description
Technical Field
The invention belongs to the technical field of simulation analysis of dielectric properties of composite materials, and particularly relates to a method for constructing a dielectric constant model of a graphene doped piezoelectric polymer matrix composite material.
Background
Along with the characteristics of increasingly lighter and more complicated aircraft structures, the development of the flexible piezoelectric sensing technology has great significance for solving the problem of difficult detection of complex curved surface damage. The piezoelectric polymer matrix composite material has the advantages of piezoelectricity, flexibility, workability and the like, and is a common flexible piezoelectric sensor functional phase material. But the material typically has a low dielectric constant, limiting the detection performance of the flexible sensor. Therefore, research and preparation of polymer-based dielectric composite materials with high dielectric constant and breakdown field strength and low dielectric loss are of great significance.
At present, in order to improve the dielectric constant of the material, a method for preparing a polymer nano composite dielectric by adding a proper amount of graphene nano sheets into a piezoelectric polymer base is often adopted. However, there are still different views of the specific mechanism by which graphene doping increases the dielectric constant. On one hand, the graphene doping changes a nonpolar phase to a polar phase in the piezoelectric polymer, and the improvement of the content fraction of the polar phase can promote the improvement of the dielectric property of the system; on the other hand, graphene is overlapped with each other in a polymer matrix to form a continuous phase, and transformation of an insulator-conductor occurs, which is called a percolation phenomenon, and a critical volume fraction of graphene when the percolation phenomenon occurs is called a percolation threshold. The dielectric constant of the composite material is greatly improved near the percolation threshold. At present, a theoretical model aiming at the phenomena of polar phase transformation and seepage is mainly an empirical model, and cannot reasonably explain the mechanism of improving the system dielectric constant by doping graphene. In addition, specific influences of variables such as the size, the morphology, the doped different volume fractions and the like of the graphene on the piezoelectric polymer matrix composite still depend on a large number of repeated experiments, and the period is long and the cost is high. Therefore, in order to solve the above-mentioned problems, it is very urgent and important to find a method for constructing a dielectric constant model of a graphene doped piezoelectric polymer matrix composite material to simulate the dielectric constant of the piezoelectric polymer matrix composite material doped with graphene nanoplatelets.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a method for constructing a dielectric constant model of a graphene doped piezoelectric polymer matrix composite. The method comprises the steps of setting model parameters, calculating the number of graphene nano sheets in a piezoelectric polymer simulation space, randomly generating position distribution of the graphene nano sheets, dividing a piezoelectric polymer simulation space grid, calculating the distance from each grid point to the nearest graphene nano sheet, calculating interface region parameters of the graphene nano sheets, calculating local electric fields and local dielectric constants of grid points in the piezoelectric polymer simulation space, calculating the interface polarization dielectric constants of the model according to an interface dielectric theory, obtaining multiple interface polarization dielectric constants, selecting an average value as a theoretical interface polarization dielectric constant of the model, and calculating the effective dielectric constant of the graphene-doped piezoelectric polymer matrix composite material. According to the invention, through the interfacial dielectric theory, the seepage phenomenon of the graphene nano sheet can be better explained, and the dielectric property of the composite material doped with the conductive filler can be simulated.
