Molecular Mechanistic Origin of the Mechanical Properties of Nacre

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Molecular Mechanistic Origin of the Mechanical Properties of Nacre
Zhang, Ning
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[Gainesville, Fla.]
University of Florida
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1 online resource (159 p.)

Thesis/Dissertation Information

Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Mechanical Engineering
Mechanical and Aerospace Engineering
Committee Chair:
Chen, Youping
Committee Members:
Sawyer, Wallace Gregory
Gower, Laurie B
Taylor, Curtis
Phillpot, Simon R
Graduation Date:


Subjects / Keywords:
Aragonite ( jstor )
Atoms ( jstor )
Deformation ( jstor )
Eggshells ( jstor )
Grain boundaries ( jstor )
Mechanical properties ( jstor )
Minerals ( jstor )
Silicon ( jstor )
Simulations ( jstor )
Writing tablets ( jstor )
Mechanical and Aerospace Engineering -- Dissertations, Academic -- UF
biomineral -- md -- nacre -- protein -- toughness
bibliography ( marcgt )
theses ( marcgt )
government publication (state, provincial, terriorial, dependent) ( marcgt )
born-digital ( sobekcm )
Electronic Thesis or Dissertation
Mechanical Engineering thesis, Ph.D.


The objective of my dissertation research is to identify the mechanisms that give rise to the remarkable mechanical performances of nacre –combinations of stiffness, low weight, strength and toughness, which are unmatched by synthetic materials. Nacre is a hard iridescent biological composite found in the inner layer of some seashells such as oyster or abalone.It is a composite material that mainly composed of microscopic ceramic (an aragonite phase) tablets arranged in layers and tightly stacked to form a three-dimensional “brick-and-mortar” structure, where the mortar is a thin layer of bio-polymers with thickness of 20–30nm. Although aragonite is a very brittle ceramic, the addition of a small amount of organic polymer and the well-designed micro-structure make the toughness of nacre is several orders of magnitudes larger than that of aragonite.The toughening mechanisms involved in nacre have been the focus of numerous studies over the past two decades, because such understanding may inspire novel composite designs through bio-mimetics. In this work, molecular dynamics (MD)simulations and steered molecular dynamics (SMD) simulations are employed to investigate the mechanical properties of nacre tablet and to reveal the underlying deformation mechanism that give rise to the unbelievable mechanical performances. Firstly,we measured the mechanical properties of aragonite through nano-indentation,compression and tension. Simulation results were validated through comparison with experiment data and it is found that they are in good agreement with each other. Deformation mechanisms, for instance, phase transformation, dislocation and structure twinning was at the first time reported. ( en )
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Thesis (Ph.D.)--University of Florida, 2013.
Adviser: Chen, Youping.
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by Ning Zhang.

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2 2013 Ning Zhang


3 To my parents, my husband and my son


4 ACKNOWLEDGMENTS I would never have been able to fini sh my dissertation without the guidance of my committee members, help from friends, and support from my parents, my son and my husband. Firs t and foremost, I w ould like to express my sinc ere gratitude to my advisor Professor Youping Chen for t he continuous support of my Ph D study and research, for her excellent guidance, caring, patience, motivation, enthusiasm, immense knowledge and providing me with an exce llent atmosphere for doing research. Her guidance helped me in all the time of research, patiently correcting conference presentation slides, editing peer reviewed journal papers and writi ng of this dissertation. I could not have imagined having a better advisor and mentor for my Ph. D st udy. Without her guidance and persistent help this dissertat ion would not have been possible. Secondly, I would like to thank my Ph. D dissertation committee members, Prof. Laurie Gower, Prof. Simon Phillpot, Prof. Gregory Sawyer and Prof. Curtis Taylor for their encouragement, insightful comments, and hard questions. My sincere thanks also go to my fellow labmates in Multiscale Mechanics group Dr. Liming Xiong, Dr. Qian Deng, Mr. Shi Li, Mr. Shengfen g Yang, Ms. Xiang Chen, Mr. Rui Che, Mr. Zexi Zheng, Mr. Shikai Wang and Mr. Chen Zhang, for the stimulating discussion s, for the sleepless nights we were working together before deadlin es, and for all the fun we have had in the last four years. I would like to thank my parents and my little sister. They are always supporting me and encouraging me with their best wishes. Finally I would like to thank my husband,


5 Yu Hong, and my son, Eric Hong. They are always there cheering me up and stand by me through the good and bad times.


6 TABLE OF CONTENTS page ACKNOWLEDG MENTS .................................................................................................. 4 LIST OF TABLES ............................................................................................................ 8 LIST OF FI GURES .......................................................................................................... 9 LIST OF ABBREVI ATIONS ........................................................................................... 13 ABSTRACT ................................................................................................................... 14 CHAPTER 1 INTR ODUCTION .................................................................................................... 16 1.1 Background and Mo tivation .............................................................................. 16 1.2 Objectiv es ......................................................................................................... 17 2 STATE OF UNDERSTANDING .............................................................................. 22 2.1 Hierarchical Struct ure of Na cre ......................................................................... 22 2.2 Constituent I: Ar agonite Cryst al ........................................................................ 23 2.3 Constituent II: Nacr e Organic Matr ix ................................................................. 24 2.3.1 Interlamellar Po lymer – Chit in ................................................................. 25 2.3.2 Intracrystalline Pr otein Perl ucin ............................................................ 26 2.3.3 Intracrystalline Pr otein Lustr in A ........................................................... 27 2.3.4 Other Intracryst alline Protei ns ................................................................. 28 3 STATE OF ART RESEARCH .................................................................................. 34 3.1 Mechanical Perform ance of Na cre ................................................................... 34 3.2 Currently Proposed Toughe ning Mechanism of Nacre ...................................... 36 4 RESEARCH METHODS ........................................................................................ 44 4.1 Atomistic and Mole cular Dyna mics ................................................................... 44 4.1.1 Deformation Mechanisms in Silicon Nano-par ticles ................................ 47 Computer model and simulation det ails ........................................ 49 Resu lts .......................................................................................... 50 Summary and discussion s ............................................................ 57 4.2 Steered Molecula r Dynami cs ............................................................................ 58


7 5 NANOSCALE PLASTIC DEFORMATION MECHANISM IN SINGLE CRYSTALLINE ARAGONIT E .......................................................................................................... 67 5.1 Computation and Modeli ng ............................................................................... 69 5.1.1 The Comput er Model .............................................................................. 69 5.1.2 Interatomic Potentia l ............................................................................... 70 5.2 Results and Di scussion .................................................................................... 71 5.2.1 Nanoindent ation ...................................................................................... 72 The effect of peri odic boundary cond ition ...................................... 72 The effect of loading ra te ............................................................... 73 The crystallographic or ientation-dependent properties .................. 73 5.2.2 Uniaxial Tension ...................................................................................... 79 5.2.3 Uniaxial Co mpression ............................................................................. 81 5.3 Conclusi ons ...................................................................................................... 84 6 MOLECULAR ORIGIN OF THE SA WTOOTH BEHAVIOR AND THE TOUGHNESS OF NACR E ........................................................................................................... 101 6.1 Model and Method .......................................................................................... 103 6.2 Results and Discussions ................................................................................. 106 6.2.1 Protein Pulli ng Simulati ons ................................................................... 106 6.2.2 Water Effect on Protei n-mineral Inte raction .......................................... 109 6.3 Summa ry ......................................................................................................... 110 7 A NEW INSIGHT INTO TOUGHENING MECHANISM OF A MIMIC NACRE TABLET: MINERAL-PROTEI N COMPOS ITE ....................................................................... 119 7.1 Simulati on Details ............................................................................................ 119 7.2 Results and Di scussion .................................................................................. 124 7.3 Conclusi ons .................................................................................................... 128 8 DISCU SSION ........................................................................................................ 139 LIST OF REFE RENCES ............................................................................................. 142 PUBLICATIONS, CONFERENCES, POSTERS AND AWARD .................................... 156 BIOGRAPHICAL SK ETCH .......................................................................................... 159


8 LIST OF TABLES Table page 2-1 Organic matrices in biom enerals of aquatic animals ............................................ 30 3-1 Mechanical properti es of abalone nacre .............................................................. 40 4-1 Summary of silicon nanospher es ......................................................................... 60 5-1 A summary of the pot ential parameters of differen t models for ar agonite ............ 86 5-2 A summary of the co mputer models of nanoindentation ....................................... 86 5-3 Aragonite structure of CaCO3 ............................................................................... 87 5-4 Post-aragonite X structure of CaCO3 at pressure of 10GPa ................................ 87 5-5 A summary of de formation mec hanisms .............................................................. 87 6-1 The nacreous protei ns used in this study ............................................................ 112 6-2 A summary of the proper ties of the f our proteins ................................................. 112 7-1 Potential param eters for ar agonite ..................................................................... 130 7-2 A summary of de formation mec hanisms ............................................................ 130


9 LIST OF FIGURES Figure page 1-1 Performance of synthet ic and natural ma terials ................................................... 20 1-2 Single crystalline ar agonite under indentation, co mpression and t ension ............ 20 1-3 Complete amino acid s sequence of perlucin ........................................................ 20 1-4 Out-of-plane and in-pl ane pulling out si mulation. ................................................. 21 1-5 Schematic of nacr e tablets stru cture .................................................................... 21 1-6 Structure features mineral bridges, asperities, surface waviness of nacre ...... 21 1-7 Stress-strain relations of dr y and wet nacres under t ensile load ing ..................... 21 2-1 Hierarchical organizations in nacre s howing at least six stru ctural levels ............ 31 2-2 Structure of abalone shel l ................................................................................... 31 2-3 Mineral nanograins stru cture of sheet nacre ........................................................ 32 2-4 Growth bands of nacre ......................................................................................... 32 2-5 Struct ure of aragonite ........................................................................................... 32 2-6 Protein secondary structure elem ents. ................................................................. 33 2-7 Features of chitin .................................................................................................. 33 2-8 Schematic represent ation of the modular stru cture of lust rin A ............................ 33 3-1 Stress-strain curve for aragonite and nacre ......................................................... 41 3-2 Nano-asperities on the tablet surface ................................................................... 41 3-3 Mineral bridges ..................................................................................................... 41 3-4 Interlocking between platelets of nacre ................................................................ 42 3-5 Surface wavi ness of tabl et ................................................................................... 42 3-6 Models of biocomposit es ...................................................................................... 42


10 3-7 nanograins within an aragonite plat elet ................................................................ 43 4-1 The computer model of Si nanosphere under i ndentati on .................................... 61 4-2 Simulated load-displacement curves .................................................................... 61 4-3 Simulated stre ss-strain cu rves ............................................................................. 62 4-4 Side cross-section view of atomistic deformati on ................................................. 62 4-5 Side cross-sectional view of Si particle in nanoindentatio n .................................. 63 4-6 Atomic arrangments ............................................................................................. 63 4-7 Stress-strain respons es using SW potential ......................................................... 64 4-8 Stress-strain responses using Tersoff potential .................................................... 64 4-9 Snapshots of atomic structure bef ore the significant st ress dropoff .................... 64 4-10 Hardness vs model si ze in MD si mulation .......................................................... 65 4-11 Stress-strain curves of various atomis tic models ................................................ 65 4-12 Single molecule pulling experi ments .................................................................. 66 5-1 The orthorhombic unit cell of ar agonite ................................................................ 88 5-2 An MD indentati on model of ar agonite ................................................................. 88 5-3 Load-displacement (P-H) curves for sample 1 with di fferent BCs ........................ 89 5-4 Load-displacement (P-H) curves of sample 1 with different loading rates ............ 89 5-5 Load-displacement (P-h ) curves of indentation along a and c -axes .................... 90 5-6 Deformed strucutres at a displacement of 3.5 nm ................................................ 90 5-7 Side cross-sectional views of t he deformed structure in Fig. 5-6 ......................... 91 5-8 Comparison of atom ic structure diagrams ............................................................ 91 5-9 Radial distri bution functi ons ................................................................................. 92 5-10 Stress-strain curves for loading and un loading .................................................. 93


11 5-11 Atomic configurati on before and after unloading ................................................ 93 5-12 Unit cell structure of aragonite and post-a ragonite X ......................................... 94 5-13 Comparison of 3-D views of aragonite nad postaragonite X ............................. 94 5-14 Side cross-sectional view s of the transfo rmed regi on ........................................ 94 5-15 Side cross-sectional vi ews before and afte r unloading ...................................... 95 5-16 The MD computer model of aragoni te for uniaxial tensi on simulati on ................ 95 5-17 Stress-strain relation for singl e crystalline aragonite under tension ................... 96 5-18 Side cross-sectional views of aragonite under uniax ial tensio n ......................... 96 5-19 A schematic of dislocation nucleation and migration pr ocess ............................. 97 5-20 The 3-D MD model for single cr ystalline aragonite under compression ............. 97 5-21 Stress-strain curves for single crystalline aragonite under compression ............ 98 5-22 Snapshots of aragoni te under comp ression ....................................................... 98 5-23 Cross sectional view of atomic a rrangement ...................................................... 99 5-24 Side cross sectional vi ews of deformed structure .............................................. 99 5-25 Comparison of in itial aragonite structur e and compressed structure ................ 100 6-1 Schematic repr esentation of the init ial computer model ...................................... 113 6-2 Potential energy versus time during energy minimiza tion ................................... 113 6-3 Molecular structures of different proteins ............................................................ 114 6-4 Top views of computer models ............................................................................ 114 6-5 Force-extension curves measured in t he simula tions ......................................... 115 6-6 Snapshots of the atomic trajectory during pulling out si mulations ....................... 116 6-7 Comparison of the force-extensi on curves .......................................................... 117 6-8 Snapshots of the at omic arrangements before, at and after plateau region ........ 118


