Organic Filling Mitigates Flaw-Sensitivity of ... - ACS Publications

Subscriber access provided by Washington University | Libraries

Article

Organic Filling Mitigates Flaw-Sensitivity of Nanoscale Aragonite Eduardo R. Cruz-Chu, Shijun Xiao, Sandeep Patil, Konstantinos Gkagkas, and Frauke Gräter ACS Biomater. Sci. Eng., Just Accepted Manuscript • DOI: 10.1021/acsbiomaterials.6b00504 • Publication Date (Web): 23 Dec 2016 Downloaded from http://pubs.acs.org on January 17, 2017

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a free service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are accessible to all readers and citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

ACS Biomaterials Science & Engineering is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

ACS Biomaterials Science & Engineering

Organic Filling Mitigates Flaw-Sensitivity of Nanoscale Aragonite Eduardo R. Cruz-Chú,†,‡ Shijun Xiao,¶,‡ Sandeep P. Patil,§,‡ Konstantinos Gkagkas,k and Frauke Gräter∗,⊥,‡ Computational Science and Engineering Laboratory, ETH Z¨ urich, Clausiusstrasse 33, Z¨ urich, Switzerland., Molecular Biomechanics Group, Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, Heidelberg, Germany., CAS-MPG Partner Institute and Key Laboratory for Computational Biology, Shanghai, China., Institute of General Mechanics, RWTH Aachen University, Aachen, Germany., Technical Center, Toyota Motor Europe NV SA, Zaventem, Belgium., and Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, INF 368, Heidelberg, Germany. E-mail: [email protected] Phone: +49 (0) 6221 533 267. Fax: +49 (0) 6221 533 298

∗

To whom correspondence should be addressed Computational Science and Engineering Laboratory, ETH Z¨ urich, Clausiusstrasse 33, Z¨ urich, Switzerland. ‡ Molecular Biomechanics Group, Heidelberg Institute for Theoretical Studies, Schloss-Wolfsbrunnenweg 35, Heidelberg, Germany. ¶ CAS-MPG Partner Institute and Key Laboratory for Computational Biology, Shanghai, China. § Institute of General Mechanics, RWTH Aachen University, Aachen, Germany. k Technical Center, Toyota Motor Europe NVSA, Zaventem, Belgium. ⊥ Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, INF 368, Heidelberg, Germany. †

1

ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Abstract Engineering at nanoscale holds the promise of tuning materials with extraordinary properties. However, macroscopic approaches commonly used to predict mechanical properties do not fully apply at nanoscale level. A controversial feature is the presence of nanoflaws in aragonite nacre, as it is expected that flaws would weaken the material, while nacre still shows high toughness and rupture strength. Here, we performed molecular dynamics and finite element simulations emulating flaws found in aragonite nacre. Our simulations reveal two regimes for fracture: nacre remains flaw-insensitive only for flaws smaller than 1.2 nm depth, or flaws of a few atoms, while larger flaws follow a Griffith-like trend resembling macroscopic fracture. We tested an alternative mechanism for flaw-insensitivity in nacre, and investigated the mechanical effect of organic filling to mitigate fracture. We found that a single nacre protein, perlucin, decreases the stress concentration at the fracture point, producing enhancements of up to 15 % in rupture strength. Our study reveals a more comprehensive understanding of mechanical stability at the nanoscale and offers new routes towards hybrid nanomaterials. Keywords : nacre, flaw-insensitive, Griffith’s theory, punctual stress, aragonite, perlucin

2


Page 2 of 39

Page 3 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Introduction Improving the mechanical properties of hierarchically structured materials relies on the characterization and understanding of their microstructure. A classical example is the increase in strength of a bulk material by adding microparticles that block lattice dislocations, hampering mechanical disruption. 1 Current advances in nanofabrication now allow us to tune materials even further, as the components can be adjusted all the way down to the nanoscale. However, size-dependent rules used to predict mechanical properties at the microscale do not necessarily apply within the dimensions of nanometers. 2 The key for understanding the mechanical properties of nanomaterials lies in a detailed characterization of their microstructure and their dynamics under load conditions. Nature offers us several working examples of mechanically robust materials built from nanoscale components. Nacre, tooth enamel, and bone combine inorganic nanocrystals with thin organic layers. 3,4 Although these biological materials are assembled using common natural constituents and mild conditions inside cells, their mechanical properties outperform any synthetic material, inspiring researchers to try to mimic nature to produce the next-generation of materials. 5–7 A thoroughly studied biological material is nacre, 8–10 which is located at the inner layer of seashells. Nacre features exceptional mechanical properties, such as fracture resistance, toughness and strength. Its high stability relies on the integration of CaCO3 crystal tablets (95%) and organic layers (5%) through elaborate hierarchical nanostructures. The CaCO3 tablets are shaped as polygonal disks of 5 to 10 µm in diameter and 0.5 µm in thickness, arranged parallel to the shell surface and piled over each other. The ordering also reaches the atomic level: CaCO3 crystals are present in the aragonite polyform with the [001] axis perpendicular to the disk surface. The platelets are nanocomposites formed from single aragonite crystals of about 30 nm depth. Remarkably, nacre is three orders of magnitude tougher than pure aragonite. 11,12 Such enhancement has been attributed to a combination of factors at the nano-scale level: interlocks between platelets through dovetail-shaped disks and mineral bridges across tablets, the nano-grained aragonite structure within platelets, 3