The invention provides a method for constructing a dielectric constant model of a graphene doped piezoelectric polymer matrix composite, which comprises the following steps:
s1, setting model parameters, and calculating the number of graphene nano sheets in a piezoelectric polymer simulation space; the model parameters comprise a piezoelectric polymer simulation space size, a piezoelectric polymer simulation space performance parameter, a graphene nano sheet size, a graphene nano sheet performance parameter and a graphene nano sheet volume fraction;
s2, randomly generating position distribution of graphene nano sheets: generating a piezoelectric polymer simulation space according to the model parameters set in the step S1, and randomly generating graphene nano sheets in the piezoelectric polymer simulation space;
s3, dividing a piezoelectric polymer simulation space grid: setting the grid number of the simulation space of the piezoelectric polymer, dividing grid lines for the simulation space of the piezoelectric polymer along three mutually perpendicular coordinate axes in a three-dimensional space, marking the intersection points of the grid lines as grid points, and numbering i { a, b, c } for each grid point according to the sequence of the coordinate axes;
s4, calculating the distance r between each grid point i { a, b, c } and the nearest graphene nano-sheet i ；
S5, calculating the interface region parameters of the graphene nano-sheets according to the performance parameters of the graphene nano-sheets, and based on a uniform and strong electric field E where a piezoelectric polymer simulation space is located 0 Calculating local electric field E (r) of each grid point in piezoelectric polymer simulation space i ) And interface region thickness r t ；
S6, r is calculated according to the step S4 i Calculating the local dielectric constant epsilon (r) of each grid point i )：
ε(r i )＝ε m +(ε′ g -ε m +ε c )e -g (9)
Wherein g represents a relative distance parameter and has g= (r) i /r t ) 2 The method comprises the steps of carrying out a first treatment on the surface of the Epsilon' represents the increase in critical dielectric constant of the interfacial region; epsilon m ，ε c Respectively representing a first dielectric constant and a second dielectric constant;
s7, calculating the model interface polarization dielectric constant epsilon according to the interface dielectric theory int The model interface polarization dielectric constant epsilon int The method meets the following conditions:
wherein </SUB > represents the average value of each grid point;
s8, repeatedly executing the steps S2 to S7 to obtain the dielectric constant epsilon of the multiple interface polarizations int And selecting an average valueTheoretical interfacial polarization permittivity as a model;
s9, calculating static dielectric constant epsilon of the composite material s And calculating the effective dielectric constant epsilon of the composite material of the graphene-doped piezoelectric polymer-based composite material eff ；
S91, calculating static dielectric constant epsilon of composite material s ：
Wherein N is A Representing the avogalileo constant; k represents boltzmann constant; t represents absolute temperature; ρ represents the composite density; m represents the molecular weight of the composite material; mu (mu) x ，f x Respectively representing dipole moment and phase content of different phases x in the piezoelectric polymer; epsilon e Represents the electron polarization dielectric constant of the composite material, and has:
wherein n is e Representing the refractive index; k (k) e Represents an extinction coefficient; the refractive index n e And extinction coefficient k e Detecting and determining the material by an ellipsometer;
s92, comprehensively considering the polar phase transition and the interface polarization caused by adding the graphene nano-sheets to obtain the effective dielectric constant epsilon of the graphene-doped piezoelectric polymer matrix composite material eff ：
Further, the step S1 specifically includes the following steps:
s11, setting a simulation space size of a piezoelectric polymer and a size of a graphene nano sheet: the piezoelectric polymer simulation space is a cube with one side of L, the graphene nano sheet is a cylinder with radius of R and thickness of h, and the range of R/h is 200-2000;
s12, setting simulation space performance parameters of the piezoelectric polymer: providing a piezoelectric polymer simulation space uniformly filled with a composite material, wherein the piezoelectric polymer simulation space performance parameter comprises a first dielectric constant epsilon m And a first conductivity sigma m ；
S13, setting performance parameters of the graphene nano sheet: the graphene nanoplatelet performance parameter comprises a second dielectric constant epsilon c Second conductivity sigma c Separation distance d c Barrier height lambda and percolation threshold volume fraction
S14, calculating the integral number of different graphene nanosheets according to the simulation space size of the piezoelectric polymer and the size of the graphene nanosheets set in S11Number of graphene nanoplatelets N:
wherein V is Composite material Representing the volume of the composite material that is space-filled with the piezoelectric polymer simulation; v (V) Graphene Representing the volume of graphene nanoplatelets.
Preferably, the step S2 specifically includes the following steps:
s21, setting position requirements of randomly generated graphene nano sheets: the center position of the graphene nano sheet is required to fall in the piezoelectric polymer simulation space, and other parts can exceed the piezoelectric polymer simulation space; the graphene nano sheets are uniformly distributed in the piezoelectric polymer simulation space without overlapping parts;
s22, randomly generating the center position and the normal vector of the graphene nano sheet in a piezoelectric polymer simulation space;
s221, randomly generating six random numbers between 0 and 1, and forming a first random vector A= (x) 1 ，y 1 ，z 1 ) And a second random vector b= (x) 2 ，y 2 ，z 2 )；
S222, multiplying the first random vector A by the length, width and height of the simulation space of the piezoelectric polymer to obtain the center position (Lx) of the graphene nano-sheet 1 ，Ly 1 ，Lz 1 ) The second random vector B is a normal vector of the graphene nano-sheets;
s23, judging whether the center position and the normal vector of the generated graphene nano-sheets meet the requirements according to the requirements set in the S21, if so, continuing to execute the step S22 to generate the next graphene nano-sheets until all the graphene nano-sheets N calculated in the step S14 are generated; otherwise, the point is removed and step S22 is re-executed.
