Optimization design on simultaneously strengthening and toughening graphene-based nacre-like materials through noncovalent interaction

Journal of the Mechanics and Physics of Solids 133 (2019) 103706

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Optimization design on simultaneously strengthening and toughening graphene-based nacre-like materials through noncovalent interaction ZeZhou He, YinBo Zhu∗, Jun Xia, HengAn Wu CAS Key Laboratory of Mechanical Behavior and Design of Materials, Department of Modern Mechanics, CAS Center for Excellence in Complex System Mechanics, University of Science and Technology of China, Hefei 230027, China

a r t i c l e

i n f o

Article history: Received 18 June 2019 Revised 10 August 2019 Accepted 2 September 2019 Available online 3 September 2019 Keywords: Artificial nacre Graphene oxide Noncovalent interaction Shear-lag model Optimization design

∗

Corresponding author. E-mail address: [email protected] (Y. Zhu).

https://doi.org/10.1016/j.jmps.2019.103706 0022-5096/© 2019 Elsevier Ltd. All rights reserved.

a b s t r a c t Nacre exhibits outstanding mechanical properties due to its hierarchically microstructural features and associated multiscale deformation behaviors, enlightening human to design high-performance graphene-based nacre-like materials (GNMs) in the past decade. However, those GNMs mimicking brick-and-mortar microstructure always cannot give consideration to both strength and toughness because the pullout process of graphene oxide (GO) sheets that amplifies toughness in GNMs is extremely limited compared to natural nacre. Toward this end, a combination of modified shear-lag model and atomic simulations is proposed to investigate the optimal strategy of simultaneously strengthening and toughening for GNMs reinforced by strong noncovalent interfacial interactions. The modified shear-lag model can well couple the interlayer sliding and structural stability to characterize the toughening effect during the pullout process. We demonstrate that the interfacial toughness and shear strength tuned by interlayer noncovalent interactions significantly impact the effective tensile strength of GNMs, while toughness is mainly dominated by the interlayer sliding before strain localization during the pullout process of GO sheets. Melamine molecule is chosen as the representative interlayer crosslink agent owing to the ultrastrong noncovalent interaction between melamine and GO. Our atomic simulations indicate that melamine bound to GO by anomalous hydrogen bonding can greatly improve the interfacial shear stress and maintain the interlayer energy-dissipation efficiency resulting from the breaking and reforming of hydrogen bonds. An optimal range of melamine content and GO oxidation degree is then explored for synchronously superior strength and toughness by balancing the competitions among the reduction of intralayer tensile limit of GO sheets, the improvement of the interlayer shear strength, and the reduction of interfacial toughness. In particular, a scaling law is proposed as the evaluation criterion to correlate the inner inelastic deformation of GNMs and their mechanical properties, revealing why interlayer noncovalent interaction can optimize strength and toughness simultaneously while most other crosslinks usually cannot. © 2019 Elsevier Ltd. All rights reserved.

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Z. He, Y. Zhu and J. Xia et al. / Journal of the Mechanics and Physics of Solids 133 (2019) 103706

1. Introduction Structural biological materials such as bone, cellulose nanofibers or mollusk shells often exhibit outstanding mechanical properties, which possess unique and attractive combinations of stiffness, strength and toughness, and in some cases unmatched by conventional synthetic materials (Liu et al., 2017b; Meyers et al., 2008; Munch et al., 2008). Nacre as a prominent nanocomposite in these materials has been reported that its fracture toughness is several orders of magnitude higher than that of the mineral constituent, while its strength closely equals the value of yield stress in the mineral under uniform rupture. This remarkable performance can be attributed to its hierarchical “brick and mortar” (BM) architecture and finetuned interfaces that join building bricks. (Barthelat and Rabiei, 2011; Barthelat et al., 2016; Espinosa et al., 2009). These special structural features leads to building blocks able to slide on one another through large inelastic deformation at interface, which not only alleviates locally stress concentration but also generates crack deflection and bridging at process zones (Abid et al., 2019; Barthelat and Rabiei, 2011; Ritchie, 2011; Shao et al., 2012). Inspired by the architecture of natural nacre, many synthetic materials with high strength and toughness have been successfully engineered over the last two decades (Bouville et al., 2014; Munch et al., 2008; Tang et al., 2003). Graphene as a typical multifunctional two-dimensional material possesses extraordinary electrical, thermal and mechanical properties with extensive applications involving composites (Novoselov and Geim, 2007; Papageorgiou et al., 2017). Due to the layered structures, graphene or graphene oxide (GO) has been widely chosen as a prior candidate of building bricks assembled layer-by-layer into nacre-like microstructure with combined various interface engineering (Dikin et al., 2007; Zhang et al., 2016). With respect to the disordered graphene assembly, these graphene-based nacre-like materials (GNMs) well transfer the excellent mechanical combinations as well as exceptional electrical and thermal properties from the nanoscale to the macroscale of bulk materials, and shows the potential to surpass natural nacre and many engineering materials (Wan et al., 2019; Zhang et al., 2016; Zhang et al., 2018). However, the weak native interlayer crosslink between adjacent graphene sheets extremely prevents the transfer of the distinguished performance of graphene across multiple length scale up to macroscale (Gong et al., 2010; Lin et al., 2018; Young et al., 2012). Many interfacial crosslinking mechanisms, including self-healing, sacrificial bond, multimodality, and synergistic effects etc., have been recommended to enhance interfacial crosslinks in experiments and theoretical studies, through introducing varies of functional groups and molecules, such as hydrogen, covalent, ionic, π -π bonding etc., during the irradiation, oxidation and reduction treatments (Cheng et al., 2015; Liu et al., 2012; Liu and Xu, 2014; Zhang et al., 2016). According to the classic shear-lag model for nacreous composites under uniaxial tension, these enhancement strategies are attributed to the improving of interfacial load transfer capability compared with the weaker one between bare graphene sheets governed by van der Waals interactions (Gong et al., 2010; Liu et al., 2012). Yet, up to now the toughness in reference to strength reported in most graphene-based materials are still much lower than theoretical prediction (Chen et al., 2015; Chen et al., 2018; Dikin et al., 2007; Gao et al., 2011). There remain necessities for optimal design on interlayer crosslink selection of such graphene-based materials. Although the hierarchical staggered BM structure and interfacial reinforcement have been widely exploited in synthetic graphene-based materials (Cheng et al., 2014; Zhang et al., 2016), the mechanisms for redistributing locally stresses through limited inelastic deformation to provide for intrinsic toughness, e.g. the fibrillar sliding and mineral-platelet sliding in seashells, are neglected (Barthelat et al., 2016; Ritchie, 2011; Wang and Gupta, 2011; Yin et al., 2019). It has been indicated that the inner distinct inelastic deformation involved by periodic dilatation bands in nacre leads to its stress hardening and structural robustness (Evans et al., 2001; Wang et al., 2001), while the GO film behaves plasticity owing to the shear slip between individual layers and the interaction between functional groups (Vinod et al., 2016). These studies declared that plenty of inner interlayer slip in nacre or artificial nacre contribute the evident macroscopic plastic plateau in the stressstrain curves under uniaxial tension, by which the evaluation of toughness is amplified. To incorporate the inner sliding mechanism in GNMs, the interlayer crosslink should provide slip lubrication within the sliding band and sufficient adhesion to ensure stress transfer to the staggered BM structures and overall strength (Barthelat et al., 2016; Wang and Gupta, 2011). The challenge is to find a suitable crosslink agent that can establish strong and reversible interactions within neighboring graphene layers. However, the conventional interlayer crosslinks, such as hydrogen, covalent, ionic, π -π bonds etc., seem to be not competent in these requirements, for the reason that covalent and ionic bonding are brittle and unrecoverable while hydrogen and π -π bonding are relatively weak (Wan et al., 2016). Recently, quantification of interactions between GO sheet and small molecules, including fatty amines, aromatic amines, and amino-group triazines, were experimentally measured through AFM-based single-molecule force spectroscopy. It was surprisingly found that melamine molecule shows the strongest noncovalent interaction with GO, exhibiting a rupture force of more than 1 nN, comparable with the strength of typical covalent bonds (Wang et al., 2018). We then carried out first-principle calculations to reveal the atomistic origin of superstrong noncovalent interaction between the melamine molecule and the GO sheet, and elucidated that the anomalous tri-N···OH-GO hydrogen bonding cooperatively enhanced by the pin-like NH2 −π interaction is responsible for the ultra-strong noncovalent interface (Xia et al., 2019). Therefore, it is possible to achieve simultaneously ultrahigh strength and toughness in graphene-based materials, where strong noncovalent interaction provides sufficient interfacial adhesion to keep the staggered BM structure intact and provide adequate load transfer, while the reversible bonding brings large-scale deformation bands and efficient energy dissipation. The shear-lag model based on the representative volume element (RVE) has been extensively used to investigate the deformation and mechanical properties of nacre and artificial nacreous nanocomposites, and evaluate the effects of brick staggering mode, overlap length and interfacial parameters (Begley et al., 2012; Chen et al., 2009; Kotha et al., 2001;

