Anomalous scaling law of strength and toughness ofcellulose nanopaperHongli Zhua,1, Shuze Zhub,1, Zheng Jiab,1, Sepideh Parviniana, Yuanyuan Lia, Oeyvind Vaalandb, Liangbing Hua,2,and Teng Lib,2

aDepartment of Materials Science and Engineering, University of Maryland, College Park, MD 20742; and bDepartment of Mechanical Engineering,University of Maryland, College Park, MD 20742

Edited by William D. Nix, Stanford University, Stanford, CA, and approved June 10, 2015 (received for review February 14, 2015)

The quest for both strength and toughness is perpetual in ad-vanced material design; unfortunately, these two mechanicalproperties are generally mutually exclusive. So far there existsonly limited success of attaining both strength and toughness, whichoften needs material-specific, complicated, or expensive synthesisprocesses and thus can hardly be applicable to other materials. Ageneral mechanism to address the conflict between strength andtoughness still remains elusive. Here we report a first-of-its-kindstudy of the dependence of strength and toughness of cellulosenanopaper on the size of the constituent cellulose fibers. Surpris-ingly, we find that both the strength and toughness of cellulosenanopaper increase simultaneously (40 and 130 times, respectively)as the size of the constituent cellulose fibers decreases (from ameandiameter of 27 μm to 11 nm), revealing an anomalous but highlydesirable scaling law of the mechanical properties of cellulose nano-paper: the smaller, the stronger and the tougher. Further fundamen-tal mechanistic studies reveal that reduced intrinsic defect size andfacile (re)formation of strong hydrogen bonding among cellulosemolecular chains is the underlying key to this new scaling law ofmechanical properties. These mechanistic findings are generallyapplicable to other material building blocks, and therefore openup abundant opportunities to use the fundamental bottom-upstrategy to design a new class of functional materials that are bothstrong and tough.

strength | toughness | scaling law | cellulose | hydrogen bond

The need for engineering materials that are both strong andtough is ubiquitous. However, the design of strong and tough

materials is often inevitably a compromise as these two proper-ties generally contradict each other (1). Toughness requires amaterial’s ability of dissipating local high stress by enduring de-formation. Consequently, hard materials tend to be brittle (lesstough); lower-strength materials, which can deform more readily,tend to be tougher (2, 3). For example, the toughness of metalsand alloys is usually inversely proportional to their strength (4).Acknowledging such a necessary compromise, one would expectthat research on advanced material design would be focused onachieving an optimum combination of these two properties. In-deed much research effort is focused on pursuing higher strength,with rather limited corresponding regard for toughness (5–10).One example is the enthusiasm sparked by the discovery ofcarbon nanotubes (CNTs), which exhibit remarkably high strength.However, it still remains uncertain how such a strong materialcan be incorporated with bulk materials to benefit from its highstrength without sacrificing toughness.There have been tremendous efforts recently to develop ma-

terials with higher strength using smaller material structures. Forexample, by decreasing the grain size of metals, dislocation mo-tions (thus plasticity) are more restricted, leading to a higherstrength (5–10). However, such treatments also minimize possiblemechanisms (e.g., crack-tip blunting) to relieve local high stress,resulting in lower toughness. The atomic scale origins of highstrength of a material, e.g., strong directional bonding and lim-ited dislocation mobility, are also essentially the roots for

brittleness of the material. In short, the well-recognized scalinglaw of “the smaller, the stronger” comes at a price of sacrificingtoughness (Fig. 1).The prevailing toughening mechanisms can be categorized

