Carbon 117 (2017) 476e487. Contents lists available at ScienceDirect. Carbon. journal homepage:

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1 Carbon 117 (2017) 476e487 Contents lists available at ScienceDirect Carbon journal homeage: A coarse-grained model for the mechanical behavior of grahene oxide Zhaoxu Meng a, 1, Rafael A. Soler-Creso b, 1, Wenjie Xia a, Wei Gao c, Luis Ruiz b, d, Horacio D. Esinosa b, c, ** a, b, *, Sinan Keten a Deartment of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL , United States b Theoretical and Alied Mechanics Program, Northwestern University, 2145 Sheridan Road, Evanston, IL , United States c Deartment of Mechanical Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL , United States d Chemical Sciences Division, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, United States article info abstract Article history: Received 2 November 2016 Received in revised form 25 January 2017 Acceted 20 February 2017 Available online 14 March 2017 Grahene oxide (GO) shows romise as a nanocomosite building block due to its excetional mechanical roerties. While atomistic simulations have become central to investigating its mechanical roerties, the method remains rohibitively exensive for large deformations and mesoscale failure mechanisms. To overcome this, we establish a coarse-grained (CG) model that catures key mechanical and interfacial roerties, and the non-homogeneous effect of oxidation in GO sheets. The CG model consists of three tyes of CG beads, reresenting grous of ristine s 2 carbon atoms, and hydroxyl and eoxide functionalized regions. The CG force field is arameterized based on density functional-based tight binding simulations on three extreme cases. It accurately quantifies deterioration of tensile modulus and strength at the exense of imroving interlayer adhesion with increasing oxidation of varying chemical comositions. We demonstrate the alicability of the model to study mesoscale henomena by reroducing different force vs. indentation curves in silico, corroborating recent exerimental observations on how chemistry near contact oint influences roerties. Finally, we aly the model to measure the fracture toughness of ristine grahene and GO. The critical stress intensity factor ðk c Þ of grahene is found to be the highest, and eoxide-rich GO also ossesses higher K c comared to hydroxyl-rich GO Elsevier Ltd. All rights reserved. 1. Introduction Grahene has emerged as a romising building block that can be used in nanocomosites and nanoelectronic devices to gain advances in mechanical and electronical erformance [1e6]. However, it has been shown through exeriments and theory that load transfer between stacked grahene sheets, and between grahene sheets and olymer matrices is oor as it emloys weak van der * Corresonding author. Deartment of Civil and Environmental Engineering, Northwestern University, 2145 Sheridan Road, Evanston, IL , United States. ** Corresonding author. Theoretical and Alied Mechanics Program, Northwestern University, 2145 Sheridan Road, Evanston, IL , United States addresses: esinosa@northwestern.edu (H.D. Esinosa), s-keten@ northwestern.edu (S. Keten). 1 These authors contributed equally to this work. Waals forces [7e10]. Grahene oxide (GO), a derivative of grahene, contains oxygen-rich functional grous caable of hydrogen bonding, which addresses this issue [11e13], and allows disersion of grahitic sheets in many solvents and olymer matrices in nanocomosites [14e16]. Although the existence of functional grous in GO deteriorates its in-lane mechanical roerties, i.e. Young s modulus and intrinsic strength, comared to ure grahene, significant enhancement in its caability of damage tolerance and the interfacial interactions ossible between GO and matrix materials makes GO favorable in many alications [17e23]. GO-based fillers have been used in olymer nanocomosites [24e26], and recent studies have emhasized the imortance of surface functionalization for a number of reasons. For examle, recent studies have shown that increasing the adhesion energy between grahitic sheets and reducing the tensile modulus of each sheet, as in the case of oxidation, allows multi-layer grahitic systems to attain high strength with little sheet overla [27]. In addition, nanoconfinement of olymers in nanocomosites htt://dx.doi.org/ /j.carbon / 2017 Elsevier Ltd. All rights reserved.

2 Z. Meng et al. / Carbon 117 (2017) 476e systems becomes effective only when the olymer-grahitic filler interactions are highly attractive, leading to matrix stiffening in nanocomosites [28,29]. Moreover, it has been reorted that thermal stability [30e33] and electrical roerties [34e37] of olymers could be greatly imroved by incororation of GO nanosheets. Atomistic modeling has been extensively utilized to investigate and redict the mechanical roerties of GO. Most rior investigations on GO modeling were carried out using all-atomistic (AA) simulations or first rinciles calculations, which rovide valuable insights into ecular mechanisms governing constitutive behavior while retaining critical chemical details. It is exected that the surface functional grous have considerable effects on the mechanical roerties of GO [38]. It has been shown that the inlane roerties, i.e. Young s modulus and intrinsic strength, monotonically decrease with increasing degree of oxidation [39,40]. Wang et al. have investigated the atomic-scale frictional behavior of GO sheets using density functional theory (DFT) including disersion corrections (DFT-D), and found moderately higher friction forces in GO comared with grahene [41]. More recently, Soler-Creso et al. have found that the comosition of GO also affects the mechanical behavior of GO [42] by using density functional-based tight binding (DFTB) technique to systematically characterize the effect of the degree of oxidation and the ratio of functional grous (i.e., eoxide grou (eoe) and hydroxyl grou (eoh)) on the mechanical erformance of GO. They reort that eoxide-oxidized GO has relatively larger failure strain than hydroxyl-oxidized GO [42]. Desite tremendous success in understanding and redicting the mechanical behaviors of GO through AA simulations, there are still drawbacks for these comutational aroaches. The most critical one is that the simulated domain of GO systems is mostly limited to sizes lower than 10 nm, as these aroaches are extremely demanding in comutational ower. This makes it very challenging to assess the mechanical behavior of GObased systems at larger scales, limiting our understanding of the behavior of crumled nanoaers [43], multilayer nanosheets [44], and GO-olymer nanocomosites [21,23,45]. Discrete article methods that avoid artificial homogenization in the mechanical roerties of the material are necessary to cature key traits of these systems. To address these scale-related issues, an uscaling comutational technique is required to simulate GO systems beyond current satiotemoral limitations. Coarse-grained ecular dynamics (CG-MD) simulations aimed at redicting the key roerties of nanomaterials offer insights into the ecular scale dynamic rocesses over extended scales and increase comutational efficiency dramatically comared to AA simulations [46e49]. Recently, we have resented a novel CG-MD model of grahene achieving ~200-fold increase in comutational seed comared to AA simulations. The model can cature the mechanical roerties of multilayer grahene (MLG), including non-linear elasticity, anisotroy at large-deformations and fracture, and also the comlex interlayer shear resonse of grahene [48]. The CG model of MLG is also able to reach exerimentally relevant satio-temoral scales, allowing us to investigate size-deendent mechanical roerties of MLG via nanoindentation and tensile deformation simulations [27,50,51]. The quantitative agreement between CG simulations of grahene and exeriments demonstrates the alicability and redictive ower of the CG modeling technique on caturing the mesoscale henomena as well as exlaining hysical mechanisms at the ecular level. Building uon our revious CG framework, here we roose a novel CG modeling framework of GO for its mechanical behavior via a bottom-u aroach. In this aer, we first rovide a descrition of the CG-MD model of GO and characterize its atomistic roerties using DFTB, followed by calibrating the force field arameters using the CG aroach. Next, we comare the mechanical roerties of GO from both CG-MD and DFTB results. Finally, we demonstrate the alicability of the model by simulating nanoindentation on monolayer GO and measuring the fracture toughness of monolayer GO sheets with different comositions. The CG simulation results agree reasonably well with recent exerimental results. 2. Methods 2.1. CG model descrition Earlier studies have shown that GO ossesses a lanar structure with functional grous (mainly eoxide and hydroxyl grous) on both the basal lane and free edges [5,12,38,52]. The roosed CG GO model conserves a similar hexagonal lattice structure of grahene with a 4-to-1 maing scheme for the s 2 carbon network. Different from the grahene case, the CG model of GO also includes two other different tyes of beads, reresenting hydroxyl- and eoxide-oxidized functional regions as illustrated in Fig. 1. While it is extremely difficult to exactly ma every GO structure to a CG model, by directly varying the ercentages of each tye of beads in the CG model, we are able to generate CG GO structures with different degrees of oxidation and comositions, which are key material arameters that govern the mechanical behavior of GO. Note that the degree of oxidation in the CG model is defined as the total ercentage of both hydroxyl- (tye H) and eoxide-oxidized Fig. 1. Schematic illustration of coarse-grained (CG) grahene oxide (GO) model. Panel A shows the all-atomistic (AA) GO structure and the AA to CG maing scheme, where three tyes of CG beads (non-oxidized (C), hydroxyl-oxidized (H) and eoxide-oxidized bead (E)) reresent different lattices. Panel B shows the resulting CG structure with different tyes of CG beads and the classification of bond and angle tyes. Note that Panel B is not a direct CG reresentation of the structure in Panel A. (A colour version of this figure can be viewed online.)

3 478 Z. Meng et al. / Carbon 117 (2017) 476e487 (tye E) beads. By also differentiating the bonded interactions between different tyes of beads, the CG model is able to cature the diversity of mechanical roerties of GO arising from different functional tyes and degrees of oxidation. The force field of the CG model includes both bonded (bond and angle terms) and non-bonded interactions. Thus, the total otential energy of the system can be written as: E ot ¼ E b þ E a þ E nb (1) where E b, E a and E nb are the sum of the energies of all the bonds, angles and non-bonded interactions of the system, resectively. In this model, we do not include the dihedral term since excluding it simlifies the force field arameterization significantly and increases comutational efficiency. Additionally, we have two major considerations to justify this choice. First, we seek to emhasize the in-lane roerties for GO (i.e. elastic modulus and uniaxial tensile strength) and interlayer adhesion energies, which are sufficiently catured by the force field given by Eq. (1). Second, the dihedral term only affects the out-of-lane bending stiffness of GO membranes, not the roerties resented herein. Dihedral terms could be added onto the force field resented here when data on the distribution of grahene (Tye I bonds), and GO s maximally functionalized with hydroxyl and eoxide chemistry (Tye II and III bonds, resectively). The average equilibrium bond length in the CG model is taken as double the measured length er our maing scheme, results in Table 2. The equilibrium angle is maintained at 120, given that for each singular CG case with only one tye of bead, the lattice structure maintains the hexagonal symmetry. The functional form of bond tye I ðv b;i Þ is the same as that of the bond in our former CG model for ristine grahene, which is reresented by the Morse otential form [48]. The reason for using a Morse otential is to cature smooth bond ruture at large strains [53]. For bond tyes II and III ðv b;ii&iii Þ, we choose a iecewise harmonic functional form in order to cature the non-linear behavior of GO. We adot a harmonic function for all the angle interactions ðv a Þ, and adot the 6e12 Lennard-Jones (LJ) otential for non-bonded interactions ðv nb Þ. The detailed functional forms are as follows and also in Table 2: V b;i ðdþ ¼D 0 h 1 e aðd d0þi 2 (2a) 8 V b;ii&iii ðdþ ¼ >< >: k be ðd d 0 Þ 2 d < d c1 k b ðd d c1 Þ 2 þ 2k be ðd c1 d 0 Þðd d c1 ÞþC 1 d c1 < d < d h i c2 k bf ðd d c2 Þ 2 þ 2k b ðd c2 d c1 Þþ2k be ðd c1 d 0 Þ ðd d c2 ÞþC 2 C 1 ¼ k be ðd c1 d 0 Þ 2 C 2 ¼ k b ðd c2 d c1 Þ 2 þ 2k be ðd c1 d 0 Þðd c2 d c1 ÞþC 1 d > d c2 (2b) bending stiffness and its deendence on oxidation becomes available in the future [48]. Accordingly, we define three tyes of bonds and three tyes of angles: tye I reresents the non-oxidized ones, tye II reresents the hydroxyl-oxidized ones, and tye III reresents the eoxideoxidized ones. The classification of bond tye is given by the following convention: if and only if both the two beads in a bond are tye C, the bond is tye I; if there is at least one tye H bead and no tye E bead in the same bond, the bond belongs to tye II; otherwise, the bond is tye III, as shown in Fig. 1. For angle tyes: if there is more than one tye C bead in an angle, then the angle is tye I, similarly, angle tye II is assigned when at least one of the involved atoms is tye H. All other cases belong to angle tye III. The hysical basis for the convention is that functional grous affect local regions and a higher amount of functional grous leads to small atches with a bulk resonse substantially different from ristine grahene. In addition, eoxide grous connect two adjacent carbon atoms, affecting a larger local area; as a result, the tye E bead dominates in the bond and angle classification. In our CG model, the ercentage of bonds and angles can simly be changed by rescribing the ercentage of different beads. Later we show in the Results section that by using this convention of classification, we are able to cature the deendence of in-lane roerties and interlayer adhesion energy of GO sheets on comosition and degree of oxidation in good agreement with DFTB calculations. We use