Z. He, Y. Zhu and J. Xia et al. / Journal of the Mechanics and Physics of Solids 133 (2019) 103706

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Liu et al., 2012; Ni et al., 2015; Wei et al., 2012). There have been also growing academic interests to study the effects of various interlayer crosslinks and their optimal densities, through which the GNMs are optimized toward maximum strength and toughness (Gao et al., 2017; Wu et al., 2018). Besides, to settle the matter that the classical shear-lag model failed to describe the behavior of characterizing the macroscopic mechanical behavior in experiments and simulations, Song et al. (2016) and Yu et al. (2018) extended the shear-lag model by considering interfacial crack propagation and stability of the RVE. Sun et al. (2015) developed an elastic model considering interface failure for the bioinspired design of carbon nanotube bundles. These efforts have deepened our comprehension on the deformation and strengthen-toughening mechanisms of nacreous nanocomposites. While these modified shear-lag models emerge from the crack propagation, they are still unsuitable to explain interlayer sliding and strain localization in graphene-based laminate composites, where interfaces function through reversible bond. Moreover, it should be noted that the aspect ratio (length to thickness) of GO sheet is on the order of 30 0 0 much larger than that of the building brick (∼100) in natural nacre (Barthelat et al., 2007; Lin et al., 2012; Wan et al., 2018), so we expect there is more obvious interlayer sliding in GNMs. So far, it is currently unknown the quantitative correlation between interlayer sliding and toughening of GNMs. In this work, optimization design that combines theoretical analysis and atomic simulations is established to simultaneously strengthen and toughen GNMs through interlayer noncovalent interaction. A modified shear-lag model accounting for the interlayer sliding and stability of staggered BM microstructure in the RVE is proposed to characterize the toughening effect during pullout process. Then, based on recent experimental measurement, effects of melamine as an optimally screened small molecule are investigated by atomic simulations on interfacial shear strength and toughness. The optimal melamine content and GO oxidation degree based on the modified shear-lag model and molecular dynamics (MD) simulations are suggested to achieve simultaneously high strength and toughness for GNMs. At last, a scaling law as the evaluation criterion is given to correlate the inner inelastic deformation and mechanical properties of artificial nacres. It is found that the GNMs enhanced by melamine can achieve synchronously superior strength and toughness as compared to existing synthesized graphene-based artificial nacre nanocomposites. 2. Deformation of graphene-based nacre-like materials Generally, there are two failure modes for GNMs under uniaxial stretching load, i.e. the fracture of the functionalized graphene (or GO) sheets when the maximum stress in graphene (or GO) sheets exceed its strength σ cr (denoted as mode G), or the failure of interlayer crosslink when the maximum shear strain of the interface reaches its failure strain (denoted as mode I) (Liu and Xu, 2014). These failure modes has well described the deformation of GNMs with unrecoverable interlayer crosslink such as covalent bonds and ion coordination bonds both in experiments as well as simulations (Gao et al., 2017; Wu et al., 2018). However, for recoverable interlayer interactions such as van der Waals adhesion, π -π interaction and hydrogen bonds, there is no obvious critical failure strain of interface during the pullout process (mode I) of GO sheets. Thus, there is an urgent need to modify the classical shear-lag model based on the representative volume element (RVE). 2.1. Elastic-plastic deformation As illustrated in Fig. 1(a) and (b), the GO sheets staggered with a regular manner in the GNM can be regarded as brittle bricks with Young’s modulus Eg and tensile strength σ cr , while the interlayer crosslink (or interaction) can be reduced to continuum mortar phase with shear modulus Gc and shear strength τ cr . To simplify analysis, the interfacial mortar phase is assumed to be elastic perfectly plastic with yield displacement e and failure displacement f , as shown in Fig. 1(d). In the RVE, hg is the thickness of GO sheet and hc is the interlayer distance. Due to the symmetry in length direction, the RVE under uniaxial stretching can be reduced to the schematic model shown in Fig. 1(c), in which a displacement  is applied at the right end of the top sheet, and the left edge of the bottom sheet is constrained in the x direction. The equilibrium equations of GO sheets #1 and #2 are governed by

∂σ ∂τ + =0 ∂x ∂y

(1)

where τ = Gc γ is the constitutive equation for elastic zone, and τ = τ cr for plastic zones. Substituting equations σ = Eg du1 /dx, ∂ τ /∂ y = 2τ /hg for GO sheet #1, and σ = Eg du2 /dx, ∂ τ /∂ y = −2τ /hg for GO sheet #2 into Eq. (1), the solutions of the displacement fields u1 and u2 in the GO sheets #1 and #2 can be obtained, respectively (detailed process exhibited  1/2 in Appendix A). The average tensile stress in the unit cell is calculated by σs = 2Eg 0 σ dx, where x = x/lg with lg is the length of GO sheet and σ is the dimensionless tensile stress in the GO sheet. So the average tensile stress of RVE can be written as

σs =







 2τcr l0 1  2l p k + tanh k 1 − 4l p hg 2

(2)

and the maximum stretching stress in GO sheet is σm = 2σs , where lp is the length of plastic zone, l p = l p /lg with range of 0



∼ 1/4, k = lg /2l0 , and l0 = Dg hc /4Gc is a shear-lag characteristic length below which the interfacial shear stress distribution is uniform. According to the tension-shear chain (TSC) model (Ji and Gao, 2004; Zhang et al., 2010b), the effect of interlayer

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Z. He, Y. Zhu and J. Xia et al. / Journal of the Mechanics and Physics of Solids 133 (2019) 103706

(a)