into two types: intrinsic and extrinsic. Intrinsic toughening oper-ates ahead of a crack tip to suppress its propagation; it is primarilyrelated to plasticity, and thus the primary source of fracture tough-ness in ductile materials. Recent progress involves introducing high-density nanotwin boundaries in metals to achieve high strength andtoughness (11–15). Intrinsic toughening mechanisms are essen-tially ineffective with brittle materials, e.g., ceramics, which in-variably must rely on extrinsic toughening (2). Extrinsic tougheningacts mainly behind the crack tip to effectively reduce the crack-driving force by microstructural mechanisms, e.g., crack bridgingand meandering and crack surface sliding (16–18). A counterintu-itive but successful example is the development of bulk metallicglass (BMG)-based composites, in which a crystalline dendritesecond phase is introduced into the BMG matrix to promote theformation of multiple shear bands, leading to a strong and alsotough material (3, 9, 16, 19–21). Intrinsic and extrinsic tougheningmechanisms are also found to be effective in natural materials (e.g.,bones and nacres), which often involve the hierarchical structureand/or a “brick-and-mortar” hybrid microstructure of the material(22–26). Nature-inspired toughening mechanisms are alsoused to synthesize biomimetic structural materials. Nonetheless,so far, there exists only rather limited success in attaining bothstrength and toughness, which often involve material-specific,complicated (e.g., growing high density nanotwins), or expensive

Significance

A long-standing challenge in material design is to overcomethe conflict between strength and toughness, because they aregenerally mutually exclusive. To address this challenge, werationally design cellulose-based nanopaper and investigatethe dependence of their mechanical properties on constituentcellulose fiber size. Surprisingly, we find that both the strengthand toughness of the nanopaper increase simultaneously (40and 130 times, respectively) as the average diameter of con-stituent cellulose fibers decreases from 27 μm to 11 nm, sug-gesting the promising potential toward an anomalous buthighly desirable scaling law: the smaller, the stronger and thetougher. There are abundant opportunities to use the funda-mental bottom-up strategy to design a novel class of functionalmaterials that are both strong and tough.

Author contributions: L.H. and T.L. designed research; H.Z., S.Z., Z.J., S.P., Y.L., O.V., L.H.,and T.L. performed research; H.Z., S.Z., Z.J., L.H., and T.L. analyzed data; and H.Z., S.Z., Z.J.,L.H., and T.L. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission.1H.Z., S.Z., and Z.J. contributed equally to this work.2To whom correspondence may be addressed. Email: lit@umd.edu or binghu@umd.edu.

This article contains supporting information online at www.pnas.org/lookup/suppl/doi:10.1073/pnas.1502870112/-/DCSupplemental.

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(e.g., BMG-dendrite composites) synthesis processes and thus arehardly applicable to other materials. A general and feasible mech-anism to address the conflict between strength and toughness stillremains elusive.Aiming to shed insight on the long-sought strategy addressing

the conflict between strength and toughness, we rationally designcellulose-based nanopaper and investigate the dependence oftheir mechanical properties on constituent cellulose fiber size.Surprisingly, we find that both the strength and toughness of thenanopaper increase simultaneously (40 and 130 times, respec-tively) as the size of the constituent cellulose building blocksdecreases (from a mean diameter of 27 μm to 11 nm). Thesestimulating results suggest the promising potential toward a newand highly desirable scaling law: the smaller, the stronger and thetougher (Fig. 1). Though the increasing strength as the diameterof cellulose fiber decreases can be attributed to reduced intrinsicdefect size, and the dependence is well captured by a continuumfracture mechanics model, our atomistic simulations reveal thatfacile formation and reformation of strong hydrogen bondingamong cellulose chains is the key to the simultaneously increasingtoughness. These mechanistic findings that underpin the highlydesirable scaling law of mechanical properties suggest a funda-mental bottom-up material design strategy generally applicableto other material building blocks as well, and therefore openup abundant opportunities toward a novel class of engineeringmaterials that are both strong and tough.Cellulose is the most abundant biopolymer on Earth and has