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 4 of 39

and mineral-protein interactions with organic molecules located between platelets 6,13 and inside single crystals. 14,15 The apparent simplicity of the nacre components (aragonite crystals, sugars and proteins) provides a good opportunity to test hypotheses about the organic-inorganic interface through modeling and simulations, which can contribute to our understanding of more complex biological materials or man-made nanocomposites. 16,17 Indeed, computer simulations have complemented benchwork studies, providing nanoscale views on nacre mechanics not available by experimental means; for example, revealing optimal ratios for flexible/brittle layers, 18 proposing nucleation mechanisms for aragonite tablets, 19 and dissecting the contribution of different nanoscale features to overall nacre toughness. 20 In this study, we focused on a controversial feature present in aragonite tablets, namely flaws of nano-scale depth. 21 Flaws are expected to be initiation points for cracks, thereby weakening the material. In contrast to this inherent destabilizing effect of flaws, Gao et al. 22 proposed that mineral tablets with a thickness of a few dozen nanometers or less are not weakened by flaws. This flaw-insensitive theory has been widely accepted and successfully applied to different systems. 23 Still, there is an active discussion about its validity, 24 and it has been proposed that other mechanisms present in biological materials may overcome the weakening caused by flaws. Under the effect of a disrupting load, a flaw focuses the mechanical stress at its tip. When the load reaches a critical stress value, so-called rupture strength, fracture strength, or σf , the stress at the tip is high enough to overcome the cohesive energy among molecules, forcing the material to separate into two surfaces. The cornerstone criteria for fracture of brittle materials was proposed by A. A. Griffith 25 as:

2Eγ σf = πa

1/2

,

(1)

which relates σf to the flaw depth a. The Young’s modulus E and the surface energy γ

4


Page 5 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


depend on physical characteristics of the material. In order to reconcile the high σf and the presence of flaws in nacre, flaw-insensitive theory states that a tablet is linked to a critical length (Wcr ); if the tablet depth is below Wcr , it has the intrinsic capability to tolerate flaws. 22,26 Since Wcr ≈ E γ σ −2 , where σ is the rupture strength for a flawless material, high strength samples as aragonite should require Wcr values in the order of dozens of nanometers. In the context of flaw-insensitivity theory, stress should concentrate around flaws to a smaller extent in nanometer-scale specimen than in macroscopic counterparts. Initial support for this theory came from computer simulations on graphene layers. 23 Nonetheless, an additional validation should come from an atomicdetailed model of aragonite. All-atom Molecular Dynamics (MD) simulations have previously been used to study crack propagation 27 for a variety of inorganic crystals, such as Si3 N4 , 28 SiO2 , 29 and GaAs. 30 Although those studies provided valuable insight into crack dynamics, a systematic analysis of aragonite flaw tolerance at nanometer scale is lacking. Moreover, the multiple roles of the organic layer in biological materials are still to be discovered. It is known that organic molecules regulate the entire mineralization process in nacre; namely calcium carbonate nucleation, inhibition, polyform selection, tablet morphology, and crystal orientation. 11 The fine-details of how those molecules work together are still concealed. Another open question is how the organic molecules contribute to the mechanical properties. Previously, atomic force microscopy and nanoindentation experiments have been used to study the mechanical response of the organic molecules with aragonite 31,32 and calcite, 33 revealing high strength at the mineral-organic interface. The presence of water at the interface 34 has been confirmed by fourier transform spectroscopy experiments, although how the solvent contributes to nacre mechanics is not clear yet. Moreover, Smith et al. 35 have shown that the thin organic matrices can bear large deformations, increasing the energy required to separate tablets in nacre. Computational studies have also been focused in this direction, 36,37 showing that the mechanical response of nacre proteins is enhanced by molecular contacts

5



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 ACS Paragon Plus Environment

Page 6 of 39

Page 7 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


aragonite tablets under load conditions using MD simulations (Figure 1), compare the results to macroscopic predictions carried out by Finite Element Analysis (FEA) and study a potential role for the organic molecules as fillings that mitigate the mechanical failure of nanoflaws. We chose a flaw geometry that closely resembles realistic nanoflaws in aragonite nacre. We found that aragonite tablets follow flaw-insensitivity theory only if very few CaCO3 atoms are removed; otherwise, nanoflaws weaken aragonite according to Griffith’s criterion. Subsequent analyses of the discrete stress distribution within a notched aragonite tablet revealed a force concentration that closely follows the continuum description used for macroscopic specimen. Finally, we show that an organic molecule can partially attenuate the destabilizing effect of nanoflaws, by balancing the internal stress acting on aragonite atoms at the rupture point. Our results provide a bridge between dynamics at atomic detail and current fracture mechanics theories used for biological materials and highlight the hybrid nature of nanocomposites to develop novel materials.

7



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 8 of 39

Methods Molecular dynamics (MD) simulations were carried out with the molecular dynamics program GROMACS. 40 Detailed description of the MD protocols are included in Supporting Information. For aragonite interactions, we used a modified version of a recently developed CaCO3 forcefield. 41 This force field have been shown to better reproduce aragonite mechanics than previously used force fields. Validation of the force field, parameter files, and a script-based tool to build aragonite crystals are provided in the Supporting Information. According to flaw-insensitive theory, a notched aragonite tablet with a flaw half its depth should behaves as a perfect flawless material as long as the tablet’s depth is below a critical length:

Wcr = α2

γE , σf2

where α is a geometry correction factor proportional to

(2) √

π. 22 Replacing the mechanical

values obtained from our aragonite model; 41 namely, E of 147.95 GPa, γ of 1.203 J m−2 , and σf of 5.2 GPa, we obtain a Wcr of 20.7 nm. We note that Gao et al. presented a variation based on a Dugdale model, 26 where the geometry correction has been replaced by:

Wcr = 1.87

γE , σf2

(3)

which results in Wcr of 12.5 nm for aragonite. Thus, the geometry factor can shift the estimated value Wcr . Therefore, to assess flaw-insensitivity on aragonite, we built aragonite models with a depth of 11.15 nm, which is smaller than the previous values and should remain flaw-insensitive for flaws up to 5.58 nm depth. All-atom aragonite tablets were built by replicating an aragonite unit cell. 41 We built two tablets with sizes of 15.38 × 11.15 × 2.30 nm and 25.30 × 11.15 × 2.30 nm along X-, Y- and Z-axes. The two tablets were minimized and equilibrated in the NpT ensemble for 10 ns at 300 K and 1.013 bar. The tablets did not show any significant changes in structural ordering nor cell dimensions. The last 8


Page 9 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


frames were used to create notched systems as follows: The simulation boxes were extended 12 nm along the X- and Y- directions; leaving empty space as required for tablet extension during pulling simulations. The periodic vector in the Z-axis was not extended, resulting in tablets of infinite length along Z-direction. By imposing periodic contacts at Z-axis, while adding empty space in X- and Y- axes, we are mimicking a 2-D system; thus, our results can be compared with previous studies about nanoflaw mechanics 23,42 that employ similar 2-D systems. Then, V-shaped flaws were introduced by removing atoms. Our flaw geometry was chosen to closely match experimental data about nacre flaws reported by K. Gries et al. 21 The cut lines followed the (101) and (¯101) lattice planes, 21 which resulted in an opening angle of 63.8◦ . Such cut lines impose the removal of one calcium atom per carbonate group, preserving the electroneutrality of the systems. The flaws were created using the formula: a = 0.4 nm × n; where a is the flaw depth in nm, and n is an integer that ranges from 0 to 22. Figure 1a shows an aragonite flaw model with n=7. Although our systems are highly simplified, their geometry is similar to the experimentally reported nacre voids (77±4◦ of opening angle and depths > 2.5 nm). 21 Since nacre flaws have hexagonal volumes, our edge-cracked systems can be considered as the tips of the voids. Different flaw geometries, such as circles or squares, would not represent the shape of nacre flaws. Moreover, round flaws are unstable at short times: flaw cuts must follow the crystal lattice planes; otherwise, aragonite charged ions would rearrange due to local charge imbalance, resulting in thin amorphous sub-regions at the flaw. Also, different angles for the cut lines would require the removal of additional atoms to keep electroneutrality, introducing extra crack points besides the tip. In total, 46 systems were built, ranging from 24,600 to 57,120 atoms. All systems were further equilibrated in the NVT ensemble for 10 ns at 300 K. To avoid tablet drifting, two cuboid volumes parallel to the (100) lattice plane were restrained, each cuboid volume containing the three outmost layers of CaCO3 atoms. After completing equilibration, we performed two groups of MD simulations in the NVT

9



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 10 of 39

ensemble. In the first group, we simulated the rupture of tablets. To mimic an external load, we performed Force Probe MD (FPMD) simulations. 43,44 The restrained layers were released and pulled outwards along the X-axis with a constant velocity of 1 nm ns−1 and a spring constant of 1000 kJ mol−1 nm−2 . This FPMD configuration, where the load is applied normal to the flaw axis, is known in mechanical engineering as loading mode I. 45 FPMD simulations were performed until tablet rupture, which usually occurred within 10 ns (Figure 1b). The point of σf is revealed in stress-strain curves as the only maximum, which is followed by a sharp drop. For each system, ten FPMD simulations were performed. Afterwards, we compared the rupture stresses from FPMD simulations to Griffith’s prediction (Equation 1). 25 We employed a geometry correction factor α which takes the dependence of √ the stress intensity factor, which for the opening mode I equals 2Eγ. For single edge notched tension of a semi-infinite tablet with flaw depth a and tablet height h, α reads: 46

α = 1.12 − 0.23

hai h

+ 10.55

h a i2 h

− 21.71

h a i3 h

+ 30.38

h a i4 h

.

In the second group, we evaluated the force concentration around flaws. We computed the atomic punctual stress using Force Distribution Analysis 47,48 (FDA), which allows to visualize the stress distribution induced by the external load. FDA compares the difference of internal forces of a system in stressed and relaxed states. For the stressed state, Force Clamp MD (FCMD) simulations were performed at constant force. The outermost layers were pulled, and the magnitude of the force was chosen to stretch but not to break the tablets. We applied forces of 41.5, 49.8, 58.1, and 66.4 nN, which correspond to 1.71, 2.05, 2.40 and 2.73 GPa of stress, respectively. For the relaxed state, the systems were equilibrated without any pulling. To prevent rotation of the tablets, four carbon atoms at the edges were restrained. For each system and state tested, ten independent FCMD simulations were performed, each one lasting 50 ns. For organic-aragonite simulations, we created an additional aragonite tablet of 25.30 × 11.15 × 4.60 nm with a V-shaped flaw of 3.6 nm depth. The increment in the Z-direction 10