different equilibrium bond lengths ðd 0 Þ for the three tyes of bonds herein, given that functional grous transform ristine s 2 bonds to s 3 bonds differently. Similar to the CG model of grahene, in which the bond length is double the equilibrium s 2 bond length, here we first measure three tyes of equilibrium bond lengths from a DFTB calculation. We calculate the bond length V a ðþ¼k q q ðq q 0 Þ 2 (3) V nb ðrþ ¼4ε LJ s LJ r 12 s 6 LJ r r < r c (4) Fig. 2(a) (b) show the tyical energy and force rofiles for bond tye II and III, Eq. (2b), resectively. The initial harmonic art in the otential gives rise to linear elastic roerties. The change of the sloe in the force rofile at d c1 results in non-linear behavior in the stress vs. strain curve of GO sheets, as shown in Fig. 2(c). Additionally, similar to the Morse otential [53], the otential V b;ii&iii can also enable bond ruture, and bond failure strain is only controlled by the critical bond length where the maximum force is achieved (i.e., the bond length d c2 in Fig. 2(b)). Through this aroach, the nonlinearity of the stress-strain behavior of GO can be catured henomenologically. Post-failure lastic behavior and bond reformation events are unlikely to be accurately reresented in any coarse-graining aroach. Caturing the softening behavior due to lasticity and dynamic bond breaking and reformation accurately requires reactive atomistic force fields that are orders of magnitude slower than the current CG model. Finally, for interlayer interactions in AA systems, there are contributions from van der Waals, electrostatic and directional H- bonding interactions. We use a simle LJ otential to account for all interactions as a mean field aroach, and in the CG model, all beads interact with other beads within a cutoff distance. Although this choice loses some directional behavior such as H-bonding, the gain in comutational efficiency is significant. We note that simle LJ otentials are generally used in other force fields with a similar

4 Z. Meng et al. / Carbon 117 (2017) 476e Fig. 2. Tyical energy (a) and force (b) rofiles for bond tye II and III otentials. The first kink in the force curve at d c1 induces the nonlinearity in the stress vs. strain curve. The second kink in the force at d c2 results in the failure behavior in the stress vs. strain. (c). Reresentative stress vs. strain curve of a GO sheet with 60% degree of oxidation having the eoxide-rich comosition using the bond otential shown in (a) (b). (A colour version of this figure can be viewed online.) degree of coarse-graining, such as CG force fields for synthetic olymers and the MARTINI force field for bioolymers [46,47,54] Characterization of atomistic GO roerties The AA simulations are carried out through a series of semiemirical DFTB calculations using the oen-source code CP2K (htt:// to determine the mechanical roerties of GO as a function of its chemical comosition. Through the calculations, we determin the elastic modulus, failure strain under uniaxial tension and interlayer adhesion energy of GO. We first generate AA A 2 GO monolayer sheets for different degrees of oxidation, based on eoxide or hydroxyl rich comositions. In this study, the term eoxide or hydroxyl rich refers to GO sheets that are only functionalized with eoxide or hydroxyl functional grous resectively. Additionally, GO sheets with a fixed degree of oxidation but variable chemical comositions are generated. A Monte Carlo-based algorithm is emloyed to determine the favorable locations for functional grous from random choices according to a Boltzmann-like distribution, as discussed in revious work [22,38,42]. It should be noted that 72% hydroxyl-rich oxidation and 80% eoxide-rich oxidation are the maximum oxidation cases that are admissible for each functionalization tye. Further increasing functional grou coverage results in chemical instability of the system during DFTB calculations. Stress-strain curves are determined by assuming the effective monolayer thickness as Dz eq ¼ 7:5 A, which is consistent with revious studies [22,42]. The Young s moduli ðeþ are obtained by fitting the material elastic constants in the stress vs. strain curves and using continuum mechanics formulation, as reviously shown [42]. The in-lane shear moduli ðsþ are calculated by using the linear-elastic relationshi S ¼ E=2ð1 þ nþ, assuming the Poisson s ratio n is a constant equal to 0.16 for all GO sheets, which is taken as the average value for all the degree of oxidation cases according to DFTB calculation results. More details about the comutational method and the validation of DFTB calculations are rovided in our revious study [42]. To characterize the interlayer adhesion energy, we generate bilayer GO sheets with different comositions and degrees of oxidation. The UFF force field is included to account for disersion effects in the material, as imlemented in CP2K. The adhesion energy can be determined by calculating the total energy of the bilayer system after otimization and subtracting the energy of two searate single sheets. The adhesion energies are calculated for different tyes of GO bilayer systems, including ure grahene sheets, eoxide-rich GO sheets, hydroxyl-rich GO sheets and GO sheets whose comosition results from a combination of both functional grous. We aim to cature the general trends of adhesion energy as the degree of oxidation and comosition varies for relatively homogenized systems. While we exected variations across different configurations with the same comosition but different distributions, (e.g. localized random atches instead of a homogeneous distribution of functional grous), these features are not considered here for calibrating the CG model Derivation of coarse-grained force field arameters Next, we roceed to derive the force field of the CG model by emloying the strain energy conservation aroach based on DFTB calculations. To calibrate the CG force field arameters, we only choose DFTB results in the armchair direction of three extreme scenarios as references. We use the ure grahene uniaxial tensile results to calibrate bond tye I and angle tye I arameters, the maximally oxidized hydroxyl-rich comosition (72% degree of oxidation) to calibrate bond tye II and angle tye II arameters, and finally the maximally oxidized eoxide-rich case (80% degree of oxidation) to calibrate bond tye III and angle tye III arameters. Both results from DFTB calculation and CG model verify that the in-lane roerties, i.e., the Young s modulus and uniaxial tensile strength, differ only a little when the degree of oxidation is larger than 70%. This is because in AA simulations the effect of functional grous saturates fairly quickly. The corresonding classification of bond and angle tyes in the CG model leads to a raid decrease of tye I bonds and angles with increasing ercentage of either tye H or E beads. Thus, the structures at high degrees of Table 1 Target roerties for GO. Young s modulus (E) GPa In-lane shear modulus (S) GPa Elastic strain ðε ela Þ Failure strain ðε maxþ Adhesion energy mj=m 2 Grahene e 21% 31 Hydroxyl-oxidized GO % 10% 156 Eoxide-oxidized GO % 25% 97 *The elastic modulus is calculated by assuming the effective thickness of the monolayer GO as 7:5 A [42].

