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Materials Today Volume 00, Number 00 October 2015

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RESEARCH: Review

Wrinkled, rippled and crumpled graphene: an overview of formation mechanism, electronic properties, and applications Shikai Deng and Vikas Berry* Department of Chemical Engineering, University of Illinois at Chicago, 810 S. Clinton, Chicago, IL 60607, USA

Distinctive from their 1D and 0D counterparts, 2D nanomaterials (2DNs) exhibit surface corrugations (wrinkles and ripples) and crumples. Thermal vibrations, edge instabilities, thermodynamically unstable (interatomic) interactions, strain in 2D crystals, thermal contraction, dislocations, solvent trapping, pre-strained substrate-relaxation, surface anchorage and high solvent surface tension during transfer cause wrinkles or ripples to form on graphene. These corrugations on graphene can modify its electronic structure, create polarized carrier puddles, induce pseudomagnetic field in bilayers and alter surface properties. This review outlines the different mechanisms of wrinkle, ripple and crumple formation, and the interplay between wrinkles’ and ripples’ attributes (wavelength/width, amplitude/ height, length/size, and bending radius) and graphene’s electronic properties and other mechanical, optical, surface, and chemical properties. Also included are brief discussions on corrugation-induced reversible wettability and transmittance in graphene, modulation of its chemical potential, enhanced energy storage and strain sensing via relaxation of corrugations. Finally, the review summarizes the future areas of research for 2D corrugations and crumples. Introduction Graphene, a two-dimensional (2D) monolayer of sp2 hybridized carbon atoms arranged in honeycomb lattice, has received significant interest since it was conclusively isolated in 2004 via the Scotch tape method [1,2]. Due to a unique combination of its crystallographic, electronic and chemical structure, graphene exhibits extraordinary properties, including highest room-temperature carrier mobility [3], a weak optical absorptivity (2.3%) [4], high thermal conductivity (25 times that of silicon) [5], and high mechanical strength (strongest nanomaterial measured, tensile strength of 130 GPa and a Young’s modulus of 1 TPa) [6,7]. Graphene can be produced via graphite exfoliation (Scotch tape method) [1], chemical vapor deposition (CVD) [8–10], sublimation of silicon from SiC [11], and reduction of graphene oxide [12]. Currently, CVD is widely employed to produce graphene with controlled number of layers, large area and high quality. Here, metal catalysts at high temperature help in dissociation of carbon precursors into carbon atoms which bind together to form graphene. These graphene sheets are *Corresponding author: Berry, V. ([email protected])

then transferred to arbitrary substrates for further study and/or applications [8,10,13,14]. Apart from chemical functionalization, substrate interaction, crystallography, and size, the surface corrugation on graphene can also modify its properties. From literature (which is conflicted in nomenclature) and our understanding, we categorize these corrugations as wrinkles, ripples and crumples based on their aspect ratio, physical dimensions, topology and order, as follows: wrinkles and ripples occur nominally on twodimensional plane, where wrinkles have a high aspect ratio with width between one and tens of nm, height below 15 nm, and length above 100 nm (aspect ratio > 10); and ripples are more isotropic (aspect ratio 1) valleys and peaks with feature size below 10 nm (Fig. 1) [15]. On the other hand, crumples are dense deformations (folds and wrinkles) occurring isotropically (ordered or unordered) in two or three dimensions (similar to crumpled paper) [16,17]. In this review, we outline different mechanisms of wrinkles, ripples and crumples formation in graphene, such as (a) thermal vibration of the 2D lattice, (b) edge instability, defect and dislocation, (c) negative thermal expansion (oppose to the positive thermal expansion for the substrate); (d) trapped solvent evaporation/removal, (e)

1369-7021/ß 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/). http://dx.doi.org/10.1016/ j.mattod.2015.10.002

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RESEARCH: Review FIGURE 1

Wrinkled, Rippled and crumpled graphene. (a) Rippled graphene; (b) wrinkled graphene and (c) crumpled graphene. Nature 446 (2007) 60–63, Nat. Nano 4 (2009) 562–566, Sci. Rep. (2014) 4.

relaxation of pre-strained substrate, (f) anchorage on substrate, (g) substrate’s surface potential, and (h) solvent surface tension. Graphene’s deformation is governed by its mechanical properties (Young’s modulus, interfacial energy and number of layers) and the resultant corrugations modify its electronic structure (band-gap opening (potentially > 1 eV) [18–20], pseudomagnetic field in bilayers [18], electron/hole puddle formation [21], and carrier transport [22]). These, in turn can be employed to modify graphene’s wettability, transmittance, chemical potential, expansion for energy storage, and conductivity. Futuristically, it is important to (a) enable control of the physical attribute of these corrugations; (b) thoroughly study the influence of wrinkles on electronic, optical, mechanical and chemical properties [23,24]; and (c) study these effects on other 2D nanomaterials.

Ripples, wrinkles and crumples formation Ripples formation Strictly, 2D crystals are expected to be unstable due to the thermodynamic requirement for the existence of out-of-plane bending with interatomic interaction generating a mathematical paradox [25,26]. The stability of the pseudo 2D material is achieved by ripple formation resulting from the partially decoupled bending and stretching modes [27,28]. The fact that free-suspended graphene is not strictly 2D was revealed by transmission electron microscopy (TEM) experiments, where suspended graphene

