Capacitance Values Research Articles

Optimizing Energy Storage Performance: In situ Synthesized Manganese Oxide (Mn3O4) Nanoparticle‐Based Symmetric Supercapacitor on a Paper Substrate

AbstractIn this study, a redox reaction is employed to synthesize manganese oxide (Mn3O4) nanoparticles using potassium permanganate as a precursor in the presence of diethyl amine. The structural characterization reveals the formation of the tetragonal phase of Mn3O4 nanoparticles with a space group of I41/amd. A free‐standing Mn3O4‐based paper electrode is fabricated and its electrochemical performances are investigated. The electrode exhibits a maximum specific capacitance value of ~353 F g−1 and an areal capacitance of ~530 mF cm−2 at a current density of 0.2 A g−1. A symmetric supercapacitor‐based device is also designed using Mn3O4 nanoparticles as an active material in a gel electrolyte configuration. The Mn3O4 device achieves specific and areal capacity values of ~208 mAh g−1 and 260 mA cm−2, respectively, at a current density of 0.3 A g−1. The device delivers maximum energy and power density values of ~104 Wh kg−1 and ~220 W kg−1, respectively, with ~92 % specific capacity retention at 0.3 A g−1 after 5000 cycles. The above results suggest that the Mn3O4‐based device has the potential for energy storage applications.

Pseudocapacitive Electrode Based on MnO2 Loaded Activated Charcoal on Graphite Paper for Sustainable Energy Storage

AbstractThe design of high‐performance electrode material without compromising energy and power density is critical for the advancement in hybrid electric vehicle technology. In this perspective, we have fabricated a MnO2 loaded activated charcoal‐based electrode on graphite paper as an endeavour to improve the energy storage capabilities. The electrode material is synthesized by employing a sustainable route and the structural, microstructural, and textural properties have been investigated. The electrochemical performance for energy storage is evaluated and the fabricated electrode on graphite paper exhibits remarkably high‐power density (811 W kg−1) maintaining high energy density (106 Wh kg−1) at the same time, along with high gravimetric specific capacitance value of 768 F g−1 at 2 mA cm−2. The obtained results demonstrate the excellent performance of the electrode material, suggesting MnO2 loaded activated charcoal as a prospective electrode material to meet the demand of hybrid electric vehicles as well as to contribute to our transitioning towards low‐to‐zero carbon emission technology.

Supercapacitor properties of partially oxidised-MXene quantum dots/graphene hybrids: Fabrication of flexible/wearable micro-supercapacitor devices

Recently, combining the synergistic properties of two-dimensional (2D) and zero-dimensional (0D) materials has attracted significant attention for energy applications. Here, we report the synthesis and characterization of partially oxidised-MXene quantum dots (PO-MXQDs) and reduced graphene oxide composite (PO-MXQDs/rGO) and investigate the resulting composites for energy storage applications towards supercapacitors. Density functional theory (DFT) simulations are used to examine the electrical and structural features of PO-MXQDs/rGO by predicting the chemical interaction involving charge transfer from PO-MXQDs to rGO. The multilayer Artificial Neural Network (ANN) model with hyperparameter tuning was developed at different input parameters to optimize material compositions, concentrations, and types of electrolytes to obtain the suitable conditions for best supercapacitive performance. The optimized PO-MXQDs/rGO showed a specific capacitance value of 1137.8 F.g−1 and was utilized for the fabrication of flexible micro-supercapacitors (FMSCs) device through the mask-assisted vacuum filtration process and asymmetric coin-cell type supercapacitor devices (ACCDs). The FMSCs deliver a higher areal capacitance (5.26 mF.cm−2), high areal energy density (0.46 μWh.cm−2), high areal power density (210.48 μW.cm−2), and the FMSC device has ultra-high cyclic stability up to 30000 cyclic voltammetry (CV) cycles. This method provides an in-depth study on developing 0D-2D hybrid materials with the wisdom of machine learning (ML) and DFT toward energy storage applications.

