# Expanding Horizons: Taking Advantage of Graphene's Surface Area for Advanced Applications
## 2 Increasing the Surface Area of Graphene
### Surface Enhancement by Creating Ripples  
Two-dimensional (2D) crystals are expected to be unstable because of thermodynamic requirements that require the formation of out-of-plane bending, which creates a theoretical conundrum when combined with interatomic interactions. The substantially isolated stretching and bending processes result in the production of ripples, which provide durability intrinsic to fictitious 2D materials [33; 34]. Transmission electron microscopy (TEM) investigations revealed that free-suspended graphite fails to adhere to the two-dimension paradigm. These tests showed that suspended graphene membranes exhibited notable out-of-plane distortions (ripples) with altitudes as high as 1 nm [35]. Scanning probe microscopy (SPM) studies of graphene in SiO\({}_{2}\) surfaces also revealed nanometer-scalefluctuations that were analogous to those found in independent graphene [36]. The AFM images in Figure 3a,b illustrate the buckling-induced formation of ripples in 500 nm wide monolayer graphene ribbon arrays, achieved by releasing a 30% pre-strain. The buckled ribbons consistently exhibited a regular surface morphology characterized by periodic ripple structures with an approximate amplitude of 80 nm and a periodicity of 340 nm. Rippling was consistently observed on the graphene-covered areas of the ribbons, which typically had a length of 10 \(\upmu\)m and a width of up to 1.2 \(\upmu\)m, following the strain release. Additionally, the study explored how varying the pre-strain influenced the resulting surface morphologies of these monolayer graphene ripples [37]. Carbon atoms occupy the third spatial dimension because of the spatial and temporal variability in carbon-carbon bond dimensions, which are influenced by vibrations caused by heat and interatomic connections [34]. This facilitates the formation of active ripples as well as a reduction in the total independent energy, as demonstrated in autonomous graphene. Additionally, the unequal distribution of bond lengths is a result of electron delocalization inside the \(\pi\)-cloud along with the resulting e-hole puddle. To reduce free energy, this asymmetry forces the lattice to take on a non-planar form. Notably, scanning tunneling microscopy (STM) shows that heat fluctuation-induced ripples on free-standing graphene display temporal dynamics. Graphene's bond length asymmetry is most noticeable at the edges and near defects, which increases the density of ripples in these areas [34]. In a thorough study of edge-stress-induced ripples using a deformation warping mode, [PERSON] et al. [38] used graphene-simulated edges as elastic strings attached to the material. The stretching of atomic connections caused by the out-of-plane movement of carbon reduced compressible edge stresses. Figure 3: AFM images comparing graphene ribbon arrays before and after the formation of ripples (**a**) show the flat ribbons on a SiO\({}_{2}\)/Si substrate before the release of pre-strain and (**b**) illustrate the buckled ribbons with their characteristic ripple pattern after the pre-strain was released. The figure is adapted with permission from [37]. American Chemical Society, 2010. All rights reserved. Polycrystallinity and defect development are common outcomes of large-scale graphene sheet synthesis using chemical vapor deposition (CVD) techniques. Wrinkles and ripples are examples of out-of-plane deformations that have the potential to greatly reduce the number of in-plane stresses caused by stacking faults [39]. Thus, wrinkles and ripples on graphene can be caused by atomic line defects, such as grain boundaries (or dislocations). To characterize ripples that are adjacent to defects, such as disclinations (heptagons or pentagons) and dislocations (heptagon-pentagon di-poles), in graphene, and to predict large-scale configurations of graphene under specific defect distributions, a theoretical model was generalized by the von Karman equation for a flexible solid membrane. In the study by [PERSON] et al.