membranes exhibited pronounced out-of-plane deformations (ripples) with height up to 1 nm [29]. Nanometer-sized ripples, similar to those found on free-standing graphene, were also reported in scanning-probe microscopy studies of graphene on SiO2 substrates [30]. Mechanistically, the temporal and spatial modulation of the C–C bond-lengths due to thermal-vibrations and interatomic interactions induce carbon to occupy space in the third dimension [27,28,31,32]; thus forming dynamic ripples and minimizing the total free energy, as observed in free-standing graphene [33]. Further, the delocalized electrons in the p-cloud (and associated electron–hole puddles formed) lead to asymmetric distribution of bond lengths. This asymmetry forces the lattice to become non-planar to minimize free energy. It is important to note that the thermal-fluctuation-induced ripples on free-standing graphene dynamically change with time as observed via scanning tunneling microscopy (STM) [33]. The asymmetry of bond-lengths in graphene is amplified on the edges and near defects, thus increasing the ripples density in these regions [28,34]. Shenoy et al. comprehensively studied the edge-stressinduced ripples by a deformation warping mode with simulation edges of graphene as elastic string anchoring on graphene and stretching of the atomic bonds brought about by out-of-plane movement of carbon to lower the compressive edge stresses [34]. CVD based production of graphene sheets at large scale commonly leads to polycrystallinity and defects. Out-of-plane

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deformation (wrinkles and ripples) can significantly reduce the magnitude of in-plane stresses generated by the defects [35]. Therefore, atomic line defects like grain boundaries (or dislocations) can induce wrinkles and ripples on graphene. Zhang et al. developed a model by generalizing von Karman equation for a flexible solid membrane to describe ripples near defects such as disclinations (heptagons or pentagons) and dislocations (heptagon–pentagon dipoles) on graphene and predicted the large scale graphene configurations under specific defect distributions [36]. Such defect-guided ripples in graphene were also simulated and discussed in the work of Wang et al. [37]. By introducing the line defect, which is an extended one-dimensional periodic Stone– Wales defect, the researchers found the ripples wavelength (distance between peak to peak of periodical ripples) and amplitude (height difference between peak to peak) decrease as the angle between the line-defect and strain-direction increases [38,39].

Wrinkle formation Growing graphene on metal substrates via CVD process and epitaxially on SiC The interaction between the substrate and graphene strongly influences wrinkle- and ripple-formation. Graphene grown on metallic catalysts exhibits high densities of wrinkles due to the opposite polarity of thermal expansion coefficients (TEC) of graphene and the metal [40]. This is because the TEC of graphene is negative, which attributed to the horizontal displacement of the graphene sheet resulting from the flexural phonon modes with little contribution from the in-plane phonons [22,41]. As graphene is cooled (the last step of CVD growth), the number of flexural modes is reduced, which increases the horizontal length of the graphene sheet. However, the value of TEC and the point of transition of TEC from negative to positive value are still being debated. Yoon et al. experimentally measured a room-temperature TEC of 8 0.7 106 K1, and Bao et al. measured a consistent

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value of 7 106 K1 [14,42,43]. However, while Bao et al. predicted the negative-to-positive transition temperatures of TEC at 350 K, Yoon et al. suggested that the TEC stays negative between 300 and 400 K. To study TEC, Bao et al. measured the initial (at 700 K) and final lengths of graphene at different temperatures; while, Yoon et al. studied Raman shifts as a function of temperature. Also, the first principle calculations by Mounet and Marzari [44] predicted that this transition should occur at 2250 K and calculated the TEC at room temperature to be 3.6 106 K1. In an experiment where a crystalline island of graphene was grown on copper, isotropic and self-similar wrinkles were achieved as shown in Fig. 2a [20,45,46]. Besides the opposite thermal deformation, the defect lines on metal substrates also play an important role in the formation of wrinkles on graphene [47]. Liu et al. showed that the wrinkle attributes and density are governed by the growth substrates (nickel in this case), its thickness and the process employed to transfer graphene. With increase in the thickness of nickel, graphene’s grain-size reduces, resulting in higher-density (and smaller) of wrinkles on graphene [41]. Graphene grown epitaxially on SiC (a semiconductor substrate) [11] also produces wrinkles due to thermal expansion of graphene during the cooling step in this process [48,49].

Graphene transfer process Graphene grown on metals is routinely transferred to other substrates and tends to form wrinkles. Here, a layer of polymer (such as poly (methyl methacrylate) or others) is spin-coated on grapheneon-metal, and the metal catalyst is dissolved in an etchant. The polymer-on-graphene layer is then transferred to a desired substrate, where the polymer is dissolved off. Calado et al. showed that water drainage between graphene and substrate plays an important role in wrinkle formation. Here, the wrinkles form on and along the water drain channels (Fig. 3a–g). The out-of-plane

FIGURE 2

Wrinkles formation in CVD process. (a) An AFM image of a hexagonal graphene flake on Cu surface. (b) Schematic diagram showing the top view of a hexagonal graphene flake on Cu (110). (c) Schematic diagrams showing the effect of thermal expansion mismatch on the formation of graphene ripples. Ripples formed only on X axis, which resulted from anisotropy strain in cooling process. (d,e) Schematic diagrams of wrinkle formation on multilayer graphene on Ni in CVD process: (d) generation of wrinkles from nucleation of defect lines on step edges between Ni terraces and (e) thermal-stress-induced formation of wrinkles around step edges and defect lines on multilayer graphene. Appl. Phys. Lett. 103 (2013), Adv. Mater. 21 (2009) 2328–2333. 3 Please cite this article in press as: S. Deng, V. Berry, Mater. Today (2015), http://dx.doi.org/10.1016/j.mattod.2015.10.002

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Wrinkles formation on substrates in transferring process. (a–c) Schematic diagrams of transferring process. (a) A SiO2 substrate with graphitic flakes covered with a polymer. (b,c) The polymer film is removed from the substrate and floats on water. (d–g) Wrinkles formation in a wet transfer process seen through an optical microscope. Wrinkles form from a large corrugation on the water drain channel. The scale-bar is 50 mm. (h) AFM image of monolayer graphene transferred onto a periodic step structure (orange steps). The wrinkles (white lines) tend to align perpendicularly to the steps. Appl. Phys. Lett. 101 (2012).

deformation of graphene (as compared to rigid films) allows its ultrastrong adhesion to different substrates [50]. Moreover, the morphology of underlying substrates can control the orientation of the wrinkles (Fig. 3h) [51]. For rough surfaces, the additional stress due to adhesion may increase number of wrinkles. Here, wrinkles (white lines) are formed in the direction perpendicular to periodic strips (orange ranges) on the substrate. For example, Lanza et al. showed that the strain-induced wrinkles on graphene can be significantly reduced by improving the adhesion between graphene and rough substrates [52]. The stresses due to interaction with anchorage on surfaces cause formation of wrinkles [53,54].