12 7-1 Initial atomic confi gurations of single crystalline an d polycrystalline aragonite .. 131 7-2 Schematic repres entation of protein-mineral composite model .......................... 132 7-3 Top views of miner al-protein composite model ................................................... 133 7-4 Stress-strain curves fo r different comput er models ............................................ 134 7-5 Snapshots of single cryst alline aragonite under tension .................................... 135 7-6 Side cross-sectional views of deforme d structure of polycryst alline aragonite ... 136 7-7 Comparison of atom ic structure diagrams .......................................................... 137 7-8 Radial distribution functi on (RDF) of calciu m-calcium ........................................ 137 7-9 Top views of atomic arr angement of mineral-p rotein composite ......................... 138


13 LIST OF ABBREVIATIONS AFM Atomic Force Microscopy MD Molecular Dynamics SMD Steered Molecular Dynamics


14 Abstract of Dissertation Pres ented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for t he Degree of Doctor of Philosophy MOLECULAR MECHANISTI C ORIGIN OF THE MECHANICAL PROPERTIES OF NACRE By Ning Zhang May 2013 Chair: Youping Chen Major: Mechanical Engineering The objective of my dissertation research is to identify the mechanisms that give rise to the remarkable mechanical performanc es of nacre – combinations of high stiffness, strength and toughness, low wei ght, which are unmatched by synthetic materials. In this dissertation, classi cal molecular dynamics (MD) simulations and steered molecular dynamics (SMD) simulati ons are employed to investigate the mechanical properties of nacre tablets and to reveal the underlying deformation mechanism that gives rise to t he unbelievable mechanical performances. Nacre is a hard ir idescent biological composite f ound in the inner layer of some seashells such as oyster or abalone. It is composed of 95-99% (by weight) calcium carbonate (calcite and aragonite). Although aragonite is a very brittle ceramic, combined with small percent (< 5%) of organic matrix it becomes much stronger and significantly much tougher than calcium carbonate crystals. Motivated by the exceptional mechanical properties of nacre, investigations on single crystalline aragonite, polycrystalline aragonite, and mineral-protein composites have been done in this dissertation.


15 MD simulation re sults show that mechanical properties of single crystalline aragonite strongly depend on the crystallographic orientati ons and loading conditions, which is demonstrated to be attributed to different deformation mechanisms, i.e., phase transformation, amorphous phase fo rmation, dislocation nucleat ion and crystal twinning. Different from the existing belief that protei n unfolding is the origin of the “saw-tooth” behavior in force-extension curves in AFM experiments, we have found that electrostatic interactions between protein and mineral are responsible for the “saw-tooth” behavior. Uniaxial tension simulation result s suggest that different computer models have different failure mechanisms. Com pared to single crystalline aragonite and polycrystalline aragonite, it is surprisingly obs erved from the mineral-protein composite that the ionic interaction between acidic/bas ic amino acids and calcium carbonate ions is so strong that Intr a-granular fracture is induced, whic h is believed to be a significant source of the high toughness of nacre.


16 CHAPTER 1 INTRODUCTION 1.1 Background and Motivation Natural materials can exhibi t superior mechanical properties and structural robustness, despite the brittle nature of t heir constituents. Bone, teeth and mollusk shell are fascinating examples of such high performance organic/mineral bio-composite materials, which exhibits incredible mechanical performances: high elastic modulus, high strength and high toughne ss. Generally speaking, t hese excellent mechanical properties of biomaterials cannot reach by synthetic materials, for instance, metals, alloy and ceramics. Fig. 1-1 (Espinosa et al. 2009) illustrates compared the different mechanical properties of syn thetic and bio-materials. The abalone nacre the inner layer of the shell, is one of the most extraordinary mineralized materials produced in biology. It is a remarkable biogenic composite material, which consists of 95 wt% ca lcium carbonate (aragonite) and 5 wt% organic materials but is 3000 tougher than aragonite (Wegst and Ashby, 2004). Nacre is made up of hexagonal tablets of ar agonite that arranged to form a “brick-and-mortar” structure. The width and thickness of “brick” are about 10-20 m and 0.5 m, respectively. The “mortar” is composed of biopolymers, whose thickness is around 20-30nm.Owing to its remarkable mechanical performance, nacre ha s caused a great interest to material researchers. The novelty of nacre has stim ulated many materials-oriented scientists to understand its mechanical properties and to fi gure out design strategies. During the past two decades, considerable research work has been carried out in designing artificial nacre-inspired materials, whic h could combine high modulus, high strength and


17 high toughness. However, almost all the me thods that have been devoted to producing artificial nacre are based on laminate pr ocessing, which proved to be unreachable currently. Therefore, to elucidate how nacre turns brittle minerals in to tougher materials presents a big challenge for t he material-oriented researcher. To elucidate the microstructu re mechanisms that govern remarkable mechanical properties of nacre, numerous studies hav e been done over the past decades including experimental, theoretical and computational approaches. Spec ial attention is given to simulation techniques that only Finite Elem ent (FE) method is adopted to measure the structural features effect, such as tablet interlocking (Katti et al., 2005) and surface waviness (Barthelat et al., 2007). However, c onsidering the hierarch ical structure of nacre from nano to micro scale Finite Element (FE) met hod is incapable of gaining insight into the deformation mechanisms from atomistic scale, which may significantly improve the toughness of nacre. Molecular dynam ics (MD) simulations are ideally suited for this purpose. It can reveal the underly ing deformation mechanisms from atomic nano-scale and to identify the chemical bonds rupture phenomen a. Accordingly, researchers can figure out the relation between deformation mechanisms and macroscale failure observations. 1.2 Objectives The objectives of this research includes investigating the deformation mechanisms of single crystalline aragonite under different loading conditions, revealing the molecular origin of “saw-tooth” behavior in forceextension curves from AFM experiment, and testing the role that protein plays in improving the work-offracture of mineral-protein composite in uniaxial tension simulations.


18 It is necessary to introduce the bi g picture of bio-inspired material development procedure. At the first st age, structure and mechanisms behind the performance of biological materials need to be understood. Then go to the next stage that design and fabricate tough bio-inspired com posites. Great attention will be given to the first stage, which could be divided into three steps. Firs t, optical microcopies such as AFM, SEM and TEM are needed to identify the structure characteristics of nacre. And then mechanical experiments like indentation and three-point bending need to be carried out to measure the mechanical properties of nacre After that, computat ional techniques, for instance, finite element (FE) and molecula r dynamics (MD) methods, are required to explore the underlying deformation mechani sm, which is happened to be my research objective, and provide clues for designing new materials. In this disse rtation, red abalone nacre was chosen to be investigated, based on how the hierarchical structure and other st ructural features, which have been detected through experimental techniques, control the outstanding mechanical performance of nacre. Based on atomistic molecular dynam ics (MD) and steered molecular dynamics (SMD) methods, the procedure and goals of our research are listed as following step by step: (1). The mechanical properties of nanograins i.e., single crystalline aragonite, in the tablet are first investigated through indentat ion, compression and tension as illustrated in Fig. 1-2. Simulation results are validated through comparison with experiment measurements. (2). Protein chains (Fig. 1-3) are gener ated through complete amino acids sequences as shown in Fig. 1-3, and then they are dragged into the grain boundaries of


19 polycrystalline aragonite using steered mole cular dynamics (SMD), through which a mimic tablet structure (mineral-p rotein composite) is built up. The complete amino acid sequence of perlucin (Weiss et al., 2000) is: G C P L G F H Q N R R S C Y W F S T I K S S F A E A A G Y C R Y L E S H L A I I S N K D E D S F I R G Y A T R L G E A F N Y W L G A S D L N I E G R W L W E G Q R R M N Y T N W S P G Q P D N A G G I E H C L E L R R D L G N Y L W N D Y Q C Q K P S H F I C E K E R I P Y T N S L H A N S Q Q R D S L H A N L Q Q R (3). Protein-mineral interaction is simulat ed through out-of-plane pulling (Fig. 1-4 (a)) to model the AFM experiment (Smith et al., 1999) of nacre. In-plane dragging (Fig. 1-4 (b)) is also simulated to measure the effect of water. (4). A 3-D tablet structure is generated and wate r is introduced into the grain boundaries. Indentation, bending, compression, tension simu lation of tablet structure is simulated and mechanical properties are com pared with the experiment results. (5). A “brick-and-mortar” tabl ets structure (Fig. 1-5) is built through the joining of interlamellar proteins. (6). Structural features such as mineral brid ges (Fig. 1-6 (a)) (Lin et al., 2007), asperities (Fig. 1-6 (b)) (Wang et al., 2001) and surface waviness (Fig. 16 (c)) (Barthelat et al., 2007) are brought into consideration. (7). Reproduce the high toughness (Fig. 1-7) of nacre as measured from experiment and reveal the underlyi ng toughening mechanism.


20 Figure 1-1. Performance of (a) synthetic and (b) natural materials in the stiffnesstoughness domain. (from Espinosa et al. 2009) Figure 1-2. Single crystalline aragonite under (a) indentation, (b) compression and (c) tension. Figure 1-3. Complete amino acids sequenc e of perlucin and one perlucin chain with green, red, blue and white color to denot e polar, acidic basic and nonpolar residues, respectively. (c) (b) (a) Nonpolar Basic Acidic Polar


21 Figure 1-4. (a) Out-of-plane and (b) In-plane pulling out simulation. Figure 1-5. Schematic of nacre tablets structure. Figure 1-6. Structure features (a) mineral bridges (b) asperities (c) surface waviness of nacre detected from experiments. Figure 1-7. Stress-strain re lations of dry and wet nacres under tensile loading. (from Barthelat, F et al., Phil. Trans. R. Soc. 2007) (b) (a) (c) (b) (a)


22 CHAPTER 2 STATE OF UNDERSTANDING 2.1 Hierarchical St ructure of Nacre As in most biologic al materials, nacre also exhibits hierarchical structures (Fig. 2-1) arranged from nanoto microscale. At m illimeter scale abalone shell exhibits two layers with distinct microstructures: a harder prismatic calcite outer layer (Fig 2-1, Fig 22(a)) and an iridescent softer and more ductile inner nacreous layer (Fig 2-1, Fig 2-2(b)), which is made of orthorhombic aragonite and various proteins. In the next micro-meter level, one can detected that aragonite t ablets are organized in “brick-and-mortar” structure and the inter-tablet boundaries are filled with bio-polymer s with thickness of 20nm to 50nm. It is usually believe that the polymers on grai n boundaries play a significant role in gluing aragonite platel ets together. The stack ed tablets are around 0.5 m in thickness and are aligned in horizontal lamellae and arranged in the vertical direction. In a high magnification level (nano-me ter), it is reported t hat the single tablet structure is composed of nanograins, whic h are divided by a continuous organic framework (Fig 2-1). With a hetero-epitaxy mechanism, nanogr ains in each tablet are proposed to have same crystal orientations wit h c-axis perpendicular to tablet surfaces (Rousseau, et al., 2005). Employed by atomic force microscopy (AFM) that can detect phase imaging, Figure 2-3 present s the structure of nacre tabl ets (Liu et al., 1992). It is widely believe that nanograins in tablets are flat with hexag onal shape (45nm in average length). TEM (Liu et al., 1992) was performed and evidences demonstrated that the some of the intr acrystalline aragonite nanograins responds as single crystal. Thus, the mineral phase although is divided by bio-polymers, still has the performance of single crystalline aragonite.


23 The second element in the hierarchical structure is the growth bands, which is also known as mesolayers, as presented in Fig. 2-4 (Lin et al, 2005). It can be seen that a mesolayers with approximately 300 m in thickness are separated by the organic material layers which are around 20 m in thickness. Although these layer were identified from experimental observation (Menig, 2000; Su, 2002; Lin and Meyers, 2005), they were seldom mentioned in the paper s with a purpose to measure mechanical properties of abalone shell. The hi ghly ordered hierarchical st ructure (Laraia et al., 1989; Vincent, 1991; Srinivasan et al., 1991; B aer, 1992; Heuer, 1992; Mayer, 2002 and Sarikaya, 1994), as illustrated in Fig. 2-1, has been speculated to have a significant influence on producing high strength and high toughness properties of nacre. 2.2 Constituent I: Aragonite Crystal Calcium carbonate, particularly in its aragonite phase, is a mineral of great geochemical and geophysical importance due to its being ubiquitous in natural systems, in both living organisms and inor ganic precipitates and sedi mentary rocks. Of all the many organisms, mollusk shell is one of the mo st extraordinary examples that is made up of calcite and aragonite with 95-99% in weight. Geologically, aragonite is predominantly found in the upper mantle. Although aragonite and calcite have t he same chemical formula, aragonite is served as a polymorph of calcite at room temperature and ambient pressure. They have different crystal structure, such as t he symmetry and crystal shapes. Aragonite, one of the carbonate minerals, has orth orhombic structure symmetry, as shown in Fig. 2-5 (a). It is made up of carbonate ion groups (CO3 2-) with triangular shape, in which a carbon atom is located in the center and three oxyg en atoms are located in the three corners.


