Anomalous scaling law of strength and toughness of cellulose nanopaper

The quest for both strength and toughness is perpetual in advanced material design; unfortunately, these two mechanical properties are generally mutually exclusive. So far there exists only limited success of attaining both strength and toughness, which often needs material-specific, complicated, or expensive synthesis processes and thus can hardly be applicable to other materials. A general mechanism to address the conflict between strength and toughness still remains elusive. Here we report a first-of-its-kind study of the dependence of strength and toughness of cellulose nanopaper on the size of the constituent cellulose fibers. Surprisingly, we find that both the strength and toughness of cellulose nanopaper increase simultaneously (40 and 130 times, respectively) as the size of the constituent cellulose fibers decreases (from a mean diameter of 27 μm to 11 nm), revealing an anomalous but highly desirable scaling law of the mechanical properties of cellulose nanopaper: the smaller, the stronger and the tougher. Further fundamental mechanistic studies reveal that reduced intrinsic defect size and facile (re)formation of strong hydrogen bonding among cellulose molecular chains is the underlying key to this new scaling law of mechanical properties. These mechanistic findings are generally applicable to other material building blocks, and therefore open up abundant opportunities to use the fundamental bottom-up strategy to design a new class of functional materials that are both strong and tough.The need for engineering materials that are both strong and tough is ubiquitous. However, the design of strong and tough materials is often inevitably a compromise as these two properties generally contradict each other (1). Toughness requires a material’s ability of dissipating local high stress by enduring deformation. Consequently, hard materials tend to be brittle (less tough); lower-strength materials, which can deform more readily, tend to be tougher (2, 3). For example, the toughness of metals and alloys is usually inversely proportional to their strength (4). Acknowledging such a necessary compromise, one would expect that research on advanced material design would be focused on achieving an optimum combination of these two properties. Indeed 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 of carbon nanotubes (CNTs), which exhibit remarkably high strength. However, it still remains uncertain how such a strong material can be incorporated with bulk materials to benefit from its high strength without sacrificing toughness.There have been tremendous efforts recently to develop materials with higher strength using smaller material structures. For example, by decreasing the grain size of metals, dislocation motions (thus plasticity) are more restricted, leading to a higher strength (5–10). However, such treatments also minimize possible mechanisms (e.g., crack-tip blunting) to relieve local high stress, resulting in lower toughness. The atomic scale origins of high strength of a material, e.g., strong directional bonding and limited dislocation mobility, are also essentially the roots for brittleness of the material. In short, the well-recognized scaling law of “the smaller, the stronger” comes at a price of sacrificing toughness (Fig. 1).Open in a separate windowFig. 1.An anomalous but desirable scaling law of mechanical properties requires defeating the conventional conflict between strength and toughness.The prevailing toughening mechanisms can be categorized into two types: intrinsic and extrinsic. Intrinsic toughening operates ahead of a crack tip to suppress its propagation; it is primarily related to plasticity, and thus the primary source of fracture toughness in ductile materials. Recent progress involves introducing high-density nanotwin boundaries in metals to achieve high strength and toughness (11–15). Intrinsic toughening mechanisms are essentially ineffective with brittle materials, e.g., ceramics, which invariably must rely on extrinsic toughening (2). Extrinsic toughening acts mainly behind the crack tip to effectively reduce the crack-driving force by microstructural mechanisms, e.g., crack bridging and meandering and crack surface sliding (16–18). A counterintuitive but successful example is the development of bulk metallic glass (BMG)-based composites, in which a crystalline dendrite second phase is introduced into the BMG matrix to promote the formation of multiple shear bands, leading to a strong and also tough material (3, 9, 16, 19–21). Intrinsic and extrinsic toughening mechanisms are also found to be effective in natural materials (e.g., bones and nacres), which often involve the hierarchical structure and/or a “brick-and-mortar” hybrid microstructure of the material (22–26). Nature-inspired toughening mechanisms are also used to synthesize biomimetic structural materials. Nonetheless, so far, there exists only rather limited success in attaining both strength and toughness, which often involve material-specific, complicated (e.g., growing high density nanotwins), or expensive (e.g., BMG-dendrite composites) synthesis processes and thus are hardly applicable to other materials. A general and feasible mechanism to address the conflict between strength and toughness still remains elusive.Aiming to shed insight on the long-sought strategy addressing the conflict between strength and toughness, we rationally design cellulose-based nanopaper and investigate the dependence of their mechanical properties on constituent cellulose fiber size. Surprisingly, we find that both the strength and toughness of the nanopaper increase simultaneously (40 and 130 times, respectively) as the size of the constituent cellulose building blocks decreases (from a mean diameter of 27 µm to 11 nm). These stimulating results suggest the promising potential toward a new and highly desirable scaling law: the smaller, the stronger and the tougher (Fig. 1). Though the increasing strength as the diameter of cellulose fiber decreases can be attributed to reduced intrinsic defect size, and the dependence is well captured by a continuum fracture mechanics model, our atomistic simulations reveal that facile formation and reformation of strong hydrogen bonding among cellulose chains is the key to the simultaneously increasing toughness. These mechanistic findings that underpin the highly desirable scaling law of mechanical properties suggest a fundamental bottom-up material design strategy generally applicable to other material building blocks as well, and therefore open up abundant opportunities toward a novel class of engineering materials 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 conventional paper. Cellulose has appealing mechanical properties, with specific modulus [∼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 and structural materials (27). Wood fibers are the main natural source of cellulose and have an intrinsically hierarchical structure (Fig. 2). A 20- to ∼50-µm-thick native wood fiber comprises thousands of nanofibrillated cellulose (CNF) fibers (5–50 nm in diameter), each of which can be disintegrated into finer elementary 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 hydroxyl groups in cellulose molecule (six in each repeat unit) enable facile formation of hydrogen bonds, both intrachain and interchain (Fig. 2). Whereas the intrachain hydrogen bonding stabilizes the linkage and results in the linear configuration of the cellulose chain, interchain hydrogen bonding among neighboring cellulose molecules plays a pivotal role in the deformation and failure behaviors of cellulose-based materials.Open in a separate windowFig. 2.Hierarchical structure of wood fibers and the characteristic of cellulose fibrils. Note the rich interchain hydrogen bonds among neighboring cellulose molecular chains.Open in a separate windowFig. S1.Atomic structure of a cellulose chain repeat unit. Note the six hydroxyl groups (red circles) in each repeat unit.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 (SI Text and Figs. S2 and ​andS3).S3). Cellulose nanopaper is made of a highly entangled random network of CNF fibers (Fig. 3A; Materials and Methods). Regular paper made of 27-μm native cellulose fibers with the same mass per area as the nanopaper is also fabricated as the control. The mechanical properties of both the cellulose nanopaper and regular paper are measured according to ASTM Standard D638 (details in SI Text).Open in a separate windowFig. 3.An anomalous scaling law of strength and toughness of cellulose nanopaper. (A) Schematic of cellulose nanopaper, made of a random network of CNF fibers. (Inset) High-resolution transmission electron microscopy (HRTEM) image of an ∼11-nm CNF fiber. (B) Stress–strain curves of cellulose paper made of cellulose fibers of various mean diameters. As the cellulose fiber diameter decreases from micrometer scale to nanometer scale, both tensile strength and ductility of the cellulose paper increases significantly, leading to an anomalous scaling law (C): the smaller, the stronger and the tougher. (D) Reveals that the ultimate tensile strength scales inversely with the square root of cellulose fiber diameter.Open in a separate windowFig. S2.(A) Optical microscope image of native cellulose fiber with a mean diameter of 27 μm. (B) Size distribution histogram. (C) AFM image of cellulose fibers with mean diameters of 28 nm. (D) Size distribution histogram. (E) HRTEM crystalline lattice image of fiber with a mean diameter of 11 nm. (F) Size distribution histogram.Open in a separate windowFig. S3.(A) A picture of a transparent cellulose nanopaper (made of CNF fibers of a mean diameter of 11 nm) on the university logo (Left). A schematic of fibrous nanostructure of the nanopaper is also shown (Right). (B) Optical transmittance of transparent cellulose nanopaper in visible and near-infrared range. (C) AFM image of cellulose nanopaper made of CNF fibers of a mean diameter of 28 nm. (D) AFM image and height scan of cellulose nanopaper made of CNF fibers of a mean diameter of 11 nm, showing rms at 1 × 1-μm scan size is 1.5 nm.