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B. Mark Heron - One of the best experts on this subject based on the ideXlab platform.
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Influence of a local electric field on the light Harvesting Efficiency of a cyclopentadithiophene-bridged D-A-π-A indoline dye on pure and N-doped TiO2 surfaces
Dyes and Pigments, 2017Co-Authors: Kadali Chaitanya, B. Mark HeronAbstract:Abstract The primary objective of this paper is to study the influence of the local electric field at the dye/semiconductor (pure and nitrogen doped TiO2) interface on the performance of dye sensitized solar cells (DSSCs). In this regard, as a first step, we explored the influence of electric field on the performance of the WS-51 dye by computing its properties in an electric field up to 15 × 10−4 a.u. The electronic and optical properties of an established, efficient, donor-acceptor-π-acceptor dye in different electric field strengths were probed with density functional theory (DFT) and time-dependent DFT. The calculated results indicate that, under an electric field, the dye shows significant changes in absorption spectrum due to considerable changes in molecular structure. The TD-DFT results indicate that the absorption spectrum of the dye in acetonitrile solution have shown a blue shift with decreasing molecular extinction coefficient by rising electric field strength. Secondly, we investigated the dye adsorbed on Ti48O96 and Ti48O95N clusters. In the applied field off state, the absorption spectrum of the dye/Ti48O95N system is red shifted with an improved molecular extinction coefficient as compared to the dye/Ti48O96 system, indicating that the nitrogen doped TiO2 surface is more favourable for enhancing the Efficiency of the DSSCs. Finally, the calculated results suggested that the light Harvesting Efficiency (LHE) of the dye/Ti48O95N system is higher than that of the dye/Ti48O96 system. But, under an electric field the LHE of the dye on Ti48O96 and Ti48O95N clusters is likely to decrease with increasing electric field strength. The photon to current response of the DSSCs is limited by the local electric field generated at the dye – semiconductor interface. Finally, results indicate that the doping of a nitrogen atom in TiO2 moderates the electric field intensity at the dye – semiconductor interface. Therefore, the results obtained in this study will provide a valuable reference for understanding the role of local electric field for the further optimization of DSSCs.
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Can elongation of the π-system in triarylamine derived sensitizers with either benzothiadiazole and/or ortho-fluorophenyl moieties enrich their light Harvesting Efficiency? – a theoretical study
RSC Advances, 2015Co-Authors: Kadali Chaitanya, B. Mark HeronAbstract:The structural and electronic properties of five known triarylamine derived sensitizers (A1, A1-F, C218, D2 and Y123) and their associated hypothetical dyes (C218-F, D2-F, Y123-F, Y1234 and Y1234-F) have been studied using density functional theory and time-dependent density functional theory. The sensitizers primarily comprise of a triphenylamine, a 4,4′-dihexylcyclopenta[2,1-b:3,4-b]dithiophene and a cyanoacrylic acid as the electron donating, π-spacer and accepting units, respectively. The π-system is extended by incorporation of either a benzo[c][1,2,5]thiadiazol-4,7-diyl unit or an ortho-fluorophenyl unit or both. To gain insight into the effect of elongation of the π-system on the electronic properties of dye sensitized TiO2 interfaces, first-principles calculations have been carried out on sensitizer molecules co-adsorbed on the (101) surface of the anatase TiO2. The theoretical results revealed that elongating the π-system of the sensitizers with both the benzothiadiazole and ortho-fluorophenyl units increases the molecular extinction coefficient, the excited state lifetime and the light Harvesting Efficiency but decreases the band gap and the reorganization energy relative to the structurally comparable reference dye Y123. The calculated short circuit current density and level alignment quality showed that the π-system in the triarylamine sensitizers elongated with both benzothiadiazole and ortho-fluorophenyl units broadens their potential use in DSSCs due to the enhanced values as compared to the reference dye. The results obtained in this study will provide a valuable reference for the strategy of inserting various π-spacers in triarylamine sensitizers for dye sensitized solar cell applications.