long been used as the sustainable building block for conventionalpaper. Cellulose has appealing mechanical properties, with specificmodulus [∼100 GPa/(g/cm3)] and specific strength [∼4 GPa/(g/cm3)]higher than most metals and composites, and many ceramics,making it as a promising building block for functional andstructural materials (27). Wood fibers are the main naturalsource of cellulose and have an intrinsically hierarchical struc-ture (Fig. 2). A 20- to ∼50-μm-thick native wood fiber comprisesthousands of nanofibrillated cellulose (CNF) fibers (5–50 nm indiameter), each of which can be disintegrated into finer ele-mentary fibrils consisting of cellulose molecular chains (27–36).Cellulose molecule is a linear chain of ringed glucose molecules,with a repeat unit (Fig. S1) comprising two anhydroglucose rings(C6H10O5) linked through C–O–C covalent bond. Rich hydroxylgroups in cellulose molecule (six in each repeat unit) enable facileformation of hydrogen bonds, both intrachain and interchain(Fig. 2). Whereas the intrachain hydrogen bonding stabilizes thelinkage and results in the linear configuration of the cellulosechain, interchain hydrogen bonding among neighboring cellulosemolecules plays a pivotal role in the deformation and failurebehaviors of cellulose-based materials.In this study, cellulose fibers of different mean diameters [27 μm

(native fiber), 28 nm, and 11 nm, respectively] are isolated from

wood cell walls using a top-down approach and characterized (SIText and Figs. S2 and S3). Cellulose nanopaper is made of ahighly entangled random network of CNF fibers (Fig. 3A; Ma-terials and Methods). Regular paper made of 27-μm native cel-lulose fibers with the same mass per area as the nanopaper is alsofabricated as the control. The mechanical properties of both thecellulose nanopaper and regular paper are measured accordingto ASTM Standard D638 (details in SI Text).

Results and DiscussionsFig. 3B shows the typical tensile stress–strain curves of cellulosenanopaper made of fibers of mean diameters of 11 and 28 nm,and that of regular paper made of fibers of mean diameter of27 μm, respectively. Five samples of each mean fiber diameterare tested and the resulting stress–strain curves are consistent.The stress–strain curve of cellulose nanopaper made of 20 nmfibers in ref. 37 is also plotted in Fig. 3B.Table 1 lists the mechanical properties of the cellulose nano-

paper and regular paper measured from the stress–strain curves:ultimate tensile strength (measured by the maximum stress thatthe paper can sustain before fracture), toughness (work to frac-ture, measured by the area under a stress–strain curve), and tensilestrain at fracture, for mean fiber diameter of 11 nm, 20 nm, 28 nm,and 27 μm, respectively. The mean value and standard deviationof each property for each mean fiber diameter are calculated fromthe measurement of five samples.Fig. 3C shows the ultimate tensile strength and toughness of

the cellulose nanopaper and regular paper for four differentmean diameters of cellulose fibers. Surprisingly, as cellulose fiberdiameter decreases, both the ultimate tensile strength and tough-ness of the cellulose paper increase dramatically. As the meanfiber diameter decreases from 27 μm to 11 nm, the ultimate tensilestrength increases more than 40 times from 6.7 MPa (regularpaper) to 275.2 MPa (11 nm nanopaper); the toughness increasesnearly 130 times from 0.13 MJ/m3 (regular paper) to 11.68 MJ/m3

(11-nm nanopaper). Further measurements of the fracturetoughness (resistance to crack propagation) of the cellulose paperreveals the similar trend: the fracture toughness increases morethan 10 times (from 143.3 to 1,481.4 J/m2) as the mean cellulosefiber diameter decreases from 27 μm to 11 nm (Figs. S4 and S5).The increased toughness is a result of increased ultimate tensilestrength and failure strain with decreasing fiber diameters, as ev-ident in Fig. 3B. In other words, by tuning the constituent fiberdiameter, we demonstrate an anomalous scaling law of mechanicalproperties of cellulose nanopaper: the smaller, the stronger and

Fig. 1. An anomalous but desirable scaling law of mechanical properties re-quires defeating the conventional conflict between strength and toughness.