Pulsed laser-modified zinc anode with improved dendrite and corrosion resistance for sustainable high performance zinc ion hybrid supercapacitors

This research explores the development and evaluation of zinc ion hybrid supercapacitors (ZIHSCs) with a focus on the enhanced performance and low corrosion attributes of pulsed laser-modified zinc anodes compared to their non-modified counterparts. These anodes, paired with cathodes crafted from activated carbon derived from jute sticks on graphite foil, were immersed in a 2 M zinc sulfate electrolyte. A pivotal aspect of the study is improving the electrochemical properties and corrosion resistance of zinc anodes achieved through precise pulsed laser modification. Extensive electrochemical testing was conducted to assess the capacitive behavior, energy storage capabilities, and durability of the supercapacitors during prolonged cycling. Hence, using the laser modified anode, we attain remarkable stability in Zn||Zn symmetric cells for 1000 h at high current density of 10 mA cm−2 with a capacity of 1 mAh cm−2, and ZIHSCs achieving specific capicitance up to 287 F/g at a current density of 0.1 A/g, and reaching an energy density of 102 Wh/kg while sustaining a power density of 80 W/kg. After 10,000 galvanostatic charge-discharge cycles, these supercapacitors maintained high capacitance values, underscoring their resilience. Notably, charge transfer resistance reduction, improved ion diffusion and enhanced corrosion resistance contributes to the supercapacitors' longevity and efficiency, which can be attributed to these anodes laser-induced surface alterations. This study highlights the crucial role of pulsed laser-modified zinc anodes in advancing ZIHSCs performance, marking a significant step towards achieving efficient and sustainable energy storage solutions.

An efficient and green strategy for the synthesis of graphene with aqueous polyphenol extracts of orchid flower (Dendrobium Anosmum) for charge storage

This study introduces the use of orchid flower extract as a green reducing agent for the first time to produce reduced graphene oxide (ORGO). Raman, XRD and FTIR confirmed the reduction process whereas TGA analysis provides the thermal stability of the prepared samples. SEM imaging validates the improved morphology of ORGO as compared to the crumpled and folded region of graphene oxide (GO). Electrochemical tests reveal ORGO’s superior specific capacitance (489.8F/g) value at scan rate of 20 mV/s, low charge transfer resistance (2.1 Ω) and high specific capacity retention (96.63 %) after 10,000 cycles, highlighting its potential application for charge storage devices.

A novel capacitive sensor interface based on a simple capacitance-to-phase converter

Abstract A novel room temperature capacitive sensor interface circuit is proposed and successfully tested, which uses a modified All-Pass filter architecture combined with a simple series resonant tank circuit with a moderate Q-factor. It is fashioned from a discrete inductor with small dissipation resonating with a grounded capacitor acting as the sensing element to obtain a resolution of ∆C ~ 2 zF in a capacitance range of 10 – 30 pF. The circuit converts the change in capacitance to the change in the phase of a carrier signal in a frequency range with a central frequency set up by the tank circuit’s resonant frequency and is configured to act as a close approximation of the ideal All-Pass filter. This cancels out the effects of amplitude modulation when the carrier signal is imperfectly tuned to the resonance. The proposed capacitive sensor interface has been specifically developed for use as a front-end constituent in ultra-precision mechanical displacement measurement systems, such as accelerometers, seismometers, gravimeters and gravity gradiometers, where moving plate grounded air gap capacitors are frequently used. Some other applications of the proposed circuit are possible including the measurement of the electric field, where the sensing capacitor depends on the applied electric field, and cost effective capacitive gas sensors. In addition, the circuit can be easily adapted to function with very small capacitance values (1 - 2 pF) as is typical in MEMS-based transducers.

Fault diagnosis and analysis of automobile capacitive touch display false triggering

Abstract Nowadays, automobile handling is mainly concentrated in the central control display. The use of high-definition and large-size capacitive touch displays has become the mainstream trend. Driving information and entertainment information are displayed on it, and the operation of the electronic control function of the car is generally realized by touching the touch panel of the central control display. As the integration of the central control display becomes higher, the fault of the display needs to be paid more attention to. The common faults include display faults and touch faults. The display fault will affect the display of vehicle information, and the driver cannot obtain vehicle status information; the touch fault will affect the car operation and can not carry out human-machine interaction. Therefore, once the central control display fails, it will affect the safety driving of the car. This paper studies the false triggering failure which is a kind of touch fault of the vehicle’s 9-inch capacitive touch display. Firstly, we test the parasitic capacitance of faulty parts and repeat the touch failure. After testing and analyzing, it has been found that the mechanical structure design of the display and the air gap bonding process can change the value of parasitic capacitance which leads to false triggering. This paper proposes solutions to solve this failure which are changing the wideness of glue to avoid glue overflow and strengthening size management to improve the spacing between the touch panel and the TFT display screen. After the implementation of the solutions, the false triggering failure no longer occurs, which proves that the solutions are effective and feasible.

