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Scaling laws for van der Waals interactions in nanostructured materials.

Gobre VV, Tkatchenko A - Nat Commun (2013)

Bottom Line: Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons.As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture.We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.

View Article: PubMed Central - PubMed

Affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany.

ABSTRACT
Van der Waals interactions have a fundamental role in biology, physics and chemistry, in particular in the self-assembly and the ensuing function of nanostructured materials. Here we utilize an efficient microscopic method to demonstrate that van der Waals interactions in nanomaterials act at distances greater than typically assumed, and can be characterized by different scaling laws depending on the dimensionality and size of the system. Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons. As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture. We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.

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Scaling laws for vdW coefficients.vdW C6 coefficients per carbon atom (the C6 of the full system divided by NC2, where NC is the number of carbon atoms) for nanostructures of different dimensionality, as calculated by the electrodynamic response model of ref. 11. The size ranges for different systems are as follows: (1) the radius of fullerenes is varied from 2 to 12 Å; (2) the radius of single-wall carbon nanotubes (SWCNT)-Armchair(n,n) and SWCNT-Zigzag(n,0) vary between 2 and 60 Å; (3) the graphene nanoribbons (GNRs) vary in radius from 5 to 50 Å; (4) the number of layers in multilayer graphene (MLG) varies from 2 to 30, where each point on the plot corresponds to an increase of two layers.
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f1: Scaling laws for vdW coefficients.vdW C6 coefficients per carbon atom (the C6 of the full system divided by NC2, where NC is the number of carbon atoms) for nanostructures of different dimensionality, as calculated by the electrodynamic response model of ref. 11. The size ranges for different systems are as follows: (1) the radius of fullerenes is varied from 2 to 12 Å; (2) the radius of single-wall carbon nanotubes (SWCNT)-Armchair(n,n) and SWCNT-Zigzag(n,0) vary between 2 and 60 Å; (3) the graphene nanoribbons (GNRs) vary in radius from 5 to 50 Å; (4) the number of layers in multilayer graphene (MLG) varies from 2 to 30, where each point on the plot corresponds to an increase of two layers.

Mentions: The main results are summarized in Fig. 1, where we present the C6 coefficient per carbon atom (see definition in the Methods section) for nanostructures of different dimensionality, including zero-dimensional fullerenes, one-dimensional single-wall carbon nanotubes, two-dimensional single-layer and MLG, and three-dimensional graphite and diamond. The C6 coefficient per carbon atom varies by almost an order of magnitude among the different nanostructures, with the lowest value found for small fullerenes and the largest for graphene. These findings demonstrate that the conventional approximation of fixed carbon–carbon C6 coefficient fails dramatically when modelling vdW interactions between nanostructures. The pairwise approximation is especially problematic when the interaction between different nanostructures is studied, for example, binding between fullerenes/nanotubes with graphene layers or graphite surface (see below).


Scaling laws for van der Waals interactions in nanostructured materials.

Gobre VV, Tkatchenko A - Nat Commun (2013)

Scaling laws for vdW coefficients.vdW C6 coefficients per carbon atom (the C6 of the full system divided by NC2, where NC is the number of carbon atoms) for nanostructures of different dimensionality, as calculated by the electrodynamic response model of ref. 11. The size ranges for different systems are as follows: (1) the radius of fullerenes is varied from 2 to 12 Å; (2) the radius of single-wall carbon nanotubes (SWCNT)-Armchair(n,n) and SWCNT-Zigzag(n,0) vary between 2 and 60 Å; (3) the graphene nanoribbons (GNRs) vary in radius from 5 to 50 Å; (4) the number of layers in multilayer graphene (MLG) varies from 2 to 30, where each point on the plot corresponds to an increase of two layers.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3753541&req=5

f1: Scaling laws for vdW coefficients.vdW C6 coefficients per carbon atom (the C6 of the full system divided by NC2, where NC is the number of carbon atoms) for nanostructures of different dimensionality, as calculated by the electrodynamic response model of ref. 11. The size ranges for different systems are as follows: (1) the radius of fullerenes is varied from 2 to 12 Å; (2) the radius of single-wall carbon nanotubes (SWCNT)-Armchair(n,n) and SWCNT-Zigzag(n,0) vary between 2 and 60 Å; (3) the graphene nanoribbons (GNRs) vary in radius from 5 to 50 Å; (4) the number of layers in multilayer graphene (MLG) varies from 2 to 30, where each point on the plot corresponds to an increase of two layers.
Mentions: The main results are summarized in Fig. 1, where we present the C6 coefficient per carbon atom (see definition in the Methods section) for nanostructures of different dimensionality, including zero-dimensional fullerenes, one-dimensional single-wall carbon nanotubes, two-dimensional single-layer and MLG, and three-dimensional graphite and diamond. The C6 coefficient per carbon atom varies by almost an order of magnitude among the different nanostructures, with the lowest value found for small fullerenes and the largest for graphene. These findings demonstrate that the conventional approximation of fixed carbon–carbon C6 coefficient fails dramatically when modelling vdW interactions between nanostructures. The pairwise approximation is especially problematic when the interaction between different nanostructures is studied, for example, binding between fullerenes/nanotubes with graphene layers or graphite surface (see below).

Bottom Line: Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons.As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture.We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.

View Article: PubMed Central - PubMed

Affiliation: Fritz-Haber-Institut der Max-Planck-Gesellschaft, Faradayweg 4-6, 14195 Berlin, Germany.

ABSTRACT
Van der Waals interactions have a fundamental role in biology, physics and chemistry, in particular in the self-assembly and the ensuing function of nanostructured materials. Here we utilize an efficient microscopic method to demonstrate that van der Waals interactions in nanomaterials act at distances greater than typically assumed, and can be characterized by different scaling laws depending on the dimensionality and size of the system. Specifically, we study the behaviour of van der Waals interactions in single-layer and multilayer graphene, fullerenes of varying size, single-wall carbon nanotubes and graphene nanoribbons. As a function of nanostructure size, the van der Waals coefficients follow unusual trends for all of the considered systems, and deviate significantly from the conventionally employed pairwise-additive picture. We propose that the peculiar van der Waals interactions in nanostructured materials could be exploited to control their self-assembly.

Show MeSH