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Theoretical study on the light Harvesting Efficiency of zinc porphyrin sensitizers for DSSCs
RSC Adv., 2014Co-Authors: Kadali Chaitanya, B. Mark HeronAbstract:The density functional theory and time-dependent density functional theory calculations of the electronic structures and electronic absorption spectra of a series of zinc porphyrin based sensitizers were reported. The sensitizers comprise of either 10H-phenothiazin-3-yl or bis(4-(hexyloxy)phenyl)amino and acene bridged carboxylic acid as electron donating and accepting units, respectively. The dye–(TiO2)36 anatase nanoparticle systems were also simulated to show the electronic structure on the interface. The calculated results show that a strong electron-donating capacity of the donor group attached at the meso-position opposite to the anchoring group of the dye will increase the molecular extinction coefficient, excited state lifetime, light Harvesting Efficiency and decrease the reorganization energy as compared to the structurally similar reference dye YD2-o-C8. The calculated short circuit current density and level alignment quality clearly indicate that the zinc-porphyrin dyes substituted with 10H-phenothiazin-3-yl donor and either 4-ethynylbenzoic acid or 4-ethynyl-1-naphthoic acid offer potential for use in DSSCs due to their large values when compared to the reference dye. The results obtained in this study will certainly provide a useful reference to the future design of tetra-substituted zinc porphyrins for dye sensitized solar cell applications.
Akira Shinpo - One of the best experts on this subject based on the ideXlab platform.
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a high light Harvesting Efficiency coumarin dye for stable dye sensitized solar cells
Advanced Materials, 2007Co-Authors: Zhongsheng Wang, Kohjiro Hara, Yasufumi Danoh, Chiaki Kasada, Akira ShinpoAbstract:Dye-sensitized solar cells (DSSCs) have been studied extensively as potential alternatives to conventional inorganic solid solar cells, by using wide-bandgap nanocrystalline TiO2 sensitized with ruthenium polypyridine complexes or metal-free organic dyes as photoelectrodes. Through molecular design, ruthenium complexes have achieved power-conversion efficiencies of over 11 %, while metal-free organic dyes have reached ca. 9 % power-conversion Efficiency under AM 1.5 (AM: air mass) simulated solar light of 100 mW cm (1 sun). Several ruthenium polypyridyl complexes have shown their ability to withstand thermal or light-soaking stress tests for at least 1000 h while retaining an Efficiency above 7 %, whereas for organic-dye-based DSSCs the longterm stability, which is the critical requirement for practical applications, so far remains a serious problem. Organic dyes are also promising for applications in DSSCs in that they have much higher molar extinction coefficients than those for ruthenium polypyridine complexes, which are favorable for light-Harvesting Efficiency (LHE) and hence photocurrent generation. Among the organic dye sensitizers tested in DSSCs, coumarin dyes are strong candidates because of their good photoelectric conversion properties. However, one of their drawbacks is that a high concentration of 4-tert-butylpyridine (TBP) is usually required for a high power-conversion Efficiency. Under continuous light soaking of 1 sun for a short period of one day, the photovoltaic performance was observed to drop dramatically because of the dissolution of the dye into electrolyte containing 0.5 M or more TBP. Therefore, it still remains a great challenge to acquire a DSSC based on a metal-free organic dye with high Efficiency that is stable in the long term. In this paper, we report a new coumarin dye, 2-cyano-3-{5′-[1-cyano-2-(1,1,6,6tetramethyl-10-oxo-2,3,5,6-tetrahydro-1H,4H,10H-11-oxa-3aaza-benzo[de]anthracen-9-yl)-vinyl]-[2,2′]bithiophenyl-5-yl}acrylic acid (NKX-2883), shown in Figure 1, for use in DSSCs. These DSSCs exhibited LHE values of near unity, incident photon-to-electron conversion Efficiency (IPCE) over a wide spectral region on transparent TiO2 films of only 6 lm thickness, and maintained ca. 6 % power-conversion Efficiency under continuous light soaking of 1 sun at 50–55 °C for 1000 h. Figure 2a shows the UV-vis absorption spectrum for NKX2883 in an ethanol solution. NKX-2883 exhibited two p–p* electron-transition peaks (426 and 552 nm) in the visible region. Compared to NKX-2677 (2-cyano-3-[5’-(1,1,6,6-tetramethyl-10-oxo-2,3,5,6-tetrahydro-1H,4H,10H-11-oxa-3a-azabenzo[de]anthracen-9-yl)-[2,2’]bithiophenyl-5-yl]acrylic acid), one of the best organic dyes for DSSCs reported