Preferably, the step S3 specifically includes the following steps:
s31, giving a grid number G, dividing a piezoelectric polymer simulation space from an original point along three mutually perpendicular coordinate axes in a three-dimensional space into grid lines according to the distance L/(G-1);
s32, marking the intersection points of every three grid lines as grid points, and numbering each grid point as i { a, b, c } according to the sequence of coordinate axes, wherein a, b, c are positive integers in [1, G ];
s33, the coordinates of grid points i { a, b, c } are found as follows:
preferably, the step S4 specifically includes the following steps:
s41, calculating the distance from the grid point i { a, b, c } to the center positions of all the graphene nanoplatelets:
s42, screening all graphene nano sheets to meet D ic ＜R+r E The conditioned graphene nanoplatelets perform step S43, where r E Represents a cut-off distance; if the screened graphene nano sheets which do not meet the condition, defining the distance r from the grid points i { a, b, c } to the nearest graphene nano sheets i ＝R+r E ；
S43, calculating the distance from grid points i { a, b, c } to the plane where the screened graphene nano-sheets are located:
s44, continuously screening the graphene nano sheets screened in the step S42 to meet the requirement D ic′ ＜r E Wherein the distance r of grid points i { a, b, c } to the nearest graphene nanoplatelet i ＝(D ic′ ) min The method comprises the steps of carrying out a first treatment on the surface of the If the screened graphene nano sheets which do not meet the condition, defining the distance r from the grid points i { a, b, c } to the nearest graphene nano sheets i ＝r E ；
S45, repeatedly executing the steps S41 to S44, calculating the distance from all grid points to the nearest graphene nano-sheet, and calculating r i ＝R+r E ，r i ＝r E Is classified by grid points.
Preferably, the step S5 specifically includes the following steps:
s51, calculating parameters of an interface region of the graphene nano sheet, wherein the parameters of the interface region of the graphene nano sheet comprise the thickness r of the interface region of the graphene nano sheet t And interfacial region conductivity sigma int ：
Wherein e represents an electron quantity and e= -1.6x10% 19 C, performing operation; m represents an electron mass and m=9.1×10 -31 kg；Represents the Planck constant and +.>r t Representing the interface region thickness;
s52, uniform and strong electric field E based on piezoelectric polymer simulation space 0 And define the distribution along the vertical axis of the three-dimensional space, calculate the local electric field E (r) of grid points i { a, b, c }, and i )：
wherein θ represents an included angle between a normal vector of the graphene nanoplatelets and a vertical axis in a three-dimensional space; phi (phi) i The electric potential of the graphene nano-sheet is represented, and the calculation formula is as follows:
wherein r is c Representing half thickness of nanosheets, i.e. r c =h/2; a represents a relative conductivity parameter, an
And S53, repeatedly executing the step S52, and calculating the local electric fields of all grid points.
Preferably, the step S7 specifically includes the following steps:
s71, local Joule heat Q (r) defining grid points i )＝ε(r i )E(r i ) 2 And calculates the average joule heating of the model:
s72, calculating the interfacial polarization dielectric constant epsilon of the model according to the interfacial dielectric theory int ：
Preferably, in the step S6, r is t The site obtains ε (r) i ) Maximum value ε (r) t ) Taking into account ε (r) t ) Integral with graphene nanoplateletsIn relation to, and at the percolation threshold volume fraction +.>The vicinity is distributed in class index, defined as
Compared with the prior art, the invention has the technical effects that:
1. according to the method for constructing the dielectric constant model of the graphene doped piezoelectric polymer matrix composite material, the seepage phenomenon of the graphene nano sheet can be better explained relative to an empirical model through an interface dielectric theory; the effective dielectric constant of the overall material can be obtained by calculating the local electric field intensity and the local dielectric constant of each grid point in the composite material model.
2. The method for constructing the dielectric constant model of the graphene doped piezoelectric polymer matrix composite material can simulate the dielectric property of the composite material doped with the conductive filler, provides a theoretical basis for the conductive seepage phenomenon of the composite material, and provides a method support for the preparation of the dielectric energy storage material.