5 480 Z. Meng et al. / Carbon 117 (2017) 476e487 oxidation have aroximately the same bond and angle comositions. For instance, examining one secific CG structure with 72% ercent of tye H beads reveals that 92% of the bonds are tye II and 81% of the angles are tye II. This justifies our ractice to use these three extreme cases to calibrate the bond and angle arameters. Similarly, we use the bilayer airwise energies of these extreme cases to calibrate non-bonded interactions. However, we note that the airwise energy only deends on LJ interactions of beads, so it does not saturate at high degree of oxidation level. Since we use ~80% degree of oxidation AA structure to calibrate the arameter for 100% degree of oxidation in the CG structure, we need to unify the degree of oxidation concets by using scaling arguments between AA and CG models to be able to comare the interlayer adhesion energy results. This asect is discussed further in the Results section. The necessary mechanical roerties to calculate the bond and angle arameters are Young s modulus, in-lane shear modulus, elastic strain and failure strain. LJ arameters are calibrated to match the adhesion energy of bilayer systems with constant interlayer sacing. A summary of the target roerties is shown in Table 1. After having established target roerties, we roceed to describe the calibration strategy. Since the Morse otential (bond tye I) can be aroximated by a harmonic function V b; I ðdþ ¼D 0 ½1 e aðd d0þ Š 2 zk be ðd d 0 Þ 2, where k be ¼ D 0 a 2, all bond tyes can be aroximated as harmonic in the small deformation regime. Gillis has derived the relationshi between the force constants of the harmonic bonds and angles of the hexagonal lattice and the elastic constants of the total sheet [55], which we have utilized in our revious CG model of grahene [48]: ffiffiffi 3 ces k b ¼ 2ð4S EÞ ffiffiffi 3 d 2 k q ¼ 0 ces 12ð3E 4SÞ (5) (6) where c ¼ 2Dz eq, and Dz eq ¼ 7:5 A. Thus, all arameters involved in the angle otentials and k be of bond otentials can be calculated directly. It should be noted that the arameters calculated using Eqs. (5) and (6) do not deend on the value of Dz eq as long as it is ket the same as the assumed effective monolayer thickness for DFTB calculation, since k b and k q scales linearly with the 2D modulus, Dz eq E. For the Morse bond otential (i.e., bond tye I) in MD simulations, a bond tyically breaks at the elongation where the force reaches a maximum, or equivalently the inflection oint in the energy rofile [53]. The arameter a is directly related to this inflection oint in the energy rofile. We set the failure criterion of the bonds according to the failure strain of GO sheets, as the same in the CG model of grahene [48]. Thus, we can calculate the arameter a as a ¼ log2=ðε max d 0 Þ, where ε max is the failure strain as obtained from DFTB results. Once k be and a have been determined, the arameter D 0 can be calculated using the relation D 0 ¼ k be =a 2. For bond tyes II and III, the arameter d c1 linearly scales with the linear elastic limit strain ε ela. We conduct uniaxial tensile simulations using the CG model with different values of d c1 and ick a value that conserves ε ela of DFTB results. The sloe of the second linear art is related to the nonlinearity in the stress vs. strain curve before failure. The average sloe of the ost-elastic region observed from DFTB calculations is conserved by choosing a corresonding k b value. Similar to the Morse bond otential, the d c2 arameter is directly related to failure strain, and is calibrated to match the failure strain from DFTB calculations. Our CG results also suggest that the sloe arameter k bf does not affect the failure strain and stress vs. strain curve, and thus we secify it as k bf ¼ 2k be. During simulations, we delete bonds once they are stretched to d cut, which is slightly larger than d c2. Thus, all the arameters of the bond and angle otentials can be determined. The only term left for the force-field that requires calibration is the non-bonded interaction, which is imortant for caturing the roerties of multilayer GO assemblies. The arameter ε LJ reresents the deth of the otential well and directly relates to the adhesion energy, and the arameter s LJ controls the interlayer Table 2 Functional forms and calibrated arameters of the CG model force-field. Interaction Functional form Parameters Bond Tye I: V b;i ðdþ ¼D 0 ½1 e aðd d0þ Š 2 d 0 ¼ 2:86 A D 0 ¼ 443:07 kcal a ¼ 1:154 d cut ¼ 3:7 A Tye II & III: Tye II: 8 k be ðd d 0 Þ 2 d < d c1 d 0 ¼ 2:94 A d c1 ¼ 3:12 A d c2 ¼ 3:46 A >< k b ðd d c1 Þ 2 þ 2k be ðd c1 d 0 Þðd d c1 ÞþC 1 d c1 < d < d h i c2 d cut ¼ 3:5 A k be ¼ 317:34 kcal V b;ii&iii ðdþ ¼ k bf ðd d c2 Þ 2 A 2 þ 2k b ðd c2 d c1 Þþ2k be ðd c1 d 0 Þ ðd d c2 ÞþC 2 d > d c2 k bf ¼ 634:68 kcal A 2 Tye III: Angle Non-bonded V a ðþ¼k q q ðq q 0 Þ 2 C >: 1 ¼ k be ðd c1 d 0 Þ 2 C 2 ¼ k b ðd c2 d c1 Þ 2 þ 2k be ðd c1 d 0 Þðd c2 d c1 ÞþC 1 slj 12 6 slj V nb ðþ¼4ε r LJ r r k b ¼ 126:94 kcal A 2 d 0 ¼ 2:80 A d c1 ¼ 3:00 A d c2 ¼ 4:20 A d cut ¼ 4:3 A k be ¼ 256:10 kcal k A 2 b ¼ 21:34 kcal A 2 k bf ¼ 512:20 kcal A 2 q 0 ¼ 120 Tye I: k q ¼ 456:61 kcal Tye II: k q ¼ 259:47 kcal Tye III: k q ¼ 189:93 kcal s LJ ¼ 7:48 A Tye C: ε LJ ¼ 0:0255 kcal Tye H: ε LJ ¼ 0:128 kcal Tye E: ε LJ ¼ 0:0797 kcal