previously, the introduction of one more CN group into the molecular frame decreases the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), thus extending the maximum absorption from 511 to 552 nm. This red-shift may favor light Harvesting and hence photocurrent generation in DSSCs, as will be discussed below. The 552 nm peak showed a broad feature with a full width at half-maximum absorbance of ca. 110 nm, comparable to that for ruthenium polypyridyl complexes, contributing broadly to the high LHE. The molar extinction coefficient (e) of NKX-2883 in ethanol was determined to be 9.74 × 10 dm mol cm at 552 nm, which is about seven times larger than that of N3 (cis-di(thiocyanate)-bis(2,2’-bipyridyl-4,4’-dicarboxylic acid); e= 1.42 × 10 dm mol cm at 532 nm), and 60 % larger than that for NKX-2677 (e= 6.43 × 10 dm mol cm at 511 nm). The LUMO (–0.69 V vs the normal hydrogen electrode (NHE)) of NKX-2883 is more negative than the conduction-band edge of TiO2 (–0.5 V vs NHE), [23] ensuring that electron injection from the excited dye to the conduction band of TiO2 is thermodynamically favorable. The dye-loaded films were obtained by dipping the TiO2 film in dye solutions with different concentrations: 0.02, 0.1, 0.3, and 1.0 mM. The normalized UV-vis absorption spectra for dye-loaded films are plotted in Figure 2b. It is evident that the spectrum becomes slightly broader with an increasing conC O M M U N IC A TI O N
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A High‐Light‐Harvesting‐Efficiency Coumarin Dye for Stable Dye‐Sensitized Solar Cells
Advanced Materials, 2007Co-Authors: Zhongsheng Wang, Kohjiro Hara, Chiaki Kasada, Yan Cui, Yasufumi Dan-oh, Akira ShinpoAbstract:Dye-sensitized solar cells (DSSCs) have been studied extensively as potential alternatives to conventional inorganic solid solar cells, by using wide-bandgap nanocrystalline TiO2 sensitized with ruthenium polypyridine complexes or metal-free organic dyes as photoelectrodes. Through molecular design, ruthenium complexes have achieved power-conversion efficiencies of over 11 %, while metal-free organic dyes have reached ca. 9 % power-conversion Efficiency under AM 1.5 (AM: air mass) simulated solar light of 100 mW cm (1 sun). Several ruthenium polypyridyl complexes have shown their ability to withstand thermal or light-soaking stress tests for at least 1000 h while retaining an Efficiency above 7 %, whereas for organic-dye-based DSSCs the longterm stability, which is the critical requirement for practical applications, so far remains a serious problem. Organic dyes are also promising for applications in DSSCs in that they have much higher molar extinction coefficients than those for ruthenium polypyridine complexes, which are favorable for light-Harvesting Efficiency (LHE) and hence photocurrent generation. Among the organic dye sensitizers tested in DSSCs, coumarin dyes are strong candidates because of their good photoelectric conversion properties. However, one of their drawbacks is that a high concentration of 4-tert-butylpyridine (TBP) is usually required for a high power-conversion Efficiency. Under continuous light soaking of 1 sun for a short period of one day, the photovoltaic performance was observed to drop dramatically because of the dissolution of the dye into electrolyte containing 0.5 M or more TBP. Therefore, it still remains a great challenge to acquire a DSSC based on a metal-free organic dye with high Efficiency that is stable in the long term. In this paper, we report a new coumarin dye, 2-cyano-3-{5′-[1-cyano-2-(1,1,6,6tetramethyl-10-oxo-2,3,5,6-tetrahydro-1H,4H,10H-11-oxa-3aaza-benzo[de]anthracen-9-yl)-vinyl]-[2,2′]bithiophenyl-5-yl}acrylic acid (NKX-2883), shown in Figure 1, for use in DSSCs. These DSSCs exhibited LHE values of near unity, incident photon-to-electron conversion Efficiency (IPCE) over a wide spectral region on transparent TiO2 films of only 6 lm thickness, and maintained ca. 6 % power-conversion Efficiency under continuous light soaking of 1 sun at 50–55 °C for 1000 h. Figure 2a shows the UV-vis absorption spectrum for NKX2883 in an ethanol solution. NKX-2883 exhibited two p–p* electron-transition peaks (426 and 552 nm) in the visible region. Compared to NKX-2677 (2-cyano-3-[5’-(1,1,6,6-tetramethyl-10-oxo-2,3,5,6-tetrahydro-1H,4H,10H-11-oxa-3a-azabenzo[de]anthracen-9-yl)-[2,2’]bithiophenyl-5-yl]acrylic acid), one of the best organic dyes for DSSCs reported previously, the introduction of one more CN group into the molecular frame decreases the gap between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), thus extending the maximum absorption from 511 to 552 nm. This red-shift may favor light