Breaking of Icosahedral Symmetry: C60 to C70

Bodner, Mark; Patera, J.; Szajewska, Marzena

doi:10.1371/journal.pone.0084079

Cited by 10 publications

(8 citation statements)

References 20 publications

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“…The differences between and can be explained through a symmetry breaking process. The highly symmetric structure of , which belong to the icosahedral symmetry group , is transformed to the dihedral symmetry group by adding one more decagonal term, creating the structure 117 .…”

Section: Resultsmentioning

confidence: 99%

Quantum transport on honeycomb networks

Batalha

Volta²,

Strunz

et al. 2022

Sci Rep

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We study the transport properties on honeycomb networks motivated by graphene structures by using the continuous-time quantum walk (CTQW) model. For various relevant topologies we consider the average return probability and its long-time average as measures for the transport efficiency. These quantities are fully determined by the eigenvalues and the eigenvectors of the connectivity matrix of the network. For all networks derived from graphene structures we notice a nontrivial interplay between good spreading and localization effects. Flat graphene with similar number of hexagons along both directions shows a decrease in transport efficiency compared to more one-dimensional structures. This loss can be overcome by increasing the number of layers, thus creating a graphite network, but it gets less efficient when rolling up the sheets so that a nanotube structure is considered. We found peculiar results for honeycomb networks constructed from square graphene, i.e. the same number of hexagons along both directions of the graphene sheet. For these kind of networks we encounter significant differences between networks with an even or odd number of hexagons along one of the axes.

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Section: Resultsmentioning

confidence: 99%

Quantum transport on honeycomb networks

Batalha

Volta²,

Strunz

et al. 2022

Sci Rep

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“…Many properties of the graphene, including colouring, can be extended to nanotubes, which are strips of the graphene of appropriate width, rolled into a cylinder [8,14]. Different nanotubes are obtained by different orientations of the strips [2][3][4][5].…”

Section: Discussionmentioning

confidence: 99%

Group theoretical methods to construct the graphene

Grabowiecka,

Patera,

Szajewska

2016

Preprint

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In this paper, the tiling of the Euclidean plane with regular hexagons whose vertices are occupied by carbon atoms is called the graphene. We describe six different ways to generate the graphene by the means of group theory. There are two ways starting from the triangular lattice of Lie algebra A2 and G2, and one way for each of the Lie algebras B3, C3 and A3, by projecting the weight system of their lowest representation to the hexagons of A2. Colouring of the graphene is presented. Changing from one colouring to another is called phase transition. Multistep refinements of the graphene are described.

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“…The uniqueness of closed‐cage, nearly spherical C 60 and related fullerene molecules has attracted considerable attention. The icosahedral symmetry and numerous possibilities of functionalization allow the modulation of their optoelectronic properties, leading to unabated interest in these intriguing carbon allotropes. The chemistry of fullerenes is that of electron‐poor olefins, with sp 2 carbon atoms constrained into a pyramidalized geometry.…”

Section: Methodsmentioning

confidence: 99%

Novel 5‐(Benzo[b]thiophen‐3‐yl)pyridine‐3‐carbaldehyde (BTPA) Functionalization Framework For Modulating Fullerene Electronics

et al. 2017

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Through ac ycloaddition reaction, fullerene( C 60 )w as derivatized with an ovel organic compound 5-(benzo [b]thiophen-3-yl)pyridine-3-carbaldehyde to form the processable and stable 3-(benzo [b]thiophene-3yl)-5-fullero-1-methylpyrrolidinepyridine (BTFP) compound. BTFP exhibits close similarities to phenyl-C61-butyric-acid-methyl-ester (PCBM)i nt erms of first reduction potentialv alues (À0.62 and À0.61 Vv s. Ag/AgCl, for BTFP and PCBM, respectively)a nd lowest occupied molecular orbital (LUMO) energy level values (3.93 eV in both cases). In chloroform, BTFP exhibits ab athochromic shift in the l max of BTFP (l max, BTFP = 290 nm and l max, PCBM = 260 nm), owing to the graftedb enzo [b]thiophene-3-yl)pyridinem oiety.D espite the similarityi nL UMO (3.93 eV) energy values, BTFP and PCBM differ in their luminescence-quenching ability.T he bathochromic shift in the l max of BTFP (relative to PCMB) is likely to contribute to improved light absorption of as uitable donor for photovoltaic applications.The uniquenesso fc losed-cage, nearly spherical C 60 and related fullerenem olecules has attracted considerable attention. The icosahedrals ymmetry [1] and numerousp ossibilities of functionalizationa llow the modulation of their optoelectronic properties, [2] leading to unabated interest in these intriguing carbon allotropes. The chemistry of fullerenes is that of electron-poor olefins, with sp 2 carbon atoms constrained into apyramidalized geometry.M ultiple double bonds are available on the carbon backbone, making multiple functionalization [3] an interesting route towards new functional materials.This has led to avariety of novel compoundsw ithf inely tunable features thath ave found applicationsa sc atalysts [4] and antioxidants, [5] as well as in sensors [6] and solar cells. [2a, 7] The functionalization of fullerenes does not only modifyt heir properties, but converts them into more processable forms, as pristine C 60 is only sparselys oluble in most solvents, making it intractable. Indeed, the quest for soluble fullerenes was (and still is) one of the main driving forces in the field of covalent modification of carbon nanostructures. Phenyl-C61-butyric-acid-methyl-ester (PCBM), af ullerened erivative, is as olution-processable n-type organic semiconductor,w hich is commonly blended with ptype conjugated polymers to make photovoltaic( PV) cells. However,o wing to the dependence of PV properties on frontier orbital energy levels of donor and acceptors, the application of PCBM to all donorp olymers irrespective of their optoelectronic properties leads to untrue PV properties. For instance,r eports by Susarova et al. [8] and Kästnere tal. [9] compared the PV responses of as et of polymers with PCBM and other functionalized fullerenes and observed that PCBM gave just moderate efficiencies in combination with the polymers, whereas the best PV performances were obtained with ab lend of each polymerw ith specific fullerened erivatives possessing better-suiting molecularstructures. Herein, we describe afulleropyrrolid...

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Breaking of Icosahedral Symmetry: C60 to C70

Cited by 10 publications

References 20 publications

Quantum transport on honeycomb networks

Quantum transport on honeycomb networks

Group theoretical methods to construct the graphene

Novel 5‐(Benzo[b]thiophen‐3‐yl)pyridine‐3‐carbaldehyde (BTPA) Functionalization Framework For Modulating Fullerene Electronics

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