24 Under standard temperature and pressures aragonite is technically unstable. But at higher pressures and lower temperature ar agonite could keep stable. With the increasing in temperature, it may transform into calcite, wh ich is the stable polymorph of calcium carbonate (Lucas et al., 1999). The mo st common crystal feat ure of aragonite is the twinned pseudo-hexa gonal prismatic crystal with what appears to be hexagonal surfaces (Fig. 2-5 (b-c)), which is wide-sp read in nature. These twinned crystals are considered as “triple twin”, in which each crystal takes 1200 of a hexagon. Thanks to the wide distribution and applications, aragonite has been comprehensively studied from both experimental and theoretic al viewpoints, including high pressure phase transition and mechanical behavior in nano-indentation. 2.3 Constituent II: Nacre Organic Matrix The organic elemen t, takes up to 1-5% in weight of nacre (Hare, 1965), is distributed in-between ( interlamellar ) (Nakahara, 1982; Belcher, 1996) and inside single tablets ( intracrystalline ) with strong connections (and St empfle et al., 2010;). The organic matrix between the mineral layers fo rms interlamellar horizontal sheets of 40 nm thickness, which are composed of s ublayers. The core is a highly ordered -chitin. In following chapters, the structure and characteri stic of interlamellar protein (chitin) and intracrystalline proteins (lustrin A, per lucin etc.) will be introduced in detail. The shell formation of mollusk is a ttributed to the highly cr oss-linked bio-polymers and the calcium carbonate crystals, which is the epithelial composite of mantle. During the formation process, these two kinds of ma terials elaborate a matrix, in which the spaces are filled with various macromolecul es (Addadi, et al., 2006). These matrices play a significant role both in nucleating and directing the growth of mineral element and


25 prevent the cracks protrusion through t he shell. The organic matrix has been conventionally classified as water-insoluble and water-soluble, based on its solubility in aqueous media after decalcification of the mineral phase. The aragonite tablets have hexagonal shape but with differences in si ze. They are trapped by the biopolymers (Nakahara, 1979, Weiner, et al., 1983), which consists of interlamellar horizontal sheets with 40 nm in thickness and intracrystalline proteins that distributed on the grain boundaries in a single tablet (Nakahara et al., 1982; Friz et al., 1994; Belcher, 1996). The interlamellar polymers are believed to connect aragonite tablets. According to Schaffer (1997), the interlamellar polymers hav e an insoluble core, mostly are highly ordered crystalline polymer -chitin. These chitins are tightly connected to form insoluble bio-polymer layers. It is widely accept ed that the intracryst alline organic matrix is mainly composed of aspartic acid proteins, such as glycine or serine, and in many cases glycosylated (Cusack and Freer, 2008). And intracrystalline proteins seem to influence and regulate the mineralization process, which include in ducing oriented nucleation, inhibition of crystal growth and control of polymorph sele ction (Cusack and Freer, 2008). It has been demonstrated in In vitro experiments that proteins in solu tion interact with calcite crystal and also induce the oriented nucleation of aragonite (Thompson et al., 2000). 2.3.1 Interlamellar Polymer– Chitin The major compoment of interlamellar organic matrix of nacre is chitin (Fig. 2-6 (a)). It is a nitrogen containing pol ysaccharide, which is made up of acetylglucosamine (Nacetyl-D-glucos-2-amine) units. T hese units are linked together with -1, 4 glucosidic bonds. According to Jeunieux (1971), chitin is in the -form with parallel chains (Fig. 2-6


26 (a)). Chitin is not only relatively hydrophobic silk polymer but also act as a complicated assemblage of hydrophilic organic matrices. It is reported that there are plentiful aspartic acid, on which proteins are bound, in -chitins (Lowenstam, 1989). According to the observations from X-ray (Weiner, et al., 1980, 1983) and the lattice images from TEM (Levi-Kalisman, 2001) the highly ordered -chitin has a unique crystallographic orientation, which usually can extend to mi cro-scale (Falini et al., 2003). In some uncommon situations, the orientation is observed to extend much longer. Chitin with the c hemical formula shown in Figure 27 (a), obtained after dissolution of the nacreous mineral phase Fig. 2-7 (b), presents a peculiar honeycomb pattern (Fig. 2-7 (c)) with 7-12 m in diameter. Chitin honeycombs are delimited by twisted protein filaments which form a network along the inte rspaces between aragonite tablets. Pores of 150 nm in diameter are obser ved in the middle of each comb as presented in Fig. 2-7 (d). Chitin is reported to be permeable to i ons and proteins that can easily diffuse during the shell growth (Weiss et al., 2000; Blank et al., 2003). It is hypothesized that the surface of the insoluble chitin matrix is coated with hydrophilic proteins, some of which are in contact with the mineral phase. These hydrophilic proteins may adopt a -sheet conformation similar to that of silk-fibroin protein and they may be orthogonally aligned with the chitin layer forming a plywood-like structure (Levi-Kalism an et al., 2001). 2.3.2 Intracrystalline Protein – Perlucin Perlucin (Fig. 2-6 (b)), one of the intracrystalline pr oteins, is the first water-soluble protein isolated from the nacre of H. laevigata It contains 155 amino acids and shows a molecular weight of ~17 kDa. These am imo acids include glycosylated asparagines (Mann et al., 2000). Perlucin has lots of ca rbohydrate-binding spots. It is a C-type


27 lectine organic matrix, in which the C-ty pe domain is made up of a C-terminal domain (short) and long residues (135 amino acids). The C-terminal domain is made up of two repeats of same residues (10 amino acids). Six cysteines were observed in the lectine domain, which is believed to act as a fo rmation of disulfide bonds (Weiss et al., 2000). In addition, perlucin has an am ino acid sequence similar to the “C-type carbohydrate-recognition domains of asialoglyc oprotein receptors” (B immler et al., 1997) of various organisms and lithostathine, a human pancreatic stone protein. Both of them are involved in the precipitation of CaCO3. Particularly, lithostathine seems to inhibit the precipitation of CaCO3. It also induces the formati on of stone after proteolytic processing in pancreatitis (G erbaud et al., 2000). Perlucin has been observed as a nucleation promoter of CaCO3 in solutions through in vitro studies (Weiss et al., 2001). It can also modify the morphol ogy of a calcite crystal su rface inducing the epitactic growth of new mineral layers, which show a peculiar round shape (Treccani et al., 2006; Blank et al., 2003). 2.3.3 Intracrystalline Protein Lustrin A Lustrin A (Fig. 2-6 (c)) from Ha liotis Rufescens, is a large multi-domain protein known to perform several functions (Smi th, et al., 1999) that has been most widely studied. Through analyzing the modul ar structure, people found t hat lustrin A consists of both proline(8) and cysteine(10) rich dom ains, as presented in Fig. 2-8. These proline-rich domain act as extenders to allow the cysteine-rich domain work independently. Shen et al. (1997) have demons trated that the cysteine-rich domain controls the mineralization of nacre. Proline -rich domains are typically considered to act as spacers between cysteine domains. During the shell formation, the arginineand


28 lysine-rich basic residues at the end of the cysteine domain wil l be interacted with anionic residues. Additionally, Lustrin A has a domai n of 275 residues (Fig. 2-8), of which 250 are either glycine (G) or serine (S). This is one of the largest discrete structural domains in Lustrin A. The secondary stru cture analysis of this domain in dicates that it is not only rich in “turns” but also rich in glyci ne loops. These types of domains have close homology with proteins such as keratin and lo ricrin (Hohl et al., 1991). Concerning the mechanical properties, as suggested by S hen et al. (1997), th is type of domain possesses high elastic property that enables it to function as an extensor molecule. Zhang et al. (2002) have shown that elastic GS loops, which are characteristics of this domain, could prevent the fracture and s eparation of mineral phase. Functional and structural homology study of this domain leads to the understanding that this domain has significant structural contribution as fa r as the overall behavior of the whole protein Lustrin A is concerned. 2.3.4 Other Intracrystalline Proteins Perlwapin is a recently identified solubl e protein from the abalone shell Haliotis laevigata Compared with other proteins, the am ino acid sequence of perlwapin shows a high relation with whey acidic protein (WAP) which are small domains consisting of 40 50 amino acid residues with a characteristic four disulphide-core pattern (Simpson, 2002), and a WAP domain has been also identifi ed in lustrin A. Since perlwapin shows a specific binding affinity for certain calcit e surface with consequent inhibition of crystal growth, it may have an effect on the growth of single aragonite tablet, which present uniform size in the three spatial directions. Pe rlwapin also plays an important role in the


29 polymorph transition, which inhibits calcit e growth and meanwhile allows aragonite formation (Treccani et al., 2006). Perlinhibin is a minor component of the water-soluble protein fraction (approximately 3 g/shell) in nacre. Perlinhibin inhibits in vitro the growth of calcium carbonate crystals. Similar to perlwapin, perlinhi bin binds specifically to certain faces of calcite crystals and inhibits the growth of new crystal layers at its binding sites (Treccani et al., 2006). Perlustrin is also a minor component of the so luble protein fraction that isolated from abalone Haliotis laevigata (approximately 10 g/shell). Perlustrin is a member of the IGFBP family. It is the first time one of them are isolated from the invertebrate. The presence of an IGFBP in nacre could suppor t the idea that biominerals such as bone and nacre may contain elements generated fr om the ancestors (Weiss et al., 2001). Perlbikunin is a very minor component of the water-soluble nacre proteins (approximately 0.1 g/shell). It seems be involved in the stabilization of the nacre organic matrix and controlling of mineralizat ion processes (Mann et al., 2007) but its role is still under investigation. To sum up, Table 2-1 lists the intracrysta lline proteins that have been identified from aquatic animals through experiment al investigation so far.


30 Table 2-1. Organic matrices in biominerals of aquatic animals. Species Compound No. of aa residues or molecule mass Reference Haliotis rufescens Lunstrin A 1,428 aa (116 kDa)Shen et al., 1997 Haliotis laevigata Perlucin 17 kDaWeiss et al., 2000 Haliotis laevigata Perlustrin 13 kDaWeiss et al., 2000 Haliotis laevigata Perlwapin 25 kDaTreccani et al., 2006 Pinctada fucata Nacrein 429 aaMiyamoto et al., 1996 Pinctada fucata MSI60 717 aa (60 kDa)Sudo et al., 1997 Pinctada fucata MSI31 315 aa (31 kDa)Sudo et al., 1997 Pinctada fucata N16 108 (110) aa (16 kDa)Samata et al. 1999 Pinctada fucata Pearlin 108 aaMiyashita et al. 2000 Pinctada maxima N66 546 aaKono et al. 2000 Pinctada maxima N14 115 aaKono et al. 2000 Patinopecten yessoensis MSP-1 820 aa (97 kDa)Sarashina et al, 2001 Pinctada fucata N19 19 kDaYano M et al., 2007


31 Figure 2-1. Hierarchical organizations in nacre showing at least six structural levels. Figure 2-2. Abalone shell (a) Outer calc ite layer and (b) Inner nacreous layer. (a) (b)


32 Figure 2-3. Structure of tablet (a) denotes mineral nanograins are surrounded by organic frameworks (b) is another phas e-contrast picture recorded on a wider field of 11 m2. The organic matrix is or ganized as in the form of ‘foam’ with very thin walls and closed cells. The mineral nanograins are thus encapsulated inside t he organic framework. Figure 2-4. Growth bands are observed separat ing larger regions of nacre. (from Lin et al, 2005) Figure 2-5. Structure of ar agonite (a) Orthorhombic unit cell structure of aragonite; (b) Aragonite natural twinning stru cture. (from wikipedia) (a) (b) (a) (b)


33 Figure 2-6. (a) Chitin and Protein secondary st ructure elements: (b) Perlucin; (c) Lustrin A. Figure 2-7. Structure of chit in (a) Chemical formula of chitin; (b) Cleavage planes of nacre tablets; (c) AFM deflection image of nacre ground parallel to the aragonite layers. The organic matrix shows a hole above each aragonite tablet with a diameter of 150 nm. (d) Enlargement of (c). Black arrow points to the hole in the organic sheet in t he middle of each aragoni te tablet (from S. Blank, et al., 2003). Figure 2-8. Schematic representation of t he modular structure of Lustrin A (from Shen et al., 1997). (a) (b) (c) (b) (a) (c) (d)