Harvesting and hence photocurrent generation in DSSCs, as will be discussed below. The 552 nm peak showed a broad feature with a full width at half-maximum absorbance of ca. 110 nm, comparable to that for ruthenium polypyridyl complexes, contributing broadly to the high LHE. The molar extinction coefficient (e) of NKX-2883 in ethanol was determined to be 9.74 × 10 dm mol cm at 552 nm, which is about seven times larger than that of N3 (cis-di(thiocyanate)-bis(2,2’-bipyridyl-4,4’-dicarboxylic acid); e= 1.42 × 10 dm mol cm at 532 nm), and 60 % larger than that for NKX-2677 (e= 6.43 × 10 dm mol cm at 511 nm). The LUMO (–0.69 V vs the normal hydrogen electrode (NHE)) of NKX-2883 is more negative than the conduction-band edge of TiO2 (–0.5 V vs NHE), [23] ensuring that electron injection from the excited dye to the conduction band of TiO2 is thermodynamically favorable. The dye-loaded films were obtained by dipping the TiO2 film in dye solutions with different concentrations: 0.02, 0.1, 0.3, and 1.0 mM. The normalized UV-vis absorption spectra for dye-loaded films are plotted in Figure 2b. It is evident that the spectrum becomes slightly broader with an increasing conC O M M U N IC A TI O N
Guy A. E. Vandenbosch - One of the best experts on this subject based on the ideXlab platform.
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On the Solar Energy Harvesting Efficiency of Nano-antennas
Rectenna Solar Cells, 2013Co-Authors: Guy A. E. VandenboschAbstract:The radiation Efficiency of nano-antennas is a key parameter in the emerging field of IR and optical energy Harvesting. This parameter is the first factor in the total Efficiency product by which nano-antennas are able to convert incident light into useful energy. The second factor is the matching Efficiency due to the unavoidable mismatch between nantenna and rectifier impedance. The radiation Efficiency is investigated in terms of the metal used as conductor and the dimensions of the nano-antenna. The results set upper bounds for any possible process transforming light into electrical energy. Combined with the theoretical upper bounds involving the matching and rectifying process (see Chap. 3), these upper bounds are the equivalent of the theoretical upper bounds for the Efficiency of conventional solar cells. Silver shows the highest efficiencies, both in free space and on top of a glass (SiO2) substrate, with radiation efficiencies near or slightly above 90 % and a total solar power Harvesting Efficiency of about 60–70 %. This is considerably higher than conventional solar cells. It is found that fine-tuning of the dipole dimensions is crucial to optimize the Efficiency.
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optimal solar energy Harvesting Efficiency of nano rectenna systems
Solar Energy, 2013Co-Authors: Guy A. E. VandenboschAbstract:Abstract Recently, upper bounds have been derived for the Efficiency of nantenna(=nano antenna) systems for solar energy Harvesting. The maximum upper bounds were found to be in the order of 60–70% for dipoles made of silver. These upper bounds are determined solely by the losses in the nantenna. In this paper, the second crucial factor in the Efficiency product for a real nano-rectenna topology is studied: the matching Efficiency due to the unavoidable mismatch between nantenna and rectifier impedance. Since suitable rectifiers do not exist yet, and since it would be totally unfeasible to optimize the nantenna – rectifier system based on experiments, for obvious reasons of cost per fabricated sample, an optimization technique is used based on full-wave simulations to assess the Efficiency that can be reached when the two impedances are optimally compatible. To this goal, first a comprehensive numerical study is made of the impedance of nano dipoles made from three different metals and deposited on a glass substrate. Then the rectifier impedance is determined for which the matching Efficiency is maximum. Two different rectifier impedance models are involved. They are (1) the polynomial (0th, 1st, and 2nd order) model and (2) the equivalent circuit (EC) model for the non-packaged case. The result is that a maximum matching Efficiency of about 97% can be reached for Al dipoles, while a maximum Efficiency product of upper bound and matching Efficiency of about 54% can be reached, in this case for Ag dipoles. These values are reached for a 2nd order polynomial model. Important is also that the results for the EC model are almost identical to the results of the 0th order polynomial model. Finally, the maximum power delivered by a single linearly polarized dipole is shown to be in the order of 5–10 pW.