3. The invention designs a method for constructing a dielectric constant model of a graphene doped piezoelectric polymer matrix composite, which aims at the specific influence of variables such as the size, the morphology, the doped different volume fractions and the like of graphene on the piezoelectric polymer matrix composite, and effectively solves the practical problems of long period and high cost caused by a large number of repeated experiments in the past.
Drawings
Other features, objects and advantages of the present application will become more apparent upon reading of the detailed description of non-limiting embodiments made with reference to the following drawings.
FIG. 1 is a flow chart of a method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material;
FIG. 2 is a graph of the position distribution of randomly generated graphene nanoplatelets in an embodiment of the present invention;
fig. 3 is a graph comparing theoretical and experimental values of dielectric constants of different graphene nanoplatelet volume fractions generated in an embodiment of the present invention.
Detailed Description
The present application is described in further detail below with reference to the drawings and examples. It is to be understood that the specific embodiments described herein are merely illustrative of the invention and are not limiting of the invention. It should be noted that, for convenience of description, only the portions related to the present invention are shown in the drawings.
It should be noted that, in the case of no conflict, the embodiments and features in the embodiments may be combined with each other. The present application will be described in detail below with reference to the accompanying drawings in conjunction with embodiments.
Fig. 1 shows a method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material, which comprises the following steps:
s1, setting model parameters, and calculating the number of graphene nano sheets in a piezoelectric polymer simulation space, wherein the model parameters comprise the piezoelectric polymer simulation space size, the piezoelectric polymer simulation space performance parameters, the graphene nano sheet size, the graphene nano sheet performance parameters and the volume fraction of the graphene nano sheets. In one embodiment the length units are μm.
S11, setting a simulation space size of a piezoelectric polymer and a size of a graphene nano sheet: the piezoelectric polymer simulation space is a cube with a side length L, the graphene nano sheet is a cylinder with a radius of R and a thickness of h, wherein the range of R/h satisfies 200-2000, and in one specific embodiment, L=10 μm, R=1.41 μm and h=0.001 μm.
S12, setting simulation space performance parameters of the piezoelectric polymer: providing the piezoelectric polymer simulation space to be uniformly filled with the composite material, wherein the performance parameters of the piezoelectric polymer simulation space comprise a first dielectric constant epsilon m And a first conductivity sigma m 。
S13, setting performance parameters of the graphene nano sheet: the graphene nanoplatelet performance parameter comprises a second dielectric constant epsilon c Second conductivity sigma c Separation distance d c Barrier height lambda and percolation threshold volume fraction
S14, calculating the integral number of different graphene nanosheets according to the simulation space size of the piezoelectric polymer and the size of the graphene nanosheets set in S11Number of graphene nanoplatelets N:
wherein V is Composite material Representing the volume of the composite material that is space-filled with the piezoelectric polymer simulation; v (V) Graphene Representing the volume of graphene nanoplatelets.
S2, randomly generating position distribution of graphene nano sheets: and (3) generating a piezoelectric polymer simulation space according to the model parameters set in the step (S1), and randomly generating graphene nano sheets in the piezoelectric polymer simulation space.
S21, setting position requirements of randomly generated graphene nano sheets: the center position of the graphene nano sheet is required to fall in the piezoelectric polymer simulation space, and other parts can exceed the piezoelectric polymer simulation space; there is no overlapping part between graphene nano sheets, and the graphene nano sheets are uniformly distributed in the piezoelectric polymer simulation space.
S22, randomly generating the center position and the normal vector of the graphene nano sheet in the piezoelectric polymer simulation space.
S221, randomly generating six random numbers between 0 and 1, and forming a first random vector A= (x) 1 ，y 1 ，z 1 ) And a second random vector b= (x) 2 ，y 2 ，z 2 )。
S222, multiplying the first random vector A by the length, width and height of the simulation space of the piezoelectric polymer to obtain the center position (Lx) of the graphene nano-sheet 1 ，Ly 1 ，Lz 1 ) The second random vector B is the normal vector of the graphene nano-sheets.
S23, judging whether the center position and the normal vector of the generated graphene nano-sheets meet the requirements according to the requirements set in the S21, if so, continuing to execute the step S22 to generate the next graphene nano-sheets until all the graphene nano-sheets N calculated in the step S14 are generated; otherwise, the point is removed and step S22 is re-executed. In one particular embodiment, the randomly generated graphene nanoplatelet location profile is shown in fig. 2.