Page 11 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


allows enough space to fit a biomolecule in the flaw. The tablet was equilibrated as described before. Our choice of organic molecule was perlucin (uniprot code P82596), a C-type lectin protein composed of 155 aminoacids (see Results and Discussion). We have chosen perlucin because its location at the aragonite surface through interactions with acidic side chains has been previously established. 11 We used a homology model 49 that covers residues 2-131. The missing residues were completed as random coils. An all-atom perlucin model was solvated in a water box of 10 nm, minimized and then equilibrated as follows: 1 ns in NVT ensemble with positional restraints in the protein, 10 ns in NpT ensemble and 100 ns in NVT ensemble without restraints. After that, the perlucin model was removed from the water box and placed above the aragonite flaw. The simulation box was extended 86 nm and 12 nm along the X- and Y- directions, the large empty space was needed to observe protein unfolding. In order to provide different organic-aragonite contacts, we used six different perlucin orientations, so-called conformations. Each conformation was obtained by 90◦ rotations around the X-, Y- and Z- protein axes. The six nacre-perlucin systems were equilibrated using two different protocols in NVT ensemble. In the first protocol, the tablet was restrained and perlucin was pushed downward with a force of 3.3 nN for 30 ns, forcing the protein to reach the flaw tip. Then, the pushing forces were removed and the system was further equilibrated for 30 ns. Finally, the tablet restraints were applied to only four carbon atoms at the edges and the system was equilibrated for 40 ns. In the second protocol, the tablet was restrained and perlucin was allowed to freely diffuse inside the flaw for 100 ns. In the Supporting Information, we include the root-mean-square deviation (RMSD) of perlucin equilibration, free in solution and within flaws. The RMSD plots show that perlucin structure is stable in both cases. After equilibration, each system was simulated ten times using FPMD setup. The core calculation for the atomic punctual stress relies on computing the sum of the P absolute values of the scalar pairwise forces acting on a atom i; that is: Fi = j |Fij |. Fi fluctuates strongly over time, and it was averaged over all trajectories. Fi was obtained

11



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

separately for stressed (Fis ) and relaxed (Fir ) states, and the difference ∆Fi = |Fis − Fir | reflects the corresponding atomic force change due to external stress. A common analysis tool for stress distribution is the virial calculation, which has extensively been used for fluid systems with high mobility, such as lipid membranes. 50,51 Compared to the virial calculation, FDA does not divide the system into spatial grids; thus, it has the advantage to pinpoint the force acting on specific aragonite atoms at the flaw tip, which is required as our system is a brittle solid. For Finite Element Analysis (FEA) of an aragonite tablet model, the commercial finite element analysis solver LS-DYNA (version: ls971s R5.1.1) 52 was used together with the analysis tool LS-Pre-Post. 53 Here, von Mises’s stresses are calculated. The concept of von Mises stress arises from the distortion energy theory, which is the most preferred theory in materials science and engineering. Stress is the internal resistance, or counter-force, of a material to the distorting effects of an external force or load. The dimensions of the aragonite tablets, including V-shaped flaws, were the same as in MD simulations. We used solid 8 node hexahedron elements (brick8), which are fully integrated solid elements (elform=2). A fine mesh was used near the flaw tip (see Supporting Information for a snapshot with a mesh). Analogous to the MD simulations, pulling forces were applied outwards on both sides. We considered two material models; an isotropic elastic material (∗mat elastic), and an elastic-orthotropic material (∗mat orthotropic elastic). For the former material, we considered a density of 2.95 g cm−3 , an elastic modulus of 144 GPa, and a Poisson’s ratio of 0.44. For the latter material, we considered a density of 2.95 g cm−3 ; elastic moduli of 144, 76, and 82 GPa for E1, E2, and E3, respectively. The Poisson’s ratios were 0.44 for V12, 0.06 for V13, and 0.18 for V23; and the shear moduli were 47.2 GPa for G12, 25.6 GPa for G13, and 41.3 GPa for G23. Both materials showed very similar stress distributions, and results of only the isotropically elastic model are shown.

12


Page 12 of 39

Page 13 of 39




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Next, we tested the cornerstone criterion for the fracture of brittle materials proposed by A. A. Griffith 25 (Equation 1), and asked how flaws impair the rupture strength of aragonite tablets at the nano-scale. Figure 2 presents the dependence of σf on flaw depth a. Overall, we find flaws larger than 1.2 nm (region II) to cause a significant drop in σf (triangles and squares). In region II, all fracture events occur at the flaw tips. The hyperbolic decay resembles the typical Griffith’s curve and shows nearly quantitative agreement with the macroscopic theory, when using typical values for E from 100 to 144 GPa and for γ from 1.20 to 1.87 J m−2 (grey shade). 54–56 For flaws smaller than 1.2 nm (region I), σf approaches a plateau around 5.2 GPa, which also is the rupture strength of flawless aragonite in our simulations. This value is near the theoretical strength of flawless minerals, which was estimated to lie in the range of 5 to 10 GPa. 57 In region I, our data strongly diverges from Griffith’s theory and show flaw-insensitivity. This mismatch can partially be attributed to a caveat in the continuum description: Equation 1 shows a singularity at a=0 and for low values of a overestimates σf . The tablet with the smallest flaws (a = 0.4 nm) was always torn at the pulling layer. For flaws with depths of 0.8 and 1.2 nm, 30% of the FPMD simulations showed tablet fracture at the flaw tip, the remaining 70% broke at one pulling layer. This suggests that beyond a critical size of the flaw (> 1.2 nm), stress sufficiently concentrates such that it initiates the crack right at the flaw, thereby impairing the rupture strength. Our findings show a discrepancy with the flaw-insensitivity theory, according to which a tablet smaller than 30 nm 22 (or 13.7 nm according to a later version of the theory 26 ) with a flaw of 50% of this depth should be flaw-insensitive. In our case, aragonite tablets with a depth of 11.15 nm are flaw-insensitive only for flaws smaller than 1.2 nm; about 10% of the tablet depth. Indeed, a flaw of half-depth results in a pronounced drop in σf from 5.2 GPa to 1.5 GPa (see Figure 2). The question arises if further reducing the width of nanocrystals to sizes below 11 nm might render crystals flaw-insensitive, which remains to be tested. However, the quantitative agreement between the atomistic (FDA) and continuum analysis (FEA) suggests the flaw-sensitivity to be a general phenomenon independent from the exact

14


Page 14 of 39

Page 15 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


length scales of the specimen. Also, nanocrystals within aragonite tablets have been found to be about 30 nm in size, rendering this question irrelevant to nacre. We note that we here considered crystals of a fixed height featuring flaws of increasing height, along Griffith’s theory, while flaw-insentivity assumed that flaw depths decrease with crystal size. 22

