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Percolation-Modeling Comparison Between the Conductivities of Zinc-Graphene Quantum Dot Nanocomposite and Graphite during Extracellular Electron Transfer in Microbial Fuel Cell Electrodes
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The anode and cathode electrodes of a microbial fuel cell (MFC) stack, composed of 28 single MFCs, were used as the negative and positive electrodes, respectively of an internal self-charged supercapacitor. Particularly, carbon veil was used as the negative electrode and activated carbon with a Fe-based catalyst as the positive electrode. The red-ox reactions on the anode and cathode, self-charged these electrodes creating an internal electro-chemical double layer capacitor. Galvanostatic discharges were performed at different current and time pulses. Supercapacitive-MFC (SC-MFC) was also tested at four different solution conductivities. SC-MFC had an equivalent series resistance (ESR) decreasing from 6.00 Ω to 3.42 Ω in four solutions with conductivity between 2.5 mScm −1 and 40 mScm −1. The ohmic resistance of the positive electrode corresponded to 75-80% of the overall ESR. The highest performance was achieved with a solution conductivity of 40 mS cm −1 and this was due to the positive electrode potential enhancement for the utilization of Fe-based catalysts. Maximum power was 36.9 mW (36.9 W m −3) that decreased with increasing pulse time. SC-MFC was subjected to 4520 cycles (8 days) with a pulse time of 5 s (i pulse 55 mA) and a self-recharging time of 150 s showing robust reproducibility.
Global integration of information in the brain results from complex interactions of segregated brain networks. Identifying the most influential neuronal populations that efficiently bind these networks is a fundamental problem of systems neuroscience. Here, we apply optimal percolation theory and pharmacogenetic interventions in vivo to predict and subsequently target nodes that are essential for global integration of a memory network in rodents. The theory predicts that integration in the memory network is mediated by a set of low-degree nodes located in the nucleus accumbens. This result is confirmed with pharmacogenetic inactivation of the nucleus accumbens, which eliminates the formation of the memory network, while inactivations of other brain areas leave the network intact. Thus, optimal percolation theory predicts essential nodes in brain networks. This could be used to identify targets of interventions to modulate brain function.
Selective localization of conductive nanofillers in one phase of co-continuous polymer blends provides an efficient method to greatly reduce the electrical percolation threshold of conductive polymer composites. However, it is still a big challenge to achieve very low percolation thresholds because the critical content for the complete continuity of the selectively filled phase is generally high. In this contribution, taking poly(L-lactide)/thermoplastic polyurethane/carbon nanotubes (PLLA/TPU/CNTs) composite as an example, we demonstrate a facile and versatile strategy for the fabrication of highly conductive PLLA-based composites with very low percolation threshold as well as excellent stiffness–toughness balance via constructing stereocomplex (SC) crystallites in PLLA melt to effectively tailor the phase transition behavior of the blend matrices. To do this, small amounts of poly(D-lactide) (PDLA) capable of co-crystallizing with the PLLA chains to form SC crystallites were incorporated into the composites by melt mixing at 190 °C. These SC crystallites can serve as physical cross-linking points to significantly increase PLLA melt-viscosity and subsequently induce the formation of co-continuous structure in the PLLA/TPU blend matrix at a much lower content of the CNTs-filled TPU phase. As a result, the obtained composites not only show a dramatically reduced percolation threshold (0.3 wt%) but also exhibit a balanced impact toughness and mechanical strength. Importantly, the strategy to promote the complete continuity of the CNTs-filled phase in blend matrix is low-cost and scalable, opening up a new avenue for the design and engineering of highly conductive PLLA-based composites.
The critical curves of the q-state Potts model can be determined exactly for
regular two-dimensional lattices G that are of the three-terminal type.
Jacobsen and Scullard have defined a graph polynomial P_B(q,v) that gives
access to the critical manifold for general lattices. It depends on a finite
repeating part of the lattice, called the basis B, and its real roots in the
temperature variable v = e^K - 1 provide increasingly accurate approximations
to the critical manifolds upon increasing the size of B. These authors computed
P_B(q,v) for large bases (up to 243 edges), obtaining determinations of the
ferromagnetic critical point v_c > 0 for the (4,8^2), kagome, and (3,12^2)
lattices to a precision (of the order 10^{-8}) slightly superior to that of the
best available Monte Carlo simulations.
In this paper we describe a more efficient transfer matrix approach to the
computation of P_B(q,v) that relies on a formulation within the periodic
Temperley-Lieb algebra. This makes possible computations for substantially
larger bases (up to 882 edges), and the precision on v_c is hence taken to the
range 10^{-13}. We further show that a large variety of regular lattices can be
cast in a form suitable for this approach. This includes all Archimedean
lattices, their duals and their medials. For all these lattices we tabulate
high-precision estimates of the bond percolation thresholds p_c and Potts
critical points v_c. We also trace and discuss the full Potts critical manifold
in the (q,v) plane, paying special attention to the antiferromagnetic region v
< 0. Finally, we adapt the technique to site percolation as well, and compute
the polynomials P_B(p) for certain Archimedean and dual lattices (those having
only cubic and quartic vertices), using very large bases (up to 243 vertices).