(b)

hc

Graphene

τ

Δ

Interlayer crosslink

Elastic-plastic deformation

Δ #3

#2 #1

RVE

C O H

2hc

Interfacial failure Failure propagation

Δ

Δ

#3

#2

z #1 y

lg Elastic-plastic deformation

lp

(c)

a

x

(d) τ

Δ

τcr

#2 Elastic zone #1 Plastic zones

Interfacial failure

Γ

Δ-a

#2 #1

a lg/2

O

0

x

Δe

Δf

Δ

Fig. 1. (a) Schematics of regular staggered BM structure and the RVE highlighted by blue dash box. (b) Illustration of two deformation stages of GNMs, i.e. elastic-plastic deformation and interfacial failure (pull-out process). The three GO sheets in RVE are marked as #1, #2, and #3. (c) Sketch of shear-lag model of two deformation stages, plastic zones colored as red zones, elastic zone colored as green zone, reversible interlayer interaction highlighted by yellow zone. (d) Profile of the effective interface constitutive relation (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.).

volume should be considered on the bioinspired composites here. Since the interlayer phase does not carry tensile load, the effective tensile stress in the nacreous nanocomposites is

σe = σs

(3)

where  = h0c /hc is the volume fraction of GO sheet, and h0c is the intrinsic interlayer distance of GO sheets. The volume fraction here slightly differs from previous reference in which  = hg / hc (Liu and Xu, 2014), due to the fact that the thickness of GO sheet hg is defined by mechanical properties such as stiffness of GO sheet, but the interlayer distance hc is determined by its geometry structure. For the composites only assembled by graphene or GO,  = 1, while the volume fraction  is always less than 1 when there exists interlayer atoms or molecules. Under displacement controlled deformation, the effective strain of the RVE is ε =2/lg . The applied displacement  as a function of plastic zone length lp is expressed as

=

τcr hc  Gc

2

1 + l p k2 + 2l p k2 +





  1  1  k 1 + 4l p tanh k 1 − 4l p 2 2

(4)

As l p → 0, Eq. (4) is simplified as the result of linear elastic deformation. Combining Eqs. (2)–(4) with l p → 0 yields the effective Young’s modulus of the nacreous nanocomposites as

Ee =

Eg k tanh 2 + k tanh

k  2k 

(5)

2

which recovers the previous result when the RVE is without offset (Liu et al., 2012). From Eq. (2), we can find the effective tensile strength is determined by the length of plastic zone. In the case of l p = 0, Eq. (2) is reduced to

σe =

2τcr l0 tanh hg

 k 2

(6)

Z. He, Y. Zhu and J. Xia et al. / Journal of the Mechanics and Physics of Solids 133 (2019) 103706

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Fig. 2. Mechanical properties as functions of the normalized length of RVE. (a) Tensile strength defined as the maximum stress under uniaxial stretching. (b) Young’s modulus obtained by fitting the linear stage of stress-strain curves. Circle and triangle symbols denote MLG obtained from (Xia et al., 2016a,b;) and MLP obtained from (Liu et al., 2017a), respectively.

Table 1 Structural and mechanical parameters on interlayer and in-plane properties of GNMs, constructed by MLG, MLP and GO (ϕ = 30%), respectively. The characteristic shear-lag length of MLG and MLP is obtained by fitting the MD simulation results in Fig. 2(a).

MLGs MLPs GO

Eg (GPa)

Gc (GPa)

τ cr (MPa)

hg (nm)

hc (nm)

l0 (nm)

950 105.5 175.7

— — 0.173

— — 68.4

0.335 0.554 0.34

0.335 0.554 0.7

7.93 2.73 7.77

which recovers the result obtained by deformation tension-shear (DTS) chain model (Liu et al., 2012). In the case of l p = 1/4, Eq. (2) is simplified as

σe =

τcr lg

(7)

2 hg

which is same as the result obtained from TSC model (Zhang et al., 2010a). As shown in Fig. 2(a), DTS model well fits the results obtained from MD simulation for multilayer graphene (MLG) (Xia et al., 2016a) and multilayer phosphorus (MLP) (Liu et al., 2017a), while the staggered structure assembled by GO with oxidation degree (defined as the ratio of oxygen to carbon atoms in GO) of ϕ = 30% is well fitted by TSC model. All parameters used to fit simulation results are listed in Table 1. Based on the characteristic shear-lag length acquired from Fig. 2(a), we can find Eq. (5) well predicts the Young’s modulus of MLG, MLP as well as GO with staggered BM structure. Eqs. (2), (6), and (7) demonstrate that the dimensionless length of plastic zone l p within 0 ∼ 1/4 directly impacts the effective tensile strength. Therefore, the maximum length of plastic zone l m p is necessary to be precisely determined as we calculate the effective tensile strength. Previous research manifested that l m p could be determined by γ (x = 0 ) =  f /hc , where γ is the shear strain of interlayer phase (Ni et al., 2015). Then, the maximum length of plastic zone can be calculated m m by solving the transcendental equation, which is defined as the ratio f /e as a nonlinear function of l m p , where l p = l p /lg . Here, we rewrite the maximum length of plastic zone as a function of interfacial toughness  , which reflects the intrinsic interlayer plasticity of functionalized graphene sheet. The interfacial toughness  is the energy determined by the area of the trapezoid in Fig. 1(d), written as  =τcr  f − τcr e /2, then the ratio is  f /e = ( + 1 )/2, where  = 2Gc  /τcr2 hc . The maximum length of the plastic zone can be determined by 2

2 m  = 1 + 4l m p k + 4l p k tanh

1  2

k 1 − 4l m p



(8)

We note that the dimensionless interfacial toughness  characterizes the interfacial elasto-plasticity before the pullout process, and always satisfies  ≥ 1. In case of  = 1, the maximum length of plastic zone is l m p = 0, and Eq. (2) is m reduce to Eq. (6). For  ≥ 1 + k2 /4, the maximum length of plastic zone is always l m p = 1/4. From Eq. (7), it is clear that l p

increases with the improvement of  , which results in the raising of effective tensile strength obtained by Eq. (2). To make it more intuitive, various combinations of three interfacial parameters, i.e. normalized stiffness Gc hg /Eg hc , strength τ cr /Eg ,

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and toughness  /Eg hg , have been employed for the RVE combining Eqs. (2), (4), and (8), some of which are mapped into a scatter plot shown in Fig. S2(a). By correlating the scatter plot and stress-strain curves shown in Fig. S2(b), we can find that the effective modulus of the RVE is positively related to the stiffness of the interlayer crosslink, while the effective strength and toughness of the RVE can be improved by enhancing the interfacial shear strength and toughness of the interlayer crosslink with identical interfacial stiffness. In this case, the failure of the RVE depends on the interfacial failure (mode I) instead of the fracture of functionalized graphene sheet (mode G). Combining the interfacial failure (mode I) and the fracture of GO sheet (mode G), the tensile strength of the RVE can be concluded as



