Research Papers

Self-Folding Mechanics of Surface Wettability Patterned Graphene Nanoribbons by Liquid Evaporation

[+] Author and Article Information
Yue Zhang, Qingchang Liu

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904

Baoxing Xu

Department of Mechanical and
Aerospace Engineering,
University of Virginia,
Charlottesville, VA 22904
e-mail: bx4c@virginia.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 19, 2017; final manuscript received November 29, 2017; published online December 20, 2017. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 85(2), 021006 (Dec 20, 2017) (9 pages) Paper No: JAM-17-1524; doi: 10.1115/1.4038683 History: Received September 19, 2017; Revised November 29, 2017

The control of geometric shapes is well acknowledged as one of the facile routes to regulate properties of graphene. Here, we conduct a theoretical study on the evaporation-driven self-folding of a single piece of graphene nanoribbon that is immersed inside a liquid droplet prior, and demonstrate the folded pattern, which is significantly affected by the surface wettability gradient of the graphene nanoribbon. On the basis of energy competition among elastic bending deformation, liquid–graphene interaction and van der Waals force interaction of folded nanoribbons, we propose a theoretical mechanics model to quantitatively probe the relationship among self-folding, surface wettability gradient, and pattern and size of ultimate folded graphene. Full-scale molecular dynamics (MD) simulations are performed to validate the energy competition and the self-folded patterns, and the results show good agreement with theoretical analyses. This study sheds novel insight on folding graphene nanoribbons by leveraging surface wettability and will serve as a theoretical guidance for the controllable shape design of graphene nanoribbons.

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Grahic Jump Location
Fig. 2

Variation of elastic bending energy of graphene nanoribbon Ebending plus graphene–graphene binding energy Ebinding of the overlap parts in folded patterns, Ebending+Ebinding,withtheoverlaplengthl0, after water molecules are completely evaporated for the folded (a) racket-like pattern and (b) spiral pattern. Bending stiffness of graphene is D=1.44 eV, binding energy density is γbinding=1.45 eV/nm2, and the interlayer distance between graphene is t=0.34 nm.

Grahic Jump Location
Fig. 1

Schematic illustrations of the self-folding behavior of a single flexible graphene nanoribbon with surface wettability gradients by liquid evaporation. (a) Mixture of water and graphene with a surface wettability gradient, where the surface wettability of each graphene strip highlighted in different colors is represented by their contact angle between water θ1, θ2,…, θn. (b) Wrapping status of graphene with water droplet at the equilibrium. (c) Folded pattern of graphene after complete evaporation of liquid, determined by the wrapping status and energy condition Eg−w+Ebending of graphene at the equilibrium.

Grahic Jump Location
Fig. 3

MD simulation snapshots of wrapping status of graphene nanoribbons with different surface wettability gradient conditions in water droplet at the equilibrium: (a)λ1=3.5,Δλ=0.2,n=6, (b) λ1=2.2,Δλ=0.4,n=6, and (c) λ1=1.2,Δλ=0.4,n=6

Grahic Jump Location
Fig. 4

Water–graphene interactive energy Eg−w and elastic bending energy of graphene nanoribbon Ebending during equilibrium. Variation of Eg−w and Ebending for graphene with the equilibrium time at wettability condition for (a) λ1=1 and (b) n=5. Comparison of the stable Eg−w+Ebending from simulations and theory at final equilibrium at wettability condition with (c) λ1=1 and (d) n=5.

Grahic Jump Location
Fig. 5

Comparison of Eg−w+Ebendingatthestableequilibriumstagebetweensimulationsandtheoryforgraphenenanoribbons:(a)λ1=2.6, (b) n=6, (c) λ1=3.5, and (d) n=3

Grahic Jump Location
Fig. 6

MD simulation snapshots of folding behavior of graphene nanoribbons during evaporation process for different surface wettability gradient conditions. (a) (i) λ1=1,Δλ=0.4,n=6 and (ii) λ1=1,Δλ=0.1,n=6. (b) (i) λ1=2.6,Δλ=0.4,n=6 and (ii) λ1=2.6,Δλ=0.3,n=6. (c) (i) λ1=3.5,Δλ=0.4,n=6 and (ii) λ1=3.5,Δλ=0,n=6.

Grahic Jump Location
Fig. 7

Self-folding map of graphene nanoribbons with surface wettability gradients by water evaporation

Grahic Jump Location
Fig. 8

Characterization of folded configuration of graphene nanoribbons after complete evaporation of water: (a) variation of overlap length l0 as function of evaporation time in MD simulations and (b) comparison of overlap length l0 in the stable folded patterns with wettability gradient Δλ between theory and MD simulations



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