Controlled wrinkles Due to the intimate interplay between wrinkle attributes and graphene properties, controllable fabrication of wrinkles on graphene is important. Bao et al. [43] reported that controlled and organized microscale wrinkles can be produced by thermal manipulation, leveraging the negative TEC of graphene (Fig. 4a–c). In their work, graphene and ultrathin graphite membranes were transferred and suspended across predefined trenches on SiO2/Si substrates (Fig. 4d). By annealing suspended graphene in a furnace, wrinkles were formed perpendicularly to the trench direction. Importantly, the orientation, wavelength and amplitude of wrinkles are influenced by the structure, shape and temperature of the substrate (Fig. 4e) [43]. A related work was conducted by Zhang et al., where graphene was grown on pre-trenched copper foils. One-dimensional periodic wrinkles of nanoscale dimensions (2 nm to 10s of nm) were shown on copper substrates via thermal strain engineering [20]. Wrinkles’ position was influenced by the

morphology of copper surface and was retained after transfer to smooth SiO2/Si substrates [46,55].

Crumples formation Among several methods to synthesize crumpled graphene, thermal expansion and reduction of graphite oxide [12,56] have gained tremendous attention. For example, ‘‘paper-ball like’’ crumpled graphene structure can be produced by rapid evaporation of aerosol droplets as shown in Fig. 5. The aqueous dispersion of micrometersize graphene oxide sheets was transported into a tube furnace by N2 gas. The graphene oxide experiences an isotropic compression and thermal reduction to form submicrometer-size crumpled graphene balls [57]. Few hundred nanometer scale graphene balls were also synthesized by Ma et al. [58] through rapid drying of graphene oxide. Zang et al. reported that the crumpling and uncrumpling of large-area graphene can be controllably achieved [17] by applying a pre-stretched elastomer film substrate via regulating relaxation and pre-strain order (Fig. 6). Graphene (3–10 layers) grown on nickel substrates was transferred to polydimethylsiloxane (PDMS) stamps. An elastomer film based on acrylic was biaxially stretched three to five times its original dimensions (pre-strain = 200–400%) to use as a pre-stretched substrate. The graphene on PDMS was stamp-transferred to this elastomer film. Relaxing one pre-stretched direction produced unidirectional wrinkles (Fig. 6b), which were well developed (Fig. 6c). This was followed by biaxial relaxation of the film to produce wrinkles from two dimensions to form crumpled graphene (Fig. 6d). Further, this crumpled graphene would unfold as the substrate film is biaxially re-stretched (Fig. 6e). The unidirectional wrinkle wavelength achieved in this work was 0.6–2.1 mm.



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FIGURE 4

Dependence of wrinkle morphology on temperature. (a) SEM images of graphene on trench before, during and after annealing and wrinkles formed on trench. (b) Graphene on trench in annealing process and higher magnification images of the edge of the graphene membrane, which shows graphene after annealing sags into the trench. (c) Schematic of buckling of a graphene membrane due to thermal contraction. From left to right, the panels depict the membrane in its original state, during heating and during cooling, respectively. The red arrows indicate the contraction/expansion of the substrate and graphene. (d) Schematic of the graphene on substrates. (e) Different orientations on graphene at different boundary shape. Nat. Nano 4 (2009) 562–566.

Mechanical models for ripples, wrinkles and crumples Mechanical models for ripples

theory (Fig. 7a) [60–62]:

In elasticity theory for the origin of spontaneous ripples, due to the absence of neighboring atoms above or below the graphene, the restoring forces perpendicular to the graphene sheet are bounded by perpendicular displacements. In other words, the perpendicular displacements induced strain energy, which limits the out of plane deformation (ripples). The amplitude size of ripples increases with the size of graphene sheet until graphene breaks up into smaller ones [59]. The spatial distribution of the ripples on graphene can be estimated by the equation [28]: rffiffiffiffiffiffiffiffiffi 2p L ¼ 4pk 3TB

l ¼ 2pt

where L is a typical linear sample size of ripple distribution, k is the bending rigidity, T is the temperature and B is the two-dimensional bulk modulus. As the temperature approaches 0 K, the distance between two ripples approaches infinity, which means, there is no ripple on graphene at 0 K. In other words, number of ripples increases along with temperature.