This produces the site percolation thresholds p_c to a precision of the order
10^{-9}.
We show analytically that the $[0,1]$, $[1,1]$ and $[2,1]$ Pad{\'e}
approximants of the mean cluster number $S(p)$ for site and bond percolation on
general $d$-dimensional lattices are upper bounds on this quantity in any
Euclidean dimension $d$, where $p$ is the occupation probability. These results
lead to certain lower bounds on the percolation threshold $p_c$ that become
progressively tighter as $d$ increases and asymptotically exact as $d$ becomes
large. These lower-bound estimates depend on the structure of the
$d$-dimensional lattice and whether site or bond percolation is being
considered. We obtain explicit bounds on $p_c$ for both site and bond
percolation on five different lattices: $d$-dimensional generalizations of the
simple-cubic, body-centered-cubic and face-centered-cubic Bravais lattices as
well as the $d$-dimensional generalizations of the diamond and kagom{\'e} (or
pyrochlore) non-Bravais lattices. These analytical estimates are used to assess
available simulation results across dimensions (up through $d=13$ in some
cases). It is noteworthy that the tightest lower bound provides reasonable
estimates of $p_c$ in relatively low dimensions and becomes increasingly
accurate as $d$ grows. We also derive high-dimensional asymptotic expansions
for $p_c$ for the ten percolation problems and compare them to the
Bethe-lattice approximation. Finally, we remark on the radius of convergence of
the series expansion of $S$ in powers of $p$ as the dimension grows.
Extensive Monte-Carlo simulations were performed in order to determine the precise values of the critical thresholds for site ($p^{hcp}_{c,S} = 0.199 255 5 \pm 0.000 001 0$) and bond ($p^{hcp}_{c,B} = 0.120 164 0 \pm 0.000 001 0$) percolation on the hcp lattice to compare with previous precise measuremens on the fcc lattice. Also, exact enumeration of the hcp and fcc lattices was performed and yielded generating functions and series for the zeroth, first, and second moments of both lattices. When these series and the values of $p_c$ are compared to those for the fcc lattice, it is apparent that the site percolation thresholds are different; however, the bond percolation thresholds are equal within error bars, and the series only differ slightly in the higher order terms, suggesting the actual values are very close to each other, if not identical.
Graphene quantum dots (GQD) with an average size of 3.1 nm were incorporated into a mesoporous porphyrinic zirconium-based metal–organic framework (MOF) by direct impregnation to render the donor-acceptor charge transfer from GQD to porphyrinic linkers. The hybrid material still possesses around half porosity of the pristine MOF and shows a hundredfold higher electrical conductivity compared to the parent MOF. By utilizing the porphyrinic linkers as catalytically active units, the GQD-MOF material exhibits a better electrochemical sensing activity toward nitrite in aqueous solutions compared to both the pristine MOF and GQD.
Research into alternative renewable energy generation is a priority, due to the ever-increasing concern of climate change. Microbial fuel cells (MFCs) are one potential avenue to be explored, as a partial solution towards combating the over-reliance on fossil fuel based electricity. Limitations have slowed the advancement of MFC development, including low power generation, expensive electrode materials and the inability to scale up MFCs to industrially relevant capacities. However, utilisation of new advanced electrode-materials (i.e. 2D nanomaterials), has promise to advance the field of electromicrobiology. New electrode materials coupled with a more thorough understanding of the mechanisms in which electrogenic bacteria partake in electron transfer could dramatically increase power outputs, potentially reaching the upper extremities of theoretical limits. Continued research into both the electrochemistry and microbiology is of paramount importance in order to achieve industrial scale development of MFCs. This review gives an overview of the current field and knowledge in regards to MFCs and discusses the known mechanisms underpinning MFC technology, which allows bacteria to facilitate in electron transfer processes. This review focusses specifically on enhancing the performance of MFCs, with the key intrinsic factor currently limiting power output from MFCs being the rate of electron transfer to/from the anode; the use of advanced carbon-based materials as electrode surfaces is discussed.