Stress Distribution at Flaw The good agreement with the Griffith’s criterion for a > 1.2 nm suggests stress concentration to occur at the nanometer scale to the same extent as at macroscopic scale. To quantify stress concentration, we calculated the internal stress distribution at the atomic level using Force Distribution Analysis (FDA) 47,48 and compared it to the macroscopic level using Finite Element Analysis (FEA) 58,59 based on a continuum description. Figure 3a shows the punctual stress as obtained from FDA for a tablet of 25.28 × 11.03 × 2.2 nm3 with a flaw of 3.6 nm depth, where fracture occurs at the flaw tip. We equilibrated this tablet in Force Clamp MD (FCMD) simulations at a constant external stress of 1.7 GPa, below the rupture strength of 2.7 GPa (see Figure 2). We obtained the molecular distribution of the external force within the calcium carbonate structure by computing the punctual stresses from the differences in forces of stressed and relaxed aragonite tablets (see Methods). The punctual stress exhibited a butterfly-like distribution, 42 with tilted elliptical panels on the sides that focus the stress intensity at the flaw tip. The stress distribution from FEA closely reproduced these features (Figure 3.b). Note that punctual stress distribution is slightly asymmetric; the reason being two-fold, namely the asymmetric molecular properties (or asymmetry in the unit cell) and in addition noise due to thermal fluctuations. To quantify the similarity between FDA and FEA, we superimposed those values. We compared the average punctual stress acting on carbon atoms from FDA to the stress value of each hexahedron element from FEA, both along the vertical (Figure 3c) and horizontal (Figure 3d) cross-sections encompassing the flaw tip. While both FDA and FEA show similar trends, they diverge within 2 nm towards the flaw tip and the boundary layers 15




Page 16 of 39

Page 17 of 39




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

acts as a nucleation center for crack propagation. Then, there is a competition of stress concentration between the flaw tip and the crystal defects at the pulling layers. For flaws ≤ 1.2 nm, the pulling layers tend to concentrate more stress than the flaw tip for different loads. Then, the fracture occurs close to the theoretical rupture strength, as if the tablets were flawless. For flaws > 1.2 nm, initially the pulling layers concentrate more stress than the flaw; however, as the load increases, the stress concentration at the flaw tip spikes, and fracture occurs along Griffith’s prediction; that is, σf decreases as the flaw depth increases.

Organic Filling in Nano-scale flaws As mentioned before, experimental studies have shown that nacre aragonite contains organic material within the nanoflaws. 21,38,39 We decided to investigate if such organic filling can contribute to the mechanical properties. It has not been possible yet to unambiguously identify those organic molecules; thus, we had to make some assumptions about the chosen molecule and its conformations within the void, which are justified below. Based on solubility assays and amino acid analysis, a set of putative candidates has been proposed, which includes the proteins perlucin, perlustrin and pelwapin. 11 Our choice of organic molecule was perlucin, 60,61 which is one of the most abundant proteins in Haliotis laevigata nacre and has been previously catalogued as intracrystalline protein. 11,62 In vitro studies have shown that perlucin promotes the formation of calcium carbonate crystals, 49,63 which further speaks for this choice: it has been proposed that proteins participating in crystal nucleation become incorporated into nanoflaws as the tablet grows in the interlamellar space. 64 To our knowledge, there is no high resolution structure of perlucin available yet, nor information about its epitaxial contacts with the aragonite surface. Thus, we resorted to a homology model. 49 Perlucin was placed on top of a notched tablet of 25.30 × 11.15 × 4.60 nm with a 3.6 nm flaw (Figure 5.a). To provide variability for the protein-aragonite contacts, we used six perlucin conformations (Figure 5.d), each conformation obtained by rotations 18


Page 18 of 39

Page 19 of 39




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

matter and aragonite surface. In group F, perlucin was pressed firmly against the void, reaching the flaw tip and increasing the contact surface. For group D, perlucin rested at the top of the flaw (Figure 5.c) and only for conformation number 6 the protein residues reached the flaw tip; this conformation also shows the highest σf in group D. To clarify this point, Figure 6 shows the number of residues in contact with the aragonite tablet. Panel 6.a shows two FPMD simulations, one for group F (black line) and one for group D (gray line), the protein in conformation 6 (see Figure 5.d). As expected, the system in group F has more protein-aragonite contacts than the system in group D. Moreover, group F trace requires more time to break than group D, resulting in a larger σf . For both F and D groups, the number of contacts oscillates around a constant value and finishes with a sharp drop, a confirmation that the protein remains strongly attached to the tablet until fracture. Panel 6.b shows the dependance of the number of contact residues with σf . The linear relationship is very clear, with a slope of 7.48 MPa per contact residue. The more contact residues, the higher σf . A plot showing the relationship between σf and different residue types is included in the Supporting Information. In previous studies, Ghosh et al. have reported a related result, 36,37 namely that the close contact between aragonite and Lustrin-A protein hardens the organic material. Our results reveal a tight and mutual interplay between both materials, as the mineral integrity also benefits from the organic molecules, which not only transfers load among tablets, but also stabilizes mechanical defects such as flaws. We note that even though confinements stabilize proteins in general, 65 we can not exclude the aragonite environment to strongly destabilize and structurally deform perlucin. However, our results suggest the strengthening effect not to depend on structural details but instead to represent a general phenomenon that primarily relies on number of contacts. The protein stretching was explored beyond the point of rupture strength. For group F, the FPMD trajectories show that perlucin keeps stretching, connecting both flaw sides even after complete aragonite rupture. A movie is included in the Supporting Information. In