6 Z. Meng et al. / Carbon 117 (2017) 476e sacing. In this study, we use constant interlayer sacing 7:5 A for different cases given that the interlayer sacing increases immediately with the resence of functional grous and it differs less than 10% at high functional grou density according to DFTB results. The constant interlayer sacing also simlifies our model and results in an identical s LJ value of 7:48 A for all bead tyes. An identical cutoff value of 20 A is chosen to balance between including as much ortion of the attractive well as needed and without exeriencing too much comutational slowdown. Secifically, the adhesion energy calculated using cutoff value of 20 A is in less than 5% difference with that calculated using cutoff value of 40 A.By testing different values of ε LJ for a system with only one tye of bead at low temerature (i.e., negligible entroic effects), we find that ε LJ linearly scales with the non-bonded interaction energy of bilayer systems. We calibrate the arameter ε LJ for three tyes of beads according to the DFTB results of the three scenarios in Table 1 at fixed interlayer sacing 7:5 A. The air coefficient for interactions between different tyes of beads is obtained via a Lorentz-Berthelot mixing rule: s AB ¼ðs AA þ s BB Þ=2; ε AB ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffi ε AA ε BB. A summary of all the CG force-field functional forms and the corresonding calibrated arameters is resented in Table Protocols for the CG-MD simulations The ecular dynamics code LAMMPS [56] is used to conduct all the CG-MD simulations. We choose the same time-ste of 4 fs as that used in the CG model of grahene [48]. To simulate the in-lane mechanical resonse, we use a monolayer sheet of dimensions nm 2. The system contains ~24000 beads in total and eriodic boundary conditions (PBCs) are alied in all the directions, while a 10 nm emty sace exists on either side of the sheet in the out-of-lane direction. This aroriate model size is determined by running multile simulations with increasing size until convergence is achieved in the stress-strain results. We find that for smaller systems, the failure strain and maximum stress are relatively higher, and this size effect might arise from the secific classification of bonds and angles in the CG model. The systems are first minimized and equilibrated in a NPT assemble at T ¼ 300K and zero ressure in the in-lane directions. After equilibration, the strain-controlled uniaxial tensile test is erformed by deforming the simulation box at a constant strain rate of s 1 in the armchair direction. During deformation, we constrained the out of lane dislacements of all the beads in order to maintain the uniaxial tensile condition and minimize entroic elastic behavior [57], given that there is negligible entroic elastic behavior in DFTB calculations on uniaxial tension of small sheets. Because of the large box size in the dimension normal to the sheet, the stress comuted using the virial theorem for the box does not corresond to the actual stress in the sheet, and needs to be corrected by multilying with the ratio of the box dimension to the actual monolayer sheet thickness. We use the same effective monolayer thickness 7.5 A used in DFTB calculations for this urose. We calibrate the arameters at 300 K since DFTB calculations have been shown to match exerimental results at room temerature [42]. Moreover, our CG model is anticiated to be alied more often to study room temerature scenarios. However, we note that the Young s modulus is not sensitive to the temerature, and by decreasing the temerature to 10 K, the Young s modulus only increases less than 2%. The strength shows a decrease with increasing temerature, and the difference is u to 20% between 10 K and 300 K for all the cases resented herein. The failure strain of the CG model is mainly governed by the bond elongation, and higher temerature increases the robability of the bonds to reach cutoff bond length. As a result, higher temerature leads to earlier failure of the sheet. The deendency of Young s modulus and strength on temerature is similar to an earlier study on ristine grahene using the adative interecular reactive emirical bond order (AIREBO) otential [58,59]. The bilayer adhesion simulations involve two GO sheets arallel to each other with dimensions nm 2. PBCs are alied in the in-lane dimensions, and again there is a 10 nm emty sace on either side of the sheets in the out-of-lane direction. We use a relatively large system to get a better statistical samling. We also test different sizes of systems ranging from 8 8nm 2 to nm 2, and the variation of the adhesion energy calculated is within 5%. After initial minimization, the system is equilibrated in the NVT ensemble at temerature T ¼ 300K. After equilibration, the energy due to the interlayer air-wise non-bonded interactions is measured with the intralayer non-bonded interactions being turned off. The adhesion energy at 10 K is also calculated, and it is found to be less than 5% larger than the adhesion energy at room temerature, thus verifying that the entroic effect on the adhesion energy is negligible. To test the redictive caabilities of the develoed CG model, we erform nanoindentation simulations of monolayer GO sheets. We use a similar size as our revious study on ristine grahene (indenter radius, R ¼ 4 nm, and membrane radius, a ¼ 25 nm) for the simulation [50]. Although the size selected is still 20 times smaller than those used in recent exeriments [22], revious studies show that this size is enough to illustrate mesoscale mechanisms by using size-scaling analysis [48]. The circular indentation region is in the center of a square sheet with length ~60 nm. In order to resemble the exerimental setting that a square sheet is susended over a circular hole, during the indentation rocess, the beads outside of the circular region are fixed by a stiff harmonic sring with sring constant kcal=$ A 2 and the beads within the circular region are set freestanding without any constraints. Noneriodic boundary conditions are emloyed due to the finite nature of the system. The simulation is also conducted at 300 K. We simulate the indenter as a rigid shere that interacts with GO beads via a reulsive force F ¼ Kðr RÞ 2, where r is the distance from the bead to the center of the indenter, and the force constant K is set to be 1000 kcal=$ A 3. The indenter is moved Fig. 3. Uniaxial stress vs. strain results (armchair direction) from CG simulations and DFTB calculations for GO sheets with hydroxyl-rich comositions at different degrees of oxidation. (A colour version of this figure can be viewed online.)

