Fractal Electrodes Research Articles

Theory for admittance voltammetry of reversible two step electron transfer process with DC bias at rough and fractal electrodes

We developed a phenomenological theory for DC-bias dependent electrochemical impedance response and admittance voltammetry of reversible two-step electron transfer (EE) process at randomly rough and fractal electrodes. The power spectrum of roughness is used to incorporate the statistical information of surface randomness. For the finite fractal model, statistical morphological parameters of roughness, viz., fractal dimension (DH), topothesy length (ℓτ) and lower cut-off length (ℓ), significantly influence the admittance response. The magnitude of admittance increases with an increase in the roughness of fractal electrode (e.g. increase in the value of DH or ℓτ or decrease in ℓ) for both the electron transfer steps. The magnitude of admittance with the variation of DC potential at fixed temporal frequency unravels the multi-electron transfer process. The two step electron transfer process has two characteristic peaks in their plot. The enhanced roughness of electrode increases the height of the admittance peaks and the regions around it (obtained at different fixed frequencies). Our theory is validated with experimental data for the ethyl viologen system at a moderately rough Pt electrode. Finally, our current methodology for admittance voltammetry has the dual advantage of impedance as well as of voltammetry.

Resistance-Capacitance Gas Sensor Based on Fractal Geometry

An important component of any chemiresistive gas sensor is the way in which the resistance of the sensing film is interrogated. The geometrical structure of an electrode can enhance the performance of a gas-sensing device and in particular the performance of sensing films with large surface areas, such as carbon nanotubes. In this study, we investigated the influence of geometrical structure on the performance of gas sensors, combining the characteristics of carbon nanotubes with a novel gas sensor electrode structure based on fractal geometry. The fabricated sensors were tested with exposure to nitric oxide, measuring both the sensor resistance and capacitance (RC) of the sensor responses. Experimental results showed that the sensors with fractal electrode structures had a superior performance over sensors with traditional geometrical structures. Moreover, the RC characteristics of these fractal sensors could be further improved by using different test frequencies that could aid in the identification and quantification of a target gas.

Ceramic materials and energy—Extended Coble’s model and fractal nature

The new frontiers open different directions within the higher and deeper knowledge structure using unemployed nano sizes domains. The BaTiO3 and other ceramic materials have fractal configuration nature based on three phenomena. First, ceramic grains have fractal shape looking as a contour in cross section or as a surface. Second, there is the so-called “negative space” made of pores and intergranular space. Third, there is fractal Brownian motion (fBm) within the material, during and after sintering, in the form of microparticle flow: ions, atoms, and electrons. Here, we took upon ourselves the task of extending Coble’s model, with already generalized Euclidean geometries, by fractal nature correction. These triple factors make the very peculiar microelectronic environment electro-static/dynamic combination. The stress is here set on inter-granular micro-capacity in function of higher energy harvesting and storage. Constructive fractal theory allows identifying micro-capacitors with fractal electrodes. The method is based on the iterative process of interpolation which is compatible with the grain model itself. Inter-granular permeability is taken as the fundamental thermodynamic parameter function of temperature and enthalpy (Gibbs free energy), which are very important for a structure-energy relation.

Numerical simulation of a novel microfluidic electroosmotic micromixer with Cantor fractal structure

In this paper, we design a novel low voltage of electroosmotic micromixer with fractal structure. Because of the influence of high voltage on electrode and solution, we propose an electroosmotic micromixer of low voltage. In order to optimize the electrode position, we design the Cantor fractal according to Cantor principle, and arrange the electrode pairs on the fractal. Then we study the mixing effect of the electrode pairs length on the mixing performance, the effect of the electrode position and the effect of fractal electrode group spacing on the mixing efficiency. When the electroosmotic micromixer has three electrode groups at alternating voltage of 5 V and alternating frequency of 8 Hz, the best mixing efficiency can reach 95.2% in one second. We call this micromixer Cantor fractal electroosmotic micromixer (CFEM). At the same Re, the mixing efficiency of CFEM is higher than the electrodeless micromixer 50%.

