<i>Introduction to Percolation Theory</i>

Stauffer, Dietrich; Aharony, Amnon; Redner, S.

doi:10.1063/1.2808877

Cited by 2,149 publications

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“…The strength of the network is the probability that a given nanotube belongs to the network and is given by . 53 We propose that stronger networks are more able to deliver electrons to lithium storage sites throughout the film. This results in the power law scaling of CN=50 with .…”

Section: Percolation Of Capacitymentioning

confidence: 98%

“…53 In this framework, at low nanotube loading levels (usually expressed as volume fractions ), the conductors form no conducting path through the composite. However, at some critical volume fraction, the electrical percolation threshold, ϕc,e, the first conducting path is formed and the composite conductivity increases substantially above that of the matrix.…”

Section: / ( )mentioning

confidence: 99%

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Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS₂/Nanotube Composite Lithium Ion Battery Electrodes

et al. 2016

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Advances in lithium ion batteries would facilitate technological developments inareas from electrical vehicles to mobile communications. While 2-dimensional systems like MoS2 are promising electrode materials due to their potentially high capacity, their poor ratecapability and low cycle-stability are severe handicaps. Here we study the electrical, mechanical and lithium storage properties of solution-processed MoS2/carbon nanotube anodes.Nanotube addition gives up to ×10 10 and ×40 increases in electrical conductivity and mechanical toughness respectively. The increased conductivity results in up to a ×100 capacity enhancement to ~1200 mAh/g (~3000 mAh/cm 3 ) at 0.1 A/g, while the improved toughness significantly boosts cycle stability. Composites with 20 wt% nanotubes combined high reversible capacity with excellent cycling stability (e.g. ~950 mAh/g after 500 cycles at 2 A/g) and high-rate capability (~600 mAh/g at 20 A/g). The conductivity, toughness and capacity scaled with nanotube content according to percolation theory while the stability increased sharply at the mechanical percolation threshold. We believe the improvements in conductivity and toughness obtained after addition of nanotubes can be transferred to other electrode materials such as silicon nanoparticles.Keywords: percolating, network, anode, mechanical 2 In recent years, lithium ion batteries (LIBs) have become the most common rechargeable power sources for portable electronic devices and electric vehicles. 1, 2 Nevertheless, they still suffer from several problems; their energy and especially power densities have not fulfilled their ultimate potential while their safety record is not unblemished. 3 A significant problem is that graphite, the dominant anode material used in LIBs, is limited by a relatively low theoretical capacity of 372 mAh/g. 4 As such, the development of the next-generation of LIBs, is expected to see the replacement of graphite-based anodes with alternative materials having higher capacity at similarly low cost. While a range of materials, including silicon, have been envisaged as future LIB anode materials, 4 of particular interest are 2-dimensional (2D) nanomaterials 5 such as graphene 6 and MoS2. 7 Over the last decade, 2D nano-materials have generated much excitement in the nanomaterials science community. [8][9][10] They come in many types including graphene, transition metal dichalcogenides (TMDs) and transition metal oxides (TMOs). These materials consist of covalently bonded monolayers which can stack via van der Waals interactions to form layered crystals. 8,9 Such 2D nanomaterials are often found as nanosheets with lateral size ranging from 10s of nm to microns and thickness of ~nm. 9 These materials have shown potential for applications 5 in both energy generation 11 and storage. 12 In the context of LIBs, exfoliated TMDs have received significant attention as prospective anode materials. 13,14 While bulk MoS2 was proposed 15 as a Li ion battery electrode material as early as 1980 due to its hi...

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Section: Percolation Of Capacitymentioning

confidence: 98%

Section: / ( )mentioning

confidence: 99%

Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS₂/Nanotube Composite Lithium Ion Battery Electrodes

et al. 2016

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“…We also consider that a cluster is percolating if contains a path connecting a particle to one of its periodic images. From the high-temperature exponential law indicating the formation of short-lived clusters upon particle collisions, by lowering the temperature the cluster size distribution becomes nonmonotonic, with dimers having a higher statistical frequency than monomers, and eventually develops a power-law tail, compatible with a percolation phenomenon [48]. The fraction P of particles belonging to a percolating cluster shows a sudden increase when the temperature drops below 0.1, where the mean cluster size χ, defined as ∞ s=1 s 2 n s / ∞ s=1 sn s , also displays a peak (inset of Fig.…”

Section: Self-assembly Spatial Correlations and Network Structurementioning

confidence: 99%

Self-assembly and cooperative dynamics of a model colloidal gel network

Colombo

Gado

2014

Soft Matter

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We study the assembly into a gel network of colloidal particles, via effective interactions that yield local rigidity and make dilute network structures mechanically stable. The self-assembly process can be described by a Flory-Huggins theory, until a network of chains forms, whose mesh size is on the order of, or smaller than, the persistence length of the chains. The localization of the particles in the network, akin to some extent to caging in dense glasses, is determined by the network topology, and the network restructuring, which takes place via bond breaking and recombination, is characterized by highly cooperative dynamics. We use N V E and N V T Molecular Dynamics as well as Langevin Dynamics and find a qualitatively similar time dependence of time correlations and of the dynamical susceptibility of the restructuring gel. This confirms that the cooperative dynamics emerge from the mesoscale organization of the network.

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“…In the vicinity of the percolation threshold, σ c can be described using the following equation, [ 66 ] in terms of the volume fraction of the fi ller, ϕ :…”

Section: Electrical Propertiesmentioning

confidence: 99%

Interphases in Graphene Polymer‐based Nanocomposites: Achievements and Challenges

et al. 2011

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Graphene constitutes a two dimensional sp2 hybridized carbon material with outstanding electrical and mechanical properties. To date, novel methods for producing large quantities of graphene and its derivatives (doped or functionalized graphenes, nanoribbons and nanoplatelets) are emerging, and research dedicated to the fabrication of polymer nanocomposites using graphenes has started. In this Research News, we summarize the synthesis and properties of graphene and its derivatives, and provide an overview of the latest research dedicated to the fabrication of polymer composites for different applications, including mechanical, electrical, optical and thermal. Some of the recently fabricated composites exhibit outstanding properties, however, it is vital to understand the chemistry and physics of the interphases established between the polymer and the graphene surfaces. The challenges in the fabrication of super robust and highly conducting composites using graphenes are also discussed. It is believed that graphene‐based polymer composites will result in commercial products if their interphases and reactivity are carefully controlled.

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Introduction to Percolation Theory

Cited by 2,149 publications

References 0 publications

Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS₂/Nanotube Composite Lithium Ion Battery Electrodes

Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS₂/Nanotube Composite Lithium Ion Battery Electrodes

Self-assembly and cooperative dynamics of a model colloidal gel network

Interphases in Graphene Polymer‐based Nanocomposites: Achievements and Challenges

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Introduction to Percolation Theory

Cited by 2,149 publications

References 0 publications

Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS2/Nanotube Composite Lithium Ion Battery Electrodes

Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS2/Nanotube Composite Lithium Ion Battery Electrodes

Self-assembly and cooperative dynamics of a model colloidal gel network

Interphases in Graphene Polymer‐based Nanocomposites: Achievements and Challenges

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Product

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Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS₂/Nanotube Composite Lithium Ion Battery Electrodes

Electrical, Mechanical, and Capacity Percolation Leads to High-Performance MoS₂/Nanotube Composite Lithium Ion Battery Electrodes