34 CHAPTER 3 STATE OF ART RESEARCH 3.1 Mechanical Performance of Nacre Various experimental techniques incl uding uniaxial tension (C urrey, 1977; Barthelat, 2007; Barthelat and Espinosa, 2007), uniaxial co mpression (Barthelat et al, 2006; Menig et al, 2000), material bending test (Wang et al, 2001; Jackson et al, 1988) and shearing test (Barthelat and Espinosa, 2007; Barthelat et al, 2007) have been employed to study the mechanical behavior of nacre. Most of th ese experimental works were performed at the millimeter size scale. At the macro-scale, the most interesting deformation mode is uniaxial tension of tablets (Rim et al., 2011). The mechanical propertie s of the individual elements of nacre were studies by t he advanced experimental techniques on nanoscale, such as AFM study on organic matrix (Smith et al., 1999), indentation test on nacre tablet (Tai et al, 2006; Bruet et al ., 2005) and magnetic and optical tweezers (Sun et al, 2004; Dao et al, 2003) to analyze biological materials (Lim et al, 2006). In addition, the relation between different scales (nanoand macroscale) was studies through approaches that developed based on MEMS test (Eppell et al, 2006; Zhu et al, 2005; Espinosa et al, 2007; Peng et al, 2008). The mechanical properties of nacre were first measure by Currey (1977). In that study, the nacre was got from gastropods, bivalves and a variety of bivalves, cephalopods. Through three-point bending test, the fracture strength of nacre is measured between the range of 56~116 MPa. In 1988, Jackson re-measured the mechanical properties of nacre and got results. The tested elastic modulus for dry nacre was 70 GPa, but for wet nacre it reduced to 60 GPa. The tensile strength was also tested. For dry nacre it was 170 MPa, but for wet nacre it was 140 MPa. Work of


35 fracture were measured to be 350 ~ 1240 J/m2 according to the condition of hydration and span-to-depth ratio. However, the work of fracture of calcium carbonate mineral is about 3000 times smaller. Therefore, wet nacre presents significantly higher toughness by the increase of plastic work. Then, some other mechanical test s (Sarikaya et al., 1990; Sarikaya and Aksay, 1992, and Sarikaya 1994) were carried out on abalone shell nacre. Based on bending tests, the fracture strength is measured to be 185 20 MPa. While the fracture toughness is measured to be 8 3 MPa m1/2. It can be noted that the fracture toughness of nacre is about eightfold bigger than that of calcium carbonate. Some natural defects and waved tablet surface were employed to explain the observed phenomena. To explain the variation, Weibu ll statistics (Weibull, 1939) were adopted (Menig et al., 2000). Obtained results show that when tested parallel to the tablet surface, the tensile strength is about 177 MPa. While in the case of testing perpendicular to the surface, the tested tensile st rength is 197 MPa. These results are consistent with the experim ental measurements (Sarikay a and Aksay, 1992; Jackson et al., 1988; Sarikaya, 1994 and Sarikaya et al ., 1990). In 2001 (Wang et al., 2001), the tensile strength of nacre is also test ed through applying loading along different directions (perpendicular and parallel to t ablet surface). The obtained results for perpendicular and parallel to tablet were 223 and 194 MPa, respectively. Compression experiments (Menig et al., 2000) is carried out on nacre based on different loading ways as previous ones. The compressive strength is measured to be 540 MPa when parallel to tablet and 235 MPa when perpendicular to tabl et. Menig et al. (2000) believed that it is the microplastic buckling that leads to the lower value. Therefore, the ratio of strength obtained from compress and tension test is about 1.5~3. While for pure mineral, this


36 ratio is about 8~15. To sum up, Table 3-1 li sts the mechanical proper ties of nacre those have been measured through experi ment technique so far. 3.2 Currently Proposed Toughe ning Mechanism of Nacre It has been spec ulated that the main toughening mechanisms of nacre are the hierarchical structure and the structural feature of nacre t ablet surfaces. Some of the toughening mechanisms of nacre will be presented below. 1. The organization of ta blets and the associated organic matrix Facilitated by tran smission electron microscopy (TE M), the mechanical behavior of organic matrix in nacre is studied by Sumito mo et al. (2008). T hey proposed a crackbridging toughening mechanism based the obser vations that the bio-polymers strongly adhere to the mineral surfaces and they show ed superior ductile properties. Toughening mechanism of outstanding fracture (Barthelat et al., 2007) was also proposed. In this mechanism, the “viscoplastic energy dissipate at the biopolymer between tablets” was responsible for the high toughnes s of nacre. Through tensile an d fracture tests, tensile deformation with a relatively large inelasti c deformation was obtained as shown in Fig 31 (a). By using atomic force microscope (Smi th et al., 1999), the organic matrix on nacre surface was stretched and a final conclusi on was obtained that the key fracture resistance of nacre resides in the polym er adhesive. In addition, they proposed a `modular' elongation mechanism (Fig 3-1 (b)) which is similar to the traditionally accepted protein domain unfolding behavior (Li, et al., 2002; Rief et al., 1997; Cieplak, et al., 2005; Keten and Buehler, 2008; Li et al., 2001; Pabon and Amzel, 2006; Lu and Schulten, 1999; Rief et al., 1997) 2. Asperities on surfaces of aragonite tablets


37 In this mechani sm, the plastic deformation was m easured by shearing and tension test on nacre tablets. The pl astic deformation is controlled by the asperities on nacre tablets surfaces (Wang et al., 2001), as shown in Fig. 3-2. It is also argued (Wang et al., 2001; Evans et al., 2001) that the interposing arrangement s of asperities between layers of tablets act as a sliding resistance, which eventually lead to the high ductility of nacre tablet. 3. Mineral br idges between tablet lamellae The organic scaffolding – mineral br idges, as shown in Fig. 3-3, are observed during the growth of nacre t ablets (Song et al., 2003, Lin et al., 2007 and Gries et al., 2009). Facilitated by transmission electron micr oscopy (TEM), a strong “correlation of the orientation of stacked aragonite platelets” is showed (Gries et al., 2009). Such mineral bridges enhance the nacre toughness by reinforcing the weak interfaces (Song et al. 2003). 4. Tablet interlocks The important role of nanoscale asperities and mineral bridges played on the toughening of nacre is denied by Katti et al (Katti et al., 20 06); meanwhile they proposed another nacre tougheni ng and strengthening mechanisms: tablet interlocks (Fig. 3-4 (a)). Three-dimensiona l finite element models (Fig. 3-4 (b)) of nacre integrated with experiment were conducted to investigate the effect of structure on stress-strain relation of nacre tablet. Tablet interlocks we re simulated and Fig. 3-4 (c) presented the obtained stress-strain relation. It is suggested fr om that picture that the high strength and toughness of nacre were attributed to the interlocks and the deformation of both organic and mineral component of nacre tablet.


38 5. Ta blet surface waviness Uniaxial tensile experiments we re conducted to measure tensile properties of nacre and relatively large deformations accompanied by hardening were observed (Barthelat, 2007). A new toughe ning mechanism is proposed that the waviness of the tablets surfaces (Fig. 3-5) is essent ial to generate hardening and spreading of deformations. 6. Hi erarchical structure Hierarchical struct ures were observed from natural materials, such as sea shells. As shown in Fig. 3-6 (a) and (b), to ens ure reach the highest strength and highest tolerance of defects, the size of mineral par ticle is carefully selected. At nano-scale, the general concepts of stress concentration at defects are no longer workable. When the sample size reaches a critical value, materi als will become not as sensitive to defects as observed from micro-scale (Gao et al. 2003). Mechanical analysis show that materials like nacre, which is composed of two com ponents (organic matrix and mineral) with very different mechanical properties, may lead to diffe rent fracture process. As illustrated in Fig. 3-6, the crack tip will be shielded. Accordingly, the crack driving force and energy dissipation will be changed (Fratzl et al. 2007). 7. Nanograins in nacre tablet It is reported that the basic building blocks of indi vidual aragonite tablets (Fig. 3-7 (a)) is cobble-like polygonal nanograins. T he average size of nanograins is about 32nm (Li et al. 2004). Due to the polycrystalline stru cture, nacre tablet shows ductile property rather than brittle fracture as the mineral nanograin shows. Th is ductility was believed to make a big contribution to the fracture toughness of nacre. AFM observation evidenced


39 that the deformation and rotation of nanograi ns were responsible for the energy dissipation of tablet, as shown in Fig. 3-7 (b) and (c). The rotation process is facilitated by the organic matrix spacing on grain boundaries (Li et al. 2006).


40 Table 3-1. Mechanical properties of abalone nacre. Author Sample Flexural tensile stress (MPa) Compressive strength YoungÂ’s modulus (GPa) Fracture strength(in bending) (MPa) Fracture toughness (MPam) Work fracture (J/m2) Currey, 1977 Nacre 56~116 Jackson, 1988 Nacre (bivave) 170 (dry)70 (dry) 350~ 1240 140 (wet)60 (wet) Sarikaya, 1990 Sarikaya, 1992 Sarikaya, 1994 Nacre (red abalone) 185 20 83 Sarikaya, 1990 Sarikaya, 1992 Sarikaya, 1994 Monolithic aragonite 1 Menig, 2000 Nacre(red abalone) 177 (parallel)235Mpa (parallel) 197 perpendicular 540Mpa perpendicular Bruet, 2005 Aragonite tiles 11Gpa(dry)79 (dry) 9Gpa(wet)92 (wet) Wang, 2001 Nacre (red abalone) 194 (parallel) 223 perpendicular Shapiro, 1996 aragonite 205 organic 0.005 Park and Lakes, 1992 aragonite 140 (yield)99.5 organic 5 (yield)20


41 Figure 3-1. (a) Stress–strain curve in t ension along the tablets for pure aragonite, dry nacre and hydrated nacre (Barthelat, F et al., 2007). (b) Diagram of long polymers behaving as entropic springs (Smith et al. 1999). (c) Proposed force–extension curves for three different kinds of molecules (Smith et al. 1999). Figure 3-2. Nano-asperities on the tablet surface (a) Nano-asperities on the tablet surface (Wang et al., 2001). (b) Cross se ction of abalone nacre showing the detailed structure at t he lamellae boundaries. Arrows highlight locations where the nano-asperities interpose (Wang et al., 2001). (c) Schematic illustration of the nano-asperities and th ree typical pairing topologies at neighboring aragonite plates (Wang et al., 2001). Figure 3-3. Mineral bridges (a) SEM micr ograph showing mineral bridges between tiles after deproteination (from Lin et al 2007). (b) TEM micrograph of nacre cross-section showing mineral bridges (from Lin et al. 2007). (c) TEM bright field image of a cross-sectional na cre specimen. The arrow marks a mineral bridge (from Gr ies et al., 2009). (a) (b) (a) (b) (c) (a) (b) (c)


42 Figure 3-4. (a) Presence of interlocking bet ween platelets of nacre (from Katti et al., 2005). (b) The interlock model with tw o bricks placed one on the top of another (from Katti et al. 2005). (c) St ress–strain response in the presence and absence of platelet interlocks, res pectively (from Katti et al., 2006). Figure 3-5. (a) SEM image showing dove-tail tablet ends (from Barthelat 2007). (b) Mechanism associated with the wavi ness: under tension, compressive stress builds up (black arrows), balanc ed by a tensile stress (grey arrows) outside of the sliding area. The resu lt is progressive locking and local hardening (from Barthelat 2007). (c) Fini te element model (from Barthelat 2007). Figure 3-6. Models of biocomposites. ( a ) A schematic diagram of staggered mineral crystals embedded in protein matrix. ( b ) A simplified model showing the load-carrying structure of the mineral–protein compos ites. Most of the load is carried by the mineral platelets wher eas the protein transfers load via the high shear zones between mineral platel ets. (c) Crack advance, leaving a wake of inelastic deformations. (a) (b) (c) (c) c


43 Figure 3-7. (a) AFM images of the nanogr ains within an aragonite platelet; (b-c) Schematics of grain rotation and defo rmation mechanisms in an aragonite platelet. (a) (b) (c)


44 CHAPTER 4 RESEARCH METHODS It is a crucia l issue to understand deformation mechanisms of bio-materials at nano-scale because of their hierarchical struct ures. It is speculated that mechanical properties of material hav e strong dependence of length scale. Thanks to the nanoscale experiments and computer simula tions, people may obtain good understandings of how structures govern the mechanical properties of materi al. As predictive tools, simulation and modeling can facilitate t he analyses of experimental phenomena at proper time-scale and length-scale. Classica l molecular dynamics (MD) or steered molecular dynamics (SMD) are well know n as bottom-up atomistic modeling. The fundamental of these tw o approaches are the chemical st ructure of material. They have been demonstrated to be very useful in revea ling the mechanical behavior of materials, especially some complex and biomaterials. 4.1 Atomistic and Molecular Dynamics Using atoms as the basic objective, molecular dynamics (MD) simulation has been considered to be fundamental and useful approach. Curr ently, MD can simulate materials with size of hundreds nanometers, even micro-meter. At the same time, this approach can elucidate deformation mechanism fr om the atomic view. It can also track the behavior of specific chemical bonds: br eaking and reforming from the atomic scale. In this way, people may find the relation between atomic information and the failure phenomena at macro-scale. Theref ore, MD simulation has been considered to be a first principles approach in under standing the mechanical behav ior of material. In MD simulation, information of atoms, such as position, velocity and acceleration can be obtained through considering interatomic pot ential and solving equation of motion:


