A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Merli, R.; Lázaro, Carlos; Monleón, S.; Domingo, Alberto

doi:10.1016/j.compstruc.2012.11.023

Cited by 18 publications

(18 citation statements)

References 43 publications

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“…In [8], the model of [7] is extended to chiral CNTs, an issue addressed also in [9]. Recently, a discrete model allowing to treat general load conditions, arbitrary chirality, and an initially stressed state, has been proposed in [38], and a geometrically nonlinear theory of discrete elastic structures accounting for the effects of self-stress has been presented in [16]. Discrete mechanics has also served as a scale-bridging tool to build shell theories [6,1,17].…”

Section: Introductionmentioning

confidence: 99%

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

Favata

Micheletti

Podio–Guidugli

et al. 2016

J Elast

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The main purpose of this paper is to evaluate the self-stress state of single-wall carbon nanotubes (CNTs) and flat graphene strips (FGSs) in their natural equilibrium state, that is, the state prior to the application of external loads. We model CNTs as discrete elastic structures, whose shape and volume changes are governed by a Reactive Empirical Bond-Order (REBO) interatomic potential of second generation. The kinematical variables we consider are bond lengths, bond angles, and dihedral angles; to changes of each of these variables we associate a work-conjugate nanostress. To determine the self-stress state in a given CNT, we formulate the load-free equilibrium problem as a minimum problem for the interatomic potential, whose solution yields the equilibrium nanostresses; next, by exploiting the nonlinear constitutive dependence we derive for nanostresses in terms of a list of kinematical variables, we determine the equilibrium values of the latter; finally, from the equilibrium values of the kinematical variables we deduce the natural geometry and, in particular, the natural radius.Our theoretical framework accommodates CNTs of whatever chirality. In the achiral case, when we can count on maximal intrinsic symmetries and hence the number of independent unknowns is reduced to a minimum, the stationarity conditions implied by energy minimization are relatively easy to derive and solve numerically; for chiral CNTs, we prefer to solve the minimum problem directly.The natural-radius predictions we achieve within our discrete-mechanics framework are in good agreement with the results of DFT-and TB-based calculations; the same is true for our predictions of the self-energy, that is, the energy associated with self-stress (called cohesive energy in the literature); we surmise that our discrete mechanical model may serve as a source of benchmarks for MD simulation algorithms.We find that self-stress depends on changes in both bond and dihedral angles in achiral CNTs and, in addition, on changes in bond length in chiral CNTs. Our analysis applies also to FGSs, whose self-stress and self-energy we evaluate; we find that, in FGSs self-stress is associated exclusively with changes in bond angle. 1 arXiv:1409.8619v2 [cond-mat.mtrl-sci] 5 Mar 2015 2 A. Favata, A. Micheletti, P. Podio-Guidugli, N.M. Pugno

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Section: Introductionmentioning

confidence: 99%

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

Favata

Micheletti

Podio–Guidugli

et al. 2016

J Elast

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“…The following approach may be regarded as the geometrical nonlinear extension of the equations developed in our previous work (Merli et al, 2013) by using the same energy approach. The small displacements assumption has been removed in this case and the necessary nonlinear terms have been included.…”

Section: Bar Elementmentioning

confidence: 99%

“…Moreover, the equations included herein may be regarded as the geometrically nonlinear extension of our previous work (Merli et al, 2013) in which a review of some mechanical parameters of SWCNTs by means of the same MSM model was provided. In addition, our numerical treatment is rather in the Molecular Mechanics (MM) approach of Cao and Chen (2006).…”

Section: Introductionmentioning

confidence: 99%

Geometrical nonlinear formulation of a Molecular Mechanics model applied to the structural analysis of single-walled carbon nanotubes