Mechanical models for wrinkles Classical buckling theory for free-edge suspended graphene The wrinkle wavelength for the free-edge thin film, such as suspended graphene on a trench can be calculated by linear buckling

E¯ f 3E¯s

1=3

where t is the thickness of the graphene, E¯ f is the strain-dependent elastic modulus of the graphene film and E¯s is the strain-dependent elastic modulus of the substrate. E f ¼ E=ð1 n2 Þ, with E, Young’s modulus, and n, the Poisson’s ratio. In this case, the wrinkle wavelength depends only on its strain-dependent elastic modulus and that of the substrate. Therefore, the wavelength and amplitude of wrinkles formed on monolayer graphene can be adjusted by modifying the trench dimensions with respect to graphene (thickness and strain-dependent elastic modulus are constants). The relationship between amplitude and wavelength for wrinkles produced spontaneously on suspended few layers graphene was described by: 1=2 Al 8n ¼t L 3ð1 n2 Þ where n is Poisson’s ratio, which is predicted to be in the range from 0.1 to 0.3 for single-layer graphene (Fig. 7b) [43,63]. Thin confined sheets under strain spontaneously generate a universal self-similar hierarchy of wrinkles. This is true for strained suspended graphene or ordinary hanging curtains (Fig. 7d), where wrinklons – a localized transition zone where two wrinkles merge 5





Crumpled graphene balls. (a) Schematic showing the experimental setup and the evaporation-induced crumpling process. (b) The size of the crumpled graphene balls and the degree of crumpling can be tuned by the concentration of GO in the aerosol droplets as shown in the low magnification overview and representative high magnification single particle SEM images. Concentration of GO from left (low) to right (high). ACS Nano 5(11) (2011) 8943.



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FIGURE 6

Controlled crumpling and unfolding of large-area graphene. (a) Schematic illustration of macroscopic deformation of a graphene sheet on a biaxial prestretched substrate and followed by relaxation of the substrate. (b–e) SEM images of patterns developed on the graphene sheet, (b) graphene transfer to a biaxial pre-stretched substrate, (c) wrinkles on graphene as the substrate is uniaxially relaxed, (d) crumpled graphene formed as the substrate is biaxially relaxed (d), (e) graphene unfolds as the substrate is biaxially stretched back. Nat. Mater. 12 (2013) 321–325.

or diverge–are formed (Fig. 7c). The length of a wrinklon, L(l), found from the minimization of total energy of distorted membrane is: l2 T 1=2 LðlÞ h Eh where T is longitudinal tensile strain, E is Young modulus and h is the thickness of the sheet. In addition, the wavelength (l) along the thin membrane is a function of the distance to the constrained edge (x): 1=4 1=2 lðxÞ Eh x h T h Furthermore, as the tension increases, a wrinklon pattern of wrinkle is expected to transform to a purely cylindrical pattern along the sheet with a single wavelength, which is described by the linear buckling model [64].

Buckling theory for substrate-supported graphene For graphene supported on a pre-strained substrate, Zang et al. revealed that wavelength of wrinkles is a function of graphene’s Young’s modulus (E) and the shear modulus of the substrate (ms) as given by: 1=3 E l0 ¼ 2pt 12Lms ð1 n2 Þ Here, the substrate is assumed to be a neo-Hookean material (with stress-strain behavior similar to Hooke’s law initially, but nonlinear at larger deformations) and L = (1 + (1 + epre)3)/2(1 + epre), where epre = (Lpre L0)/L0, where Lpre and L0 are the pre-strain and initial length of the substrate, respectively [17]. The linear buckling model has been successfully applied to describe suspended few layers graphene under large tension, however, it was proven to be invalid for nanometer scale wrinkles on monolayer graphene [21] (even for thickness of monolayer graphene from 7





Mode of wrinkles on thin film and scanning electron microscopy image of wrinkles on graphene. (a) Sketch of Herringbone mode in thin films. (b) SEM image of a bilayer suspended graphene membrane produced by thermal manipulation. (c) Evolution of the normalized length of a wrinklon, L/l, with the normalized amplitude, A/h (fixed wavelength, l = 8 mm), for different thicknesses as indicated. Insert figures of (c) left: schematic representation of the wrinklon experiments; right: morphology of the transition l to 2l for a constrained plastic sheet for A = 6 mm and l = 8 mm. (d) Left: scanning electron microscopy image of suspended graphene bilayer (scale bar is 1 mm). Right: pattern of folds obtained for a rubber curtain (scale bar is 25 cm). Phys. Rev. Lett. 90 (2003) 074302, Nat. Nano 4 (2009) 562–566, Phys. Rev. Lett. 106 (2011) 224301.

0.08 to 0.335 nm). This is because the ripples, with wavelength at subnanometer scale, are influenced by the atomic structure of graphene much more than by continuum mechanics rules [65]. Therefore, an atomic-scale graphene simulation (Fig. 8c,d) was developed and agreed with the nanoscale ripples/wrinkles observed experimentally (Fig. 8b) [21]. It is important to note that the uncertainty in thickness of graphene, known as Yakobson Paradox, can lead to a dispersion in mechanical properties. This is because the in-plane thickness of graphene can vary from 0.057 to 0.335 nm [66,67]. However, in most cases the thickness is assumed to be 0.34 nm.

Unsupported graphene Without interaction with solid substrates, flat graphene becomes unstable with increasing lateral dimensions, which can cause it to self-fold or scroll [65]. Cranford et al. studied the self-folding of mono- and multilayer graphene sheets, utilizing a coarse-grained hierarchical multi-scale model (derived directly from atomistic simulation). Through theoretical and simulation analysis for racket-type folded configuration, they showed that the critical selfpffiffiffiffiffiffiffiffiffi folded length L (as shown in Fig. 8a) is p C=g in the monolayer (at

300 K), where C (eV) and g (eV/m2) are the bending stiffness per unit length and the surface energy per unit area, respectively, and: 2 sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi3 E ðDVDW Þ3 5 3=2 n LðnÞ ¼ 4p g 12 for n layers graphene (n > 1), where DVDW is the equilibrium distance (van der Waals interface) between the layers, as shown in Fig. 9a–c [68]. The results indicate that thinner graphene sheets are expected to have finer wrinkle-wavelengths. On the other hand, a method based on wrinkling and cracking phenomena of nanoscale thin film (applying an increasing uniaxial tensile strain, the morphology of film changes from well-defined periodic wrinkling pattern to crack-formation orthogonal to the strain direction as shown in Fig. 9d–f) allows unambiguous measurements of three fundamental mechanical properties: elastic modulus, strength, and fracture strain [69].