Fig. 2. Hierarchical structure of wood fibers and the characteristic of cel-lulose fibrils. Note the rich interchain hydrogen bonds among neighboringcellulose molecular chains.

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the tougher. There is no tradeoff between tensile strength andtoughness, a highly desirable feature in advanced material design.Fig. 3D shows the tensile strength of cellulose paper as a func-

tion of the mean fiber diameter, and clearly depicts the scaling lawof the smaller, the stronger, which can be attributed to the reducedintrinsic defect size in constituent cellulose fibers as their diameterdecreases, as justified below.Under tension, the initially entangled random cellulose fiber

network deflects and twists to align parallel to the tensile di-rection. As the tensile load increases, the straightened cellulosefibers begin to fracture, resulting in an overall failure of thepaper. This failure mechanism is supported by the SEM obser-vation of the fractured cross section of test samples, showing theCNF fibers are aligned along the tensile loading direction atfailure (SI Text). In this sense, the failure stress of an individualcellulose fiber gives a reasonable estimate of the overall tensilestrength of nanopaper. A theoretical fracture mechanics model(Fig. S6, details in SI Text) predicts that the ultimate tensilestrength of the cellulose nanopaper σUTS ∝ 1=

ffiffiffiffi

Dp

, with D beingthe mean fiber diameter. Fig. 3D demonstrates excellent agree-ment between such a theoretical prediction and experimentalmeasurement (from two independent sources: present study andref. 37) of the dependence of σUTS of cellulose nanopaper andregular paper on constituent fiber diameter over three orders ofmagnitude, and thus offers strong evidence for the above mecha-nistic understanding of the scaling law of tensile strength ofcellulose nanopaper.To further shed insight on the anomalous scaling law of

strength and toughness of the cellulose nanopaper, we also fab-ricate single-walled CNT (SWCNT) films with a thickness of20 μm using the same filtration and drying method as in cellulosenanopaper fabrication. The mean diameter of the constituentSWCNT bundles is 11 nm, comparable to that of the CNF fibersin our strongest and toughest cellulose nanopaper. Tensile test ofthe SWCNT films is executed under the same conditions as for thecellulose nanopaper. The fractured cross-section of the SWCNTfilm after the tensile test is examined with SEM (Fig. S7). Theinitially random network of SWCNTs aligns parallel to the loadingdirection before fracture, suggesting the similar deformation/failure mechanism as that of the cellulose nanopaper (Fig. S8).By contrast, the comparison of the stress–strain curves of theSWCNT film and cellulose nanopaper reveals significant dif-ference. Despite the exceptional mechanical properties of in-dividual SWCNTs (e.g., with a tensile strength of ∼100 GPa), theSWCNT film yields a tensile strength of 31 MPa, and a toughnessof 0.06 MJ/m3, consistent with the data reported in literature (38)but drastically lower (9 times and 195 times, respectively) thanthose of our cellulose nanopaper made of 11-nm CNF fibers.Based on the above results, we envision the following mech-

anistic understanding on the exceptional mechanical propertiesand anomalous scaling law of cellulose nanopaper: though theincrease in tensile strength of cellulose nanopaper is attributedto reduced defect size as the constituent CNF fiber size decreases(the smaller, the stronger); the simultaneous increase in toughnessessentially results from the significant increase of strong hydrogenbonding among CNF fibers as their diameter decreases (and thustheir surface area increases). Fig. 4 further clarifies the envisionedmolecular-level toughening mechanism of cellulose nanopaper.