Wastewater is now considered to be a vital reusable source of water reuse and saving energy. However, current wastewater has multiple limitations such as high energy costs, large quantities of residuals being generated and lacking in potential resources. Recently, great attention has been paid to microbial fuel cells (MFCs) due to their mild operating conditions where a variety of biodegradable substrates can serve as fuel. MFCs can be used in wastewater treatment facilities to break down organic matter, and they have also been analysed for application as a biosensor such as a sensor for biological oxygen which demands monitoring. MFCs represent an innovation technology solution that is simple and rapid. Despite the advantages of this technology, there are still practical barriers to consider including low electricity production, current instability, high internal resistance and costly materials used. Thus, many problems must be overcome and doing this requires a more detailed analysis of energy production, consumption, and application. Currently, real-world applications of MFCs are limited due to their low power density level of only several thousand mW/m². Efforts are being made to improve the performance and reduce the construction and operating costs of MFCs. This paper explores several aspects of MFCs such as anode, cathode and membrane, and in an effort to overcome the practical challenges of this system.
Microbial fuel cells (MFCs) have attracted considerable interest due to their potential in renewable electrical power generation using the broad diversity of biomass and organic substrates. However, the difficulties in achieving high power densities and commercially affordable electrode materials have limited their industrial applications to date. Carbon materials, which can exhibit a wide range of different morphologies and structures, usually possess physiological activity to interact with microorganisms and are therefore fast-emerging electrode materials. As the anode, carbon materials can significantly promote interfacial microbial colonization and accelerate the formation of extracellular biofilms, which eventually promotes the electrical power density by providing a conductive microenvironment for extracellular electron transfer. As the cathode, carbon-based materials can function as catalysts for the oxygen-reduction reaction, showing satisfying activities and efficiencies nowadays even reaching the performance of Pt catalysts. Here, first, recent advancements on the design of carbon materials for anodes in MFCs are summarized, and the influence of structure and surface functionalization of different types of carbon materials on microorganism immobilization and electrochemical performance is elucidated. Then, synthetic strategies and structures of typical carbon-based cathodes in MFCs are briefly presented. Furthermore, future applications of carbon-electrode-based MFC devices in the energy, environmental, and biological fields are discussed, and the emerging challenges in transferring them from laboratory to industrial scale are described.
Zinc-graphene composite has been electrolytically produced for the first time using a graphene quantum dot (GQD) electrode. The electrochemical reduction of zinc ion at a GQD electrode is shifted to a lesser negative potential with the complimentary anodic peak due to the oxidation of the composite shifted towards a positive potential as compared to zinc ion reduction in the GQD bath. The coulombic efficiency of the composite represents a gain of nearly 10% over the conventional Zn/Zn²⁺ in the energy storage systems. In galvanostatic electrolysis, the deposition of zinc-graphene composite is carried out under neutral and acidic conditions. The X-ray diffraction of the electrolytically prepared composite shows distinct features of 2 theta reflection at 8° due to (001) plane of graphene, in addition to the characteristic reflections at 38.9°,43.2°, 54.3°, 70.1° and 90° arising from Zn at (002), (100), (101), (102) and (110). A large scale preparation of the zinc-graphene composite has been achieved at a zinc plate as the working electrode in the GQD bath. The composite is stable up to 250 °C. Scanning electron microscopic (SEM) and energy dispersion X-ray analysis (EDAX) shows a string like structure with peaks for carbon and zinc in EDAX.
Graphene quantum dots (GQDs), a nano version of graphene whose interesting properties
that distinguish them from bulk graphene, have recently received significant scientific attention.
The quantum confinement effect referring to the size-dependence of physical and chemical
properties opens great possibility in the practical applications of this material. However, tuning
the size of graphene quantum dots is still difficult to achieve. Here, an edge-etching mechanism
which is able to tune the size of GQDs in a quasi-continuous manner is discovered. Different
from the ‘unzipping’ mechanism which has been adopted to cut bulk graphitic materials into
small fragments and normally cut through the basal plane along the ‘zig-zag’ direction where
epoxy groups reside, the mechanism discovered in this research could gradually remove the
peripheral carbon atoms of nano-scaled graphene (i.e. GQDs) due to the higher chemical
reactivity of the edge carbon atoms than that of inner carbon atoms thereby tuning the size of
GQDs in a quasi-continuous fashion. It enables the facile manipulate of the size and properties of
GQDs through controlling merely the reaction duration. It is also believed the as discovered
mechanism could be generalized for synthesizing various sizes of GQDs from other graphitic
precursors (e.g. carbon fibres, carbon nanotubes, etc)
Electrically conductive polymer nanocomposites with rodlike fillers are a versatile class of materials that are being explored for a wide range of applications. Realizing the full commercial potential of these novel materials hinges upon our ability to produce composites with well-defined and controllable properties. This, in turn, requires an in-depth understanding of the structure-property relations for the electrical properties of polymer nanocomposites. In this chapter, we review major theoretical and fundamental experimental studies of polymer nanocomposites, with particular emphasis on the main factors that determine their electrical properties. We will also discuss the major gaps in our current understanding of these materials and the greatest opportunities in the field.