45 F=ma, in which F is force on the atom, m denotes the atom mass and a is the acceleration. The basic concept of atomistic simulation is that t he dynamic behavior of each atom can be tracked. Molecular dynamics (MD) simulati on is different to Monte Carlo method. MD simulation can provide the full dynamic trajectory, which is considered to be a crucial element in revealing deformation mec hanisms based on the observed macroscopic failure behavior. The total energy of syste m can be divided into kinetic and potential energy. Equation 4-1 presents the relation between them. EKU (4-1) the kinetic energy (K) can be expressed as, 2 11 2N j jKMv (4-2) and the temperature of system (T) is controlled by the kinetic energy, i.e., velocity for a specific material. The relation between them is, 2 13 1 33N kini i bbEp T NkNkm (4-3) The potential ener gy (U) of system, which is also known as the force field, is a function of positions (jr) of atoms, where j = 1, ., N denotes the summary of all atoms. The potential energy can be written as, ()jUUr (4-4) With a proper force field U(rj), the objective is to solve the 2nd-order differential equation (4-5). 2 2()jj rjdr mUr dt 1,, j N (4-5)


46 It should be mentioned that th is equation can only be solved when the number of atoms in system is more than two. Typically, there are two kinds of algorithm to integrate the equation of motions: update of positions, su ch as BeemanÂ’s algorithm, Leap-frog algorithm and Verlet algorithm Equation 4-6 shows the functional format of updating of positions. 21 2 rttrtvttatt (4-6) or update of velocities (equation (4-7)) in Ve locity Verlet algorithm (equation 4-7). 1 2 vttvtatattt (4-7) The basic Verlet algorithm (Allen and Tildesley, 1989) can be expressed as, 2 00002jjjjrttrttrtatt (4-8) The acceleration can be obtai ned through the equation of jjafm The forces of atoms can be obtained through derivation of interatomic potential function, 2 2jj jrjdr FmUr dt 1,, j N (4-9) The simulation objectives of MD are not limited to singl e atoms. MD can be regarded as coarse-grain method by simu late groups of atoms. Owing to its fundamental concept, MD simulation can captur e a great variety of failure behaviors, such as crack/dislocation nucleation and propagation, phase transformation. It is well known that continuum mechanics is a t op-down based approach. In contrast, in atomistic simulation no priori assump tions are needed because the properties of material have been well defined through the interatomic potentials. Therefore, MD simulation is a bottom-up modeling. However, it is very challenge but very crucial to


47 choose an appropriate interatomic potential. Ty pically, the most popular approaches to obtain a suitable potential are semi-emp irical or empirical experiment, where mathematical functions are carefully chosen to reproduce the energy surfaces. For the study of biomaterials, various interato mic potentials, such as CHARMM potential, AMBER potential, have been employed. Diffe rent protein struct ure types require different interatomic potential models. One of the drawbacks of atomistic simulations is the time limitation. No matter how powerful the computer is, the simulation time is limited at nanoseconds scale currently. Therefor e, MD simulation is restricted with the time-scale. It is very challenge to conduct a simulation to microseconds. Thus, large strain rates have been applied in many simula tions. The strain rate is usually several orders higher than that used in experiment. With the recent advances in computer technology, the simulation length has extend ed from nanometer to micrometer, which, however, is still incomparable to experiment al length scale. To make quantitative links with experimental scales, great efforts hav e been carried out in extending the length and time scales of MD simulation. Test cases of nanoindentation on silicon nano-particles were conducted to illustrate how MD simulations work: 4.1.1 Deformation Mechanisms in Silicon Nano-particles Nanoindent ation has been established as an effe ctive technique in measuring the elastic modulus, fracture toughness and hardness, at small length scales. Nanoindentation experiments can also be used to provide insights into microscopic deformation mechanisms of material s. Many new phenomena and deformation mechanisms have been discovered through nanoi ndentation experiments on nanoscale


48 materials. In a recent expe riment by Gerberich et al., unusual mechanical properties have been observed when indent ing nearly spherical, defe ct-free single crystalline silicon particles. The radiuses of parti cles are ranged between 20 nm to 50 nm. Experimental results show that the loadi ng of silicon nanosphere produces hardness is about 50 GPa, which is four time s larger than that of bulk s ilicon (Gerberich et al., 2003). The discovery of this super-high hardness in silicon nanoparticles has been followed by extensive theoretical and co mputational research to understand the deformation mechanisms (Gerberich et al., 2003; Deneen et al., 2006; Gerberich et al., 2005; Mook et al., 2007; Gerberich et al., 2006; Gerberich et al., 2009). It is believed that the high hardness in silicon nanoparticles is due to “the high level of plastic strain and work hardening experienced by very small volumes” (Deneen et al., 2006; Gerberich et al., 2005). The plastic deforma tion mechanisms were theorized to be heterogeneous dislocation nucleation at the bottom and top contact edges followed by dislocation propagation either up or down a glide cylinder (Gerberich et al., 2003). This theory of silicon dislocation plasticity was challenged by a recent paper on molecular dynamics (MD) simulations of silic on nanoparticles with sizes up to 10 nm in radius under uniaxial compression (Valentin i et al., 2007). The MD simulations showed that the diamond crystal structure to -tin structure phase transformation occurred during compression. The authors conclud ed that the phasetransition path of deformation should dominate in ultrasmall structur es where dislocation activity is either prohibited or unstable due to image forces t hat tend to push disloc ations out of the nanostructure. However, silicon diamond to -tin phase transformation has been widely observed in bulk silicon (Domnich et al., 2000; Domnich et al., 2008), whereas super-


49 high hardness has not been found in bulk silic on. This indicates that different or additional deformation mechani sms may exist in nanoscale silicon particles and structures. The objective of this study is to explore possible deformation mechanisms in silicon nanoparticles under indentation loading thr ough MD simulations. We perform MD simulations with different interatomic potent ial functions and compare the simulation results with experimental meas urements to identify the appr opriate potential model. We assess the comparability of MD simulations and indentation experiments by comparing MD simulations with different applied stra in rates. Our simulation results also demonstrate how the mechanical properti es and deformation mechanisms change with nanoparticle size. Computer model and simulation details Figure 4-1 schematic ally illustrates an indentation on a defect-free single crystalline Si nanoparticle. The Si nanoparticle was pr epared by generating a perfect diamond cubic crystal structure of Si with a lattice constant of 5.43 t hen removing all atoms outside a spherical region of a specified di ameter (5–40 nm). The particle was then placed on a fixed rigid surface with the vertic al axis of the particle oriented along the [001] crystal direction. The rigid surface is used to prevent the particle from moving due to the indenting force caused by the tip. Fina lly, a spherical indenter tip with a diameter of 1 m was positioned 5.0 above the silicon su rface, and allowed to move downward to the particle at a specifi ed velocity. The molecular dy namics code, LAMMPS (Plimpton, 1995), developed by Sandia National Laborator ies, was employed for the constant temperature MD simulations. The simulati ons were performed with the Stillinger–Weber


50 and Tersoff potentials for Si. The velocity-Ver let algorithm is used and a time step of 1 fs is set. The Nose–Hoover thermostat (H oover 1985) with a 1.0 ps relaxation time was used to maintain a constant temperature at 298 K. Results 1. Simulation results from different interatomic potential models There are severa l well-established potential model s for Si including the Stillinger– Weber (SW) and Tersoff potentials. The SW potential (Stillinger and Weber, 1985) is one of the first three-body interaction model s and one of the most widely used potentials for Si. It gives a fairly realistic description of crystalline Si equilibr ium structure, and has been shown to simulate dislocations observ ed in some Si experiments (Minor et al., 2005). The Tersoff potential function (Tersoff, 1989) is a bond order potential that can model many materials with a diamond crystal st ructure. In addition, Tersoff potential has been shown to correctly predict the pressu re-induced phase transformation, which is from cubic diamond structure to -tin structure (Valentini et al., 2007; Xiong and Chen, 2009). This conclusion is in agreement with ex perimental observations (Domnich et al., 2000; Domnich et al., 2008). To explore possible deformation mechanisms in Si nanoparticles, the MD simulations employ ed both the SW and the Tersoff potential functions, respectively. In Fig. 4-2 we present the measured lo ad-displacement curves in MD simulations of indentation of a 40nm Si sphere with Te rsoff and SW potential functions describing the atomic interaction force, respectively In Fig. 4-3 we present the corresponding stress-strain responses. Here, the stress is defined as the st ress averaged over the entire computer model and is computed by the standard virial stress formula, which,


51 when used for average stress of the entire model specimen, is identical with the continuum mechanics definition of Cauchy stress (Chen et al., 2006; Chen et al., 2009). From Fig. 4-3 and Fig. 4-4, we s ee that the Tersoff and SW curves overlap in both the load-displacement and the stress-strain curves until a significant drop-off in the stress obtained by SW potential. After this critical point, the two simulation results depart from each other. Unloading simulati on shows irreversible deformation has occurred in the MD simulation with SW potenti al. This indicates that the two different potential models predict same elastic behavior for the Si nanosphere, but not the plastic behavior. An analysis of the arrangements of atoms in t he MD simulation using the SW potential reveals that disloc ations have nucleated from t he contact regions after the stress drop. The atomic arrangements at = 0.11 are shown in Fi g. 4-4(a). Using the slip vector representation (Zimmerman et al ., 2001), the snapshots of dislocation loops at strains = 0.11 and 0.185 are pr esented in Fig. 4-4(b) and 44(c). This representation is a measure of how far an atom has moved re lative to its nearest neighbor. It is seen from Figs. 4-4(b) and 44(c) that dislocation loops are em itted from the contact surfaces and propagate along the {111} slip planes in the [110] slip directions. In contrast to the stress-strain response in MD simulation with SW potential, the stresses obtained from MD simulation with Ters off potential keep increasing with strain. At larger strains ( > 0.3), the stress-st rain curve changes its slope and the stress reaches a distinct stress plateau at stress value of about 5 GPa. After the plateau it increases sharply until the Si particl e reaches the ultimate strength ( max = 16.01 GPa).


52 After that, the stress oscillat es, and the silicon particle is no longer able to withstand an applied stress. A st ress plateau usually indicates that a phase transformation has occurred (Murakami 2002).Experimental studies have show n that the radius of the nearest four neighbors of diamond structure silicon phase (Si-I) is 2.35 In contrast, the radius of the nearest four neighbors of -tin silicon (Si-II) is 2.42 and the radius of second nearest two neighbors is 2.57 (Boyer et al., 1991). To identify the structural phase formed in the silicon nanoparticle, snapshots of deformation (employing the Tersoff potential) as a function of strain are pres ented in Fig. 4-5 using the coordinate number representation with a cutoff distance of 2. 60 chosen to calculate the coordinate number for a specified atom. In Fig. 4-5 (a) we observe that a metastable phas e with a coordination number of five was formed from top and bottom cont act areas of the Si-I nanoparticle and propagated toward the core of the nanoparticle. It should be not ed from Fig. 4-5 (b) that when the two metastable phase regions met at the core of the par ticle, another phase with sixfold coordinat ion number (Si-II, -tin phase) was formed. As the indentation depth continued to increase, the -tin phase region extended from the core [Fig. 4-5 (c)] to the contact surfaces [Fig. 4-5 (d)], then the Si nanoparticle reached the maximum stress max = 16.01 GPa. Thus, the nonlinear stress–st rain relation observed in the MD simulation using the Tersoff potential, shown in Fig. 4-3, is attr ibuted to the initial metastable phase transiti on, and the subsequent -tin phase formation leads to the stress plateau. The sharp increas e of stress with strain after the plateau is due to the higher elastic modulus of the -tin phase.


53 Further analysis of the deformed atomic struct ure reveals another surprising deformation mechanism in that the structur e failed eventually not by amorphous phase formation, but by line defects that look like di slocations [Figs. 4-5 (e) and 4-5 (f)]. To analyze the mechanism that leads to the material failure, in Fig. 4-6 we present a sidecross-sectional view of the deformed stru cture with coordination number representation [Fig. 4-6 (a)], and a zoomed-in structure [Fig 4-6 (b)], as well as its slip vector representation [Fig. 4-6 (c)], respectively, at = 0.63. We notice that, different from the dislocation nucleation in SW potential-based MD simulation, dislocations in the current deformed structure are emitt ed from the contact surfac e and propagate within the newly formed -tin phase region [the red r egion in Fig. 4-5 and Fig. 4-6 (a)] in the Tersoff potential-based MD simulation. We would like to emphasize here that dislocations did not emit and propagate in the Si-I phas e but within the Si-II phase region. It is widely accepted that the phase transiti on of silicon that tr ansformed from initial structure of diamond to -tin is a densification “sem iconductorto-ductile-metal phase transformation” (Cheong and Zhang, 2000). In other words, the density of Si-II ( -tin phase) is higher than Si-I. Higher density resu lts in a smaller magnitude Burgers vector, which makes the dislocation easier to nuc leate and migrate. In addition, since the dominant plastic deformation mechanism of metal is dislocation-mediated, it is reasonable that dislocations may prefer to nuc leate within the metallic b-tin phase Si-II than the semiconductor phase Si-I. Using a relatively large indenter tip (1 lm in diam eter), Gerberich and co-workers performed indentation tests on de fect-free Si nanospheres with diameters from 40 nm to 100 nm and reported the measured hardness to be 20–50 GPa (Gerberich et al. 2003).