Under tension, the initially entangled CNF network deflects andtwists to align parallel to the tensile direction. As the load increases,the straightened CNF fibers begin to slide relative to each other,and the pulling-off and fracture of such fibers eventually leads tothe overall failure of the nanopaper. Unlike covalent bonding,hydrogen bonding between hydroxyl groups readily reforms afterbond breaking due to interfiber sliding. If a cellulose fiber frac-tures under tension, the fractured segments remain bonded toneighboring fibers. In other words, mechanical failure of nano-paper involves both fiber fracture and a cascade of hydrogen bondbreaking and reforming events (as illustrated in Fig. 4), whichdissipate a significant amount of energy, and thus result in muchenhanced fracture toughness.By contrast, a SWCNT film lacks such a mechanism. Bonding

between SWCNTs in the film is essentially van der Waals (vdW)forces, which are much weaker than the hydrogen bonding betweenhydroxyl groups in the cellulose nanopaper. Therefore, pulling out aSWCNT from the film dissipates much less energy than pulling outa CNF fiber from the cellulose nanopaper, which explains the sig-nificantly lower toughness and tensile strength of the SWCNT filmcompared with the cellulose nanopaper.To confirm the above-envisioned mechanistic understanding, we

carry out atomistic modeling to simulate the key deformation andfailure process in both cellulose nanopaper and SWCNT films(details in SI Text).Fig. 5 illustrates the hydrogen bond breaking and reforming

process by a model that is representative of the molecular-level

Table 1. Mechanical properties for paper made from cellulose fibers with different diameters

Mean fiber diameter, nm Tensile strength, MPa Toughness, MJ/m3 Fracture strain, % Density, g/cm3 Specific strength, MPa/g/cm3

11 275.2 ± 25 16.9 ± 1 8.5 ± 0.5 1.2 229.2 ± 2120(37) 235.0 ± 21 7.26 ± 2.6 5.2 ± 1.228 208.3 ± 17 4.3 ± 0.2 2.9 ± 0.1 1.2 173.6 ± 1427,000 6.7 ± 0.7 0.13 ± 0.1 2.4 ± 0.1 0.8 8.3 ± 0.9

A C

B D

Fig. 3. An anomalous scaling law of strength and toughness of cellulosenanopaper. (A) Schematic of cellulose nanopaper, made of a random net-work of CNF fibers. (Inset) High-resolution transmission electron microscopy(HRTEM) image of an ∼11-nm CNF fiber. (B) Stress–strain curves of cellulosepaper made of cellulose fibers of various mean diameters. As the cellulosefiber diameter decreases from micrometer scale to nanometer scale, bothtensile strength and ductility of the cellulose paper increases significantly,leading to an anomalous scaling law (C): the smaller, the stronger and thetougher. (D) Reveals that the ultimate tensile strength scales inversely withthe square root of cellulose fiber diameter.

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deformation events in a cellulose nanopaper under tension. Acellulose bundle contains seven cellulose chains (each with fourrepeat units) that are packed in a pattern as in cellulose crystal sothat one cellulose chain is completely surrounded by other sixchains (Fig. 5A). We simulate the pulling out of the center chainfrom the bundle by applying a constant velocity on the right endof the center chain. Fig. 5B plots the variation of the total po-tential energy of the simulation model as a function of thepulling-out displacement, which clearly shows a zigzag fluctua-tion profile. Fig. 5B, Insets, reveal that the zigzag energy fluc-tuation captures the hydrogen bond breaking and reformingevents: the potential energy ramps up to a local maximum(e.g., first peak in Fig. 5B) as the hydrogen bond stretches tothe most, followed by a sudden drop of the potential energy to alocal minimum (the first trough), which corresponds to the hy-drogen bond with a constant velocity on the right end of thebreaking and hydroxyl groups relocating to a new bonding site.The potential energy then ramps up again and reaches next localmaximum, indicating the newly formed hydrogen bond stretchesto the most. The above events repeat until the center chain iscompletely pulled out of the bundle. Fig. 5C illustrates relativecellulose chain sliding, during which a series of hydrogen bondbreaking and reforming events happen when neighboring hydroxylgroups come close to each other. The boxed region shows theevolution of newly formed hydrogen bonding region during thepulling-out process. We believe that the combination of collec-tive strength of massive hydrogen bonds and the repeated energydissipation that is needed to completely separate two cellulosebundle surfaces (after a major series of hydrogen bond breakingand reforming events) renders the anomalous scaling law of themechanical properties of cellulose nanopaper, which is furthersupported by molecular dynamics simulation of the fiber-scaledeformation process in cellulose nanopaper and SWCNT films,as detailed below. The atomistic scale toughening mechanismenvisioned and proved above is in line with recent studies on theinterfacial energy between cellulose nanocrystals (39, 40). For