20


Page 20 of 39

Page 21 of 39





Page 22 of 39

Page 23 of 39




1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Conclusions In this article, we studied the effect of nanoflaws on aragonite fracture using MD simulations. For flaws larger than 1.2 nm, we observe a Griffith-like trend, with strongly decreased fracture strength and fracture always occurring at the flaw tip. Force Distribution Analysis revealed a high concentration of stress at the flaw tip and pulling layers, which is critical to decide where fracture occurs and closely resembles the stress distribution expected for macroscopic objects of the same geometry. Our data thus suggests that for any flaws comprising more than just a very few atoms, stress concentration inevitably renders aragonite flaw-sensitive. Our MD simulations show similar profiles for the mechanics at the nano and macro scales. Thus, insensitivity to flaws is unlikely to be caused by the nanoscale dimensions and atomistic nature of the crystal. It instead is rather a result of the assumption that flaw sizes linearly decrease with the sizes of the crystals. 26 Why then can nacre be so strong, given the many flaws detected in nacre aragonite? Many toughening mechanisms of nacre have been previously described. As a new cornerstone, the results presented here suggest rupture strength to increase upon inserting a perlucin protein into a nanosized flaw of aragonite. The general strengthening effect of fillings in flaws by itself is not new, but that protein inclusions in aragonite flaws bridge the flaw surfaces sufficiently to mitigate the flaw-sensitivity of aragonite is a new plausible mechanism hitherto overlooked in the context of nacre. It is reasonable to hypothesize that the presence of multiple organic molecules in the flaw and more optimal interactions of perlucin’s charged sidechains with ions in aragonite than those achieved with our brute force MD simulations should increase σf even further. FDA calculations revealed that perlucin significantly decreases the stress concentration at the flaw, resulting in higher strength against breakage and toughness. We speculate that proteins filling up nanoflaws play a crucial role in relieving stress concentrations, given the high mechanical stability of charged protein-CaCO3 interactions. Taken together, our findings serve as a micrscoscopic interpretation of the enhancement 24


Page 24 of 39

Page 25 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


of nacre’s mechanics by the presence of organic material as observed previously. They also show that a comprehensive understanding of nacre mechanics relies on a detailed structural description of all components. Our results highlight the need of further improvements of computational models; for example, adding various organic molecules, proper epitaxial matching at the organic-aragonite interface, and realistic flaw volumes. Testing those scenarios computationally should shed further light on the manifold determinants of nacre’s strength.

25



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Acknowledgement The authors thank Prof. Pokroy at Technion - Israel Institute of Technology for providing us a Perlucin homology model. This work was financially supported by the Klaus Tschira Foundation, the DFG grant GR 3494/7-1, and Toyota Europe. The authors gratefully acknowledge the computing time granted by the John von Neumann Institute for Computing at J¨ ulich Supercomputing Centre in Juropa supercomputer (project HHD24). We also thank the PRACE committee for granting us supercomputer time at High Performance Computing Center Stuttgart in Hermit/Hornet supercomputers (project PP14102332).

Supporting Information Available Detailed description of the MD protocols, files with CaCO3 parameters, a script builder for aragonite blocks, a plot showing the dependence of aragonite Young’s modulus with force field parameters, a snapshot of all-atom punctual stress, a figure of finite element mesh, a movie showing pulling of an aragonite-organic system, RMSD plots for MD equilibration of perlucin, and dependance of σf with residue types are provided as Supporting Information. This material is available free of charge via the Internet at http://pubs.acs.org/.

26


Page 26 of 39

Page 27 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


References (1) Arzt, E. Acta Mater. 1998, 46, 5611–5626. (2) Greer, J. R.; De Hosson, J. T. M. Prog. Mater. Sci. 2011, 56, 654–724. (3) Barthelat, F. Philos. T. R. Soc. A 2007, 365, 2907–2919. (4) Yao, H. B.; Fang, H. Y.; Wang, X. H.; Yu, S. H. Chem. Soc. Rev. 2011, 40, 3764–3785. (5) Toohey, K. S.; Sottos, N. R.; Lewis, J. A.; Moore, J. S.; White, S. R. Nature Mat. 2007, 6, 581–585. (6) Espinosa, H. D.; Juster, A. L.; Latourte, F. J.; Loh, O. Y.; Gregoire, D.; Zavattier, P. D. Nat. Commun. 2011, 2, 173–1–173–9. (7) Liu, Y.; Yuan, W.; Shi, Y.; Chen, X.; Wang, Y.; Chen, H.; Li, H. Angew. Chem. Int. Edit. 2014, 53, 4127–4131. (8) Gilbert, P. U. P. A.; Metzler, R. A.; Zhou, D.; Scholl, A.; Doran, A.; Young, A.; Kunz, M.; Tamura, N.; Coppersmith, S. N. J. Am. Chem. Soc. 2008, 130, 17519–17527. (9) Barthelat, F.; Tang, H.; Zavattieri, P. D.; Li, C. M.; Espinosa, H. D. J. Mech. Phys. Solids 2007, 55, 306–337. (10) Li, X.; Chang, W. C.; Chao, Y. J.; Wang, R.; Chang, M. Nano Lett. 2004, 4, 613–617. (11) Heinemann, F.; Launspach, M.; Gries, K.; Fritz, M. Biophys. Chem. 2011, 153, 126–153. (12) Jackson, A. P.; Vincent, J. F. V.; Turner, R. M. P. Roy. Soc. Lon. B Bio. 1988, 234, 415–440. (13) Meyers, M. A.; ; Lin, A. Y. M.; Chen, P. Y.; Muyco, J. 2008, 1, 76–85. (14) Huang, Z.; Li, X. Sci. Rep. 2013, 3, 1693. (15) Huang, Z.; Pan, Z.; Li, H.; Wei, Q.; Li, X. J. Mater. Res. 2014, 29, 1573–1578. (16) Vaia, R. A.; Wagner, H. D. Matter. Today 2004, 7, 32–37. (17) Shin, M. K.; Lee, B.; Kim, S. H.; Lee, J. A.; Spinks, G. M.; Gambhir, S.; Wallace, G. G.; Kozlov, M. E.; Baughman, R. H.; Kim, S. J. Nat. Commun. 2012, 3, 650. (18) Wilbrink, D. V.; Utz, M.; Ritchie, R. O.; Begley, M. R. Appl. Phys. Lett. 2010, 97, 193701.