Study of fractal electrode designs for buckypaper-based micro-supercapacitors

This work reports the fractal designs of planar interdigital electrodes for buckypaper-based micro-supercapacitors (MSC) and studies their influences on MSC performance for different fractal levels. The fractal designs used in this study were derived from the H-tree structure. The electrodes were realized using a standard lithography process followed by the vacuum-filtration technique. The geometrical complexity of MSC electrodes increases with the level of the fractal structures and possibly results in higher electrical capacitance. The areal capacitance as measured by cyclic voltammetry indicates that the device with the fractal design of Level 3 gives the greatest areal capacitance (18.82 mF/cm2). The measured galvanostatic charge/discharge curves reveal that as the level of the MSC fractal electrode increases the measured areal capacitance increases as well. With a measured current density of 1 mA/cm2, the areal capacitance of the Level-3 fractal-electrode MSC design (17.25 mF/cm2) is 33% greater than that of the standard interdigital-electrode design. A Ragone plot shows that the power density as well as the energy density of MSCs increases with the level of fractal design. Electrochemical impedance spectroscopy measurements are also reported. These measured results confirm that the fractal designs of interdigital electrodes improve the energy-storage performance of MSCs.

Study on Nature-inspired Fractal Design-based Flexible Counter Electrodes for Dye-Sensitized Solar Cells Fabricated using Additive Manufacturing

Dye-Sensitized Solar Cells (DSSC) are third generation solar cells used as an alternative to traditional silicon solar cells. DSSCs are characterized by their durability, easy handling and ability to perform better under diverse lighting conditions which makes them an ideal choice for indoor applications. However, DSSCs suffer from several limitations including low efficiencies, susceptibility to electrolyte leakage under extreme weather conditions, and the need for expensive materials and fabrication techniques which limits their large-scale industrial applications. Addressing these limitations through efficient design and manufacturing techniques are critical in ensuring that the DSSCs transform from the current small-scale laboratory levels to sizeable industrial production. This research attempts to address some of these significant limitations by introducing the concepts of nature-inspired fractal-based design followed by the additive manufacturing process to fabricate cost-effective, flexible counter electrodes for DSSCs. The new conceptual fractal-based design counter electrodes overcome the limitations of conventional planar designs by significantly increasing the number of active reaction sites which enhances the catalytic activity thereby improving the performance. The fabrication of these innovative fractal designs is realized through cost-effective manufacturing techniques including additive manufacturing and selective electrochemical co-deposition processes. The results of the study suggest that the fractal-based counter electrodes perform better than conventional designs. Additionally, the fractal designs and additive manufacturing technology help in addressing the problems of electrolyte leakage, cost of fabrication, and scalability of DSSCs.

Two-photon-induced stretchable graphene supercapacitors

Direct laser writing with an ultrashort laser beam pulses has emerged as a cost-effective single step technology for realizing high spatial resolution features of three-dimensional structures in confined footprints with potential for large area fabrication. Here we present the two-photon direct laser writing technology to develop high-performance stretchable biomimetic three-dimensional micro-supercapacitors with the fractal electrode distance down to 1 µm. With multilayered graphene oxide films, we show the charge transfer capability enhanced by order of 102 while the energy storage density exceeds the results in current lithium-ion batteries. The stretchability and the volumetric capacitance are increased to 150% and 86 mF/cm3 (0.181 mF/cm2), respectively. This additive nanofabrication method is highly desirable for the development of self-sustainable stretchable energy storage integrated with wearable technologies. The flexible and stretchable energy storage with a high energy density opens the new opportunity for on-chip sensing, imaging, and monitoring.