example, it is shown that hydrogen bonds can always reform de-spite the configuration of how the CNFs intersect each other (39).The deformation of cellulose nanopaper (or a SWCNT film)

under tension is accommodated by the relative sliding betweenneighboring CNF fibers (or CNT bundles). Such a relative slidingcan be decomposed into two sliding modes: parallel sliding andperpendicular sliding. Note that the surface area in direct con-tact in two neighboring fibers (e.g., within the range of effectivehydrogen bonding formation or vdW interaction) is often only asmall portion of the whole fiber surface. Under such a consid-eration, Fig. 6A shows the simulation model of the two surfaceareas in direct contact for parallel sliding between two CNF fi-bers (Fig. S9), each of which consists of an array of 6 × 3 cel-lulose chains, with 7 and 14 repeat units (i.e., 7.7 and 15.4 nm) ineach chain, and that between two SWCNT bundles, each ofwhich consists of 3 (15, 0) SWCNTs, with length of 7.8 nm and15.7 nm, respectively. Fig. 6B shows the corresponding simula-tions models for perpendicular sliding between two CNF fibersand that between two SWCNT bundles. Fig. 6C plots the vari-ation of total potential energy as a function of relative dis-placement of parallel sliding between two CNF fibers and thatbetween two SWCNT bundles. For the case of CNF fibers, zigzagfluctuation of potential energy is of substantial amplitude. Eachpeak in the curve corresponds to an energy barrier that the ex-ternal load needs to overcome (i.e., work done by the load) todrive the relative sliding between neighboring CNF fibers. Thevariation of total hydrogen bonding energy is also plotted in Fig.6C for comparison, which matches well with that of the totalpotential energy in terms of both peak location and amplitude,offering strong evidence for the cascade of events of hydrogenbond breaking and reforming during the sliding process and thedominant role of hydrogen bonding in the toughening mecha-nism of cellulose nanopaper. In other words, the sum of all of thework associated with the repeated breaking and reforming ofstrong hydrogen bonds among neighboring CNF fibers beforefinal failure essentially dominates the toughness of the cellulosenanopaper. Therefore, the scaling law of the smaller, the toughercan be readily understood by the fact that the contact area betweenneighboring CNF fibers (thus the total number of hydrogenbonds) increases significantly as the diameter of CNF fibers de-creases. By contrast, for the case of SWCNT bundles, the potentialenergy variation is of much smaller amplitude. The regular wavyprofile (with a period of ∼4.38 Å) suggests that the energy vari-ation corresponds to the periodic shift of atomic stacking (with aperiod of 4.26 Å) between the two neighboring SWCNT bundle.Parallel sliding between neighboring SWCNT bundles dissipatesmuch less energy than that between two CNF fibers.Fig. 6D plots the variation of the total potential energy as a

function of relative displacement of perpendicular sliding be-tween two CNF fibers and that between two SWCNT bundles. In

Fig. 5. Atomistic simulations to demonstrate the hy-drogen bond breaking and reforming events amongcellulose molecular chains. (A) Simulation model of acellulose bundle contains seven cellulose molecularchains. Top view only shows the middle three chainsfor visual clarity. (B) Variation of total potential energyas a function of the sliding displacement of the centercellulose chain out of the bundle. (Insets) Clearlyshown are the hydrogen bond breaking and reformingevents (dotted circles), each of which dissipates energy.(C) Relative cellulose chain-sliding, during which a se-ries of hydrogen bond breaking and reforming eventshappen (in boxed region) when neighboring hydroxylgroups come close to each other.