σe = min

σcr

2 2τcr l0 hg

2l m pk

+ tanh

1  2

k 1−

4l m p

mode G



(9)

mode I

In the case of mode G, Eq. (9) is similar to the TSC model when the platelet aspect ratio larger than its critical value (Zhang et al., 2010a), while Eq. (9) is reduced also to previous results when the volume fraction  = 1 (Wu et al., 2018). As shown in Fig. 2(a), Eq. (9) can well predict the failure of GO sheet in the RVE. 2.2. Interfacial failure As long as there is no fracture in GO sheet under uniaxial tension, GNMs will deform through the pullout of GO sheet after the energy bearing at the edges reaches its maximum interfacial toughness. The pull-out process is accompanied by the propagation of interface failure along loading direction, due to the reversible interface interaction between staggered GO. As indicated in Fig. 3(a) and (b), the deformation process of GO staggered BM structure can be also divided into four stages, including elastic stage (Ⅰ), uniform deformation (Ⅱ), localization stage (Ⅲ), and final failure (Ⅳ), similar to the MLG using coarse-grained MD simulations (Xia et al., 2016a). Taking the GO staggered structure with the length of RVE lg = 40 nm as an example, an initial elastic region (Ⅰ) is first observed with the yielding strain ε ep ≈ 0.04. After yielding, a plateau in the plastic flow stress is followed until the RVE reaches its critical stain ε f ≈ 0.24. In this stage (Ⅱ), defined as uniform deformation, the right (#2) and left (#3) GO sheets slide synchronously to the right and left, respectively, which behaves the stick-slip mechanism. Then, the right GO sheet (#2) is pinned, while the left GO sheet (#3) still slips until it slips from bottom GO sheet (#1) with the maximum strain of RVE ε m ≈ 0.62. Here, the switch between uniform deformation and strain localization seems like the behavior of bifurcation, which indicates that there exists energy instability of staggered BM structure during uniaxial stretching. In the localization stage (Ⅲ), the load-carrying capability of the RVE deceases due to the shortening of effective overlap length in staggered BM structure. We now investigate the last three deformation process (stages Ⅱ, Ⅲ, and Ⅳ) to determine the critical strain, ε f , and maximum strain, ε m . As shown in Fig. 1(b) and (c), a pullout with length, a, is placed at the right end, similar to the unit cell used by (Yu et al., 2018). The total energy of the system is given by



U = UE + 2int b

lg −a 2



(10)

where the first and second terms are the elastic and adhesion energies, respectively, b is the width of GO sheet, and  int is the interlayer adhesion energy. The elastic energy of the RVE can be estimated by



UE = hg b

lg /2 0



σ12 2Eg



 dx +

lg /2 0



σ22 2Eg

 



dx + hc b

0

lg /2



τ2 2Gc



dx

(11)

Considering that the pullout process is quasi-static, the deformation in this stage can be separated into two steps, i.e. the GO sheet #2 moves rigidly with length of a, and then the RVE deforms under stretching displacement, δ =  − a. The displacement δ can be regarded as a small disturbance for the RVE, so a linear shear-lag can be adopted here. The elastic energy of the RVE under given edge displacement δ is expressed as (more details see in Appendix B) 2

UE =

kbEg δ hg lg k(1 + 2a ) + 2 coth

1 2



k ( 1 − 2a )

(12)

where a = a/lg , δ = δ /lg . In a displacement-controlled experiment, the variation of energy is given by

dU = ∂aUE da − 2bint da

(13)

Combining Eqs. (12) and (13), the strain energy release rate for RVE under displacement control can be obtained by minimizing the system energy, dU/da = 0, and expressed as

 2 Eg hg k2 δ ∂ UE  G= − =

 2 ∂ a δ 2 + k(1 + 2a ) tanh 12 k(1 − 2a )

(14)

Z. He, Y. Zhu and J. Xia et al. / Journal of the Mechanics and Physics of Solids 133 (2019) 103706

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Fig. 3. (a) MD snapshots of the deformation process of GO staggered structure. af is the critical pullout length. The red arrow indicates the collapse of RVE. (b) The pullout length, a, (graph top) and engineering strain (graph bottom) of GO sheet as functions of the strain of RVE with length of lg = 40 nm. (c) The maximum strain of staggered structure as a function of the number of RVE. (d) The failure strain of staggered structure as a function of its normalized length, lg , of RVE. The marked green point is the failure strain of regular staggered structure with offset. The failure strain calculated by Eq. (16) of MLG is obtained from (Xia et al., 2016a) with temperature of 300 K.

Eq. (14) is similar to the result obtained by (Yu et al., 2018), which fully governs the stability of the staggered structure. The interface is stable in the case of ∂a G < 0 until the length, a, of interface failure reaches its critical value af . By solving ∂a G = 0, we can determine the critical pullout length af





 

k 1 + 2a f − sinh k 1 − 2a f



=0

(15)

where a f = a f /lg , and the failure strain of staggered BM structure is ε f = 2a f . Eq. (15) indicates that the failure strain of regular staggered structure is only a function of the dimensionless parameter k (or lg /l0 ), so the functional groups in GO sheet affect the strain localization through intralayer and interlayer mechanical properties. For Nx RVEs replicating along x direction, the maximum failure strain is given by

εm =

2(2Nx − 1 )a f + 1 2Nx

(16)

which recovers the results proposed by Xia et al., 2016a). With N → ∞, ε m → ε f . As shown in Fig. 3(c), Eq. (16) can well fit the MD simulation results with the only one fitting parameter ε f = 0.225, which corresponds to the critical strain (ε f ≈ 0.24) obtained from our MD simulation. As shown in Fig. 3(d), the failure strain of regular staggered structure increases with the normalized length of RVE, which elucidates that the plateau length of flow stress in regular staggered structure increases as the overlap length of RVE enlarges. Combining Eqs. (15) and (16), our theory predicts well the trend of failure strain, but slightly overestimates the failure strain for the large overlap length, due to the pinning probability increased by temperature and strain rate. However, there is a stacking offset of the staggered BM structure in the practical situation, i.e. the overlap length of the right (#2) and left (#3) in RVE is not the same, or the mechanical properties of these two GO sheets (#2 and #3) are different. Moreover, the staggered structure of GNMs in experiments is always randomly staggered. Therefore, the

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Fig. 4. (a) The sketch of normalized stress-strain curve for staggered structure for the configuration k = 2. (b) Plots exhibit the elastic-plastic toughness Wep , pullout toughness Wf , and the total materials toughness Wtotal (all normalized) vary with the normalized length of GO sheet with oxidation degree ϕ = 30%.

deformation of staggered structure, considering the actual situation, is asymmetric as well as nonuniform, which will result in largely reducing its failure strain and stretching strength (Ni et al., 2015). As displayed in Fig. 3(d), the failure strain of staggered structure (ε f ≈ 0.23) with RVE length of 50 nm is much larger than that (ε f ≈ 0.048) of the staggered structure with offset (the length of GO sheets #2 10 nm and #3 40 nm). Nevertheless, the interlayer sliding before strain localization is still the significant mechanism during pullout process that raises the energy dissipation. To estimate the enhancement of pullout process on material toughness, the quantitative relationships between the applied stress (and strain) and the pull-out length are investigated. Based on the mechanical model presented in Section 2.1, the effective stress in the RVE with pull-out length, a, can be obtained by replacing lg with lg – 2a in Eqs. (8) and (9). They are formulated as 2

2 2 m  = 1 + 4l m p k (1 − 2a ) + 4l p k (1 − 2a ) tanh

σea =



1 2



k ( 1 − 2a ) 1 − 4l m p



(17)





  2τcr l0 1 2l m k ( 1 − 2a ) 1 − 4l m p k (1 − 2a ) + tanh p hg 2

(18)

where the range of dimensionless pull-out length a is given by 0 ≤ a ≤ a f . Analogously, the applied displacement  as a function of pull-out length a is expressed as