Theory of generalized Gerischer impedance for quasi-reversible charge transfer at rough and finite fractal electrodes

A theoretical model for the generalized Gerischer impedance at an irregular interface under quasi-reversible heterogeneous charge transfer reaction has been developed. The dynamic impedance response is predicted to depend on three phenomenological components, viz. diffusion, charge transfer reaction and bulk homogeneous kinetics as well as roughness. The theory has been developed for both deterministic and stochastic electrode roughness. Statistical properties of the stochastic electrode roughness are characterized through their power spectral density. The impedance response is influenced by the finite self-affine fractal roughness which is analyzed in detail. Three governing phenomenological length scales are diffusion length, charge transfer length and reaction layer thickness. The anomalous impedance response of the finite fractal electrode is due to the synergistic effect of the phenomenological lengths and finite-fractal morphological parameters, namely, fractal dimension (DH), lower cut-off length (ℓ) and topothesy length (ℓτ). The impedance response has three distinct characteristic frequency regimes: the low frequency bulk kinetics controlled regime, roughness dependent intermediate frequency region and heterogeneous charge transfer controlled high frequency regime. A contrasting diffusive behavior is predicted, wherein the system switches from sub-diffusive to super-diffusive response with increase in electrode roughness. This theory unravels the influence of both bulk and interfacial kinetics on the impedance response of a rough electrode.

Modeling the Improved Visual Acuity Using Photodiode Based Retinal Implants Featuring Fractal Electrodes.

Electronically restoring vision to patients blinded by severe retinal degenerations is rapidly becoming a realizable feat through retinal implants. Upon receiving an implant, previously blind patients can now detect light, locate objects, and determine object motion direction. However, the restored visual acuity (VA) is still significantly below the legal blindness level (VA < 20/200). The goal of this research is to optimize the inner electrode geometry in photovoltaic subretinal implants in order to restore vision to a VA better than blindness level. We simulated neural stimulation by 20 μm subretinal photovoltaic implants featuring square or fractal inner electrodes by: (1) calculating the voltage generated on the inner electrode based on the amount of light entering the photodiode, (2) mapping how this voltage spreads throughout the extracellular space surrounding retinal bipolar neurons, and (3) determining if these extracellular voltages are sufficient for neural stimulation. By optimizing the fractal inner electrode geometry, we show that all neighboring neurons can be stimulated using an irradiance of 12 mW/mm2, while the optimized square only stimulates ~10% of these neurons at an equivalent irradiance. The 20 μm fractal electrode can thus theoretically restore VA up to 20/80, if other limiting factors common to retinal degenerations, such as glia scarring and rewiring of retinal circuits, could be reduced. For the optimized square to stimulate all neighboring neurons, the irradiance has to be increased by almost 300%, which is very near the maximum permissible exposure safety limit. This demonstration that fractal electrodes can stimulate targeted neurons for long periods using safe irradiance levels highlights the possibility for restoring vision to a VA better than the blindness level using photodiode-based retinal implants.

MATERIALS SCIENCE AND ENERGY FRACTAL NATURE NEW FRONTIERS

The modern material science faces very important priorities of the future new frontiers which open new directions within higher and deeper structure knowledge even down to nano and due to the lack of energy, towards new and alternative energy sources. For example, in our up to date research we have recognized that BaTiO3 and other ceramics have fractal configuration nature based on three different phenomena. First, ceramic grains have fractal shape looking as a contour in cross section or as a surface. Second, there is the so-called “negative space” made of pores and inter-granular space. Being extremely complex, the pore space plays an important role in microelectronics, micro-capacity, PTC, piezoelectric and other phenomena. Third, there is a Brownian process of fractal motions inside the material during and after sintering in the form of micro-particles flow: ions, atoms and electrons. Here we met an exciting task of the Coble model, with already extended and generalized geometries. These triple factors, in combination, make the microelectronic environment of very peculiar electro-static/dynamic combination. The stress is here set on inter-granular micro-capacity and super micro-capacitors in function of higher energy harvesting and energy storage. An attention is paid to components affecting overall impedances distribution. Con­struc­tive fractal theory allows recognizing micro-capacitors with fractal electrodes. The method is based on the iterative process of interpolation which is compatible with the model of grains itself. Inter-granular permeability is taken as a function of temperature as fundamental thermodynamic parameter.