Subject to tension

Cellulose chain Hydrogen bonding

Fracture involves a cascade of hydrogen bond breaking and re-forming events

Fig. 4. Envisioned molecular-level toughening mechanism of cellulosenanopaper. Failure involves a cascade of hydrogen bond forming, breaking,and reforming events, which dissipate a significant amount of energy, leadingto much-enhanced fracture toughness of cellulose nanopaper.

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perpendicular sliding mode, the difference between the twocases becomes even more drastic. For the case of CNF fibers,there is first a significant increase in the total potential energy,followed by the zigzag nature of the energy fluctuation similar tothat in parallel sliding mode. The initial significant increase intotal potential energy results from the severe bending of thebottom CNF fiber (Fig. 6B, Inset). Such a severe bending furtherconfirms the strong hydrogen bonding between the two CNFfibers, a feature not existing in the SWCNT bundle case, whereboth SWCNT bundles remain nearly undeformed during slidingprocess. The severe bending of CNF fibers before perpendicularsliding occurs also contributes additional external work requiredto completely separate two perpendicular CNF fibers. The col-lective effect of these deformation features at individual CNFfiber scale leads to significant enhancement of both fracturestrain and toughness of the cellulose nanopaper. However, for thecase of SWCNT bundles, the variation of total potential energy isnearly negligible, which can be attributed to further reducedcontact area and even weaker vdW interaction in lack of com-mensurate stacking between two perpendicular SWCNTs.Fig. 6 E and F plot the evolution of resistant force when two

neighboring CNF fibers (and two neighboring SWCNT bundles)slide in parallel and perpendicularly to each other, respectively.In both sliding modes, the magnitude of resistant force in CNFfiber case is substantially higher than that in the SWCNT case,shedding light on molecular scale understanding of the hugedifference in tensile strength between cellulose nanopaper andSWCNT films.

Concluding RemarksWe rationally design and fabricate cellulose nanopaper by tuningthe diameter of constituent cellulose fibers, which allows forwhat is, to our knowledge, the first-of-its-kind investigation ofthe size dependence of mechanical properties of cellulose nano-paper. Surprisingly, we find that both the ultimate tensile strengthand toughness of the cellulose nanopaper increase significantly asthe constituent cellulose fiber diameter decreases, suggesting ananomalous but highly desirable scaling law of mechanical prop-erties: the smaller, the stronger and the tougher. The increase intensile strength of cellulose nanopaper is attributed to reducedintrinsic defect size as the constituent cellulose fiber size de-creases. A fracture mechanics model predicts that the tensilestrength of cellulose nanopaper inversely scales with the squareroot of cellulose fiber diameter, in excellent agreement with

experimental measurement over three orders of magnitude offiber diameter. The simultaneous increase in toughness essen-tially results from the significant increase of strong hydrogenbonding among cellulose fibers as their diameter decreases.Further atomistic simulations reveal the key mechanism under-lying this unconventional scaling law of mechanical properties:rich hydroxyl groups along cellulose molecular chains allow forfacile formation and reformation of strong hydrogen bondingamong neighboring molecular chains, which in turn dictate sig-nificantly enhanced resistance force and energy dissipation dur-ing intercellulose fiber sliding, and thus lead to both high tensilestrength and toughness of the cellulose nanopaper. Such mech-anistic understanding is further supported by control experiment,in which films made of SWCNT bundles of diameter comparableto that of cellulose fibers are shown to have drastically lowertensile strength and toughness, essentially due to rather weakvdW-type interactions in lieu of strong hydrogen bonding amongbuilding blocks.The findings from the present study shed fundamental insight