2σea =a 1+ lg Eg

 and

a =

τcr hc Gc





+

a

(19a)

lg



m 1 + lm p + 2l p

2





2

k2 ( 1 − 2a ) +



    k k ( 1 − 2a ) 1 + 4l m ( 1 − 2a ) 1 − 4l m p tanh p 2 2

(19b)

In Eq. (19a), the first term is the contribution of pullout length, while the second term is the deformation of overlap part. It is obvious that when  = 1, Eqs. (18) and (19) can be reduced to Eqs. (S22) and (S23) (Appendix B), respectively, revealing that the mechanical model discussed in Sections 2.1 and 2.2 is consistent. Besides, during the uniform deformation (stage Ⅱ) shown in Fig. 3(b), the strain of GO sheets is small and almost constant, so the strain of the RVE during pullout process can be simplified as ε ≈ 2a + εep . The stress-strain curve exhibited in Fig. S4 can now be described by combining Eqs. (15), (17), (18) and (19). Fig. 4(a) is a sketch of normalized effective stress-strain curve for k = 2, which shows a short elastic stage followed by a long pullout process. It is recognizable that the process of interfacial failure dominates the energy dissipation. Therefore, the capability of energy absorption Wtotal (or toughness) defined as the area under the effective stress-strain curve for the RVE can be estimated by modifying the strength and critical strain ε ep herein to be these calculated in Section 2.1, respectively. The toughness can be divided into two parts named as the elasto-plastic portion Wep and pullout portion Wf

Wtotal = Wep + W f =

 εep 0

σe d ε +

 εf εep

σe d ε

(20)

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Fig. 4(b) shows how normalized Wep and Wf of staggered structure varies with lg /l0 , revealing that our assumption well predicts the toughness of staggered structure obtained from MD simulations. Besides, Wf as a part of total toughness is dominated when the dimensionless length is large enough (lg /l0 > 3), while there is a dramatic drop in the total toughness once fracture of GO sheets (mode G) occurs as shown in Fig. 4(b). Above analysis demonstrates that interfacial parameters, such as interface stiffness, strength and toughness largely govern the mechanical properties of GNMs. In addition, interface failure (mode I) is beneficial to improve the toughness of GNMs, and tensile strength can be enhanced due to interface plasticity. However, it has been widely recognized that the native interface between graphitic nanostructures and matrices creates weak crosslink, which prevents the transfer of the excellent performance of graphene (or its ramification) across multiple length scale up to macroscale. To overcome this issue, here, we propose a new strategy that screens small molecules that is simultaneously strong and reversible as the interlayer crosslink agent to enhance the interfacial mechanical properties. 3. Effects of small molecules As discussed in Section 2, the mechanical performance of GNMs is critically governed by interfacial interaction and interface failure. Here, we first explore the mechanical and failure behaviors of bilayer model with optimal adhesion molecule, screened by first principle calculations based on density functional theory (DFT), through MD simulations. Then, based on these simulation results, the mechanical properties are investigated quantitatively on the RVE. 3.1. Effects on bilayer GO interface Despite single-molecule AFM experiment can directly measure the binding strength between different organic molecules and GO sheets, atomic simulations, such as first principle calculations and MD simulations, are more efficient to screen the most suitable adhesion molecule. To screen the optimal adhesion molecule, the rupture forces, defined as the maximum force of molecule separated from GO sheet, of several adhesion molecules are first calculated by DFT simulation. A detailed methodological description can be found in our recent work (Xia et al., 2019). As shown in Fig. 5(a), the rupture force of amino-group triazines increases in turn with the increase of amino-group number compared with water, which is commonly utilized in the investigation of GNMs. This result corresponds to the experimental measurements, revealing that melamine is the optimal adhesion molecule in these candidate molecules. To detail the analysis, the rupture force of a single melamine as a function of hydrogen bond (HBond) number is calculated, shown in Fig. 5(b), demonstrating that the hydrogen bonds between nitrogen on triazine and hydroxyl (O–H···N–tri) dominates the rupture force. By fitting linearly the first three hydrogen bonds, its binding strength is obtained about 212.5 pN per HBond. In order to highlight the effects of small molecules such as melamine on mechanical improvement, the interfacial mechanical response of GO bilayer model are explored by performing MD simulations. As shown in Fig. 5(e), the interlayer of bilayer GO sheets is intercalated with a variable amount of melamine. Upon equilibration, the right edge of top GO sheet is subjected to a lateral sliding motion along x direction with a constant velocity of v = 2 m/s, whereas the lateral momentum of the left edge of bottom GO sheet is constrained to zero (Liu and Xu, 2014). Using this procedure, the interfacial shear stress can be calculated by dividing the tensile force F by the overlap area between bilayer GO sheets, and the interfacial shear strength is defined here as average interfacial shear stress during sliding. As shown in Fig. 5(f), an amount of melamine can largely enhance the interfacial shear strength from 68.4 MPa to 160.5 MPa. In addition, it also elucidates that the interfacial shear stress can be sustained to an approximately constant value around its shear strength during pullout process because of the mechanism of hydrogen-bonding breaking and reforming (Compton et al., 2012; Medhekar et al., 2010; Zhang et al., 2019). To quantitate the effects of melamine, the shear strength as a function of melamine content M, defined as the weight ratio of melamine molecules to carbon atoms in GO sheets, is investigated under various oxidation degree. As shown in Fig. 6(a), small quantities of melamine (M = 6.67%) can improve interfacial shear strength with variable oxidation degree (ϕ = 0 ∼ 50%) of GO sheet, and enhancement effect enlarges with the increase of oxidation degree ϕ . Thus, it can be concluded that low oxidation GO sheet with a little melamine can acquire higher interfacial shear strength in comparison with the native interface of high oxidation GO sheet. In other words, the interfacial shear strength for specific oxidation degree can be significantly boosted by increasing the melamine content (M = 0 ∼ 16%) of interlayer, as exhibited in Fig. 6(b). Meanwhile, comparing the increase rate in Fig. 6(a) and (b), we find that raising the melamine content in interlayer is more efficient to improve the interface shear strength than that of oxidation degree. As discussed in above DFT simulations, HBonds between melamine and GO sheets dominate the binding strength. Here, to elucidate the role of melamine in mediating interfacial load transfer, the analysis combining HBond and interfacial shear strength is adopted. Fig. 6(a) indicates that the enhancement in native interfacial shear strength of bilayer GO sheets tends to saturate with respect to the increase of oxidation degree, which extremely limit the mechanical properties of GNMs assembled by pure GO sheets. When analyzing their HBonds exhibited in Fig. 7(a), we can find that the total number of HBonds in bilayer model increases linearly with the raising of oxidation degree, while the rate of increase in HBond number between interlayer, which dominates the interfacial shear strength during sliding, drops sharply (logarithmic increase) with respect to oxidation degree ϕ , because HBonds within the GO sheets are easier to bond than that between interlayer by contrasting their donor-acceptor distance. As a result, it is not an efficient method through raising the oxidation of GO sheets to improve the number of interfacial crosslink, which has been previously expected to promote the interfacial shear

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600

(a)

1200

(c)

1000

400 800 300

O-H∙∙∙O

(d)

600 200 400

100 0

e ter azin wa tri

AT

A

ne TA mi DA mela

200

0

Adhesion molecules

2

3

4

v

fixed GO with melamine

fixed

6

O-H∙∙∙N

v

(f)0.25

M=0 M = 16.0% wt.