27



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(19) Sch¨ affer, T. E.; Ionescu-Zanetti, C.; Proksch, R.; Fritz, M.; Walters, D. A.; Almqvist, N.; Zaremba, C. M.; Belcher, A. M.; Smith, B. L.; Stucky, G. D.; Morse, D. E.; Hansma, P. K. Chem. Mater. 1997, 9, 1731–1740. (20) Askarinejad, S.; Rahbar, N. J. R. Soc. Interface 2014, 12, 20140855. (21) Gries, K.; Kr¨ oger, R.; K¨ ubel, C.; Fritz, M.; Rosenauer, A. Acta Biomater. 2009, 5, 3038–3044. (22) Gao, H.; Ji, B.; Jäger, I. L.; Arzt, E.; Fratzl, P. P. Natl. Acad. Sci. USA 2003, 100, 5597–5600. (23) Zhang, T.; Li, X.; Kadkhodaei, S.; Gao, H. Nano Lett. 2012, 12, 4605–4610. (24) Ballarini, R.; Kayacan, R.; Ulm, F. J.; Belytschko, T.; Heuer, A. H. Int. J. Fracture 2005, 135, 187–197. (25) Griffith, A. A. Philos. T. R. Soc. A 1921, 221, 163–198. (26) Gao, H.; Chen, S. ASME J. Appl. Mech. 2005, 72, 732–737. (27) Rountree, C. L.; Kalia, R. K.; Lidorikis, E.; Nakano, A.; van Brutzel, L.; Vashishta, P. Annu. Rev. Matter. Res. 2002, 32, 377–400. (28) Kalia, R. K.; Nakano, A.; Omeltchenko, A.; Tsuruta, K.; Vashishta, P. Phys. Rev. Lett. 1997, 78, 2144. (29) Rountree, C. L.; Prades, S.; Bonamy, D.; Bouchaud, E.; Kalia, R.; Guillot, C. J. Alloy. Comp. 2007, 434–435, 60–63. (30) Vashishta, P.; Bachlechner, M. E.; Campbell, T.; Kalia, R. K.; Kikuchi, H.; Kodiyalam, S.; Nakano, A.; Ogata, S.; Shimojo, F.; Walsh, P. Prog. Theor. Phys. Supplement 2000, 138, 135–170. (31) Mohanty, B.; Katti, K. S.; Katti, D. R. Mech. Res. Commun. 2008, 25, 17–23. (32) Mohanty, B.; Verma, D.; Katti, K. S.; Katti, D. R. MRS Symp. Proc. 2006, 975, 0975–DD03–03. (33) Sonnenberg, L.; Luo, Y.; Schlaad, H.; Seitz, M.; C¨ olfen, H.; Gaub, H. E. J. Am. Chem. Soc. (34) Verma, D.; Katti, K.; Katti, D. Spectrochim. Acta A 2007, 67, 784–788. (35) Smith, B. L.; Sch¨ affer, T. E.; Viani, M.; Thompson, J. B.; Frederick, N. A.; Kindt, J.; Belcher, A.; Stucky, G. D.; Morse, D. E.; Hansma, P. K. Nature 1999, 399, 761–763. (36) P. Ghosh, K. S. K., D. R. Katti Macromolecules 2007, 8, 851–856.

28


Page 28 of 39

Page 29 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(37) Ghosh, P.; Katti, D. R.; Katti, K. S. J./ Nanomater. 2008, 2008, 582973. (38) Yan, X. H.; Wang, S. N.; Zhang, X. J.; Wang, X. X.; Wang, R. CrysEngComm 2011, 13, 7202–7206. (39) Younis, S.; Kauffmann, Y.; Bloch, L.; Zolotoyabko, E. Cryst. Growth Des. 2012, 12, 4574–4579. (40) van Der Spoel, D.; Lindahl, E.; Hess, B.; Groenhof, G.; Mark, A. E.; Berendsen, H. J. C. J. Comput. Chem. 2005, 26, 1701–1718. (41) Xiao, S.; Edwards, S. A.; Gr¨ ater, F. J. Phys. Chem. C. 2011, 115, 20067–20075. (42) Buehler, M. J.; Abraham, F. F.; Gao, H. Nature 2003, 426, 141–146. (43) Grubm¨ uller, H.; Heymann, B.; Tavan, P. Science 1996, 271, 997–999. (44) Gr¨ ater, F.; Shen, J.; Jiang, H.; Gautel, M.; Grubm¨ uller, H. Biophys. J. 2005, 88, 790–804. (45) Anderson, T. L. Fracture Mechanics: Fundamentals and Applications, 3rd ed.; CRC Press, 2004. (46) Perez, N. Fracture Mechanics; Kluwer Academic Publisher Group, 2004. (47) Stacklies, W.; Seifert, C.; Graeter, F. BMC Bioinformatics 2011, 12, 101. (48) Costescu, B. I.; Gr¨ ater, F. BMC Biophysics 2013, 6, 5. (49) Weber, E.; Bloch, L.; Guth, C.; Fitch, A. N.; Weiss, I. M.; Pokroy, B. Chem. Mater. 2014, 26, 4925– 4932. (50) Gullingsrud, J.; Schulten, K. Biophys. J. 2004, 86, 3496–3509. (51) Vanegas, J. M.; Torres-Sánchez, A.; Arroyo, M. J. Chem. Theory. Comput. 2014, 10, 691–702. (52) Livermore Software Technology Corporation, LS-DYNA: Keyword User Manual ; 2010. (53) Livermore Software Technology Corporation, LS-Pre/Post; 2011. (54) Barthelat, F.; Espinosa, H. D. Elastic Properties of Nacre Aragonite Tablets. SEM Annual Conference and Exposition on Experimental and Applied Mechanics. 2003. (55) Barthelat, F.; Li, C. M.; Comi, C.; Espinosa, H. D. J. Mater. Res. 2006, 21, 1977–1986. (56) Forbes, T. Z.; Radha, A. V.; Navrotsky, A. GeoChim. Cosmochim. Ac. 2011, 75, 7893–7905.