on the long-sought strategy addressing the conflict between strengthvs. toughness in engineering material design by envisioning a bot-tom-up design strategy to achieve both high strength and tough-ness that is generally applicable for a wide range of other materialbuilding blocks. The opportunities are abundant and multifaceted.There exists a wide variety of other biodegradable cellulose fibersand manmade fibers, with rich features in morphology, length,topology, crystallinity, and surface groups that can be furtherleveraged to enable both strong and tough cellulose based mate-rials under the same bottom-up design strategy (41–46). It is wellestablished that functional groups can be introduced to the surfaceand ends of CNTs (47–49). Properly functionalized CNTs (e.g.,with carboxyl groups) can enable strong inter-CNT bonding andsmaller CNT bundle size, holding promise toward strong andtough CNT films, another long-sought solution in nanocarbon-based materials. The fundamental bottom-up strategy can essen-tially go beyond 1D building blocks (tubes, wires, filaments)toward 2D building blocks [e.g., atomic layers of graphene oxide(GO), boron nitride, and molybdenum disulfide] and 1D/2D hy-brids. For example, it has been recently shown that hybridmicrofibers containing well-aligned and mixed 2D GO sheets and1D CNF fibers are both much stronger and tougher than themicrofibers made of pure GO sheets or CNF fibers, due to syn-ergistic enhancement of bonding between GO and CNF fibers(50). These fertile opportunities could lead toward a novel class of

Fig. 6. Relative sliding between neighboring CNFfibers vs. SWCNT bundles. (A) Simulation models ofthe two surface areas in direct contact for parallelsliding between two CNF fibers (Left) and that be-tween two SWCNT bundles (Right). (C) Variation oftotal potential energy as a function of relative dis-placement of parallel sliding between two CNF fi-bers (green) and that between two SWCNT bundles(blue). The contribution from hydrogen bonds be-tween CNF fibers (red) is included for comparison.(E) The evolution of resistant force during parallelsliding of two neighboring CNF fibers (red) and twoneighboring SWCNT bundles (blue). (B, D, and F)Results for the case of perpendicular sliding, in cor-respondence to A, C, and E, respectively.

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engineering materials that are both strong and tough with an arrayof potential applications, such as lightweight composites, flexiblepaper electronics, and energy devices.

Materials and MethodsThe CNF dispersion is degassed for 20 min in a bath sonicator until no bubblesare observed in the dispersion. The dispersion is poured into the filtrationapparatus containing a nitrocellulose ester filter membrane with a 0.65-μmpore size. The filtration time depends on the desired nanopaper thicknessand CNF diameter. After filtration, a strong gel forms on top of the filtermembrane. This gel “cake” is sandwiched between two smooth substratesand placed in a 40 °C oven for 10–15 min. The final nanopaper with a 90-mmdiameter, 30- to 50-μm thickness, and ∼1.2 g/cm3 density is obtained after a

70 °C hot press for 10–15 min. For control experiment, we prepare regularpaper from the Kraft bleached softwood (Southern Yellow Pine) pulp viafiltration with the same mass per area and the same pressure as the nano-paper. The regular paper thickness is ∼60 μm, with a density ∼0.8 g/cm3.

ACKNOWLEDGMENTS. We thank Peter Ciesielski in the National BioenergyCenter at National Renewable Energy Laboratory for the SEM characteriza-tion of Southern Yellow Pine hierarchical structure, and we acknowledgethe use of the Modern Engineering Materials Instructional Laboratory at theUniversity of Maryland for mechanical testing and the sharing of the Micro-fluidizer at the Biotechnology Research and Education Center. This work wassupported by National Science Foundation Grants 1362256, 1069076, and1129826 (to S.Z., Z.J., and T.L.), Department of Defense Air Force of ScientificResearch Young Investigator Program FA95501310143 (L.H.), and the MarylandNanoCenter’s FabLab and NispLab.

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