7 482 Z. Meng et al. / Carbon 117 (2017) 476e487 Fig. 4. Comarison of the elastic moduli (a) and the tensile strengths (b) between CG model and DFTB calculations for GO sheets with hydroxyl-rich comositions at different degrees of oxidation. (A colour version of this figure can be viewed online.) with a constant downwards velocity of 5 m/s from the initial osition where it has no interaction with the GO beads. In our revious study, exlicit sensitivity analysis confirmed that the indentation rate has no observable effect on the mechanical resonse of CG system [50]. Finally, we aly our CG model to study the fracture toughness of different GO sheets with different comositions. The same Fig. 5. Uniaxial stress vs. strain results (armchair direction) from CG simulations and DFTB calculations for GO sheets with eoxide-rich comositions at different degrees of oxidation. (A colour version of this figure can be viewed online.) dimension size as the uniaxial tension case is used. Central cracks with different lengths are generated by deleting the beads and corresonding bond and angle interactions. The cracks are aligned with the zigzag direction and tensile loading is alied in the armchair direction. An equivalent deformation rocedure to that used in uniaxial tensile deformation is alied. 3. Results and discussion Having derived all of the force field arameters for the CG models based on the three extreme cases, we validate the CG model by testing it for different degrees of oxidation and comositions. In Fig. 3, we comare CG and DFTB uniaxial tensile results in the armchair direction for GO sheets with different degrees of oxidation on hydroxyl-rich comositions. We note that the CG model shows anisotroy in the uniaxial tensile results of armchair and zigzag direction since we adot a hexagonal symmetric lattice, although DFTB results do not show such an effect due to breakage of symmetry. Secifically, the failure strain and failure stress in the zigzag direction are generally ~15% larger than those in the armchair direction, and our revious results of grahene show similar anisotroy in both directions [48]. Nonetheless, the general decreasing trend of Young s modulus and strength with increasing degree of oxidation is well catured for both directions in the CG model. In addition, the brittle failure of the hydroxyl-oxidation case is catured by using the iecewise otential form for the new bond tye II. By calculating the elastic moduli and strengths for different degrees of oxidation, DFTB and CG results show that Young s modulus decreases faster at lower degrees of oxidation than that at higher degrees of oxidation, as shown in Fig. 4. In other words, a small amount of functional grou coverage results in an obvious Fig. 6. Comarison of the elastic moduli (a) and the tensile strengths (b) between CG model and DFTB calculations for GO sheets with eoxide-rich comositions at different degrees of oxidation. (A colour version of this figure can be viewed online.)

8 Z. Meng et al. / Carbon 117 (2017) 476e deterioration of both Young s modulus and strength due to disrution of the s 2 network of grahene, while the imact of further oxidation becomes diminished at higher ercentages of hydroxylation. The Young s modulus for each case is within 10% error comared with the DFTB results. It is a remarkable accomlishment of the model that the arameterization for the 72% case alone is sufficient to cature the uniaxial tensile behaviors of other degree of oxidation cases with reasonable accuracy. The strength deviation for lower degrees of oxidation cases is relatively larger than the Young s modulus case. Secifically, the deviations are 23.1%, 17.5%, 4.6% and 14.5% for the four oxidation cases listed in Fig. 3. The relatively large deviation for low degree of oxidation is due to the fact that failure strains are almost a constant for atomistic GO sheets in DFTB calculations, while in CG models, for low degree of oxidation cases, tye II bonds, with smaller force constants, are more significantly stretched than tye I bonds, and this localized behavior results in early failures of GO sheets with lower degrees of oxidation in CG simulations. It is foreseeable that more localized behavior would be resent in larger systems. Similarly, Fig. 5 shows the comarison between CG uniaxial tensile results of eoxide-rich CG and DFTB calculations. Generally seaking, GO sheets with a high eoxide comosition exhibit a relative larger failure strain and ductility, which is defined as the difference between failure strain and elastic strain. The higher ductility of eoxide-rich cases can be attributed to an eoxide-toether transformation at the atomic level [22]. For the CG model erformance, the Young s modulus and strength values and their decreasing trend agree closely with DFTB results, as shown in Fig. 6. In addition, since the arameter of bond tye III has a larger d c2, the CG model is able to reroduce the large failure strain and ductility for the eoxide-oxidation case, and it also reroduces the general increase of failure strain with increasing eoxide coverage. It should be noted that the CG model shows less variability for different initial configurations than AA models. More secifically, the Young s moduli have negligible differences with different random distributions of the beads, and the standard deviation for strength is only 1% of the averaged value. This is because the CG model treats the comlicated chemical atomistic structure with a simler lattice structure, resulting in a CG model that simlifies and stabilizes mechanical behavior during deformation. Having verified the CG model for both hydroxyl-rich and eoxide-rich comositions, we then test the CG model for a wider set of comositions that include combinations of eoxide and hydroxyl functionalization. First, we define the ratio of eoxide and hydroxyl functional grous as: N eoxides d ¼ (7) N eoxides þ N hydroxyls where N eoxides and N hydroxyls are the total number of eoxide and hydroxyl grous in DFTB calculations, while they reresent the total number of tye E and tye H beads in CG simulations. DFTB