Effect of surface functionalization on the quantum capacitance of M2CF2 (M = Ti, V, Cr, Zr, Nb, Mo) as supercapacitor electrodes

The surface charge storage capacity, atomic structures, and quantum capacitance of M2CF2 (M=Ti, V, Cr, Zr, Nb, Mo) are investigated using density functional theory (DFT). The influence of different surface functionalization methods on the capacitance performance of M2CF2 is also examined, including the introduction of vacancy defects (C-, F-, M-vacancy) and nonmetal doping (N, O, and S). The findings show that both defects and doping reduce the quantum capacitance of V2CF2, Cr2CF2, and Mo2CF2, but they have a negligible impact on the capacitance behavior of Ti2CF2, Zr2CF2 and Nb2CF2. Furthermore, the pristine Cr2CF2 system exhibits relatively high quantum capacitance and surface charge storage capacity under both positive and negative bias. However, the presence of vacancies and dopants significantly decreases its capacitance. Among the structures studied, pristine and nonmetal-doped V2CF2 demonstrate the highest quantum capacitance values (1302.02–1517.56 μF/cm2), suggesting its potential as an effective positive electrode material. Overall, the findings of this study are expected to boost the development of high-capacitance electrodes in the future.

Characterization and High‐Frequency Applications of Barium Antimonide Thin Films for Voltage‐Controlled Negative Capacitance and 6G Technology

Herein, films of barium antimonides (BaSb) are fabricated by a thermal deposition technique under a vacuum pressure of 10−5 mbar. BaSb films exhibit orthorhombic lattice. Over a wide range of scans, the films are mostly stoichiometric, displaying atomic contents of 50.17 and 49.83 at% for Ba and Sb, respectively. Morphological analyses of these films show the growth of large grains with sizes ranging from 1.64 to 4.14 μm. Dynamic electrical measurements on Ag/BaSb/Ag films are conducted in the frequency domain of 0.01–1.80 GHz. The films display features of voltage‐controlled negative capacitance source (VCNC) and resonance–antiresonance peaks at a critical frequency of 1.64 GHz. Lorentz models spectral analyses on these peaks indicate that they correspond to a high‐frequency capacitance value of 2.8 nF, a density of oscillators of 4 × 1010 cm−3, and a scattering time constant of τ = 100 ns. Additionally, Ag/BaSb/Ag films show a wide variety in the cutoff frequency spectra, making them suitable for high‐frequency applications. The cutoff frequency varies from 2.6 GHz to 1.0 THz as driving frequency increases from 1.0 to 1.64 GHz. The features of VCNC sources, resonance–antiresonance behavior, and high cutoff frequency make BaSb thin films promising for thin‐film transistors and 6 G technology applications.

A gas spark switch electrode impact pressure test platform.

The discharge arc of a high-current gas spark switch has a strong mechanical effect on the electrode and adjacent objects. The measurement of this mechanical effect on the electrode plays a very important role in switch design and the theoretical study of spark discharge. However, in traditional stress measurement systems, the spatial electromagnetic interference caused by the discharge and the high electrode voltage affects the measurement accuracy and can even damage the experimental instrument. In this paper, an electrode impact stress measurement system based on PVDF piezoelectric film is designed to measure the electrode stress under a strong spatial electromagnetic field and high voltage. The experimental results show that the system can measure the impact pressure of high-voltage and high-current gas spark switch electrodes. The starting time of the stress measurement waveform shows that the shock to the electrode is formed in the initial stage of current buildup. The measured results clearly show the high magnetic field force component in the electrode impact pressure waveform. The shock waveforms induced by different pulse capacitor values, breakdown voltages, and loads are examined. It is found that the shock stress waveforms applied to the electrodes are affected by the peak value of the current, dI/dt, and the discharge duration.