54 This experiment is repeated by Mook et al (2007). They reported that a silicon particle with a 44 nm diameter failed at a load of 45 N. Meanwhile, the measured height showed a significant decrease (Mook et al ., 2007). Note that material hardness is defined as the resistance to local permanent deformation, in many experiments it is usually determined by the ratio of maximum indentation force Pmax and the projected contact area A, Pmax/A. The obtained load–displacement relations with the two different potentials are plotted in Fig. 4-2, in which th e critical load based on the Tersoff potential reaches a value of 37.2 N at an indent depth of 24.0 nm whereas that obtained from the SW potential is only 2.8 N at a depth of 4.5 nm. Employ ing the experimentally used formula H=P/A, the hardness calculated usin g the Tersoff and SW potentials are 30.85 and 5.58 GPa, respectively. Comparing the simulation results with the experimentally measured hardness (20-50 GPa) and the crit ical load of material failure (45 N for a silicon particle with a 44 nm diameter), we c onclude that the Tersoff potential model predicts mechanical properties that are clos er to the experimental measurements than the SW potential, and hence is more appropr iate for modeling of Si nanoparticles. 2. Effect of strain rate One of the ma jor differences between experimen ts and MD simulations is the strain rate: the typical strain ra te used in MD simulations (> 107 s-1) is several orders larger than that in experiment (~1.0s-1). Therefore, there has been a great concern about the reliability of MD simulation in explanation of experimental measured properties. To gain a quantitat ive understanding of the effect of strain rate on the numerical results, MD simulations of a 10 nm spherical Si parti cle under indentation were conducted with three diffe rent strain rates: 1.0107 /s, 1.0108 /s, and 1.0109 /s.


55 In Fig. 4-7 and Fig. 4-8, we plot the stress-strain curves for the 10nm Si particle in MD simulations of SW (Fig. 4-7) and Terso ff potentials (Fig. 4-8), respectively, with 3 different strain rates. It is seen that, before the first significant stress drop in both SW and Tersoff potential-based MD simulation, t he simulation results of the stress-strain responses using SW or Tersoff potential model are almost identical among three different applied strain rates. After the stress dr op, the stress fluctuates as a result of the nucleation and migration of dislocations. We see that the magnitude of th e stress fluctuations changes with the applied strain rate. This, we belie ve, is partially caused by the numerical algorithm used for the NVT (Constant volume and temperature) ensemble. The working principle of this ensemble is similar to appl ying a damping to the s ystem to reduce the magnitude of atomic velocities so as to achi eve a target kinetic energy that serves as a measure of temperature in the MD simulation. A higher strain rate (i.e., larger applied velocity) requires a larger damping to reduce the magnitude of the mo tion of atoms. As a result, the magnitude of the stress fluctuati ons caused by the motion of dislocations is also affected by the numerical algorithm. It is interesti ng to note that the material behav ior of the Si nanoparticle in the simulations, including the critical strain, is independent of applied strain rates before the nucleation of dislocations. This means t hat the applied strain rate does not have an effect on the averaged stress–st rain response unless there is motion of dislocations, even when there is phas e transition behavior. 3. Effect of specimen size


56 It is well known t hat there is a strong effect of the size of nanostructures on the mechanical properties. Previous experimen t and simulation studies on metals have proposed two controversial models: “smaller is stronger” (Horstem ever et al., 2001; Greer et al., 2005; Greer et al., 2006), and “smaller is softer.” (Marian and Knap, 2007) Li and Bhushan reported that the bending strength of 17.5 GPa for Si nanobeams is three times higher than that of the bulk Si (6 GPa) (Li and Bhushan, 2003). They suggested that phase transformation might contri bute to the super-hig h strength of the silicon nanobeam. The indentation experiment s on Si nanospheres by Gerberich’s group showed that the hardness of Si nanospher es could be more than four times than that of bulk silicon (Gerberich et al., 2003). This group believes that the super-hardness is because of “a high level of plastic st rain and work hardening experienced by these very small volumes” (Gerberich et al., 2003). So far, studies on silicon have suggested that the smaller the silicon specimen is, the larger the hardne ss and strength are. To investigate t he size effect and the origins of the size effect in silicon nanoparticles, MD simulations were perform ed employing the Tersoff potential with nanoparticles ranging from 5 to 40 nm in diameter. The number of atoms in each computer model and the maxi mum indentation depth are summarized in Table I. Using the same formula as that in the experim ental analysis (Gerberich et al., 2003), the calculated hardness for each Si nanosphere, as well as the deformation mechanisms observed in the simulations are presented in Table I. Fig. 4-9 shows the atomic arrangements in MD simulations of Si nanopar ticles before their significant stress dropoff using coordination number representation. It is seen from Fig. 4-9 that phase


57 transformation can occur in Si nanoparticles at sizes as small as 5 nm in diameter. We have also plotted the measured hardness versus nanoparticle diameter in Fig. 4-10. Table 4-1 and Fig. 4-10 show that there is a cr itical size, around D = 10 nm, at which a transition from smaller is softer to self-similar hardening occurs. This result implies that different mec hanisms are involved in the deformation processes upon samples with various diameters. The deforma tion mechanism that is responsible for the increased strength and hardening in Si nanoparticle is the phase transition from the Si-I to the -tin silicon, followed by dislocation nucleation and motion within the newly formed metallic phase. The critical size that corresponds to the strongest specimen appears to be the smallest one that a llows dislocation nucleation. Figure 4-11 plots the stress–strain re lation with different sizes are plotted. It can be observed that the pattern of stress–strai n curve are nearly independent of specimen size before the stress drop at ~0.6, whereas after that they show different plastic flow behaviors: Si nanoparticles with diameters ranging from 10 to 40 nm display significant stress drops and large stress oscillations, w hereas particles with 5 nm in diameter present more frequent and sma ller stress fluctuations. Summary and discussions This work has shown that MD si mulations employing the Tersoff potential provide a more reasonable prediction for the hardnes s of silicon nanoparticles than with the SW potential. Simulation results have revealed a possible deformation mechanism in silicon nanoparticles under indentation: phase transition from st ructure of diamond to -tin is followed by dislocation nuc leation within newly formed -tin metallic phase region or amorphization, depending on the si ze of the particle. MD si mulation results have also


58 shown that there is critical diameter si ze, around 10 nm, upon whic h dislocation emitting within the -tin phase region is the dominant defo rmation mechanism that leads to the material failure. Below this critical size, amorphous phase formation gradually overcomes the dislocations to be the domin ant failure mechanism. This result is consistent with the well-acc epted conclusion that dislocat ion cannot nucleate below a critical size (Schall et al., 2006). Unfortunately, it is diff icult to measure an accurate critical size because a mixture of dislocation and amorphous phase exists simultaneously in a certain size range. We would like to mention that the present MD simulations differ with the experiment in a few aspects. First, the silic on particle surfaces are directly exposed to vacuum, i.e., no oxide passivation layer is tak en into consideration, which is different from the experiments of Gerb rich et al. and Mook et al ., although our MD simulation results show no noticeable difference betwe en particles with or without an amorphous layer. Also, the loading process is controlled by displacement in the simulations instead of load in the experiments. The differenc e between them may lead to considerable divergence regarding the simulation result s, but shall not af fect the underlying deformation mechanism analysis. In addition, due to the limitation of simulation time the applied strain rate is much higher than the experiment employed, which, according to our analysis, does not have a significant effe ct on the elastic behavior; the critical strains for phase transformation and disloc ation nucleation; and the deformation mechanisms. 4.2 Steered Molecular Dynamics


59 It has been demon strated that Steered molecular dynamics (SMD) simulation is a very useful tool (Lu et al 1998) in studies of bio-mole cular systems, since it could explain single molecule exper iments, and at the same time it can overcome short timescale and explore assumed conformation mechanism. The fundamental concept of SMD is to accelerate conformational change s by applying external forces. A restraint moves to the core of a gr oup of atoms according to ha rmonic potential between the restrained atom and the core atom which can be expressed as, 2 1201 ,,, 2 UrrtkvtXtXn (4-10) In equation (4-10), 0 X is original coordinates, X t denotes the position of restrained atom at time t, vis the dragging velocity and n is the dragging direction. The force on dragged atoms can be obtained through 120,,, F xxtkvtXtXn Through tracking the position of atoms and the appl ied force, one can obtain the force extension relation. The mechanical properties of materials, such as elastic modulus, strength, stiffness and toughness, can be derived from the force – extension curve. The spring constant k is set to be 10 kcal/mol/2 in this SMD study to simulate the AFM experiment, as illustrated in Fig. 4-12.


60 Table 4-1. Summary of the diamet er, D, total number of atoms, Ntot, maximum indentation depth, hmax, measured hardness, H, and deformation mechanisms measured and observed in the MD simulations of Si nanospheres. D(nm) Ntot hma x (nm) H (GPa) Deformation and failure mechanism 5 3,265 3.1 24.9 Phase transformation and amorphization 8 13,407 4.9 29.2 Phase transformation and amorphization 10 26,167 6.2 34.1 Phase transformation and Dislocation 20 231,521 12.0 31.45 Phase transformation and Dislocation 30 706,419 18.0 31.0 Phase transformation and Dislocation 40 1,673,237 24.0 30.85 Phase transformation and Dislocation


61 Figure 4-1. The computer model of Si nanosphere under indentation. Figure 4-2. Simulated load-di splacement curves. 0 5 10 15 20 25 0 10 20 30 40 (nm)P ( N) 40nm/SW 40nm/TERSOFF (2.8N,4.5nm) (37.2N,24.0nm)


62 Figure 4-3. Simulated stress-strain curves. Figure 4-4. (a) side cross-section view of atomistic deformation at =0.11. (b) dislocation loop nucleate at the contact area at ~ 0.11, (c) dislocation loop structure at ~ 0.3. Atoms are colored in the unit of Burgers vector according to their slip vectors. Red atoms indicate perfect dislocations, while other colors indicate partial dislocations. 0 0.2 0.4 0.6 0 5 10 15 StrainStress (GPa) 40nm/SW 40nm/TERSOFF


63 (a) =0.26 (b) =0.40 (c) =0.44 (d) =0.60 (e) =0.61 (f) =0.65 Figure 4-5. Side cross-sectional view of Si particle in MD simulation of nanoindentation on (0 0 1) silicon surface using coor dination number representation. Green ones are atoms with diamond cubic stru cture (Si-I). Red and yellow ones are atoms with sixfold (Si-II ) and fivefold coordination. Figure 4-6. (a) At omic arrangments at =0.63, (b) zoomed in atomic structure, and (c) slip vector presentatio n with red atoms indicati ng perfect dislocations.


64 Figure 4-7. Stress-strain res ponses using SW potential. Figure 4-8. Stress-strain responses using Tersoff potential. Figure 4-9. Snapshots of atomic structure before the signific ant stress drop-off, from left to right, D=5.0, 8.0, 10.0, 20.0, and 30nm, using coordination number representation. Atoms wit h green color stand for Si-I, red and yellow atoms represent -tin phase and metastable phase. 0 0.1 0.2 0.3 0 0.5 1 1.5 2 2.5 3 StrainStress (GPa) 1.0109 s-1 1.0108 s-1 1.0107 s-1 (a) SW potential 0 0.2 0.4 0.6 0 5 10 15 StrainStress (GPa) 1.0109 s-1 1.0108 s-1 1.0107 s-1 (b) Tersoff potential


65 Figure 4-10. Hardness vs model size in MD simulation. Figure 4-11. Stress-strain curv es of various atomistic models. 10 20 30 40 26 28 30 32 34 SNS diameter (nm)Measured hardness (GPa) 0 0.2 0.4 0.6 0 5 10 15 StrainStress (GPa) D=5.0nm D=10.0nm D=40.0nm


66 Figure 4-12. Single molecule pulling ex periments, carried out on a single protein molecule (Buehler and Ackbarow, 2007) (schematic based on Ref. (Schwaiger et al, 2002)). (a) depicts an experimental setup based on AFM, and (b) depicts a steered molecular dynam ics (SMD) analogue. During the SMD simulation, the end of the molecule is slowly pulled, which leads to a slowly increasing force over the disp lacement, as schematically shown in (c). Both AFM and SMD lead to force–di splacement relation. Besides the force-extension curve, SMD provides detailed information about associated atomistic deformation mec hanisms. Typically, the pulling rates in SMD simulation (no larger than 0. 01 m/s) are six to eight magnitudes larger than those in experiment due to the time scale limitation of MD. Thus, strain rate effect is typically r equired to consider in order to interpret MD results in light of experiment findings.