results indicate that for a given degree of oxidation (70% in this case), brittle to ductile failure behavior can be observed by increasing the eoxide grou ercentage, which also leads to an areciable enhancement in toughness, which is defined as the area below the stress vs. strain curve [42]. As shown in Fig. 7, the CG model is able to quantitatively reroduce the increasing toughness trend with increasing eoxide-oxidized beads ercentage for combined functionalization cases. Fig. 7(c) shows the comarison of ductility, which is defined as the difference between linear elastic limit strain ε ela and failure strain ε max, between DFTB results and our CG model, and the agreement is remarkable. These results demonstrate the redictive caabilities of our CG model given that the model is only Fig. 7. In-lane mechanical behavior of the DFTB results (a) and the CG results (b) for different hydroxyl/eoxide ratio at 70% degree of oxidation. In (a), d is defined as the ratio between the number of eoxide grous and the total number of eoxide and hydroxyl grous, and in (b), d is defined as the ratio between the number of tye E beads and the total number of tye H and tye E beads. (c). Ductility vs. hydroxyl/ eoxide ratio d for both DFTB (circle) and CG (square) results. (A colour version of this figure can be viewed online.) calibrated based on the three extreme cases. For the interlayer interaction erformance, Fig. 8 shows the interlayer adhesion energy difference for three functionalization cases redicted from the CG model: hydroxyl-rich, eoxide-rich and a combined comosition with a 1:1 ratio between hydroxyl and eoxide functional grous. By differentiating the interactions for the three tyes of beads, our CG model can quantitatively match the relationshi between adhesion energy and degree of oxidation, and also cature the interlayer adhesion difference resulted from different functionalization. Secifically, the CG model catures the increasing adhesion energy with increasing degree of oxidation, as well as the higher adhesion energies of hydroxyl-rich cases. The

9 484 Z. Meng et al. / Carbon 117 (2017) 476e487 Fig. 8. Comarison between the redicted adhesion energies for three functionalization cases: hydroxyl-oxidation only, eoxide-oxidation only and combined oxidation with 1:1 ratio between hydroxyl and eoxide. DFTB adhesion energy results for combined oxidation with 1:1 ratio after conversion of the degree of oxidation are shown in black solid diamonds. (A colour version of this figure can be viewed online.) resulting adhesion energies of combined comositions lie in between the two functionalization cases. We also run four atomistic cases of combined comositions in DFTB: 10%/10% hydroxyl/ eoxide, 20%/20% hydroxyl/eoxide, 30%/30% hydroxyl/eoxide and 40%/40% hydroxyl/eoxide. The DFTB results also show increasing adhesion energy with increasing degree of oxidation. We note that since we calibrate the LJ arameters according to ~80% degree of oxidation cases, we must convert the degree of oxidation of all atomistic cases by multilying 1.25 so that the degree of oxidation is comarable between DFTB calculation and CG model results, for examle, a 40%/40% hydroxyl/eoxide atomistic case corresonds to a 50%/50% hydroxyl/eoxide CG case. After the conversion of degree of oxidation, the DFTB results all lie near the CG redictions as shown in Fig. 8, and this consistency further shows the redictive caability of the CG model on the interlayer interactions. The model has been shown to quantitatively cature both the in-lane and interlayer mechanical resonses of GO sheets with different comositions and degrees of oxidation. We then aly the CG model to simulate monolayer GO nanoindentation behavior, in which the GO sheet undergoes large deformation until failure. Nanoindentation is one of the most widely used exerimental techniques to investigate the mechanical roerties of 2D materials [50,51]. Although during the nanoindentation, there is out-of-lane deformation involved, it has been verified that the in-lane biaxial tension still governs the total deformation. Secifically, by testing the CG model of ristine grahene with and without dihedral terms [48], the difference in the force-deflection curve is negligible, and even at maximum deflection, the dihedral energy contribution is less than 1% of the bond energy. As a result, even without the dihedral terms, the CG model is adequate to cature the realistic nanoindentation mechanical resonse. In our simulation, we use a 4 nm radius sherical unch to indent on 25 nm radius circular regions of three tyes of GO sheets: one without functional grous, same as a ristine grahene sheet, one with 70% hydroxyl-oxidation and the last case is a 70% oxidized eoxide-rich GO sheet. We note that it is unrealistic to simulate such systems using DFTB technique due to rohibitive comutational costs, while the same comutation takes less than 2 h of wall-clock time in 16 rocessors using our CG model. We use a theoretical model to fit the load-dislacement curve from the simulations [51], in which the force vs. deflection behavior can be aroximated using the equation: F ¼ s 0 td þ Et q 3 a 2d3 (8) Fig. 9. (a). Snashot of a 70% hydroxylerich GO sheet during indentation (we only show half of the sheet for clarity). (b). Nanoindentation simulation results of CG GO sheets (solid line) with theory fitting (dashed line) for three cases: ure grahene, 70% hydroxyl oxidation GO and 70% eoxide oxidation GO, resectively. (A colour version of this figure can be viewed online.) where F is the alied force, s 0 is the retension in the membrane, d is the central deflection or indentation deth, a is the film radius, q ¼ 1:02 is a dimensionless constant derived from the Poisson s ratio of the system, t ¼ Dz eq is the effective thickness of monolayer GO sheets. We use the Young s modulus E calculated from the uniaxial tensile test for each tye of GO sheet to fit the curves, and also s 0 ¼ 0, given that the sheets are fully relaxed before indentation loading in the simulations. Fig. 9 illustrates that the analytical fits deviate from simulation data for large deformation in the grahene and eoxide oxidation cases. The non-linear elastic behavior of grahene at large deformations corresonds to the deviation from the linear elastic assumtion of the theoretical model. For eoxide oxidized cases, the deviations after reaching an indentation deth of 5 nm is due to the non-linear ductility of eoxide oxidized GO. However, for hydroxyl oxidized case, since the sheet is linear elastic until brittle failure as shown in the uniaxial tensile results, there should not be any significant deviation from the analytical fit, which is