Mechanical models for crumples Instead of deformation by uniaxial confining force, as in the case of wrinkled graphene, crumpled graphene is mainly involved in



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FIGURE 8

STM image of a nanoscale graphene ripples and simulation of a periodic rippling morphology graphene. (a) Atomic-resolution STM image of a nanotrench exhibiting subnanometre graphene ripples. (b) Cross-section of the graphene ripples exhibiting a wavelength of 0.7 nm, and an amplitude of 0.05 nm. The extra corrugation of the line can be attributed to the positions of C atoms. (c) Simulation of a 5.7-nm-wide infinitely long graphene nanoribbon subjected to 5% in-plane compression, revealing a periodic rippling morphology. (d) Left: one wavelength ripple side structure. Right: bond length structure in simulated graphene ripples. Nat. Phys. 8 (2012) 739–742.

multidirectional compression. In a thin sheet under lateral compression mode, with increase in compression force, the sheet undergoes a transformation process, going from flat to cone to crumples and finally forms a crumpled ball. For forces larger than the crumpling threshold state (Fc), the radius of the crumpled sheet follows a power-law behavior, where dimensional analysis suggests the scaling form [70]: b Rf K0 R20 k a ¼C FR0 R0 k where Rf is the radius of sheet under force, R0 is the initial radius, K0 is the two-dimensional Young modulus, k is the bending rigidity, F is the compression force, and C, a, b are the scaling parameters. Here, the radius is nearly independent of forces and has a value of about Rf/R0 0.63. Different configurations of thin sheet under different forces are shown in Fig. 10. Therefore, the ripples on monolayer graphene are formed due to (a) the balance between the intrinsic and perpendicular restoring forces, (b) the absence of other supporting (reinforcing) layers, and (c) deformation induced strain in graphene. The pattern of ripples depends on the temperature and size of graphene sheet. Wrinkles are formed when graphene experiences a uniaxial exterior force, which arises from the supporting layer of graphene. Further, crumple formation is a consequence of multidirectional forces applied on graphene; they depend on

the original size of the sheet and the compression force on the graphene sheet.

Properties and applications of corrugations on graphene Most of the ripples on graphene data are from simulations, therefore, most of the reports of ripples are focused on the theoretical study of electronic properties. Wrinkles and crumples influence several electronic phenomena, including suppression of weak localization [71], electron–hole puddles [33,72,73], band-gap opening [18–20,74], pseudomagnetic field in bilayers [18,75], and carrier scattering [22,76]. They exhibit other atypical properties, such as surface and optical modification [17], energy storage [17,77], chemical activities enhancement [78,79] and bio-interfacing [53].

Electronic properties of ripples and wrinkles on graphene The curved geometry and strain in graphenic systems are known to couple with the 2D massless Dirac Fermions via gauge field and scattering potential to alter the electronic structure [19]. For planar graphene model (only an idealistic model) without disorder (or impurities), the Fermi level lies at the Dirac point, where the density of electronic states vanishes [80]. Both disorder and impurities in graphene introduce violation of the electronic homogeneity of graphene. Doping by defects (a transfer of charge between 9





Racket-type self-folded configurations and dependence of stiffness on folded length of graphene sheets and Strain induced wrinkles. (a) Schematic depicting adhered length and curved length. (b) Simulation results for a 2-layer coarse-grained graphene sheet width of 25 nm and length of 125 nm, respectively. (c) Simulation results for the coarse-grained graphene sheets. Folded length, L, changes with the increase in stiffness due to multilayered graphene sheets formation. (d–f ) Schematic illustrations strain-induced surface wrinkling and thin-film cracking. Appl. Phys. Lett. 95 (2009), Nano Lett. 11 (2011) 3361–3365.

the defects and the bulk) and charged impurities deviates graphene away from having the Dirac points [81,82] in the Brillouin zone. Among other causes, the corrugations on graphene suppress electron-transport [15,83], mobility, weak localization (by fluctuating position of the Dirac point [71]) and quantum corrections [84–86]. The quantum correction is a result of quantum interference of electrons moving in different trajectories [87]. It includes interference of time-reversed trajectories (weak localization correction) and elastic scattering induced interference of electrons on Friedel oscillations of the electron density (Altshuler–Aronov correction) [84,87–89].

FIGURE 10

Mechanical models for crumpled thin film. (a) A d-cone formed by applying a weak force to the sheet. (b) A crumpled sheet formed by applying a strong force. Nat. Mater. 5(3) (2006) 216.

The electron and hole puddles created due to the disorder in graphene was imaged by Suyong et al. via scanning tunneling microscopy (STM) and scanning tunneling spectroscopy (STS) [71]. The topography of monolayer graphene on a SiO2/Si substrate exhibits a height variation of about 1.2 nm. In an ideal graphene layer, the carrier density can be continuously tuned from hole to electron doping from zero density at Dirac point (ED) [90–92]. The local disorder gives rise to a spatially varying electrostatic potential that changes the relative position of ED with respect to EF. Introduction of electron–hole puddles due to surface corrugations was also studied via first principles ab initio calculations. The local graphene geometry and its carrier distribution were strongly correlated [73]. As mentioned above, wrinkling (rippling or crumpling) can tailor the electronic structure of graphene, as explained within the Slater–Koster prescription [93]. Two main effects are outlined: (a) p-s rehybridization between nearest neighbors shifts the porbital energy, resulting in an effective electrochemical-potential variation; and (b) change in the nearest-neighbor hopping integral introduces an effective ‘‘vector potential’’. The estimated electrochemical potential variation associated with the ripples (observed experimentally) is on the order of 30 meV. The bond stretching and the dipole moment created by polarized p-cloud density in wrinkled graphene can open a relatively large band-gap and also modify the local chemical potential enabling selective functionalization [22]. A band gap within 0.14–0.19 eV by both the periodic wrinkles and the surface chemistry was shown by modeling gridlike periodically modulated graphene [74].