67 CHAPTER 5 NANOSCALE PLASTIC DEFORMATION MECHANISM IN SINGLE CRYSTALLINE ARAGONITE It is reported that calcium carbonate (CaCO3) minerals are the most abundant biominerals both in terms of the quantities produced and t heir widespread distribution (Weiner and Dove, 2006). Aragonite is one of the polymorphs of calcium carbonate crystal. During the past few decades, aragonite has attracted considerable interest due to its significant role played in complex or ganic/mineral biogenic composites. Of all the many organisms, mollusk shell is one of t he most extraordinary examples, in which calcium carbonate (CaCO3) composes 95~99% in weight (Menig et al., 2000). Considering the wide distribution in nature and its mechanical function, the mechanical properties of aragonite is no doubt a critical dominanc e of its corresponding geological and biological materials. It exists at ambient c onditions with a density of 2.56 g/cm (Berg, 1986). Theoretic al and experimental studies of aragonite have mainly concentrated on the high-pressure phase transit ion behavior, rangi ng from the pioneer work of Bridgman (Bridgman, 1939) to many static and dynamic experimental studies (Tyburczy and Ahrens, 1986; Fiquet et al., 1994; Martinez et al., 1996; Lin and Liu, 1997; Biellmann et al., 1993; Luth, 2001; Suito et al., 2001; Ivano v and Deutsch, 2002; Ono et al., 2007; Santilln and Williams, 2004; Oganov et al., 2006; Ono et al., 2005), and to recent atomistic simulations (Liu et al., 2001; Bearchell and Heyes, 2002; Sekkal et al., 2008; Miyake and Kawano, 2010; Ruiz-Hernandez et al., 2010), with which the atomicscale details of the phase tr ansition processes of CaCO3 has been observed and studied.


68 Beside the phase transition behavio r of aragonite, Han et al. (1991) had measured the Knoop microhardness on different surfaces of single crystalline aragonite in 1991. Using Brillouin spectroscopy (Liu et al., 2005) the elasticity of ar agonite was examined. In 2006, Kearney et al (2006) studied the nanoscale anisotr opic elastic-plastic behavior and the hardness of single crystalline aragonite using both atomic force microscopy (AFM) and finite element method (FEM). Load plateaus were observed in the obtained force-depth curves, which were believed to be related to dislocation nucleation events. Also, preferential pileup lobes were present ed after indentation, indicating anisotropic plastic behavior. Through finite element si mulation, Kearney et al (2006) proposed that the pileup zones might result from slip activities on {110} <001> systems. Generally speaking, material hardness has an intimate relationship with crystal slip system and elastic modulus. In aragonite, the trigonal CO3 2groups is planar, which is parallel to the (001) surface. The Ca2+ ions is reported to located to resemble hexagonal packing (Han et al., 1991), as shown in Fig. 1. Experimental observation has demonstrated that the pol ar (110) face is stable and each ionic layer in this direction consists of either carbonate or Ca ions (Shindo and Kwak, 2005). In other words, (110) plane is an imperfect cleavage plane (Huggins, 1922). Very recently, Huang et al (2011) studied the fracture mechanism of nacre under high-strain-rate compression. They believe that the emission of partial dislocat ion and the onset of deformation twinning are responsible for the fracture toughness of nacre according to their high-resolution transmission electron microscopy (HRTEM) observation. Although some mechanical properti es of aragonite have been measured and many interesting deformation mechanisms have been proposed based on experimental


69 observations, the actual deformation mec hanisms of aragonite are very complex and have not been well understood. Therefore, as an alternat ive approach that allows observation of the deformation processes on atomic scale, MD simulation may be employed to study the underlying deformation mechanism of aragonite. In this work, MD simulations were use to invest igate the mechanical properties of aragonite under various loading conditions, in cluding nanoindentati on, uniaxial tension and compression. Thereafter, we will eluc idate the underlying deformation mechanisms of aragonite with atomic-scale details. 5.1 Computation and Modeling 5.1.1 The Computer Model The crystal structur e of aragonite that identified by De Villiers (1971) is used to build the computer model in this work. A primitive unit cell of aragonite contains 20 atoms and is shown in Fig. 5-1. The crystal structure of ar agonite is orthorhombic with = = =900 and the space group of aragonite is Pmcn. The lattice constants along a-, band care 4.960 7.964 5. 738 respectively (De Villiers, 1971). The computer models of indentation, tension and compre ssion simulations are composed of 100800, 105400 and 118560 unit cells, respectively. T he three-dimensiona l atomic-level computer models will be introduced in the following sections. Constant volume and temperat ure (NVT) molecular dynamics simulations are performed throughout this work. Verlet-Leapfr og algorithm is employed in integrating equation of motions. The time step is set to be 1 fs. Nose-Hoover thermostat was used. To govern the temperature at a constant value (298K) a rela xation time period of 0.1 ps


70 is set. The simulations performed in this study employ the general purpose MD simulation package DLPOLY 2.19 (Smith et al., 2007). 5.1.2. Interatomic Potential To select a suit able interatomic potential is a crucial step in MD simulations of materials behavior. Generally speaking, she ll model (SM) and the rigid ion model (RIM) are the two common potentials models for ionic material. In the rigid ion model, all ions have a fixed spherical electr on density. This electron de nsity can be represented by a point charge. To accurately describe the polarization property of anions, O2in particular, the shell model has been devel oped by dividing the anion into two particles: the shell and the core (Dick and Overhauser, 1958). However, when using shell model information on core and shell is utilized, which significantly enhance the simulation time and convergence rate (Gale, 2005). For aragonite, many potential models have been built since 1992, including both rigid ion models (Pavese et al ., 1992; Catti et al., 1993; Jackson et al., 1995; Dove et al., 1992; Jackson and Price, 1992; Jackson, 2001; Braybrook, et al., 2002) and shell models (Ca tti, et al., 1993; Pavese, et al., 1996; Archer et al., 2003; Pavese et al ., 1992; Fisler et al., 2000;). Table 5-1 lists some of the interatomic potentia l models and their parameters for aragonite. It can be seen that the major diff erences between different potential models reside in the C-O interaction. Although shell models that allow polarization of the -CO3 group can reproduce the bulk properties more a ccurately (Pavese et al., 1996; Fisler et al., 2000), the addition of core and shell func tion of oxygen atoms significantly reduces the computer efficiency. Consequently, t he simulation systems employing shell model will have to be small system s. In contrast, the ri gid ion model for CaCO3 can be


71 extended to larger size with higher co mputer efficiency. Through simulation and comparing the rigid ion models listed in table 5-1, we ha ve found that the potential model developed by Dove et al. (1992) can predict mechanical properties of material, which is in good agreement with experiment m easurement. This potential is obtained by fitting to the properties and st ructure of calcite and aragonite Therefore, the empirical potential of aragonite derived by Dove et al (1992) is employed in this study. The Dove potential func tion comprises both bonded and non-bonded parts. Coulomb interactions are calculated usi ng the Ewald sum in the non-bonded part. The short-range repulsive interactions between OO, Ca-O and C-O are treated by BornMayer potential, which can be written as, ()exp() VrAr (5-1) The bond bendin g terms of O-C-O are implem ented by using the following intermolecular harmonic function, 2 01 () 2 Vk (5-2) where 0 denotes the equilibrium angle, k denotes the constant for bond bending, denotes the angle between the O-C-O atoms. The out-of-plane potential for –CO3 group is implemented using a four-body or a torsional term, 1cos2tVk (5-3) where tk denotes force const ant due to out-of-plane, is the angle between two O-CO planes in a single molecular ion. The potent ial parameters of this model can be found in table 5-1. 5.2. Results and Discussion


72 5.2.1. Nanoindentation Figure 5-2 present s the computer model for nanoin dentation of single crystalline aragonite. The simulated system consists of an aragonite substrate and a rigid spherical indenter with the indenter tip r adius of 50 To test t he effect of periodic boundary condition and loading rate on the simulation results, we first used a smaller model containing 1.6 million atom s, labeled as sample 1 in table 5-2. To study the effect of crystal orientation on mechanical behavior of aragonite, simulations of indentations along two crystallographic orientations, namely a -axes and c -axes, were performed. These two substrates, labeled sample 2 and sample 3 in table 5-2, have similar sizes and contain about 2 million atom s, respectively. The contact forces between the substrate atoms and the indenter are modeled as repulsive forces. At the beginning of the simulations, the indenter is positioned 10 above the center of the surface, and moves at a constant velocity. In both cases, the computer models have free surfaces in the indent direction. To restri ct the rigid-body motion of the substrate, three layers of atoms on the bottom of sample are absol utely frozen. We apply periodic boundary conditions along the directions pe rpendicular to the indent axis. The effect of periodic boundary condition To ensure that t he sample sizes are large enough to avoid spurious effects of the periodic boundary conditions on simulation resu lts, preliminary ind entation simulations of sample 1 with finite size and peri odic boundary conditions were performed, respectively. The obtained load-displacement (P -H) relations are compared in Fig. 5-3, from which it is seen that the P-H curves with the tw o different boundary conditions almost overlap with each other. This implies that the current comput er models are large


73 enough and can be considered to be independent of the boundary conditions. Therefore, in the following indentation simulations, per iodic boundary conditions are applied to simulate bulk properties of aragonite. The effect of loading rate The effect of the indenter loading rate on hardness of aragonite is also investigated through indentation on sample 1. In Fig. 5-4, we compare the simulated loaddisplacement (P-H) curves with loading rates of 0.1 /ps and 0.3 /ps. It is seen that the two curves with loading rates of 0.1 /ps and 0.3 /ps are very similar and there are very small difference in the load values. This suggests that the loading rate is low enough and will not significant ly affect the mechanica l behavior of aragonite in simulations. Therefore, in the following simulations, the lower loading rate of 0.1/ps is applied. The crystallographic or ientation-dependent properties In this secti on, the crystallographic orientation-dependent pr operties of aragonite are studied through indentation along tw o crystallographic orientations, a -axes and c axes, respectively. Fig. 5-5 presents the measured load-displacement curves in the simulations of the indentat ion on different orientated cr ystal surfaces. One can note from Fig. 5-5 that in both cases the loaddisplacement curves are linear at small displacement but become increasingly nonlinear at larger displacement. In spite of some similarities in the pattern of the curves, there are several differences between them. Firs t, the slope of load-displace ment (P-H) curve shown in Fig. 5-5 for the case of indenting along c -axes is larger than that along a -axes. The displacement at which plastic flow first occu rs is 1.2 nm in the case of indentation along


74 c -axes, while 2.2 nm in t he case of indentation along a -axes. The common definition of material hardness is the local resistance to permanent deformation. Therefore, the hardness of aragonite, H can be obtained by the ratio of maximum indentation force Pmax and the projected contact area A. Accordingly, for indentation along c -axes with maximum elastic load of 300 nN and a contact area of 33.18 nm2, we obtain a hardness H[001] of 9.04 GPa. This result is in good agreement with the exper imental measurement value, 8.6 0.36 GPa (Kearney et al., 2006). With the same formula, we determine the hardness of aragonite along a -axes is 7.96 Gpa. This means that aragonite hardness is significantly affected by the crystal ori entation. The result that the hardness along c axes is larger than that along a -axes is consistent with the ex perimental finding (Han et al., 1991) that the (001) plane is harder than any other planes in aragonite. The other difference resides in the plastic regime that a se ries of load plateaus are observed in the case of indentation along c -axes, while load drops are seen in the case of indentation along a -axes. This phenomenon implies t hat the plastic behaviors of indentation on different crystallographic orie ntation surfaces may be dominated by different deformation mechanisms. To further study the deformation processes, in Fig. 5-6 we plot the atomic configurations at indentation di splacement of 3.5 nm in t he cases of indentation along c and a -axes, respectively. It is noticed that in Fig. 5-6 (a) a surrounding pileup zone is observed when indenting along c -axes. The observation of such a pileup zone is consistent with a previous reported experimental observation on aragonite (Kearney et al., 2006). In contrast, such pileup phenomenon is not clearly observed in the case of indentation along a -axes (Fig. 5-6 (b)). This phenomeno n can be further studied through


75 comparing the side cross-sectional views of the deformed structures for the two cases in Fig. 5-7 (a-b). One can note that in the case of indentation along c -axes the aragonite atoms beneath the contacted surface has trans formed into the amorphous phase, while the atoms that are several layers away from the indenter maintained the initial aragonite crystal structure; no dislocati ons or cracks are observed. In the case of the indentation along a -axes, other than small amount of atoms transform ed into amorphous phase, another regularly arranged new phase is obser ved and extends in the normal direction to the contact surface. We use both radi al distribution function (RDF) and coordination number in this study to identify the new phase. The side view s of atomic structur e of aragonite and the transformed phase induced by indentation along a -axes are presented in Fig. 5-8 (a-b). It is noticed in Fig. 5-8 that the carbonate ions in the init ial aragonite structure tend to rotate and move, which accordingly lead the correlated calcium atoms to deviate from their original positions. C onsequently, the geometry dist ribution of calcium atoms changes from the initial zigzag shape to approximately straight lines. Fig. 5-9 summarizes the radial distribution functions (RDF) of key atoms pair separations for aragonite and the transformed phase induced by indentation, tension and compression, which will be discussed in the following sections. RDF of aragonite and new transformed phase induced by indentation along a -axes are labeled as “ARA” and “INDx”, respectively. It appears that the radius of the nearest Ca-Ca nei ghbor of transformed phase is smaller than that of aragonite, whic h indicates a density increase and a volume reduction. Lacking detailed phase structures of CaCO3 from experimental studies, we propose this new phase based on our molecu lar dynamics simulation results.