Semi-cylindrical and cylindrical cross-capacitive sensors for micro-droplet detection

In drug delivery systems, the demand for precise microdroplet detection has prompted the utilization of flexible capacitive sensors. Traditional capacitive sensor structures, including coplanar electrodes and parallel plate capacitance, exhibit inherent geometric properties that significantly impact accuracy, sensitivity, and stability. This study explores the semi-cylindrical and cylindrical cross-capacitance sensor designs to enhance these performance metrics for microdroplet detection applications. This research work encompasses the development, analysis, simulation studies, fabrication process, and experimental investigations of these sensor designs. It was observed that they demonstrate notable changes in capacitance values for variations in the volume of liquid droplets, alterations in the relative permittivity of liquid samples, and the change in the velocity of free-flying liquid. The sensor structures are systematically examined across a range of liquid droplet sizes and liquids with varying dielectric constants. The response of the semi-cylindrical capacitive sensor proves to be accurate, significant, and fast, yielding high repeatability of ±0.032% and an impressive sensitivity of 0.7409 fF/μL. These findings position the presented sensor as an ideal candidate for microdroplet detection in drug delivery applications, which showcases its suitability for medical field.

Biomass-tar-derived oxygen-enriched porous carbon as a high-performance carbon electrode material for double electric layer and zinc-ion hybrid supercapacitor

Carbon-based capacitor electrodes have the advantages of high capacitance value, superior recyclability, and inexpensive raw materials, which fuel the application of capacitors in large-scale energy storage. Biomass tar is a hazardous waste that can be recycled as a low-cost carbon electrode precursor for capacitors, due to its retaining biomass-based heteroatom. In this study, hierarchically porous carbon with cross-linked structure was fabricated by using a nano-Al2O3 template combined with the KOH activation technique, in which the γ-Al2O3 has a size of only 10 nm with high specific surface area, thus optimizing the pore structure of the carbon material. The resulting optimal material, BTC-0.2-2-800, contains abundant pore structure and extremely high oxygen content, delivers low resistance and excellent rate performance with high specific capacitance of 292.1 F g−1 and 221.7 F g−1 at 1 A g−1 and 20 A g−1, respectively, in double electric layer supercapacitors (EDLCs). Besides, no significant capacity degradation after 10,000 charging and discharging cycles at 10 A g−1 was found. The two-electrode device prepared using Na2SO4 electrolyte achieves a high energy density of 43.18 Wh kg−1 at the power density of 1000 W kg−1, which can light up a 2 V LED lamp. Moreover, Zinc-ion hybrid supercapacitor (ZIHSC) fabricated with BTC-0.2-2-800 carbon electrode accounts for the energy densities of 69.82 Wh kg−1 and 49.39 Wh kg−1 at the power densities of 40 W kg−1 and 400 W kg−1, respectively. This study reveals the great potential of biomass-tar-derived carbon as a high-performance electrode material, which may provide an opportunities for the resource utilization of hazardous wastes.

A novel seven‐level inverter with high gain and reducing spike current capabilities

SummaryThis paper describes a novel seven‐level (7L) inverter. The suggested topology offers a 7L output voltage and a threefold gain by using proper capacitor values. The suggested topology reduces the spike current induced by the capacitor by the use of a resonant inductor. The suggested inverter's performance under various loads and situations is compared with those found in existing literature. The simulation findings confirm the system's strong performance in terms of component count, control circuit simplicity, and possible cost reductions, while retaining similar or enhanced performance metrics as compared with the aforementioned topologies. A laboratory setup is used to validate the feasibility of the suggested topology and provide solid evidence of its effectiveness. Furthermore, discussions about the possible uses of this structure in energy conversion are conducted.

Renewable Musa Sapientum derived porous nano spheres for efficient energy storage devices

Biomass-based carbonaceous materials derived from Musa Sapientum have gained much attention in recent years for their application in energy storage devices, especially supercapacitors. In the present work, we synthesized carbonaceous material from banana peel as the biomass precursor by using a pyrolysis method carried out at various temperatures (600, 800, and 1000 °C). The characterization of the prepared carbonaceous materials BP600, BP800 and BP1000 was done by using different characterization techniques such as FTIR, XRD, FE-SEM, and TEM, studies. The electrochemical study of the synthesized material was carried out by cyclic voltammetry (CV), galvanostatic charge–discharge (GCD) electrochemical impedance spectroscopy (EIS). The supercapacitive performance of the material was studied using a 3-electrode system with 3M KOH as an electrolyte. As a result, the BP600 exhibited a better specific capacitance with higher energy and power densities along with a maximum cyclic stability of 16,000 cycles. To show the practical applicability of the material BP 600, two electrode system studies were carried out as well, which showed preferentially good values for specific capacitance with appreciable power and energy density values. The study provides us with a green approach for the fabrication of non-toxic, low-cost, and environmentally friendly potential porous carbonaceous electrode materials by converting bio-waste into a clean and renewable source of energy.