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mobility [95]. Analogous results of anisotropic Landau levels quantization and thermal conductivity on wrinkling graphene were also demonstrated [96,97].

Surface properties and strain sensing of wrinkled and crumpled graphene Remarkably, wrinkles on single atom-thick graphene can also modulate its surface properties and transparency. Zang et al. found that crumpled graphene exhibits tunable wettability and high transparency (Fig. 11a,b). The contact angle measurement for water on crumpled graphene obeyed Wenzel and Cassie-Baxter laws for conforming and non-conforming interactions (with air gaps), respectively. Further, voltage applied across an elastomer sandwiched between crumpled graphene leads to Maxwell stress, which reduces the thickness and increases the area of the elastomer layer. It further tuned the transmittance in the visible range with voltage, as displayed in Fig. 11c,d [17]. Similarly, Wang et al. and Zang et al. demonstrated that graphene wrinkles created by releasing a pre-strained substrate can be used as a strain-sensor, where the device resistance changes with strain (Fig. 11f) [17,77].

Energy storage of wrinkled and crumpled graphene Recently, there has been a great thrust in applying graphene as electrodes for supercapacitors due to its high surface area and conductance. Wrinkled and crumpled graphene are advantageous for these applications since they make the sheets less stiff, while inhibiting stacking and retaining increased surface area. Further, graphene nanosheets, with preponderance of exposed edge planes

FIGURE 11

Properties of applications of wrinkles graphene. (a,b) Voltage-induced actuation of a crumpled graphene–elastomer laminate. (a) As voltage is applied, the laminate reduces its thickness and expands its area. The area actuation strain is over 100%. (b) Transmittance of the laminate in the visible range as a function of the area actuation strain. Values in (b) represent the mean of n tests (n = 3). (c,d) Stretchable graphene coatings capable of superhydrophobicity and tunable wettability. Images showing the contact angle of a water drop: 1528 on highly crumpled graphene (c) 1038 on unfolded graphene (d). (e) Color map of the spatial density variations in the graphene and the blue regions correspond to holes and yellow regions to electrons. Inset image is the corresponding topographic image. (f ) Resistance response of the wrinkled graphene device upon different strain. The insets are optical images of simple strain sensor. Nat. Mater. 12 (2013) 321–325, Nat. Phys. 8(10) 739–742, ACS Nano 5 (2011) 3645–3650. 11 Please cite this article in press as: S. Deng, V. Berry, Mater. Today (2015), http://dx.doi.org/10.1016/j.mattod.2015.10.002

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Yan et al. found the lattice strain and large curvature of a wrinkle in twisted bilayer graphene can result in pseudomagnetic field (100 T) interacting directly with electronic states of the sheet. Along the wrinkle, the group observed zero-field Landau level like quantization and valley polarization with a large energy gap. On strained and wrinkled monolayer graphene, this could open up a band-gap and generate hyperbolic energy dispersion. In small and moderate deformations, the energy difference of the two van Hove singularities (DEvhs) decreases as the strain increases. An energy gap in twisted graphene bilayer is opened (via wrinkle) if the strain, e is greater than 0.14. Above this value, there is a linear correlation between the band-gap and strain (caused by wrinkle) [18]. Costa et al. also reported that periodic wrinkles/folds in graphene will possess enhanced spin-orbit interaction via curvature, which can open gap and allow spin polarized transport at low magnetic fields [94]. It is important to note that inter-wrinkle spacing greater than the mean free wavelength of carriers minimizes the influence of wrinkles/corrugations on transport barriers [51]. Further, Zhu et al. found that the maximum height of a wrinkle after which graphene would fold was 6 nm [22]. A distinct anisotropy in the fold resistivity on the graphene was observed and attributed to transport along and across the folded wrinkles via diffusive transport of charge distributed across multilayered folds (increases ON/OFF ratio) and local interlayer tunneling across the collapsed region (adds resistance of the order of graphene contact resistance). The quasi-periodic nanoripple arrays of graphene not only causes anisotropy in charge transport but also affects the limitation on both the sheet resistance and the charge

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and wrinkles, enhance charge storage. Supercapacitors constructed with graphenic electrodes may be smaller than the lowvoltage aluminum electrolyte supercapacitors that are typically used in electronic devices [98–100]. Chen et al. developed a transparent (up to 57% at 550 nm) and stretchable (up to 40% strain) supercapacitor by stacking wrinkled graphene (multilayer). Here, wrinkling was important to ensure sustained stretching. The measured surface-specific capacitance was about 5.8 mF cm2 with a mass-specific capacitance of 7.6 F/g [101]. Further, the graphenic wrinkles provide fast Li+ diffusion channels with a low activation barrier of about 0.1 eV, lower than that of a smooth graphene (0.3 eV) for lithium ion battery application [102]. The wrinkles also provide the extra expansion allowance during lithiation, which addresses a major current challenge of anode cracking due to volume expansion [78,103]. Moreover,

