Based on the electric mechanical and chemical mechanical coupling theory and numerical calculation of conductive polymer materials, the electric mechanical coupling equation and chemical mechanical coupling equation are derived by using the basic equations of electrical, mechanical and chemical potential, and are derived into the equivalent integral weak form respectively. The electric mechanical coupling and chemical mechanical coupling properties are calculated by FEPG finite element programming. The results show that conductive polymer materials show obvious multi field coupling effect, and the effect of electric field and chemical potential leads to significant deformation of polymer materials.
1. Quote & nbsp; word
Conductive polymers have the same conductivity as metals through doping and electrochemical processes [1]. Conductive polymers can be divided into wet and dry. Dry polymers include electrostrictive, electrostatic, piezoelectric and ferroelectric polymers. They generally require relatively high driving voltage (& gt; 100 V/um)。 However, they can use DC voltage to induce displacement, which can improve the reliability of use. In addition, these materials have relatively large mechanical energy density. In contrast, wet polymers (ion exchange, polymer glue, etc.) require a driving voltage of only 1-2 volts. However, it must be kept wet and it is difficult to induce displacement with DC voltage. The displacement produced by dry and wet conductive polymers can be bending or stretching< br />
Conductive polymer has p-conjugated molecular chain structure. It is a heterogeneous material in mesostructure. Its conductivity depends on the chain structure and the conductivity of interchain carriers (electrons or ions). The structure and conductive mechanism of conductive polymer is that there are some structural defects in the conductive polymer chain, and the lone electrons do not participate in conjugation. It can be removed by oxidation to form carbon positive ions. On the contrary, through reduction, it can pair with foreign electrons to produce carbon negative ions. Such conjugated defects are not limited to one carbon atom, but distributed on a long conductive polymer chain segment. Many of these micro chains are combined according to certain laws to form macro conductive polymers< br />
Conductive polymer materials exhibit electrical mechanical and electro-chemical coupling properties. At present, the research work mainly focuses on the experimental test of the properties of conductive polymers. Literature [2] tested the microstructure, mechanical and electrical properties of conductive polymers. The electro-chemical-mechanical deformation and electrochemical potential of conductive polymers were studied in literature [3], and their pH correlation was analyzed. The thermomechanical behavior of conductive polymer mixtures was tested in reference [4]. The electrical and mechanical properties of conductive polymer composites were tested in reference [5]< br />
In terms of theoretical research, literature [6] used the homogenization model to predict the conductivity of conductive polymers and carbon nanotubes, because the orientation of molecular chains and the heterogeneity of microstructure will seriously affect the conductivity of materials. Using the second law of thermodynamics, literature [7] proposed a unified continuum model to simulate the multi field coupling behavior of short chain polymers subjected to electric thermal mechanical interaction and potential effect. If the electric and thermal effects are omitted, the model will degenerate to a purely mechanical nonlinear rheological equation. In fact, the electro thermal mechanical coupling behavior is manifested in many materials, such as piezoelectric ceramic materials [8-11]. However, there is little knowledge about the multi field coupling properties of polymer materials and less numerical simulation research< br />
In this paper, the electro mechanical and electro-chemical coupling equations of conductive polymers are discussed. On this basis, the finite element program is compiled to solve these equations respectively, and the material deformation induced by electro-mechanical and chemical-mechanical effects under different conditions is obtained.
2. Numerical example of electro mechanical coupling
According to the above theory, FEPG is used for finite element programming, and a typical example is calculated by the program< br />
Calculation example: a cantilever beam is fully restrained at the left end. The geometric dimensions of the beam are as follows: beam length L = 100mm, beam height 1mm, elastic modulus
, Poisson's ratio
, shear modulus
, piezoelectric stress coefficient
, dielectric stress coefficient
. A 100V voltage is applied to the upper surface of the beam, as shown in Figure 1 below to solve the deformation of the beam centerline< br />
& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; Figure 1. Schematic diagram of electrical load of beam < br / >
In the process of finite element analysis of mechanical electrical coupling, in fact, there are different orders of magnitude of elastic constants, dielectric constants and piezoelectric constants, which will lead to serious ill conditioned and unstable results of stiffness matrix. Using the above dimension changing method and FEPG finite element programming to calculate the above example, the following numerical results are obtained: < br / >
& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; Figure 2. Deformation diagram of beam < br / >
For this example, ANSYS software is used for calculation and compared with the results of flying arrow programming calculation. The results are as follows: < br / >
& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; Figure 3. Comparison of results < br / >
From the results of the above example, it can be seen that the solution results of FEPG finite element programming are consistent with those of ANSYS software, it is also more convenient and accurate to solve the coupling problem.
3. Numerical example of mechanical chemical coupling
According to the above theory, the finite element programming is carried out by using FEPG software, and a typical example is calculated by using the program< br />
Calculation example: for a flat plate with length L = 100mm and width 50mm, a force of 100N and - 100N is applied in the middle of the plate, a complete displacement constraint is applied on the lower boundary, and no constraint is applied on the concentration boundary. Calculate the concentration distribution of the plate generated by the force< br />
& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; Fig. 4 concentration distribution of concentrated force 100N load < br / >
{[ 111]}
& nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; & nbsp; Fig. 4 concentration distribution of concentrated force-100n load
4. Conclusion
In this paper, the electro mechanical and mechanochemical coupling problems of conductive polymers are discussed respectively; Based on the basic equations of mechanics, electricity and chemistry, the equivalent integral weak form of coupling is derived; The coupling equation is solved by FEPG software; The multi field coupling characteristics of conductive polymers are simulated. The numerical results show that the conductive polymer has the characteristics of electrical mechanical and mechanical chemical coupling under the coupling field, but when the effects of each field are quite different, the properties of the conductive polymer are controlled by the dominant field. Under the coupling action of electric force field, the performance of conductive polymer is controlled by environmental variables, which is the main factor for the application of conductive polymer in sensors and actuators. The work of this paper is based on the linear material model, and the correlation of parameters to field variables will lead to the nonlinear model. The experimental test of material parameters and calculation results needs to be further studied< br />
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