Understanding and strain-engineering wrinkle networks in supported graphene through simulations

Abstract

Wrinkle networks are ubiquitous buckle-induced delaminations in supported graphene, which locally modify the electronic structure and degrade device performance. Although the strong property-deformation coupling of graphene can be potentially harnessed by strain engineering, it has not been possible to precisely control the geometry of wrinkle networks. Through numerical simulations based on an atomistically informed continuum theory, we understand how strain anisotropy, adhesion and friction govern spontaneous wrinkling. We then propose a strategy to control the location of wrinkles through patterns of weaker adhesion. This strategy is deceptively simple, and can in fact fail in several ways, particularly under biaxial compression. However, within bounds set by the physics of wrinkling, it is possible to robustly create by strain a variety of wrinkle network geometries and junction configurations. Graphene is nearly unstrained in the planar regions bounded by wrinkles, highly curved along wrinkles, and highly stretched and curved at junctions, which can either locally attenuate or amplify the applied strain depending on their configuration. These mechanically self-assembled networks are stable under the pressure produced by an enclosed fluid and form continuous channels, opening the door to nano-fluidic applications.Peer ReviewedPostprint (published version

Modelling fluid deformable surfaces with an emphasis on biological interfaces

“…From a finite element method (FEM) perspective, this requires the basis functions parametrizing the surface to be in H 2 (square-integrable functions whose first-and second-order derivatives are also square-integrable). Here, we resort to subdivision surfaces, which have already been used to study the equilibrium shapes of lipid bilayers (Feng & Klug 2006;Ma & Klug 2008) and to analyze thin shells (Cirak et al 2000;Cirak & Ortiz 2001;Cirak & Long 2011;Zhang & Arroyo 2014;Li et al 2018). Based on a time-incremental version of Onsager's formalism, we develop variational time-integrators (Ortiz & Stainier 1999;Peco et al 2013), which are nonlinearly and unconditionally stable and allow us to adapt the time-step spanning orders of magnitude during the dynamics of fluid deformable surfaces.…”

Computing the volume enclosed by a periodic surface and its variation to model a follower pressure

“…As an application of the theory, we perform a simulation of a supported graphene sheet adhered to the substrate upon biaxial compression and under internal pressure in graphenesubstrate interstitial space [24]. Graphene is modeled as an elastic sheet using an atomistic-based continuum model within a geometrically exact framework, which adheres to the substrate with a continuum version of a Lennard-Jones potential and experiences a frictional sliding forces.…”

“…To obtain equilibrium configurations, we minimize the total free energy of the system using a quasi-Newton method with line-search, which evaluates the energy and its gradient with respect to the nodal degrees of freedom. See [24] for a full description of the model and a motivation of the problem, and Fig. 5 for an illustration.…”

“…We treat two cases: (1) periodic tubular surfaces and (2) doubly periodic surfaces enclosing a volume with a substrate. Our specific interest is in modeling pressurized carbon nanotubes [20] and supported graphene [23,24] enclosing a fluid or a gas [12,13,16], but the method is applicable to a wide range of problems such as supported lipid bilayers [21] or periodic structures in biomembrane tubes [7]. In the context of these applications, we provide numerical examples with Lagragian subdivision finite element calculations [8,3], showing the correctness of the proposed method to compute the volume and its variation.…”

Property control by elastic strain engineering: Application to graphene

“…However, it has not been possible to precisely and reversibly control the location of wrinkles, partly due to an insufficient theoretical understanding of wrinkling under biaxial compression [Zhu et al, 2012]. Wrinkles in suspended graphene under biaxial strain were studied by numerical simulation [Zhang et al, 2014]. The influence of strain anisotropy and the adhesive and frictional properties on the morphology of spontaneously-formed wrinkle networks was investigated.…”