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Upper bounds for the solar energy Harvesting Efficiency of nano-antennas
Nano Energy, 2012Co-Authors: Guy A. E. VandenboschAbstract:The radiation Efficiency of nano-antennas is a key parameter in the emerging field of IR and optical energy Harvesting. This parameter is the first factor in the total Efficiency product by which nano-antennas are able to convert incident light into useful energy. This Efficiency is investigated in terms of the metal used as conductor and the dimensions of the nano-antenna. The results set upper bounds for any possible process transforming light into electrical energy. These upper bounds are the equivalent of the theoretical upper bounds for the Efficiency of conventional solar cells. Silver shows the highest efficiencies, both in free space and on top of a glass (SiO2) substrate, with radiation efficiencies near or slightly above 90%, and a total solar power Harvesting Efficiency of about 60–70%. This is considerably higher than conventional solar cells. It is found that fine-tuning of the dipole dimensions is crucial to optimize the Efficiency.
Kadali Chaitanya - One of the best experts on this subject based on the ideXlab platform.
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Influence of a local electric field on the light Harvesting Efficiency of a cyclopentadithiophene-bridged D-A-π-A indoline dye on pure and N-doped TiO2 surfaces
Dyes and Pigments, 2017Co-Authors: Kadali Chaitanya, B. Mark HeronAbstract:Abstract The primary objective of this paper is to study the influence of the local electric field at the dye/semiconductor (pure and nitrogen doped TiO2) interface on the performance of dye sensitized solar cells (DSSCs). In this regard, as a first step, we explored the influence of electric field on the performance of the WS-51 dye by computing its properties in an electric field up to 15 × 10−4 a.u. The electronic and optical properties of an established, efficient, donor-acceptor-π-acceptor dye in different electric field strengths were probed with density functional theory (DFT) and time-dependent DFT. The calculated results indicate that, under an electric field, the dye shows significant changes in absorption spectrum due to considerable changes in molecular structure. The TD-DFT results indicate that the absorption spectrum of the dye in acetonitrile solution have shown a blue shift with decreasing molecular extinction coefficient by rising electric field strength. Secondly, we investigated the dye adsorbed on Ti48O96 and Ti48O95N clusters. In the applied field off state, the absorption spectrum of the dye/Ti48O95N system is red shifted with an improved molecular extinction coefficient as compared to the dye/Ti48O96 system, indicating that the nitrogen doped TiO2 surface is more favourable for enhancing the Efficiency of the DSSCs. Finally, the calculated results suggested that the light Harvesting Efficiency (LHE) of the dye/Ti48O95N system is higher than that of the dye/Ti48O96 system. But, under an electric field the LHE of the dye on Ti48O96 and Ti48O95N clusters is likely to decrease with increasing electric field strength. The photon to current response of the DSSCs is limited by the local electric field generated at the dye – semiconductor interface. Finally, results indicate that the doping of a nitrogen atom in TiO2 moderates the electric field intensity at the dye – semiconductor interface. Therefore, the results obtained in this study will provide a valuable reference for understanding the role of local electric field for the further optimization of DSSCs.