29



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(57) Scholz, C. H. The Mechanics of Earthquakes and Faulting, 2nd ed.; Cambridge University Press, 2002. (58) Patil, S. P.; Market, B.; Gr¨ ater, F. Biophys. J. 2014, 106, 2511–2518. (59) Patil, S. P.; Xiao, S.; Gkagkas, K.; Market, B.; Gr¨ ater, F. PLoS One 2014, 9, e104832. (60) Mann, K.; Weiss, I. M.; André, S.; Gabius, H. J.; Fritz, M. Eur. J. Biochem. 2000, 267, 5257–5264. (61) Weiss, I. M.; Kaufmann, S.; Mann, K.; Fritz, M. Biochem. Bioph. Res. Co. 2000, 267, 17–21. (62) Evans, J. S. Bioinformatics 2012, 28, 3182–3185. (63) Dodenhof, T.; Dietz, F.; Franken, S.; Grunwald, I.; Kelm, S. PLoS One 2014, 9, e97126. (64) Suzuki, M.; Okumura, T.; Nagasawa, H.; Kogure, T. J. Cryst. Growth 2011, 337, 24–29. (65) Mittal, J.; Best, R. B. P. Natl. Acad. Sci. USA 2008, 105, 20233–20238.

30


Page 30 of 39

Page 31 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Graphical TOC Entry

31


a

b

ACS Biomaterials Science & Engineering Page 32 of 39

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 161nm 17

0 ns

a 9.52 ns

9.54 ns

9.56 ns ACS Paragon Plus Environment

I

II

Page ACS 33Biomaterials of 39 Science & Engineering 6 1.4

σf / GPa

1.2 I

σ

1 2 3 4 5 6 7 8 9 10 11 12 13

5

1.0 0.8

4

0.6 0

3

1

2

3

a / nm

4

5

2 1 0

ACS Paragon Plus Environment 0

1

2

3

4

5

a / nm

6

7

8

9

a

nN39 ACS Biomaterials Science & Engineering Page 34 of 3 2 1 0

GPa 7.6 5.7 3.8 1.9 0.0

d

102 101 100

ACS Paragon Plus Environment 15 -5 5 6 8 -15 2 4 X from vertix / nm from vertix / nm

10

Stress / 0.5 GPa

Punc. Stress / nN

1 2 3 4 5 6 7 8b 9 10 11 12 13 14 15 16 17 18 19 c 102 20 211 10 22 230 10 24 -1 25 10 26 0 27 Y

-1

0.5 1 10 2 0.0 3 10 4 -0.5 10 5 2.7 6 a 2.4 -15 GP 7 -10 -5 2.1 / 0 8 . 1.7 5 10 s s 15 X / nm e 9 Pr 10 11 12 1.5 10 13 1.0 14 10 15 0.5 16 10 0.0 17 10 18 -0.5 19 10 2.7 20 a 2.4 21 -15 -10 GP ACS Paragon Plus Environment 2.1 -5 0 / 22 1.7 . 5 10 s 23 15 X / nm es 24 Pr

b

P. Stress / nN

1.0

10

P. Stress / nN

a

Page 35 ACS of 39 Biomaterials Science & Engineering 1.5 10

a ACS Biomaterials c 36 of 39 b Science & Engineering Page 1 2 3 4 5 6 7 1nm 8 9 10 Conf.3 Conf.1 Conf.2 11 12 13 14 15 16 17 Conf.5 Conf.6 18 Conf.4 19 20 ACS Paragon Plus Environment 21 22 23

d

60

a

# contact residues

PageACS 37 of Biomaterials 39 Science & Engineering 50

σf / GPa

1 2 3 4 40 5 6 7 30 8 9 10 11 20 8 6 2 4 12 0 time / ns 13 14 2.9 15 16 17 182.8 19 20 21 222.7 23 24 25 262.6 27 ACS Paragon Plus Environment 28 29 20 30 40 50 30 # contact residues

b

10

2.9

ACS Biomaterials Science & Engineering Page 38 of 39 2.8

σf / GPa

1 2 2.7 3 4 2.6 5 6 7 2.5 8 9 ACS Paragon Plus Environment 2.4 10 5 3 1 4 2 11 Conformation

6

16

a

Punc. Stress / nN

Page ACS 39Biomaterials of 39 Science & Engineering

12

Punc. Stress / nN

1 2 3 8 4 5 6 4 7 8 9 0 10 -5 0 10 5 11 -15 -10 12 X from vertix / nm 13 14 1516 16 17 1812 19 20 21 8 22 23 24 4 25 26 27 0 ACS Paragon Plus Environment 28 6 0 4 2 29 30 Y from vertix / nm

15

b

8

Organic Filling Mitigates Flaw-Sensitivity of ... - ACS Publications

Recommend Documents