S3, dividing a piezoelectric polymer simulation space grid: setting the grid number of the simulation space of the piezoelectric polymer, dividing grid lines for the simulation space of the piezoelectric polymer along three mutually perpendicular coordinate axes in a three-dimensional space, marking the intersection points of the grid lines as grid points, and numbering i { a, b, c } for each grid point according to the sequence of the coordinate axes.
S31, giving a grid number G, and dividing the piezoelectric polymer simulation space from an original point along three mutually perpendicular coordinate axes in the three-dimensional space into grid lines according to the distance L/(G-1).
S32, marking the intersection points of every three grid lines as grid points, and numbering each grid point as i { a, b, c } according to the sequence of coordinate axes, wherein a, b, c are positive integers in [1, G ].
S33, the coordinates of grid points i { a, b, c } are found as follows:
s4, calculating the distance r between each grid point i { a, b, c } and the nearest graphene nano-sheet i 。
S41, calculating the distance from the grid point i { a, b, c } to the center positions of all the graphene nanoplatelets:
s42, screening all graphene nano sheets to meet D ic ＜R+r E The conditioned graphene nanoplatelets perform step S43, where r E Represents the cut-off distance, r in one embodiment E =0.5; if the screened graphene nanoplatelets which do not meet the condition, defining the distance r from the grid points i { a, b, c } to the nearest graphene nanoplatelet for simplifying calculation i ＝R+r E 。
S43, calculating the distance from grid points i { a, b, c } to the plane where the screened graphene nano-sheets are located:
s44, continuously screening the graphene nano sheets screened in the step S42 to meet the requirement D ic′ ＜r E Wherein the distance r of grid points i { a, b, c } to the nearest graphene nanoplatelet i ＝(D ic′ ) min The method comprises the steps of carrying out a first treatment on the surface of the If it is not screenedGraphene nanoplatelets meeting the conditions, in order to simplify the calculation, the distance r from grid points i { a, b, c } to the nearest graphene nanoplatelet is defined i ＝r E 。
S45, repeatedly executing the steps S41 to S44, calculating the distance from all grid points to the nearest graphene nano-sheet, and calculating r i ＝R+r E ，r i ＝r E Is categorized to facilitate computation.
S5, calculating the interface region parameters of the graphene nano-sheets according to the performance parameters of the graphene nano-sheets, and based on a uniform and strong electric field E where a piezoelectric polymer simulation space is located 0 Calculating local electric field E (r) of each grid point in piezoelectric polymer simulation space i ) And interface region thickness r t 。
S51, calculating parameters of an interface region of the graphene nano sheet, wherein the parameters of the interface region of the graphene nano sheet comprise the thickness r of the interface region of the graphene nano sheet t And interfacial region conductivity sigma int ：
Wherein e represents an electron quantity and e= -1.6x10% 19 C, performing operation; m represents an electron mass and m=9.1×10 -31 kg；Represents the Planck constant and +.>r t Indicating the interface region thickness.
S52, uniform and strong electric field E based on piezoelectric polymer simulation space 0 And define the distribution along the vertical axis of the three-dimensional space, calculate the local electric field E (r) of grid points i { a, b, c }, and i )：
wherein θ represents an included angle between a normal vector of the graphene nanoplatelets and a vertical axis in a three-dimensional space; phi (phi) i The electric potential of the graphene nano-sheet is represented, and the calculation formula is as follows:
wherein r is c Representing half thickness of nanosheets, i.e. r c =h/2; a represents a relative conductivity parameter, an
And S53, repeatedly executing the step S52, and calculating the local electric fields of all grid points.
S6, r is calculated according to the step S4 i Calculating the local dielectric constant epsilon (r) of each grid point i )：
ε(r i )＝ε m +(ε′ g -ε m +ε c )e -g (9)
Wherein g represents a relative distance parameter and has g= (r) i /r t ) 2 The method comprises the steps of carrying out a first treatment on the surface of the Epsilon' represents the increase in critical permittivity of the interfacial region at boundary r of the interfacial region t The maximum value epsilon (r) is obtained t ) Taking into account ε (r) t ) Integral with graphene nanoplateletsIn relation to, and at the percolation threshold volume fraction +.>The vicinity is distributed in class index, define +.>In one particular embodiment a= 647.3.
S7, calculating the model interface polarization dielectric constant epsilon according to the interface dielectric theory int Model interfacial polarization dielectric constant ε int The method meets the following conditions:
wherein < > represents the average value of each grid point.