Theory for the chronopotentiometry on rough and finite fractal electrode: Generalized Sand equation

A theoretical model for the galvanostatic chronopotentiometry on a randomly rough electrode is developed for the diffusion controlled mass transport. The proposed model addresses the influence of various morphological characteristics of roughness on the transition time, interfacial concentration and potential transients. The potential transient and transition time of rough electrode is expressed in terms of average interfacial concentration. Expression for the average surface concentration is obtained in terms of the power spectrum of roughness while detailed analysis of simulated chronopotentiograms is performed for the finite fractal model. Power spectrum of finite fractal roughness is characterized through three controlling parameters of roughness, viz. fractal dimension (DH), lower cutoff length scale of fractality (ℓ) and topothesy length (ℓτ), significantly influence the chronopotentiometric response. Theoretical result show that the transition time at a centered random or pitted surface decreases with increase in their roughness. Experimental data on rough Pt electrode corroborate this observation and quantitative agreement over all time scale is achieved after inclusion of correction for the electric double layer and ohmic contributions.

Fractal Electrochemical Microsupercapacitors

AbstractThe first successful fabrication of microsupercapacitors (μ‐SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO2 thin‐film electrodes as prototypes, μ‐SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ‐SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin‐film RuO2 electrodes. The energy density of the Moore design is 23.2 mWh cm−3 at a volumetric power density of 769 mW cm−3. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm−3 at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ‐SCs that use thin‐film electrodes at no extra processing or fabrication cost.

Fractal Electrodes as a Generic Interface for Stimulating Neurons

The prospect of replacing damaged body parts with artificial implants is being transformed from science fiction to science fact through the increasing application of electronics to interface with human neurons in the limbs, the brain, and the retina. We propose bio-inspired electronics which adopt the fractal geometry of the neurons they interface with. Our focus is on retinal implants, although performance improvements will be generic to many neuronal types. The key component is a multifunctional electrode; light passes through this electrode into a photodiode which charges the electrode. Its electric field then stimulates the neurons. A fractal electrode might increase both light transmission and neuron proximity compared to conventional Euclidean electrodes. These advantages are negated if the fractal’s field is less effective at stimulating neurons. We present simulations demonstrating how an interplay of fractal properties generates enhanced stimulation; the electrode voltage necessary to stimulate all neighboring neurons is over 50% less for fractal than Euclidean electrodes. This smaller voltage can be achieved by a single diode compared to three diodes required for the Euclidean electrode’s higher voltage. This will allow patients, for the first time, to see with the visual acuity necessary for navigating rooms and streets.