FIGURE 12

Chemical activities enhancement and energy storage application of wrinkles and crumples on graphene. Scanning electron microscope images of fracture surface topography in expended graphite (a) and wrinkled graphene (b). (c) Schematic of copper covered by graphene with wrinkles and defects. (d) Dependence of the chemisorption energy on the curvature of the ripple. Insert figure is the schematic of chemical activities enhancement of ripples on graphene. Mass-based specific capacitance of the three graphene samples as a function of mass loading at current density of (e) 0.1 and (f ) 2 A/g. FE-SEM images of 3D-GR/PtAu with different concentration of GO of (g) 0.1 wt% and (f ) 0.25 wt%. Nat. Nano 3 (2008) 327–331, ACS Nano 7 (2013) 5763–5768, J. Phys. Chem. C 113 (32) (2009) 14176, ACS Nano 7(2) (2013) 1464, Carbon 93 (2015) 869.


graphenic materials exhibit high electrical conductivity, excellent thermal stability and remarkable mechanical and chemical robustness, which retains the structural integrity around the core despite 250% change in volume during repetitive lithiation and delithiation. Crumpled graphene is remarkably aggregation-resistant in either solution or solid state, and remains largely intact and redispersible after different treatments like, chemical treatments, wet processing, annealing, and pelletizing at high pressure. This stability and high surface area facilitate the application of crumpled graphene in energy storage applications like Li-ion batteries [57] and supercapacitors [104], as shown in Fig. 12e,f.

Chemical activities and functionalization affinity of wrinkled and crumpled graphene Partovi-Azar et al. found that the topology of graphene governs the formation of electron–hole puddles [33,73] on graphene. Further, Wang et al. [105] have shown the relationship between electron– hole puddling and functionalization affinity of graphene. Clearly, wrinkles (and other topologies) in turn influence the chemical activity of graphene, as studied by Boukhvalov and Katsnelson [106], shown in Fig. 12c,d. The study suggests that corrugations on graphene would enhance chemical activities if the ratio of height of corrugation (wrinkle or ripple) (h) to its radius (R) is larger than 0.07. For h/R smaller than 0.07, chemical activities enhancements disappear. Wrinkled graphene has also been applied as a scaffold to attach nanoparticles for energy applications [78,103]. For example, core– shell SnO2-graphene nanoparticles in wrinkled graphene matrix were synthesized by hydrothermal process by Zhou et al. [78]. The SnO2-graphene 3D nanoarchitecture showed high discharge capacities of 883.5, 845.7, and 830.5 mA h g1 in the 20th, 50th and 100th cycles in lithium storage experiments, respectively, at a current density of 200 mA g1 with desirable discharge capacity of 645.2 mA h g1 at 1680 mA g1. Further, wrinkles on graphene have been leveraged as nucleation sites for H2 generation at the cathode in brine electrolysis experiments [107] (to delaminate graphene from metals). A similar application was also demonstrated by employing platinum–gold alloy nanoparticle composited with crumpled graphene [108], as shown in Fig. 12h,g. Ramanathan et al. reported that the wrinkled nature of the functionalized graphene sheets within a composite provides for improved interlocking and better interaction with the host polymer matrix [79], as shown in Fig. 12a,b. In the presence of wrinkled graphene, polymer nanocomposites display enhanced dispersion, and uniquely increased glass transition temperature of poly(acrylonitrile) by 408C with addition of 1 wt% wrinkled graphene (or at 308C with only 0.05 wt% wrinkled graphene in PMMA). The wrinkles, ripples or crumples on graphene can also be applied for fabrication of other graphene structures. As shown in Fig. 13a–c, by designing the surface morphology of growth substrate (with microscopically parallel slip lines) and subscribing to a suitable transfer technique, wrinkled graphene was synthesized on SiO2/Si substrate. Large-area oriented graphene nanoribbons (GNRs) arrays, with width less than 10 nm, were then produced by plasma etching as confirmed by AFM and field-effect transistor studies [109]. The relative randomness and the small size of ripples restrict the modification of properties of graphene (except for its electronic



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FIGURE 13

Wrinkle engineering for fabricating GNRs and graphene nanoribbons array field-effect transistors. (a) CVD growth of graphene on nanostructured Cu foil, (b) transfer of graphene from corrugated Cu foil to flat SiO2/Si substrate by structure-preserved transfer technique, (c) fabrication of GNRs array by self-masked plasma etching, (d) AFM image of GNRs array on SiO2/Si substrate of (c), (e) schematic of a GNRs array FET device with 8 nm Cr/50 nm Au as the source/ drain, 300 nm SiO2 as the gate dielectric and highly doped Si as the back gate. (f) Transfer characteristics (current versus gate voltage) for the device of (e) in (b) at Vd = 10 mV, 100 mV, and 500 mV, respectively. J. Am. Chem. Soc. 133 (2011) 17578–17581.

structure). Therefore, the applications of rippled graphene are limited in comparison to other corrugations. On the contrary, crumples are dense deformations in two or three dimensions with dramatically modified chemical activities and functionalization affinity. Hence, the crumpled (and wrinkled) graphene are employed for energy related research (energy storage, cells and supercapacitors) where high conductive, high surface area, thermal stability and mechanical and chemical robustness are important.

Wrinkle-free graphene It is important to note that for several applications, wrinkles are undesirable. These include (i) high speed FETs and optical switches, and (ii) corrosion-inhibition (wrinkles promote corrosion) [36]. For corrosion inhibition, graphene is the thinnest membrane that is impermeable [110], and has been employed to protect metals against corrosions [111,112]. However, graphene shows more extensive corrosion and oxidation than bare, unprotected metal surface due

FIGURE 14

Wrinkle free graphene produced by CVD method. (a–d) AFM images of the transferred graphene layer synthesized on (a) Cu on SiO2 and (b) Ni on rGO/SiO2 substrates. (c,d) The line profiles along the line indicated in (a,b), respectively. (e) Schematic drawing of Ni thin film deposited sample. The rGO layer was deposited only on a part of the oxidized silicon wafer surface by spin-coating and patterning for a clear comparison of the effects of the rGO layer under the metal. Nano Lett. 13 (2013) 2496–2499. 13 Please cite this article in press as: S. Deng, V. Berry, Mater. Today (2015), http://dx.doi.org/10.1016/j.mattod.2015.10.002



TABLE 1

Summary of the correlation between corrugation attributes and graphene properties and applications.