S71, local Joule heat Q (r) defining grid points i )＝ε(r i )E(r i ) 2 And calculates the average joule heating of the model:
s72, calculating the interfacial polarization dielectric constant epsilon of the model according to the interfacial dielectric theory int ：
S8, repeatedly executing the steps S2 to S7 to obtain the dielectric constant epsilon of the multiple interface polarizations int And selecting an average valueTheoretical interfacial polarization dielectric constant as a model.
S9, calculating static dielectric constant epsilon of the composite material s And calculating the effective dielectric constant epsilon of the composite material of the graphene-doped piezoelectric polymer-based composite material eff 。
In an external electric field E 0 Under the action, besides interface polarization caused by graphene doping, the piezoelectric polymer can generate three polarization phenomena, namely electron polarization, ion polarization and orientation, in the modes of electron cloud displacement, positive and negative ion displacement, polarity phase transformation and the likePolarization. The parameter that measures the sum of the intensities of these three polarization phenomena is called the static dielectric constant ε s 。
S91, calculating static dielectric constant epsilon of composite material s ：
Wherein N is A Representing the avogalileo constant; k represents boltzmann constant; t represents absolute temperature; ρ represents the composite density; m represents the molecular weight of the composite material; mu (mu) x ，f x Respectively representing dipole moment and phase content of different phases x in the piezoelectric polymer; epsilon e Represents the electron polarization dielectric constant of the composite material, and has:
wherein n is e Representing the refractive index; k (k) e Represents an extinction coefficient; refractive index n e And extinction coefficient k e The material is detected and determined by an ellipsometer.
S92, comprehensively considering the polar phase transition and the interface polarization caused by adding the graphene nano-sheets to obtain the effective dielectric constant epsilon of the graphene-doped piezoelectric polymer matrix composite material eff ：
In a specific embodiment, a graph of comparison of dielectric constant simulation values and experimental values of volume fractions of different graphene nanoplatelets is shown in fig. 3, piezoelectric polymer composite materials with volume fractions of 0, 0.1, 0.2, 0.3, 0.4, 0.5 and 0.6 of graphene are prepared experimentally, and dielectric constant measurement is performed on four parallel samples of each batch. Meanwhile, the effective dielectric constant of the composite material with the same volume fraction is calculated by using the dielectric constant model, and the experimental error is reduced by repeating four times. Through comparison of the dielectric constant simulation value and the experimental value, the error between the simulation value and the experimental value is found to be controlled within 17%, and the proposed model can be considered to correctly reflect the dielectric property of the whole material under the statistical meaning.
According to the method for constructing the dielectric constant model of the graphene doped piezoelectric polymer matrix composite material, the seepage phenomenon of the graphene nano sheet can be better explained relative to an empirical model through an interface dielectric theory; the effective dielectric constant of the whole material can be obtained by calculating the local electric field intensity and the local dielectric constant of each grid point in the composite material model; the dielectric property of the composite material doped with the conductive filler can be simulated, so that a theoretical basis is provided for the conductive seepage phenomenon of the composite material, and a method support is provided for the preparation of the dielectric energy storage material; aiming at the specific influence of the variables such as the size, the morphology, the doped different volume fractions and the like of the graphene on the piezoelectric polymer matrix composite, the practical problems of long period and high cost caused by a large number of repeated experiments in the past are effectively solved.
Finally, what should be said is: the above embodiments are merely for illustrating the technical aspects of the present invention, and it should be understood by those skilled in the art that although the present invention has been described in detail with reference to the above embodiments: modifications and equivalents may be made thereto without departing from the spirit and scope of the invention, which is intended to be encompassed by the claims.