Editorial—Dielectrophoresis 2017

Blanca H. Lapizco-Encinas At the beginning of the 1950s, a new electrokinetic phenomenon was discovered by Dr. Herbert A. Pohl, a scientist at the Naval Research Laboratory. Dr. Pohl observed that dielectric particles could move in the presence of an inhomogeneous electrical field, he called this new phenomenon “Dielectrophoresis” 1. Pohl's discovery laid dormant for a couple of decades until the late 1980s when microfluidics and microfabrication technologies allowed a rebirth of Dielectrophoresis. Dielectrophoresis has become one of the main pillars of microfluidics, with applications in a wide range of fields, from bioanalysis to separation of carbon nanotubes. Dielectrophoresis is one of the fastest growing fields in microfluidics, with hundreds of publications every year, and topical conferences, such as the biannual Dielectrophoresis Meeting series that started at the Institute of Physics in London in 2014. It is with great pleasure that we bring to you the fourth installment of the Dielectrophoresis series; Dielectrophoresis 2011, 2013 and 2015 2-5 were very well received by our scientific community. It is an honor to organize again this special issue focused on the latest developments of this dynamic and exciting field. We are delighted to present to you the special issue “Dielectrophoresis 2017.” This issue contains 12 valuable contributions from research groups in USA, Europe, and Asia. These contributions are divided into three categories: (i) Fundamentals, (ii) Advances in Applications, and (iii) Bioanalytical and Clinical Assessments. The first section on fundamentals includes novel contributions with strong focus on modeling dielectrophoretic particle behavior. Some of these studies also include a comprehensive experimental validation. The topics covered include the modeling of a single particle, multipole moments, behavior of micro-rods in rotating fields, and particle collective dynamics in suspensions. The second section is focused on advances in applications. It starts with a study of a novel dielectrophoretic mode, isomotivedielectrophoresis (isoDEP) for the analysis of individual particles. The section has four additional contributions that cover dielectrophoretically aided droplet generation, enhancing dielectrophoresis with fractal gold nanostructured electrodes, impedance spectroscopy assisted by dielectrophoresis, and an analysis on device design under high conductance solutions. The third and last section is focused on bioanalytical and clinical assessments. This section begins with a comprehensive review on DNA dielectrophoresis that explores the polarizability of DNA, compares the distinct modes of dielectrophoresis and illustrates many of the applications for the manipulation of DNA. This review demonstrates the enormous potential of dielectrophoresis for the analysis of macromolecules. Two additional contributions study the feasibility of dielectrophoresis for enrichment of highly aggressive cancer subpopulations and manipulation of vaccinia virus with dielectrophoretically aided impedance monitoring with carbon nanoelectrodes. We would like to express our greatest appreciation to all the contributors for their excellent articles. Special thanks to Professor Mark Hayes from Arizona State University for handling the editorial process for one of the manuscripts in this issue. We gratefully acknowledge the excellent work and dedication of our reviewers. Thanks again to our authors, reviewers, and everybody else for the support that made the special issue “Dielectrophoresis 2017” possible. Blanca H. Lapizco-Encinas

Enhancement of dielectrophoresis using fractal gold nanostructured electrodes.

Dielectrophoretic motions of Saccharomyces cerevisiae (yeast) cells and colloidal gold are investigated using electrochemically modified electrodes exhibiting fractal topology. Electrodeposition of gold on electrodes generated repeated patterns with a fern-leaf type self-similarity. A particle tracking algorithm is used to extract dielectrophoretic particle velocities using fractal and planar electrodes in two different medium conductivities. The results show increased dielectrophoretic force when using fractal electrodes. Strong negative dielectrophoresis of yeast cells in high-conductivity media (1.5 S/m) is observed using fractal electrodes, while no significant motion is present using planar electrodes. Electrical impedance at the electrode/electrolyte interface is measured using impedance spectroscopy technique. Stronger electrode polarization (EP) effects are reported for planar electrodes. Decreased EP in fractal electrodes is considered as a reason for enhanced dielectrophoretic response.

Integration of Fractal Biosensor in a Digital Microfluidic Platform

The digital microfluidic (DMF) platform introduces many applications in biomedical assays. If it is to be commercially available to the public, it needs to have the essential features of smart sensing and a compact size. In this paper, we report on a fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF platforms. A simulation of the electrical field distribution shows reduced peak intensities and uniform distribution of the field. When compared with a V-notch square electrode, the fractal electrode shows a superior performance in both aspects, i.e., field uniformity and intensity. These improvements are translated into a successful and responsive actuation of a water droplet with 100 V. Likewise, the effective dielectric strength is improved by a 33% increase in the fractal electrode breakdown voltage. In addition, the capability of the fractal electrode to work as a capacitive biosensor is evaluated with CRP quantification test. Selected fractal electrodes undergo a surface treatment to immobilize anti-CRP antibodies on their surface. The measurement shows a response to the added CRP in capacitance within 3 min. When the untreated electrodes were used for quantification, there was no significant change in capacitance, and this suggested that immobilization was necessary. The electrodes configuration in the fabricated DMF platform allows the fractal electrodes to be selectively used as biosensors, which means that the device could be integrated into point-of-care applications.