10 Z. Meng et al. / Carbon 117 (2017) 476e Fig. 10. (a) Schematic of the CG ristine grahene sheet with a central crack, a 0 ¼ 3nm in this case. (b). The state of catastrohic crack roagation. (c). Stress-strain relationshis for different crack lengths. (A colour version of this figure can be viewed online.) corroborated by the data shown in Fig. 9. These findings are significant because force vs. deflection resonses for GO membranes reorted exerimentally have been classified into two classes, corresonding to ductile and brittle failure modes [22,60]. Our CG results suggests that ductile failure occurs when the indenter contact area is redominantly occuied by eoxide grous, while brittle failure is observed when the indenter interacts with a hydroxyl-rich area, or an area that has high defect density. Our findings illustrate the imortance of exlicit reresentation of these discrete heterogeneity regions in the CG model to exlain the exerimental data. We then derive the nominal strength from the eak load in the force-dislacement curve using equation s max ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi FE=ð4RtÞ (where F is the ruture force, R is the indenter radius, and t is the film thickness). We note that this equation is for a linear elastic circular membrane, and thus it would overestimate the strengths of GO sheets due to material nonlinearity. Secifically, the derived nominal strengths for the three cases in Fig. 9 are 55.3 GPa, 28.5 GPa, 35.3 GPa for grahene sheet, 70% hydroxylerich GO sheet and 70% eoxideerich GO sheet, resectively. The measured strengths for the same materials in uniaxial tests are around 49 GPa, 26 GPa and 25 GPa, resectively, taken as the average strength in both armchair and zigzag directions. The results indicate that with the highest nonlinearity for 70% eoxide-rich GO sheets, the nominal strength derived from indentation test has the most overestimation when comared to its intrinsic strength. In our revious study [50], we have shown that the effective strength extracted from indentation measurement is affected by the interlayer shear strength for multilayer systems. This study ascertains that for a monolayer system, the measurement of strength via indentation could also be affected by in-lane nonlinearity and heterogeneity, which should be considered in future strength measurements of 2D materials where better statistical samling may be needed to obtain accurate material roerties. It has been roosed that classic Griffith theory of brittle fracture may be alicable to grahene and GO [44,61]. Unlike ductile and quasi-brittle materials, such as metals and olymeric materials, which are difficult to simulate fracture in atomistic simulations due to large size of lastic zone or rocess zone [62,63], classic brittle fracture has been successfully studied with atomistic simulations [61,64]. As further validation of our model, here we measure the critical stress intensity factor K c, which determines the linearelastic fracture toughness of the material, for the same three tyes of GO sheets studied during nanoindentation using this develoed CG model. According to the Griffith fracture criterion for a central crack of length 2a 0 : s c ffiffiffiffiffiffiffiffi a 0 ¼ ffiffiffiffiffiffiffiffi 2gE where the left-hand side is the critical stress intensity factor ffiffiffiffiffiffiffiffi K c ¼ s c a 0, and the right-hand side term deends only on material roerties (E is the Young s modulus and g is the surface energy, i.e., edge energy for 2D material like grahene). To measure K c, the failure far-field stress is measured for secimens with different central crack length. Fig. 10(a) shows the initial configuration of the simulation system, and after reaching critical stress s c, the crack roagates catastrohically through the whole sheet, as catured by Fig. 10(b). Brittle fracture is also manifested by the linear resonse in the stress-strain curves, as shown in Fig. 10(c). Table 3 lists the results of critical fracture stress and K c for different secimens. Our results show that K c is aroximately constant, and for large crack lengths, K c shows even less variance, further corroborating that Eq. (9) is ideal for long and shar cracks. It should be noted that K c values in Table 3 are calculated by assuming a monolayer thickness of 0.75 nm. By converting to a monolayer thickness of 0.34 nm such as that of grahene, K c ¼ 3:77MPa ffiffiffiffi m, which is consistent to other MD studies and exerimentally measured values of 4:0±0:6MPa ffiffiffiffi m [61,64]. Since we also cature the Young s modulus of grahene accurately, according to Eq. (9), the edge energy is also conserved in our CG model, and this validates our strain energy conservation aroach. The same rocedure is adoted to measure the fracture toughness of both hydroxyl-rich and eoxide-rich GO sheets with a 70% degree of oxidation. Interestingly, although eoxide GO shows an obvious non-linear resonse during uniaxial tension, it exhibits nearly linear resonse before failure and smaller failure strain when a defect is resent. The brittle fracture of catastrohic crack roagation (Fig. 11(b)) indicates the likely alicability of Griffith theory. The measured K c is 1:00±0:04MPa ffiffiffiffi m for the hydroxyl case, and 1:16±0:03MPa ffiffiffiffi m for the eoxide case. Kc values of GO sheets Table 3 Simulation data of crack size, critical fracture stress and critical stress intensity factor K c. a 0 ðnmþ s cðgpaþ K ffiffiffiffi cðmpa m Þ Average 1.71 Standard Deviation 0.05 (9)