A wideband flexoelectric energy harvester based on graphene substrate
Introduction
Energy harvesting from ambient is sufficient for micro electro mechanical system (MEMS). Micro energy harvester plays an important role of power supply in the fields of implantable medical devices, micro electric systems, wireless sensing and etc. [1], [2]. The structure optimization and material innovation of micro energy harvester have been research hotspots in recent years.
The vibration piezoelectric energy harvesters (VPEH) can convert the vibration of the external environment into electric energy and are widely used for its simple structure and low cost. The current works about improving the efficiency of the VPEH are mainly focused on the enhancement of the piezoelectric materials. Hwang et al. [3] fabricates a high-efficient energy harvester enabled by a single crystalline piezoelectric PMT-PT thin film with an exceptional piezoelectric charge constant d33 on a PET substrate, and the output electric current is significantly increased. Karan et al. [4] makes a piezoelectric energy harvester with non-electrically poled Fe-RGO/PVDF nanocomposite film, and the open circuit output voltage and short current can reach up to 5.1 V and 0.254 , which were 12 and 105 times greater than pure PVDF respectively. Fu et al. [5] constructs a sensitive flexible piezoelectric energy harvester by filling a PVDF polymer matrix with 5 vol% BaTi2O5 nanorods. The device shows an excellent performance with a high power density of 27.4 . Few studies consider the effect of different base materials on the performance of energy harvesters. In this paper, it is found that the damping is less and performance of the device is better when graphene is used as the material of substrate layer. Pristine monocrystalline graphene is known as the strongest material with remarkable mechanical and electrical properties [6], [7]. Previous studies have discovered its advantages on enhancing the performance of piezoelectric layer and electrodes [8], [9], [10]. It is found that it can improve the conversion rate of the energy harvester when it is used as a base material.
For vibration energy harvester, bandwidth is located near the resonant frequency of the structure, and it denotes the range between two frequencies in the frequency domain where signal strength is of the maximum signal strength. The expansion of the generator working bandwidth is mainly realized by structural optimization. Many novel and practical structures have been presented in macroscopic size. Liu et al. [11] proposes two wideband PVEHs in mm size using a frequency-up-conversion cantilever stop. The method of changing stiffness is adopted for solving the contact problem. The authors of this article [12], [13] have design a high-performance tunable structure by adding balls and boxes at free edge of the cantilever. Tunable function is achieved by position variation of the balls in boxes and bandwidth is broadened. For micro energy harvester, Wang et al. [14] designs an array of flexoelectric energy harvester. Each beam of the array has a different natural frequency, which results in a wide working frequency range. It also has been found that the number of the beams has an effect on the optimal resistance of the device.
Flexoelectric effect is the relation between strain gradient and polarization and it is only significant on micro/nano scale [15], [16]. It plays a critical role for micro/nano scale as the gradient coupling property of flexural material makes it more sensitive to structural bending strain and curvature changes. Unlike piezoelectric effect, there is no limit to temperature and materials [17]. Deng et al. [2] have studied the micro energy harvester under the theory of flexoelectric for the first time. It has been found that the output power density and conversion efficiency increase significantly when the thickness reduces from 3 to 0.3, which provides the theoretical basis for designing flexoelectric energy harvester. Wang et al. [18] have developed an analytical model for unimorph piezoelectric energy harvesters with flexoelectric effect. The governing equation is derived based on the Hamilton principle. Our previous work [19] developed the model of micro bistable plate energy harvester based on strain gradient and flexoelectric effect. The output voltage and conversion rate of the harvester are analyzed.
There is a lot of research on micro energy harvester, but the study on the energy dissipation caused by substrate is still scarce. The vibration energy in the working environment of MEMS is weak, and the amount of energy loss determines the sensitivity of system to the external energy input [20], [21], [22], [23], [24]. Therefore, how to reduce energy loss is significant in design of the micro energy harvester. In this paper, graphene is selected as substrate material for high mechanical performance. It is found that the conversion rate of the energy harvester is improved significantly.
Broadening the bandwidth of the device is also a hotspot. There is little research about structure design of micro energy harvester for widening bandwidth. A simple but efficient structure composed two beams is designed in this paper and the working frequency band is widened by collision of the two beams, which offsets the effect of damping changes on bandwidth and far exceeds it. Based on flexoelectric theory, the dynamic model of the novel micro energy harvester is established, and the effect of parameters on bandwidth and power density is studied.
Section snippets
Mechanical properties of substrate
When the cantilever vibrates, the mechanical energy loss mainly includes thermoelastic loss, air damping, support loss, and surface loss. The quality factor is a performance indicator for judging energy loss, and the higher the Q factor, the lower the energy loss. The total Q factor is calculated with follow equation:
For the cantilever with thickness h and the length l, Yang and Yasumura [21], [22] report that thermoelastic loss
Dynamic modeling
It has been reported that deformation of the structure in the micron scale is size-dependent. Strain gradient theory predicts the size-dependence by introducing an intrinsic length. The strain gradient can induce polarization, even in centrosymmetric crystals, due to local breakage of the inversion symmetry, which is called the flexoelectric effect [15]. Considering flexoelectric effect, this paper designs a novel micro vibration flexoelectric energy harvester (MVFEH). As shown in Fig. 4, it is
Results and discussion
A system of ordinary differential equations is constituted by simultaneous Eq. (21) and Eq. (23). Deflection and contact force are obtained by solving the above ordinary differential equations using MATLAB software.
Conclusion
Based on theoretical analysis, numerical simulation and experimental verification, this paper presents an effective micro flexoelectric energy harvester with high conversion rate and wide bandwidth. Comparatively study shows that the selection of substrate materials has a great influence on the conversion rate. The structure with NCG substrate has the highest Q factor compared with other common materials, which means the energy dissipation of MVEH is lowest and conversion rate is highest. The
CRediT authorship contribution statement
Jiangtao Xue: Methodology, Data curation, Writing - original draft, Visualization, Investigation, Software, Validation. Lihua Chen: Conceptualization, Supervision, Methodology. Liqi Chang: Software, Validation. Wei Zhang: Supervision, Writing - review & editing, Resources.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgement
This paper is supported by the national natural science foundation of China, project No. 11472019 , project No. 11972053 and project No. 11772013. We really appreciate the assistance of the committee of the national natural science foundation of China.
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