Candle-Soot Derived Photoactive and Superamphiphobic Fractal Titania Electrode

Carbon soot is one of the oldest materials known for its hydrophobic properties, robustness, and availability, making it an ideal material for use in various applications. The drawbacks, however, are the loose structural binding between constructing carbon nanoparticles and the amorphous nature of soot itself. In this paper, we present a facile chemical vapor deposition (CVD) method that maintains the soot template structural integrity and enables its modification into a highly photoactive, self-cleaning titania fractal network. The results show that the small air pockets available on the surface combined with the salinization process produces a TiO2 fractal network with superamphiphobic properties. Given the high surface area of the fractal network structure and titania’s well-known photocatalytic activity, the designed surfaces were assessed for their photocatalytic decoloration activities. The results showed that the soot template derived TiO2 films can offer enormous potential in many different applic...

General Theory for Pulse Voltammetric Techniques at Rough Electrodes: Multistep Reversible Charge Transfer Mechanism

Theoretical model is developed for the voltammetric response of multistep reversible charge transfer mechanism at rough electrode. This theory is applicable for arbitrary as well as random roughness profiles. An explicit mathematical expression relating the staircase (SCV), cyclic staircase (CSCV), differential pulse (DPV) and square wave (SWV) voltammetric response of finite fractal electrode to the statistical morphological characteristics is obtained. The fractal characteristics, viz. fractal dimension (DH), lower length scale of fractality (ℓ) and topothesy length (ℓτ) are found to dominantly control the various voltammetric techniques responses of a multistep charge transfer mechanism. The heights of the voltammetric peaks corresponding to each charge transfer step is found to increase with increasing roughness. In CSCV, the anomalous intermediate scan rate window of Randles-Sevc˘ik plots shifts with the number of charge transfer step. The peak current for the charge transfer step occurring at lower potential has an early onset of the influence of morphology, i.e., the anomalous regime window shifts at lower scan rates compared to those occurring at higher potential values. The differential techniques show roughness induced current enhancement for all the peaks without affecting the position of the peak potential. Thus, roughness helps to overcome the major drawback of low Faradaic current in these techniques and improves their application for chemical sensing purposes.

Novel fractal planar electrode design for efficient neural stimulation.

Planar electrodes are used in epidural spinal cord stimulation and cortical stimulation. Stimulation efficiency of an electrode is characterized by its ability to activate a volume of neural tissue with lower voltage and power requirements. As current density tends to increase towards the sharp edges of an electrode, we hypothesize that electrode designs involving a greater amount of sharp edges will have higher variations of current density, and therefore increase stimulation efficiency, compared to electrodes with flat or rounded edges. This study uses three Koch snowflake fractal design iterations to compare each voltage and power requirements to those of the traditional square and circular electrode designs. Electrode geometries were constructed in COMSOL Multiphysics, each with an equal surface area. Voltages obtained from the finite element models were interpolated to determine the nodal voltages of 100 axons randomly positioned around the electrode. Threshold voltage and power for activating these model axons were simulated in NEURON. Current density variation was significantly higher on the surface of the 3rd iteration Koch snowflake electrode than the traditional square electrode. This novel electrode also activated a significantly greater number of axons with a lower threshold as compared to the traditional square electrode. The computational models used in this study demonstrated the feasibility of increasing stimulation efficiency through the design of novel planar electrodes with Koch snowflake fractal iterations. Future studies could explore and optimize efficiency when more fractal additions are taken, as well as exploiting other fractal shapes.

Aqueous synthesis of LiFePO4 with Fractal Granularity.

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.