Claims (8)
1. The method for constructing the dielectric constant model of the graphene doped piezoelectric polymer matrix composite material is characterized by comprising the following steps of:
s1, setting model parameters, and calculating the number of graphene nano sheets in a piezoelectric polymer simulation space; the model parameters comprise a piezoelectric polymer simulation space size, a piezoelectric polymer simulation space performance parameter, a graphene nano sheet size, a graphene nano sheet performance parameter and a graphene nano sheet volume fraction;
s2, randomly generating position distribution of graphene nano sheets: generating a piezoelectric polymer simulation space according to the model parameters set in the step S1, and randomly generating graphene nano sheets in the piezoelectric polymer simulation space;
s3, dividing a piezoelectric polymer simulation space grid: setting the grid number of the simulation space of the piezoelectric polymer, dividing grid lines for the simulation space of the piezoelectric polymer along three mutually perpendicular coordinate axes in a three-dimensional space, marking the intersection points of the grid lines as grid points, and numbering i { a, b and c } for each grid point according to the sequence of the coordinate axes, wherein a, b and c are positive integers in [1 and G ], and G is the grid number;
s4, calculating the distance r between each grid point i { a, b, c } and the nearest graphene nano-sheet i ；
S5, calculating the interface region parameters of the graphene nano-sheets according to the performance parameters of the graphene nano-sheets, and based on a uniform and strong electric field E where a piezoelectric polymer simulation space is located 0 Calculating local electric field E (r) of each grid point in piezoelectric polymer simulation space i ) And interface region thickness r t ；
S6, r is calculated according to the step S4 i Calculating the local dielectric constant epsilon (r) of each grid point i )：
ε(r i )＝ε m +(ε′g-ε m +ε c )e -g (9)
Wherein g represents a relative distance parameter and has g= (r) i /r t ) 2 The method comprises the steps of carrying out a first treatment on the surface of the Epsilon' represents the increase in critical dielectric constant of the interfacial region; epsilon m ,ε c Respectively representing a first dielectric constant and a second dielectric constant;
s7, calculating the model interface polarization dielectric constant epsilon according to the interface dielectric theory int The model interface polarization dielectric constant epsilon int The method meets the following conditions:
wherein </SUB > represents the average value of each grid point;
s8, repeatedly executing the steps S2 to S7 to obtain multiple interfacesPlane polarization dielectric constant ε int And selecting an average valueTheoretical interfacial polarization permittivity as a model;
s9, calculating static dielectric constant epsilon of the composite material s And calculating the effective dielectric constant epsilon of the composite material of the graphene-doped piezoelectric polymer-based composite material eff ；
S91, calculating static dielectric constant epsilon of composite material s ：
Wherein N is A Representing the avogalileo constant; k represents boltzmann constant; t represents absolute temperature; ρ represents the composite density; m represents the molecular weight of the composite material; mu (mu) x ,f x Respectively representing dipole moment and phase content of different phases x in the piezoelectric polymer; epsilon e Represents the electron polarization dielectric constant of the composite material, and has:
wherein n is e Representing the refractive index; k (k) e Represents an extinction coefficient; the refractive index n e And extinction coefficient k e Detecting and determining the material by an ellipsometer;
s92, comprehensively considering the polar phase transition and the interface polarization caused by adding the graphene nano-sheets to obtain the effective dielectric constant epsilon of the graphene-doped piezoelectric polymer matrix composite material eff ：
2. The method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 1, wherein the step S1 specifically comprises the following steps:
s11, setting a simulation space size of a piezoelectric polymer and a size of a graphene nano sheet: the piezoelectric polymer simulation space is a cube with one side of L, the graphene nano sheet is a cylinder with radius of R and thickness of h, and the range of R/h is 200-2000;
s12, setting simulation space performance parameters of the piezoelectric polymer: providing a piezoelectric polymer simulation space uniformly filled with a composite material, wherein the piezoelectric polymer simulation space performance parameter comprises a first dielectric constant epsilon m And a first conductivity sigma m ；
S13, setting performance parameters of the graphene nano sheet: the graphene nanoplatelet performance parameter comprises a second dielectric constant epsilon c Second conductivity sigma c Separation distance d c Barrier height lambda and percolation threshold volume fraction
S14, calculating the integral number of different graphene nanosheets according to the simulation space size of the piezoelectric polymer and the size of the graphene nanosheets set in S11Number of graphene nanoplatelets N:
wherein V is Composite material Representing the volume of the composite material that is space-filled with the piezoelectric polymer simulation; v (V) Graphene Representing the volume of graphene nanoplatelets.