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Wavelength/width (nm)

Height, aspect ratio or other relationship

Modified properties and/or applications

0.1–10 nm

Intrinsic ripples aspect ratio of 1 with height (H) 0.2 nm [29] Thermal contraction on Cu trench: H 0.05 nm and W 0.7 nm [21] Thermal contraction on Rh foil: H 7.9 nm and W 8.2 nm [18] Transfer of SiO2 post CVD: H 3.3 nm and W 6.8 nm [51]

Pseudomagnetic behavior [18,75] Band-gap opening [18,20,74] Carrier scattering [76] Electron–hole puddles formation [21]

10–100 nm

Simulation Studies [22]

Carrier scattering Anisotropic electron transport [22,96]

100 nm–1 mm

Thermal contraction on Cu foil: H 25 nm and W 300 nm [46] Reduced graphene oxides crumpled graphene [98] Pre-stretched H 70 nm and W 500 nm [77]

Mobility limitation Conductivity reduction Band gap opening [19] Charge storage enhancement [98] Strain sensitivity [77]

Above 1 mm

Pre-stretched crumpled graphene [17] Thermal contraction on Si trench H 30 nm and W 2 mm [43]

Tunable transparency, wettability, and thickness at different voltages [17] Chemical reactivity enhancement [114] Charge storage enhancement [101]

Relationships

Ratio between height and radius (R), H/R > 0.07 [106] pffiffiffiffiffiffiffiffi H > p C=g (C = bending stiffness and g = surface energy) [68]

Chemical activity enhancement [106] Self-folding [68]

to the existence of wrinkles, which lead to [113–115] (1) nanosized gas inlets and reaction channels; (2) strongly distorted sp2 hybridized carbon reactivity enhancement [116]; and (3) electrochemical driving force by forming graphitic cathode–metals couple.

Producing graphene with fewer wrinkles is essential in such applications. To this end, the intrinsic ripples in suspended graphene may be suppressed (or removed) by depositing graphene onto atomically smooth substrates (such as boron nitride (BN))

FIGURE 15

A summary illustration of corrugations on graphene formation, properties and application. Gray arrows stand for formation of corrugations on graphene, red arrows indicate electronic properties and blue arrows for other properties. Nat. Mater. 6 (2007) 858–861, Phys. Rev. Lett. 101 (2008) 245501, Appl. Phys. Lett. 103 (2013), Nano Res. 4 (2011) 996–1004, Nat. Nano 4 (2009) 562–566, Nat. Mater. 12 (2013) 321–325, Nature 446 (2007) 60–63, Nat. Phys. 4 (2008) 144–148, Appl. Phys. Lett. 95 (2009), ACS Nano 5 (2011) 3645–3650, J. Phys. Chem. C 113 (32) (2009) 14176, ACS Appl. Mater. Interfaces 6 (2014) 7434–7443, ACS Nano 5(11) (2011) 8943, Carbon 93 (2015) 869. 14 Please cite this article in press as: S. Deng, V. Berry, Mater. Today (2015), http://dx.doi.org/10.1016/j.mattod.2015.10.002

MATTOD-626; No of Pages 16 Materials Today Volume 00, Number 00 October 2015

Future research Futuristically, due to the several implications of wrinkles on graphene, extensive research is required to achieve a control on the wrinkle-patterns, selective areas, wavelength/width, lengthscale, amplitude/height, number density and shape, and reversibility to smooth graphene. This will have consequences in electronics, composites, microelectromechanical systems, and device [109,120] fabrication. Also, additional research is needed to understand the interplay between carrier properties, chemical potential and corrugation attributes to rationally employ wrinkled, rippled or crumpled graphene in controlled applications. Further, modified topologies can be induced by external forces including chemical environment, local humidity, temperature, stress and photo-interaction. The effect of the crystallographic orientation of the wrinkles needs to be studied to determine ease of formation and influence on properties.

Summary Graphene is a fluidic 2D nanomaterial and can exhibit several topologies, which in turn influence its properties as shown in Table 1 and Fig. 15. This review outlines (A) several mechanisms of wrinkle, ripple and crumple formation on graphene: thermal fluctuations (ripples), edge instability (ripples and wrinkles), negative thermal expansion coefficient (wrinkles), dislocations, and strain induced formation (wrinkles and crumples); (B) interplay between mechanical activities and wrinkle attributes: dependence of wavelength, amplitude, and bending radius on channel length, strain, Young’s modulus, interfacial energy and number of layers; (C) influence on the electronic structure: band-gap opening, pseudomagnetic field in bilayers, and electron/hole puddle formation; (D) properties of surfaces and composites: reversible wettability, reversible transmittance, and chemical potential; and (E) applications: energy storage, strain sensing, tunable-wettability surfaces, controllable opto-transmitter, and nanoscale devices. Futuristically, it is critical to control the physical attribute and further study the influence of wrinkles on electronic, optical, mechanical and chemical properties. Most interestingly, graphenic wrinkles can change its electronic structure, transport properties and can modify the chemical potential distribution, which can be leveraged in several applications.

Acknowledgements VB acknowledges support from the startup funds from University of Illinois at Chicago and funds from National Science Foundation (CMMI-1054877, CMMI-0939523 and CMMI-1030963). Thanks to Sanjay Behura and Bijentimala Keisham for valuable discussion. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] [52] [53] [54] [55] [56] [57] [58] [59] [60] [61] [62] [63] [64]

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