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Can elongation of the π-system in triarylamine derived sensitizers with either benzothiadiazole and/or ortho-fluorophenyl moieties enrich their light Harvesting Efficiency? – a theoretical study
RSC Advances, 2015Co-Authors: Kadali Chaitanya, B. Mark HeronAbstract:The structural and electronic properties of five known triarylamine derived sensitizers (A1, A1-F, C218, D2 and Y123) and their associated hypothetical dyes (C218-F, D2-F, Y123-F, Y1234 and Y1234-F) have been studied using density functional theory and time-dependent density functional theory. The sensitizers primarily comprise of a triphenylamine, a 4,4′-dihexylcyclopenta[2,1-b:3,4-b]dithiophene and a cyanoacrylic acid as the electron donating, π-spacer and accepting units, respectively. The π-system is extended by incorporation of either a benzo[c][1,2,5]thiadiazol-4,7-diyl unit or an ortho-fluorophenyl unit or both. To gain insight into the effect of elongation of the π-system on the electronic properties of dye sensitized TiO2 interfaces, first-principles calculations have been carried out on sensitizer molecules co-adsorbed on the (101) surface of the anatase TiO2. The theoretical results revealed that elongating the π-system of the sensitizers with both the benzothiadiazole and ortho-fluorophenyl units increases the molecular extinction coefficient, the excited state lifetime and the light Harvesting Efficiency but decreases the band gap and the reorganization energy relative to the structurally comparable reference dye Y123. The calculated short circuit current density and level alignment quality showed that the π-system in the triarylamine sensitizers elongated with both benzothiadiazole and ortho-fluorophenyl units broadens their potential use in DSSCs due to the enhanced values as compared to the reference dye. The results obtained in this study will provide a valuable reference for the strategy of inserting various π-spacers in triarylamine sensitizers for dye sensitized solar cell applications.
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Theoretical study on the light Harvesting Efficiency of zinc porphyrin sensitizers for DSSCs
RSC Adv., 2014Co-Authors: Kadali Chaitanya, B. Mark HeronAbstract:The density functional theory and time-dependent density functional theory calculations of the electronic structures and electronic absorption spectra of a series of zinc porphyrin based sensitizers were reported. The sensitizers comprise of either 10H-phenothiazin-3-yl or bis(4-(hexyloxy)phenyl)amino and acene bridged carboxylic acid as electron donating and accepting units, respectively. The dye–(TiO2)36 anatase nanoparticle systems were also simulated to show the electronic structure on the interface. The calculated results show that a strong electron-donating capacity of the donor group attached at the meso-position opposite to the anchoring group of the dye will increase the molecular extinction coefficient, excited state lifetime, light Harvesting Efficiency and decrease the reorganization energy as compared to the structurally similar reference dye YD2-o-C8. The calculated short circuit current density and level alignment quality clearly indicate that the zinc-porphyrin dyes substituted with 10H-phenothiazin-3-yl donor and either 4-ethynylbenzoic acid or 4-ethynyl-1-naphthoic acid offer potential for use in DSSCs due to their large values when compared to the reference dye. The results obtained in this study will certainly provide a useful reference to the future design of tetra-substituted zinc porphyrins for dye sensitized solar cell applications.
Xu Wang - One of the best experts on this subject based on the ideXlab platform.
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A study of harvested power and energy Harvesting Efficiency using frequency response analyses of power variables
Mechanical Systems and Signal Processing, 2019Co-Authors: Xu WangAbstract:Abstract Frequency response analysis of field variables such as force, displacement/velocity, voltage was conducted in the previous work to study Harvesting vibration energy under the base excitation of the random and sinusoidal signals. This paper proposes a unique method for conducting frequency response analysis on power variables under a new unified theoretical framework to determine the time averaged harvested power or energy Harvesting Efficiency under the excitation of the random and sinusoidal signals. The uniqueness of the method is to directly measure and calculate the time averaged output power and Efficiency for piezoelectric and electromagnetic vibration energy harvesters under different excitations regardless of the dimensions or sizes of the vibration energy harvesters. This paper has studied the frequency responses of power variables and their mean/dc values and illustrated the relationships of the mean/dc values with the mean harvested power or energy Harvesting Efficiency.
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dimensionless optimization of piezoelectric vibration energy harvesters with different interface circuits
Smart Materials and Structures, 2013Co-Authors: Xu WangAbstract:Conversion of mechanical vibration energy into electric energy could provide reliable and efficient energy utilization. Both the harvested resonant power and the energy Efficiency have been studied based on a single degree of freedom weak electromechanical coupling piezoelectric vibration energy harvester and normalized in a dimensionless form. Performance optimizations have been conducted for the energy harvester connected with different interface circuits in terms of normalized harvested resonant power and resonant energy Harvesting Efficiency to identify both qualitatively and quantitatively the best energy extraction and storage interface circuit. Both the dimensionless harvested resonant power and the resonant energy Harvesting Efficiency formulae have been normalized to contain only two normalized variables of resistance and force factor regardless of the size and excitation magnitude of the energy harvesters.