0.20

0.15

0.10

0.05

z y

5

Number of HBonds

GO

(e)

1

Shear stress (GPa)

Rupture force (pN)

500

(b)

x

melamine

0.00 0.0

0.5

1.0

1.5

2.0

2.5

3.0

Δ (nm) Fig. 5. (a) Histogram of the rupture force for 5 different adhesion molecules with GO sheets functionalized by a single hydroxyl, including water and aminogroup triazines (2-amino-1,3,5 triazine [ATA], 2,4-amino-1,3,5 triazine [DATA], and melamine) (Xia et al., 2019). (b) The rupture force as a function of the number of hydrogen bonds (HBonds) (Xia et al., 2019). The first three HBonds is between hydroxyl groups and nitrogen on triazine (O–H···N–tri), and the last point indicates the HBonds including all three interaction between hydroxyl groups and amino groups. (c) and (d) Hydrogen bond network, highlighted by green lines, in the interlayer between two GO sheets considered in MD simulations, (c) HBond formed between two hydroxyl group (O–H···O), (d) HBond formed between hydroxyl group and melamine (O–H···N–tri). (e) Two atomic structures of bilayer model, bare GO sheets and GO sheets with interlayer filled by melamine. (f) Interfacial shear stress as a function of pulling displacement with oxidation degree of 30%. The dashed lines indicates mean stress level for each set of sliding conditions.

strength (Gao et al., 2017; Wu et al., 2018). It also validates that a stronger interlayer noncovalent interaction is essential here to reinforce the native interface between GO sheets. For bilayer model with interlayer intercalated with melamine, the total number of HBonds first decreases slightly, and then increases apparently, as shown in Fig. 7(b). The effective HBond, defined as interlayer crosslink, includes O–H···N HBonds as well as O–H···O HBonds, which has opposite trends, respectively. With the increase of melamine content, O–H···N HBonds almost increases linearly, while O–H···O HBonds decreases monotonously. Consequently, there is an optimal melamine content, where the ratio between the effective HBonds and the total ones reaches its maximum value. As exhibited in Fig. 7(c), the optimal melamine content is around 10%∼13%. Obviously, the ratio of effective HBond still decreases with respect to oxidation degree. By plotting the shear force F as a function of effective HBonds with linear fitting, we observe that the binding strength of O–H···N HBond is much higher than that of O–H···O HBond, which are calculated as 262.1 pN and 49.7 pN, respectively. The binding strength of O–H···N HBond is slightly larger than that computed by DFT simulations, due to the mechanical interlocking, which enhances the interfacial sliding resistance. Overall, the enhancement of interlayer melamine mainly attributes to improving individual binding strength of HBond, rather than increasing the number of interfacial HBonds. Besides, by analyzing all these simulation results, we find that the shear modulus, obtained by fitting the linear stage of shear stress-strain curves, is nearly independent to both oxidation degree ϕ and melamine content

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Fig. 6. (a) The interfacial shear strength of bilayer GO sheets as a function of oxidation degree with different melamine contents. The solid lines are obtained by fitting MD simulation results using equation τϕ ϕ /(1 + Aϕ ). (b) The interfacial shear strength as a function of melamine content with different oxidation degree. The solid lines are fitted by formation of τM (1 + BM3/4 ) (Fitting parameters are listed in Table S1). The error bar in (a) are introduced to exhibit the fluctuation of stress during sliding.

Fig. 7. (a) Number of HBonds as a function of oxidation degree ϕ . Black points is the total HBonds of bilayer model, and red points is the effective HBonds. (b) Number of HBonds as a function of melamine content with oxidation degree ϕ = 30%. (c) The ratio of effective HBond as a function of melamine content with different oxidation degree. (d) Shear force F as a function of effective HBonds. Note that red symbols is the results deducting the contribution of O–H···O HBonds.

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Fig. 8. (a) Normalized Young’s modulus of RVE as a function of melamine content. The black solid line is obtained by Eq. (5). (b) Normalized tensile strength of RVE as a function of melamine content. The black and red solid lines are the results obtained by TSC model Eq. (7) and DTS chain model Eq. (6), respectively. The blue solid line is obtained by fitting the points between black and red solid lines.

M (seeing Fig. S5(b)). By analyzing multiple results from MD simulations, we can obtain the interfacial shear modulus about G0 = 0.173 GPa (more details can be found in Appendix D). 3.2. Effects on the RVE of staggered BM structure According to the nonlinear shear-lag proposed in Section 2, volume fraction  and interfacial toughness  should be determined by MD simulations. Here, we combine the MD simulations and shear-lag model based on the RVE to investigate the relation between the interfacial plastic properties and the interlayer intercalated with a variable amount of melamine. ˚ and the volume fraction MD simulation reveals that the distance of interlayer intercalated with melamine is about 0.8 A,  is 0.86∼0.87 with melamine content of 0 < M < 16%. According to Eq. (5), normalized Young’s modulus, Ee /Eg , is only as a function of k (k = Gc lg2 /Dg hc ), so Young’s modulus of the RVE is independent to both oxidation degree and melamine content, as shown in Fig. 8(a). However, situation is more complicated when it comes to the plastic properties of interlayer adhered by melamine. Fig. 2(a) demonstrates that the stretching strength of RVE with native interface is well described by TSC model, implying that its dimensionless interfacial toughness accords with  ≥ 1+k2 /4 for arbitrary length of RVE. As shown in Fig. 8(b), with the increase of melamine content, normalized tensile strength decreases until it reaches to the limit described by DTS chain model, in which the dimensionless interfacial toughness is assumed to be  = 1. This indicates that the interfacial toughness decreases with the increase of melamine content, because the interlayer interaction between GO sheets, dominated by the interlayer crosslinks such as π -π interaction and effective HBonds, is reducing as discussed in Section 3.1. It also exhibits that melamine molecules can provide slip lubrication for the interface between GO sheets. For simplicity, we assume that the dimensionless interfacial toughness  has a linear relationship with the melamine content M. By fitting the results shown in Fig. 8(b), the relationship between dimensionless interfacial toughness and melamine content with the RVE length of 40 nm is expressed as

=

50 13 − M 6 3

(21)

It should be pointed out that the dimensionless interfacial toughness  always satisfies  ≥ 1 given by Eq. (8). As a result, Eq. (21) is only established at M ≤ 7%, beyond which the dimensionless interfacial toughness is defined as  = 1. Therefore, there is an evident transformation of interface from completely plasticity to brittleness with the growing of melamine content. Combining the results fitted from Figs. 2(a) and 8(b), we conclude that the relationship between dimensionless interfacial toughness and melamine content for different length of RVE is approximately assumed to be a simple combination form of

  k 2  100M = 1 − 1+ 13

4

(22)

This assumption satisfies that the interface is completely plastic (TSC model) when there are no melamine molecules, while the interfacial toughness declines linearly as melamine content rises and can be reduced to Eq. (21) for the RVE length of 40 nm. Overall, this assumption is reasonable and well fits our MD simulations, suitable to be used for the following optimization design.

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Fig. 9. Representative nephograms of tensile strength in each stage as functions of oxidation degree ϕ as well as melamine content M for GNMs with different RVE length of (a) 10 nm, (b) 50 nm, (c) 100 nm, and (d) 800 nm. The red dashed line in plots indicates the transition of interfacial deformation from plasticity (below the dashed line) to brittleness (above the dashed line). The black dashed line is the boundary of failure mode between intralayer fracture (mode G, within the dashed line) and interfacial failure (mode I, outside the dashed line).