Mg2+ ion conducting Chitosan:PVP polymer blend electrolytes for electric double layer capacitor applications

Biopolymer electrolytes are prepared using Chitosan (CS) and Polyvinyl pyrrolidone (PVP) incorporated with magnesium chloride (MgCl2). The complex formation of electrolytes are confirmed by X-ray diffraction(XRD) and Fourier Transform Infrared spectrometer(FTIR) analysis. The scanning electron microscope(SEM) reveals the surface morphology and microstructure of the electrolytes while energy dispersive spectroscopy(EDS) facilitates the presence of elements. The distribution of elements are confirmed with elemental mapping analysis. DSC analysis enlightens on thermal properties, offering an understanding of phase transitions and thermal stability of the films. CS/PVP/MgCl2(50:50:25) polymer electrolyte shows higher ionic conductivity value of 5.8 × 10−4 S/cm at 30 °C and the specific capacitance value of 86.5 Fg−1 at low scan rate of 10 mVs−1. Linear Sweep Voltammetry (LSV) analysis has been used to determine the electrochemical stability window of the electrolyte and it is found to be 0.7 V. This result indicates that the CS/PVP/MgCl2 electrolyte is a suitable material for energy storage device applications.

Copper molybdenum sulfide coupled with multi-walled carbon nanotube nanocomposite for robust water splitting process

Developing eco-friendly and efficient non-noble catalysts is crucial for cleaner energy production, nevertheless, optimizing the catalyst is challengeable. The Cu2MoS4 were successfully synthesized with various amount of MWCNTs. The suitable amount of high conductivity of MWCNT can greatly accelerate its HER and OER kinetics, which was demonstrated with the obtained results. XRD spectra revealed tetragonal Cu2MoS4 structure with I 4‾ 2 m space group. Carbon existence was substantiated by Raman spectra, and the ID/IG value of Cu2MoS4/MWCNT-100 was 0.98. The Cu2MoS4 nanoplates were strongly anchored to MWCNTs, as demonstrated by the morphological analysis of SEM and TEM images. The optimized catalyst (denoted as Cu2MoS4/MWCNT-100) exhibits high bifunctional with low 140 mV overpotential value and 193 mV@10 mA/cm2 for HER and OER and a lower Tafel slope value of 93 mV/dec and 51 mV/dec for HER and OER. Moreover, it revealed good catalytic activity with high electrical conductivity (0.361 Ω and 0.897 Ω for HER and OER) and high capacitance value (5.9 mF/cm2 and 9.4 mF/cm2 for HER and OER) with better stability. Lastly, we construct overall water splitting electrolyzer by optimized electrocatalyst as both anode and cathode entail cell voltage as 1.57 V only to deliver 10 mA/cm2 with a faradaic efficiency of 98.75 % for H2 and 93.28 % for O2 and it was believed as active material for water splitting.

Biochar/poly(aniline-pyrrole) modified graphite electrode and electrochemical behavior for application in low-cost supercapacitor

An attempt is made to use biochar (BC), a carbon rich low-cost green material, as a platform to house conducting polymer for fabricating stable graphite electrodes for application in next generation supercapacitor devices. Here, BC is first prepared from sucrose solution using a simple hydrothermal method. The seeded chemical oxidative copolymerization of aniline and pyrrole is then carried out at identical comonomer weight ratio using BC as seed particles. Two different BC to mixed monomer (w/w) ratios (1:0.7 and 1:1) have been used and the prepared composites are named as BC/P(Ani-Py)1:0.7 and BC/P(Ani-Py)1:1 respectively. Independent of composition, both BC seed and composite particles are spherical. The smooth homogeneous surface of BC turned heterogeneous after composite formation. The average size of BC seed particles is 2.56 µm and those of composites prepared at weight ratios of 1:0.7 and 1:1.0 are 2.72 and 2.90 µm respectively. Cyclic voltammetry (CV), galvanostatic charging discharging (GCD), and electrochemical impedance spectroscopy (EIS) are used to evaluate the electrochemical properties. Comparatively, the BC/P(Ani-Py)1:1 composite modified graphite electrode exhibited the highest capacitance value (274.27 F g−1 at a current density of 1.0 A/g) and is capable of acting as a supercapacitor electrode. A long-term cycling test of the BC/P(Ani-Py)1:1 modified electrode at a current density of 5.0 A/g displayed a capacitance retention of 96.6 % after 1000 cycles of charge and discharge, indicating a very good cycle stability.