Merli

Lázaro

Monleón

et al. 2015

International Journal of Solids and Structures

Self Cite

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a b s t r a c tIn this paper, the post-critical behavior and buckling modes of single-walled carbon nanotubes are analyzed via a Molecular Mechanics model. The main target is to develop a general formulation for the model, which has been simplified under small strains assumption, and to implement a versatile tool for the structural analysis of carbon nanotubes in the framework of geometrical nonlinearity. For this purpose, a mechanical formulation able to reproduce any load configuration and supporting conditions has been derived by using an energy approach. Then, an incremental-iterative solution procedure has been implemented in order to trace several nonlinear equilibrium paths and to obtain the corresponding critical strains of clamped-clamped nanotubes under compressive, flexural and torsional loading distributions. The model shows a good numerical performance and results in agreement with previous atomistic works. Two interatomic potentials have been adopted in order to find out the influence of different constitutive relationships on the final nonlinear response. We have concluded that the choice of the potential function has no significant effect on the final buckling strains. Our results confirm that the final buckling response is strongly determined by geometrical imperfections in the nanotube, which can be well reproduced in the proposed model, but are much more difficult to handle in continuum models.

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“…To further explore this hypothesis, we tested the effect of nanostructure stiffness on plant cell internalization. Single-walled carbon nanotubes (SWCNTs) exhibit stiffnesses on the order of hundreds of GPa to TPa (37,38), about one thousand times stiffer than the nanostring nanostructure (several Gpa (39)). Furthermore, SWCNTs have been shown to passively internalize into the cells of a variety of plant species (40)(41)(42), with a leading hypothesis that the larger tensile strength of the SWCNT compared to that of the plant cell wall facilitates needle-like plant cell internalization (13,43,44).…”

Section: Internalization Mechanism Of Dna Nanostructures Into Plant Cmentioning

confidence: 99%

DNA Nanostructures Coordinate Gene Silencing in Mature Plants

Zhang

Demirer

Zhang

et al. 2019

Preprint

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SignificancePlant bioengineering will be necessary to sustain plant biology and agriculture, where the delivery of biomolecules such as DNA, RNA, or proteins to plant cells is at the crux of plant biotechnology. Here, we show that DNA nanostructures can passively internalize into plant cells and deliver small interfering RNA (siRNA) to mature plant tissues. Furthermore, we demonstrate that nanostructure size, shape, compactness, and stiffness, affect both nanostructure internalization into plant cells and subsequent gene silencing efficiency. Interestingly, we also find that the siRNA attachment locus affects the endogenous plant gene silencing pathway. Our work demonstrates programmable passive delivery of biomolecules to plants, and details the figures of merit for future implementation of DNA nanostructures in agriculture. AbstractPlant bioengineering may generate high yielding and stress-resistant crops amidst a changing climate and a growing global population (1-3). However, delivery of biomolecules to plants relies on Agrobacterium infection (4) or biolistic particle delivery (5), the former of which is only amenable to DNA delivery. The difficulty in delivering functional biomolecules such as RNA to plant cells is due to the plant cell wall which is absent in mammalian cells and poses the dominant physical barrier to exogenous biomolecule delivery in plants. DNA nanostructure-mediated biomolecule delivery is an effective strategy to deliver cargoes across the lipid bilayer of mammalian cells, however, nanoparticle-mediated delivery remains unexplored for passive biomolecule delivery across the cell wall in plants. Herein, we report a systematic assessment of different DNA nanostructures for their ability to internalize into cells of mature plants, deliver small interfering RNAs (siRNAs), and effectively silence a constitutivelyexpressed gene in Nicotiana benthamiana leaves. We show that nanostructure internalization into plant cells and the corresponding gene silencing efficiency depends on the DNA nanostructure size, shape, compactness, stiffness, and location of the siRNA attachment locus on the nanostructure. We further confirm that the internalization efficiency of DNA nanostructures correlates with their respective gene silencing efficiencies, but that the endogenous gene silencing pathway depends on the siRNA attachment locus. Our work establishes the feasibility of biomolecule delivery to plants with DNA nanostructures, and details both the design parameters of importance for plant cell internalization, and also assesses the impact of DNA nanostructure geometry for gene silencing mechanisms.

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A molecular structural mechanics model applied to the static behavior of single-walled carbon nanotubes: New general formulation

Cited by 18 publications

References 43 publications

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

Geometry and Self-stress of Single-Wall Carbon Nanotubes and Graphene via a Discrete Model Based on a 2nd-Generation REBO Potential

Geometrical nonlinear formulation of a Molecular Mechanics model applied to the structural analysis of single-walled carbon nanotubes

DNA Nanostructures Coordinate Gene Silencing in Mature Plants

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