4. Optimization design of graphene-based nacre-like materials 4.1. Optimal melamine content and oxidation degree The interlayer mechanical properties quantified by our MD simulations demonstrate that the introduction of melamine molecules reinforces the interfacial shear strength but weakens the interfacial toughness. Therefore, there is a pathway by optimizing the GO oxidation degree (5% ≤ ϕ ≤ 50%) and melamine content (0 ≤ M ≤ 16%) for GNMs to achieve ultrahigh strength and toughness simultaneously. Figs. 9 and 10 show the effects of these two parameters (ϕ and M) on strength and toughness changing with the length of RVE. To optimize the overall effective tensile strength of GNMs, it should be noted that there exists two distinct failure modes (the interfacial failure mode I or the fracture of GO sheet mode G), where the one with lower value is selected as the effective tensile strength. Combining Eqs. (8), (9), and (22) with parameters τ cr and σ cr calculated from MD simulations (see appendix D and E), the tensile strengths as functions of oxidation degree and melamine content varying with RVE length lg are exhibited in Fig. 9, in which four typical strength nephograms are plotted. Then, the optimal oxidation degree ϕ and melamine content M toward optimum tensile strength of GNMs as a function of GO sheet length lg can be concluded by maximizing the value in each cloud diagram of strength, as shown in Fig. 11(a). It clearly reveals that the optimization strategy can be divided into four stages varying with the length of GO sheet. When the length lg of GO sheet is less than about 48 nm, the strength increases monotonously with the melamine content, and the optimum strength is obtained at the region of brittle interface with high oxidation degree, indicating that the interfacial shear carrying capability governs the strength of materials (stage Ⅰ in Fig. 11(a)). However, beyond the length lg ≈ 48 nm, the optimum strength is achieved at the region of plastic interface with a lower melamine content of M ≈ 4.5% but high oxidation degree (stage Ⅱ). This suggests that interfacial toughness begins to dominate the strength of materials. Then, the region of fracture of GO sheet (mode G) starts to appear and broadens for the length lg of GO sheet larger than 60 nm, as shown in Fig. 9(c) and (d). In this stage (Ⅲ),

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Fig. 10. Characteristic nephograms of toughness in each stage as functions of oxidation degree ϕ as well as melamine content M for GNMs with different RVE length of (a) 10 nm, (b) 50 nm, (c) 100 nm, and (d) 800 nm.

Fig. 11. The predicted optimum oxidation degree ϕ and melamine content M toward optimal tensile strength and toughness of GNMs as a function of lg . The blue region in (a) suggests the range of optimal melamine content.

there is a competition between mode I and mode G, both of which restricts continuous raising of the optimum strength. So the optimum strength increases with the reducing of oxidation degree. At last (stage Ⅳ), the left edge of mode G reaches its left boundary of oxidation degree when the length of GO sheet larger than 610 nm, as shown in Fig. 9(d). Consequently, the optimal melamine content spreads to the interval of 0∼13% between the upper and bottom black dashed lines on the boundary of ϕ = 5%.

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Analogously, the optimum toughness of GNMs can be calculated by incorporating Eq. (20) with the effects of oxidation degree and melamine content. It should be emphasized that the toughness is mainly dominated by interfacial energy dissipation Wf during pullout process when the GO sheet is long enough, much larger than the energy We dissipated during elasto-plastic deformation, resulting in that we need to balance oxidation degree or melamine content to avoid the fracture of GO sheet. As shown in Fig. 10(a), the toughness increases monotonously with oxidation degree and melamine content for the length of GO sheet less than about 35 nm (stage Ⅰ in Fig. 11(b)). Then (stage Ⅱ), the effect of interfacial toughness gradually surpasses that of interfacial shear strength, so the optimum toughness is achieved with lower melamine content of M ≈ 5%. As the length of GO sheet exceeds the critical length lg ≈ 60 nm, the optimum toughness is greatly impacted by fracture of GO sheet. In this stage (Ⅲ), there is a dramatic drop of the toughness on the boundary of transition from interfacial failure (mode I) to intralayer fracture of GO sheets (mode G), and the optimum toughness occurs around the edge out of region of mode G, as exhibited in Fig. 10(c). For the length of GO sheet beyond 10 0 0 nm (stage Ⅳ), the optimal melamine content toward the optimum toughness increases to around 13% as the region of mode G showing in Fig. 10(d) step by step occupies the one below the black dashed line. Fig. 11 illustrates the detailed evolution of the optimal melamine content M and oxidation degree ϕ as a function of graphene length lg to optimize the strength and toughness. When the length of GO sheet is small (lg less than 48 nm), we need to increase the melamine content and oxidation degree at the same time to maximize the strength and toughness. Interestingly, it is only necessary to reduce the oxidation degree and maintain a lower melamine content around 5% to ensure simultaneously high strength and toughness as the graphene length ranges from 48 to 610 nm. Beyond this length spectrum, the optimal melamine content toward the simultaneously optimum strength and toughness escalates until accesses its limit of M = 13% recovered by Eq. (22) with k → ∞. Usually, the length of GO sheet synthesized in experiments is on the order from a few hundred nanometers to dozens of micrometers (Lin et al., 2012; Wan et al., 2018), which is slightly larger than the scope regarded in our theoretical predictions. As a result, there are two optimization strategies depending on the size of GO sheet applied in realistic experiment. In the case of GO sheet shorter than 1 μm, the melamine content is selected between 5%∼10%, and correspondingly declines the oxidation degree. When the length of GO sheet above 1 μm, the optimal melamine content ranges 11%∼13%, while reduced graphene oxide (rGO) sheet should be employed instead. To sum up, synchronal optimization of the strength and toughness can be accomplished by matching optimal melamine content and oxidation degree with suitable characteristic length of GO sheet. Furthermore, it should be highlighted that melamine molecule performs a different role on strength and toughness. While the melamine molecule can strengthen interfacial shear stress to improve the strength of materials, it also weakens the interfacial toughness that adjust the stress in GO sheet to avoid its rupture. Hence, the melamine content in conjunction with oxidation degree here behaves as pair of regulators balancing the competition among the reduction of in-plane tensile strength of GO sheets, the improvement of the shear strength of interlayer, and the reduction of interfacial toughness, to achieve optimum toughness but still sustain relatively high strength of GNM. 4.2. Additional remarks on various crosslinks To expose the inelastic deformation on the toughness of GNMs with bone (Mercer et al., 2006), nacre (Wang et al., 2001) and other graphene-based materials, we plot them together on the material property chart in Fig. 12, which exhibits the normalized toughness, W/σ e , dependent normalized strength, σ e /Ee , for several synthesis materials in previous experiments, including Al2 O3 -PMMA hybrid material (Munch et al., 2008), GO/rGO paper (Dikin et al., 2007) and a series of graphenebased artificial nacre nanocomposites with different interface interactions (Zhang et al., 2016). The toughness of nacre and artificial nacre calculated by Eq. (20) is simplified as