One-step synthesis of 2-Methyl-2,4-Diphenyl-2,3-Dihydro-1H-Benzo[b][1,4]diazepine: Investigating crystal structure, hirshfeld surface analysis and supercapacitor applications

This study reports the synthesis, spectroscopic characterization and detailed crystal structure analysis of a benzodiazepine compound, 2-methyl-2,4-diphenyl-2,3-dihydro-1H-benzo[b][1,4]diazepine, synthesized from 1,2-phenylenediamine and acetophenone. The crystal structure, determined via single crystal X-ray analysis, reveals the compound's placement within the monoclinic system with the P 21/c space group. The asymmetric unit comprises the main molecule and an uncoordinated water molecule linked through an intramolecular O–H···N hydrogen bond. The crystal packing is influenced by centrosymmetric dimers formed by uncoordinated water molecules through O–H···N hydrogen bonds, along with weak C–H···π interactions. Hirshfeld surface analysis highlights the significance of H … H and H … C/C … H interactions in the crystal packing, providing insight into the intermolecular forces at play. Supercapacitance performance of the GCPE/LDABA electrode was assessed and specific capacitance value of 17.89 mF g−1 was achieved in a 0.1 M Na2SO4 electrolyte. Long-term stability of the GCPE/LDABA electrode was maintained up to 2000 cycles. This study not only elucidates the structural features of the title compound but also sheds light on its potential utility through an investigation into its electrochemical performance via supercapacitor application.

Controllable construction of mesoporous hollow carbon spheres rich in micropores from waterborne benzoxazine and their application in supercapacitors

Mesoporous hollow carbon spheres (MHCSs) with mesoporous channels and nanocages structure have unique advantages in energy storage. However, this structure alone does not significantly enhance the electrochemical double layer capacitance (EDLC). Additionally, the current hydrophobic nature of polymer precursors with high char yield impedes effective binding with templates due to polarity differences. Moreover, the use of toxic organic solvents presents obstacles to further development. So, it remains a challenge to prepare MHCSs rich in micropores using polar polymers with high char yield in green solvent. In this work, we prepared MHCSs rich in micropores (MMHCSs) using waterborne benzoxazine as a carbon sources and dendritic/fibrous nano-silica as a sacrificial hard template using water as the solvent and combined with freeze-drying, curing, carbonization and an activation step. The optimal MMHCSs (MMHCSs306–1–7000.5h) has a large specific surface area (1057 m2 g−1), and has a maximum specific capacitance value near 221.45 F g−1 at 0.5 A g−1 in a three-electrode system, the specific capacitance still reaches 156.66 F g−1 at a high current density (20 A g−1) due to the full utilization of micropores in the presence of mesoporous-shell and hollow-core. When assembled into a symmetrical supercapacitor, the energy density reaches 5.91 Wh kg−1 when the power density is 137.5 W kg−1. The study provides an eco-friendly method for preparing MMHCSs, and the unique structure has potential application in supercapacitors.

The Behavior of Terminal Voltage and Frequency of Wind-Driven Single-Phase Induction Generators under Variations in Excitation Capacitances for Different Operating Conditions

This paper assesses the behavior of output voltage and frequency of wind-driven self-excited induction generators with variable excitation capacitances connected to the main and auxiliary windings under different operating conditions. The optimum values of the main winding excitation capacitance for fixed terminal voltage operation under different values of shunt capacitance, load, and speed are also evaluated. The obtained results show that the terminal voltage is highly affected by changing the main winding excitation capacitance. In addition, the frequency is greatly affected by changing the auxiliary winding excitation capacitance. However, under different operating conditions, variation in the output frequency under different values of the main winding capacitance, with fixed auxiliary winding capacitance, is acceptable. Extensive simulations were conducted and the results are discussed in this publication.