The aromaticity concept and the Clar sextet rule have not received their deserved attention in graphene community. In this chapter, we will show how the simple Clar rule can help us to understand aromaticity and its related properties of graphene and nanoribbons.
Due to specifi c characteristics of graphene nanosheets (GNS) and graphene oxide
(GO), they are promising candidate to fabrication, integration and applications in
nanodevices, sensors and actuators. In addition, for new application of GNS and GO
in diff erent fi elds of science and technology, one must combine them with other new
nanomaterials such as magnetic nanoparticles, carbon dots, carbon nanotubes, nanosemiconductors,
quantum dots etc. However, a prerequisite of such combinations and
development applications of graphene, is surface functionalization of GNS and GO.
Generally, the GNS and GO functionalization is done in two ways: noncovalent and
covalent functionalization. In noncovalent functionalization, a weak interaction of a
π-π, van der Waals or electrostatic type is created between GO and the target matter.
In covalent functionalization, the oxygen-containing functional groups on the surface
of graphene, including carboxylic acid groups at the edges and epoxy and hydroxyl
groups of the plane, can be used for covalent bonding. Th ere are several routes to
covalent functionalization of graphene: nucleophilic substitution, electrophilic addition,
condensation and addition reactions. In this chapter, the surface functionalization
of graphene methods are presented and recent publications in attachment of
some nanoparticles to the graphene surface are summarized and discussed.
These are lecture notes based on a mini course on percolation which was given at the Jyväskylä summer school in mathematics in Jyväskylä, Finland, August 2009. The point of the course was to try to touch on a number of different topics in percolation in order to give people some feel for the field. These notes follow fairly closely the lectures given in the summer school. However, some topics covered in these notes were not covered in the lectures (such as continuity of the percolation function above the critical value) while other topics covered in detail in the lectures are not proved in these notes (such as conformal invariance).
The standard tables used for the Kolmogorov-Smirnov test are valid when testing whether a set of observations are from a completely-specified continuous distribution. If one or more parameters must be estimated from the sample then the tables are no longer valid.A table is given in this note for use with the Kolmogorov-Smirnov statistic for testing whether a set of observations is from a normal population when the mean and variance are not specified but must be estimated from the sample. The table is obtained from a Monte Carlo calculation.A brief Monte Carlo investigation is made of the power of the test.
A calculation of percolation thresholds of 11 two-dimensional and 18 three-dimensional lattices is presented. Among the three-dimensional ones are a random lattice and its dual, plus a number of aniso- tropic regular lattices. The results are used to test universal formulas that relate the percolation thresholds of lattices to their dimension and coordination number. The evidence suggests that dimension and coordination number are not sufficient to predict percolation thresholds.
Uniqueness of the infinite cluster and continuity of connectivity functions for short-and long-range percolation
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continuity of connectivity functions for short-and long-range percolation. Comm. Math.
Phys. 111, (2015), 505-532. http://doi org/10.1007/BF01219071/
Graphene -All you need to know
- M Berger
Berger, M. (2019). Graphene -All you need to know. Nanowerk.
https://www.nanowerk.com/what_is_graphene.php
Algebra -Exponential functions
- P Dawkins
Dawkins, P. (2018). Algebra -Exponential functions.
https://tutorial.math.lamar.edu/classes/alg/expfunctions.aspx
Percolation on a square grid
- S Wolfram
Wolfram, S. (2011). Percolation on a square grid. Wolfram Demonstrations Project.
https://demonstrations.wolfram.com/PercolationOnASquareGrid/
Biscocho is a '21 graduate With High Honors from the Philippine Science High School -CALABARZON Region Campus. He earned awards for Best Presenter
- Jamme Omar
Jamme Omar A. Biscocho is a '21 graduate With High Honors from the Philippine Science
High School -CALABARZON Region Campus. He earned awards for Best Presenter, Best Research
Proposal, Best Research Paper, and Best Research Poster. He is currently pursuing BS Applied Physics
at the University of the Philippines Diliman.
Almazan is a '21 graduate from the Philippine Science High School -CALABARZON Region Campus. He received an award for Best Research Proposal in 2019. He is currently taking
- Ralph Calvin
Ralph Calvin D. Almazan is a '21 graduate from the Philippine Science High School -CALABARZON Region Campus. He received an award for Best Research Proposal in 2019. He is
currently taking BS Agricultural and Biosystems Engineering at the University of the Philippines Los
Baños.
Emralino is a Grade 12 Physics teacher at the Philippine Science High School -CALABARZON Region Campus
- Francis Murillo
Francis Murillo Emralino is a Grade 12 Physics teacher at the Philippine Science High School
-CALABARZON Region Campus. He holds a BS Applied Physics from the University of the