W ∼

σe2 2Ee

+



 ε f − εep σe

(23)

where 0 < ε ep ≤ ε f , ɛep ≈ σ e /Ee . When ε f → ε ep , Eq. (23) is reduced to W ∼ σe2 /2Ee , and the material is completely brittle. For ε f >ε ep , W > σe2 /2Ee , and the material deforms inelastically. Accordingly, the inelasticity of nacre as well as artificial nacreous nanocomposite can be described by the scaling law of W/σ e ∼ β (σ e /Ee ), where β ∼ ε f /εep − 1/2 is a dimensionless parameter. β = 1/2 means brittleness of material and ε f = ε ep , while β > 1/2 indicates the plasticity of material and ε f > εep . As displayed in Fig. 12, bone, nacre and Al2 O3 -PMMA hybrid material are far away from the line of β = 1, with scaling parameters of β = 2.78, 3.57, 6.55, respectively, which well reflects the large plastic plateau in the stress-strain curve of those materials under uniaxial tension, so the scaling law plotted in Fig. 12 can be applied as a new evaluation criterion to unite the inner inelastic deformation and high performance of those artificial nacreous nanocomposites. However, most points from previous experimental results plotted in Fig. 12 representing graphene-based materials distributes in the area below the line of β = 1, which implies that these graphene-based materials mainly deforms through the failure of GO sheets instead of inner interlayer slipping. Although there are still several graphene-based materials above the line of β = 1, such as pure GO/rGO paper (β = 2.38) and H2 O-GO paper (β = 1.33), their strength and toughness are still lower than nature nacre. We attribute this distinction to the difference of their interlayer interactions, which govern the interlayer deformation. Conventionally, there are several typical crosslinks availed of reinforcing interfacial strength, including π -π , hydrogen, covalent, ionic bonding, and synergistic effects of above interactions, whereas they performs differently inherent mechanical properties. Covalent bond and ionic bonding are strong but brittle, while π -π interaction and hydrogen

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Fig. 12. Material property chart comparing material normalized toughness against normalized strength. The theoretical results for GNMs has been included for comparison with other graphene-based materials. The dashed lines are the isolines of failure strain formulated as W/σe = ε f − σe /2Ee . The experimental data and source references used in this figure are summarized in Table S2.

bonding are weak but recoverable (Cheng et al., 2014). For instance, GA, bonding GO sheets with covalent bond, can significantly improve the strength of GO paper but largely decline its failure strain (Gao et al., 2011), because such molecular interface engineering also destroys the in-plane sp2 -bonding of graphene sheets because of electron distribution reorganization, introduces additional defects like vacancies and adatoms, and then reduces the tensile properties of graphene sheets (Papageorgiou et al., 2017). Besides, the ionic bond usually works between adjacent intralyer GO sheets at their bridging edges, which strengthens the in-plane tensile carrying capability but limits energy dissipation in graphene-based materials (Park et al., 2008). All these reasons mentioned above causing the covalent or ionic bonding dominated GNMs are generally capable to realize ultrahigh strength while the promotion of toughness is disproportionate. For π -π and hydrogen bonding, they are the interlayer interactions and continuously reversible during shear slip, which enlarges the toughness of graphenebased material but may degrade its strength. For example, water can obviously enhance the toughness and failure strain of GO paper, but almost has no improvement on its strength (Gao et al., 2011), due to the fact that water molecules improve the probability interlayer slip but not apparently reinforce the binding strength of hydrogen bond between water and GO sheet (shown in Fig. S8). Therefore, the ultrastrong and reversible noncovalent interaction (e.g. melamine interacted with GO sheet) is the optimal interlayer crosslink, which can not only greatly enhance the interfacial shear strength like covalent and ionic bonding but also retain the capability of energy-dissipation similar to hydrogen bonding during pullout process of GO sheets. As illustrated in Fig. 12, once GNMs stressed by melamine molecules (as example), its strength and toughness can be simultaneously improved through both strength optimization and toughness optimization compared with nature bone, nacre and other artificial nacreous nanocomposites. While we have performed comparison with existing experimental studies, there are distinct differences between the theoretical analysis and those experimental studies. First, the staggered BM structure in MD simulations and theoretical analysis is symmetric without offset which may lead to higher strength and toughness in the simulations as compared to those expected at experimental structure. In addition, GO sheets in our staggered BM structure are defect free and wrinkle less, whereas in the experimental study, GO sheets usually consist of vacancies and wrinkles, which may lead to different strengthening mechanisms, e.g. chelation, as compared to the defect-free and wrinkle-less GO sheets that are considered in the present MD simulations (Chen et al., 2018). Nevertheless, the optimum design indicates that the GNM with strong interlayer noncovalent interaction does well mimic the deformation and remarkable mechanical properties of nature nacre, while outperforming previous GNMs by simultaneously reaching ultrahigh strength and toughness in the mechanical property chart. 5. Conclusion In summary, we performed MD simulations in conjunction with the development of modified shear-lag model to study the optimal strategy of simultaneously enhanced strength and toughness for graphene-based nacre-like materials reinforced by strong noncovalent interfacial interactions. A modified shear-lag model on account of the interlayer sliding and stability of staggered structure was proposed to describe the toughening effects during pullout process. It was found that both the interfacial shear strength and toughness serve as significant roles in strengthening mechanisms of graphene-based nacrelike material, while interlayer sliding during pullout process dominates its toughness. Then, based on previous experimental studies and our recent first principle calculations, we chose melamine molecule as optimal interlayer crosslink to tune the interfacial shear strength and toughness of neighboring GO sheets. Our MD simulations indicate that melamine bound to

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GO by anomalous hydrogen bonding can greatly enhance the interfacial shear resistance and maintain the interlayer energydissipation efficiency because of hydrogen-boning stick-slip mechanisms. Combining the modified shear-lag model and MD simulations, we gave the optimal melamine content and GO oxidation degree to achieve simultaneously high strength and toughness. Furthermore, a comprehensible scaling law emerged from the present theoretical model can be as the evaluation criterion to capture the relation between mechanical properties and inner interlayer slipping of the artificial nacre. Significant property enhancements of artificial nacre were observed when it was reinforced through the ultrastrong noncovalent interaction, where our graphene-based materials achieved synchronously superior strength and toughness as compared to previous synthesized graphene-based artificial nacreous nanocomposites. Although various nacre-like materials have been achieved in the past two decades, the conflicts between strength and toughness have not been well solved due to the neglect (or difficult realization) of effective tablet sliding and pullout. More recently, Yin et al. (2019) applied regular three-dimensional BM assembly with large-scale sliding of the bricks to toughen glass, demonstrating that tablet sliding mechanism in nacre-like materials can trigger nonlinear deformations over large volumes to improve toughness significantly. In our study, the modified shear-lag model can well consider the interlayer sliding and the stability of BM structure, subsequently, the large-scale MD simulations and associated theoretical predictions demonstrate that crosslink agent with strong noncovalent interaction can be as a promising strategy to strengthen and toughen GNMs simultaneously. Overall, this work not only sheds light on the fundamental enhancing mechanisms of graphene-based materials from molecular scale to their structures, but also provides guidelines for the design and optimization of a wide range of advanced functional materials. Declaration of competing interest The authors declare no competing financial interest. Acknowledgments This work was jointly supported by the Strategic Priority Research Program of the Chinese Academy of Sciences (XDB22040402), the National Natural Science Foundation of China (11525211, 11872063, and 11802302), and the Fundamental Research Funds for the Central Universities (WK2090 050 040, WK2090 050 043). The numerical calculations have been done on the supercomputing system in the Supercomputing Center of University of Science and Technology of China. Supplementary material Supplementary material associated with this article can be found, in the online version, at doi:10.1016/j.jmps.2019. 103706. 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