3. The method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 2, wherein the step S2 specifically comprises the following steps:
s21, setting position requirements of randomly generated graphene nano sheets: the center position of the graphene nano sheet is required to fall in the piezoelectric polymer simulation space, and other parts can exceed the piezoelectric polymer simulation space; the graphene nano sheets are uniformly distributed in the piezoelectric polymer simulation space without overlapping parts;
s22, randomly generating the center position and the normal vector of the graphene nano sheet in a piezoelectric polymer simulation space;
s221, randomly generating six random numbers between 0 and 1, and forming a first random vector A= (x) 1 ,y 1 ,z 1 ) And a second random vector b= (x) 2 ,y 2 ,z 2 )；
S222, multiplying the first random vector A by the length, width and height of the simulation space of the piezoelectric polymer to obtain the center position (Lx) of the graphene nano-sheet 1 ,Ly 1 ,…z 1 ) The second random vector B is a normal vector of the graphene nano-sheets;
s23, judging whether the center position and the normal vector of the generated graphene nano-sheets meet the requirements according to the requirements set in the S21, if so, continuing to execute the step S22 to generate the next graphene nano-sheets until all the graphene nano-sheets N calculated in the step S14 are generated; otherwise, the point is removed and step S22 is re-executed.
4. The method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 2, wherein the step S3 specifically comprises the following steps:
s31, giving a grid number G, dividing a piezoelectric polymer simulation space from an original point along three mutually perpendicular coordinate axes in a three-dimensional space into grid lines according to the distance L/(G-1);
s32, marking the intersection points of every three grid lines as grid points, and numbering each grid point as i { a, b, c } according to the sequence of coordinate axes, wherein a, b, c are positive integers in [1, G ];
s33, the coordinates of grid points i { a, b, c } are obtained as follows:
5. the method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 2, wherein the step S4 specifically comprises the following steps:
s41, calculating the distance from the grid point i { a, b, c } to the center positions of all the graphene nanoplatelets:
s42, screening all graphene nano sheets to meet D ic <R+r E The conditioned graphene nanoplatelets perform step S43, where r E Represents a cut-off distance; if the screened graphene nano sheets which do not meet the condition, defining the distance r from the grid points i { a, b, c } to the nearest graphene nano sheets i ＝R+r E ；
S43, calculating the distance from grid points i { a, b, c } to the plane where the screened graphene nano-sheets are located:
s44, continuously screening the graphene nano sheets screened in the step S42 to meet the requirement D ic′ <r E Wherein the distance r of grid points i { a, b, c } to the nearest graphene nanoplatelet i ＝(D ic′ ) min The method comprises the steps of carrying out a first treatment on the surface of the If the screened graphene nano sheets which do not meet the condition, defining the distance r from the grid points i { a, b, c } to the nearest graphene nano sheets i ＝r E ；
S45, repeatedly executing the steps S41 to S44, and calculating all grid points to the nearest graphene nanometerDistance of the sheets, and r i ＝R+r E ，r i ＝r E Is classified by grid points.
6. The method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 2, wherein the step S5 specifically comprises the following steps:
s51, calculating parameters of an interface region of the graphene nano sheet, wherein the parameters of the interface region of the graphene nano sheet comprise the thickness r of the interface region of the graphene nano sheet t And interfacial region conductivity sigma int ：
Wherein e represents an electron quantity and e= -1.6x10% 19 C, performing operation; m represents an electron mass and m=9.1×10 -31 kg；Represents the Planck constant and +.>r t Representing the interface region thickness;
s52, uniform and strong electric field E based on piezoelectric polymer simulation space 0 And define the distribution along the vertical axis of the three-dimensional space, calculate the local electric field E (r) of grid points i { a, b, c }, and i )：
wherein θ represents an included angle between a normal vector of the graphene nanoplatelets and a vertical axis in a three-dimensional space; phi (phi) i The electric potential of the graphene nano-sheet is represented, and the calculation formula is as follows:
wherein r is c Representing half thickness of nanosheets, i.e. r c =h/2; a represents a relative conductivity parameter, an
And S53, repeatedly executing the step S52, and calculating the local electric fields of all grid points.
7. The method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 4, wherein the step S7 specifically comprises the following steps:
s71, local Joule heat Q (r) defining grid points i )＝ε(r i )E(r i ) 2 And calculates the average joule heating of the model:
s72, calculating the interfacial polarization dielectric constant epsilon of the model according to the interfacial dielectric theory int ：
8. The method for constructing a dielectric constant model of a graphene-doped piezoelectric polymer-based composite material according to claim 1, wherein in the step S6, r is as follows t The site obtains ε (r) i ) Maximum value ε (r) t ) Taking into account ε (r) t ) Integral with graphene nanoplateletsIn relation to, and at the percolation threshold volume fraction +.>The vicinity is distributed in class index, defined as
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