76 The force-di splacement curves for i ndentation and retraction along a-axes are shown in Fig. 5-10. It is noted that initially the indentat ion curve follows the elastic deformation as labeled by the black arrow. At point 1, the slope of p-h curve decrease abruptly, which indicates the plastic deformati on. Then the indenter tip is retracted after reaching point 2. It should be noted that when the indenter force dec rease to zero at point 3, there is still an indent er depth of 2.2 nm that cannot recover, which can also observed from the unloaded structure in Fig. 511 (b) and Fig. 5-15 (b ). This indicates permanent plastic deformati on after retraction. In order to st udy the plastic deformation mechanism in detail, Fig. 5-11 presents the side cross-sectional views of atomic conf iguration of deformed structures before and after unloading. It is observed from Fig. 5-11 that both amor phous phase and a new regularly arranged phase. In this study, since the phase transformed from aragonite under increasing pressure, we name this new formed phase as post-aragonite X. It is found ( Dickens and Bowen, 1971) that the unit cell of aragonite is orthorhombic with a=4. 96, b=7.96, c=5.74 and = = =900, as listed in table 5-3. In contrast, post-aragonite X has monoclinic un it cell with lattice par ameters of a=4.43, b=8.72, c=5.98 and =76.980, = =900, as illustrated in table 5-4 The bond length of Ca-O1 and C-O remain the same values as that of aragonite. The big difference happens at the distance between Ca and O. Fig. 5-12 and Fig. 5-13 present the crosssectional and 3-d views of unit cells of aragonite and post-aragonite X. The space group changes from pmcn of aragonite to pmmn of post-aragonite X.


77 To identify the distribution of post-aragonite X fo rmed in the indented region, the surrounding environments of each atom are considered and the number of nearest neighbor atoms, namely coordi nation number, is employed to study phase transition process. According to the difference in the radius of nearest Ca-Ca neighbors for aragonite and post-aragonite X, here we adopt the coordination number of calcium atoms to identify phase transformation. Aragoni te has two nearest calcium neighbors at a distance of 3.89 while post-aragonite X is detected to have two nearest calcium neighbors at a distance of 3.33 Hence, a cutoff radius of 3.4 which is between 3.33 and 3.89 is chosen to calculate t he coordinate number. Within the radius of 3.4 there are no atoms in the aragonite phase while t here are two atoms in postaragonite X. Figure 5-14 shows cross-sectional views of the distribution of the transformed phase induced by indentation along a -axes at different defo rmation stages. The atoms are colored according to the coordination nu mber of calcium atoms. The blue atoms represent the original aragonite crystalli ne structure; the ye llow and green atoms represent the ordered new phas e – post-aragonite X and t he amorphous phase that have been completely transformed into after bei ng indented, respectively. One can note from Fig. 5-14 that the phase transforma tions occur and propagate anisotropically, resulting in a symmetry petal pattern. Fig. 5-15 presents distribution of post-aragonite X before and after unloading. Blue and green atoms denote aragonite and post-aragonite X, respectively. Atoms with the other colors denote amorphous phase. From the comparison between Fig. 5-15 (a) and (b), it is observed that after unloading the penetration depth remains at 2.2 nm. In additi on, the transformed post-aragonite X area


78 decreases and the amorphous phase is still obs erved. It is believed that the postaragonite X and amorphous phase are responsible for the permanent plastic deformation after retraction, as illustrated in Fig. 5-10, Fi g. 5-11(b) and Fig. 5-15(b). Looking back at the load-displacement relationship in Fig. 5-5, it may be concluded that the observed load plateaus in the l oad-displacement (P-H) curve of indentation along c -axes is attributed to the pileup z one formation, which leads to sudden energy release and accordingly results in the decr ease of the overall sl ope, i.e., load plateaus. However, in the case of indentation along a -axes, the plastic load-drops in loaddisplacement (P-H) curve in Fig. 5-5 may be induced by the phase transformation. As indicated in Fig. 5-14, pos t-aragonite X nucleates beneat h the contact surface and grows under higher loads. Many high-pres sure phases of aragonite have been reported ex perimentally (Oganov et al., 2006) such as, post-aragoni te, phase I, phase II, phase III and phase IV. The post-aragonite phase is measured to be st able at a pressure above 40 GPa (Ono et al., 2005; Sekkal, et al., 2008). These phases are energetically com petitive structures and become stable at high-pressure (usually above 42 GPa) conditions (Ono, et al., 2007). It is well known that the basic principle to deter mine the most stable crystal structure is that the stable st ructure has the lowest possible Gibbs free energy at given P-T conditions (Oganov et al., 2006). From our simulation results it is noted that postaragonite X is stable at a pressure above or equals to 10 GPa, as denoted with green color in Fig. 5-15 (b). In summary, pos t-aragonite X is a phase of CaCO3 that different from the experimentally reported high-pressure phas es, which is usually measured above 40


79 GPa. It is a low energy phase and be stable at a pressure equals to or a little bit above 10GPa. During retraction, when pressure decreases to below 10 GPa, the postaragonite X recovers to aragonite. Therefor e, under pressure below 10 GPa, postaragonite is metastable and is not a low energy phase. 5.2.2 Uniaxial Tension In this section, we investigate the structural and mechanical properties of aragonite subjected to uniaxial tensile loading along a -axes. This simulation is motivated by the experimental tension study of nacre tablet s (Barthelat and Espinosa, 2007). Fig. 5-16 shows the three-dimensional computer model of aragonite plate. The system size is set as 50.0 nm 50.0 nm 10.0 nm and it includes 2,108,000 atoms in total. The simulation is carried out at room temperature with a loadi ng rate of 0.1 /ps. The obtained stress-strain relation is plotted in Fig. 5-17. One can notice that the simulated YoungÂ’s modulus is 142 GPa, wh ich is consistent with the experimental measured value of 144GPa of single crysta lline aragonite (Barthelat and Espinosa, 2003). Moreover, the elastic shoulder is followed by a sudden stress drop, which indicates the beginning of plastic flow. To further reveal the underlying plastic deformation mechanism, in Fig. 5-18 (a) and (b) we present the atomic configurations at strains of 0.052 and 0.056, respectively. We see that in Fig. 518 (a) dislocations nucleate and propagate along {110} slip plane, which is also one of the cleavage planes (Huggins, 1922). Voids are observed at the disl ocation tips marked with black arrows in Fig. 5-18 (b). We believe that it is dislocation nucleation that results in the sudden stress drop in stress-strain curve in Fig. 5-17. In addition, as two dislocations meet, it is


80 observed that the atomic arrangement in some areas is changed, which indicates possible occurrence of phase transformation. To further invest igate the nature of the dislocati on slip and phase transformation in aragonite during uniaxial tension, we analyz e the dislocation migration path and the phase diagram. Firstly, we zoom in the defo rmed structure to track the motion of atoms along dislocation line. Figure 519 schematically illustrate the dislocation nucleation and propagation process. As displa yed in Fig. 5-1, the prim itive unit cell of aragonite contains four CaCO3 units. One can note from Fig. 5-19 that dislocation onset is attributed to the relative motion of CaCO3 units in primitive unit cell other than the movement of atoms within a CaCO3 unit. This may be understood because the ionic attractive interaction between Ca2+ and CO3 2within a single molecule is much stronger than the interaction between CaCO3 molecules. Hence, when atoms are forced to slip under tensile loading the Ca2+ and CO3 2in a single molecule will be bonded together and move as a group. As reported by a t heoretical study (Huggi ns, 1922), the cleavage plane of crystalline aragonite tends to occur to rupture the weaker bonds in preference to the stronger bonds. Similarly, dislocations pr efer to be triggered by relative movement between CaCO3 units. Secondly, the at omic structure of aragonite and the transformed phase induced by uniaxial tension are compared in Fig. 5-8 (a ) and (c). Also, radial distribution function (RDF) is employed again to evaluate the phase transformation. RDF information of the aragonite phase and the new phase induced by t ensile loading are labeled in Fig. 5-9 as “ARA” and “TEN-x”, respectively. Through compar ison it is evident that different from aragonite structure, the transformed phase induc ed by tension is a new ordered phase.


81 5.2.3 Uniaxial Compression In this secti on, we present numerical simula tions of aragonite under uniaxial compression along a and c -axes. The computer model c onsists of 2,371,200 atoms in total with a size of 30.0 nm 30.0 nm 30.0 nm. Fig. 5-20 shows the atomic configuration of the aragonite cube adopted in our compression simulations. It is a finite size sample and no periodic boundary condition is applied. The compressive loading is applied to the atoms within four layers at the two ends along the compression axes. The strain rate is controlled at 3.33108 s-1. Figure 5-21 pres ents the stress-strain curves obtained from the compression simulations along a and c -axes, respectively. As can be seen from Fig. 5-21, the measured YoungÂ’s modulus along c -axes in the simulation is about 80GPa, which is consistent with the experiment al measurement of 82GPa (Barthelat and Espinosa, 2003). However, the Young modulus along a -axes is slightly sm aller than the one along c -axes, i.e., 67 GPa vs. 80 GPa. The other si gnificant difference between the curves is the yield stress. For the case of compression along a -axes, plastic deformation starts at the strain of 0.02 corresponding to a yiel d stress of 120 MPa. A stress plateau is observed after the yield point, which imp lies possible structural change and atomic rearrangement. Thereafter, the st ress increases dramatically a nd the material fails. If we define the fracture toughness as the energy required to make a crack propagates, which can be calculated through the area under stress-strain curves, we find that the fracture toughness of aragonite is also highly cr ystallographic ori entation dependent. In order to i dentify the plastic deformation mec hanism, snapshots of the deformed structure at different plastic stage are present ed in Fig. 5-22. It is seen that voids,


82 marked with black arrows, are formed due to the propagation of disl ocations along [110] direction. A more detailed study of dynamic process indicates t hat the nucleation and propagation of dislocations follow the same path as schematically explained in Fig. 5-19. In addition, it is observed in Fig. 5-22 (a-c) that the new arrangement of atoms in the compressed region differs considerably from the init ial structure. The crystal structure before and after deformation is plotted in Fig. 5-8 (a) and (d ), respectively. We find that the atoms in trans formed phase still maintain a long-range crystalline order. This suggests that a phase transformation of aragonite has occurred. Using the radial distribution function (RDF), it is found that this phase is very similar to the transformed new phase induced by indentation along a -axes. Note that in Fig. 5-9 (b) this new phase has two nearest Ca neighbors at a shorter di stance of 3.33 than that of aragonite (3.89 ). Hence a cutoff radius of 3.6 which is between 3.33 and 3.89 is chosen to calculate the coordinate number of Ca. Fig. 5-23 (b) presents the new phase distribution at a strain of 0.12. The atoms are colored a ccording to coordination number with red for the new phase, blue for aragonite and other colors for amorphous phase. It is worth emphasizing that different from the dislocation propagat ion observed in the tension simulation, dislocations trigger ed by compressive loading cannot propagate to the free surface of the comput er model due to the obstacle of newly transformed phase. Furthermore, it is surprising to note from Fig. 523 (b) that the newly formed phase twinned together, which is especially clear in the lower half region of model specimen. The twinning boundaries that marked by blue or yellow atoms between red regions can be clearly identified. To further investigate the nature of the twi nning structure, we picked the lower half region of the specimen before and after compression to trace the


83 deformation process and compare them in Fig. 5-23 (a) and (c). It is seen that the transformed phase is symmetric to twin boundar y (TB) planes with an inclination angle of 68.2o, which is comparable to the experiment observation of 63.8o that reported by Huang et al (2011). However, no phase transforma tion was reported in their study. Very recently, it is reported that a well-def ined twinning structur e could highly promote material strength (Lu et al., 2009; Zhang and H uang, 2008; Li et al., 2010). Recalling the stress-strain curve in Fig. 5-21, there is no doubt that the gradual stress increasing after the plateau region is attribut ed to the deformation resistance from the twinned structure. As for t he case of compression along c -axes, Fig. 5-21 shows that the material yields at a larger strain of 0.09 with a yi eld stress of 600 MPa that is higher than the counterparts of compression along a -axes. This result again correlates with the experimental observation that (001) plane is harder than (100) plane (Han et al., 1991). From this viewpoint we can, to some ex tent, explain why nacre develops a “brick-andmortar” tablet arrangement with the c -axes of aragonite perpendicular to the surface to protect itself from a harsh predatory penetrating attack. The oscillations in the stressstrain curve in elastic region are believed to be induced by thermal fluctuation of atoms in the room temperature env ironment employed in this study. A short stress plateau region is observed after yield point. Diffe rent from the case of compression along a -axes, stress-strain curve shows a sudden drop after the stress plateau. To rev eal the underlying deformation mechani sm, in Fig. 5-24 we present the snapshots of the deformed structure at strains of 0.12 and 0.17, respectively. It is seen from Fig. 5-24 (a) that the stress plateau in the stress-strain curve corresponds to the process of the rearrangement of atoms. In Fig. 5-25 we compare the arrangements of


84 atoms in the squared region in Fig. 5-24 (a) before and after compression. One may observed from Fig. 5-25 (a-b) that the initial overlapped -CO3 groups from side view tend to slip and rearrange to a straight line to resist the continuous compressive loading until the strain reaches about 0. 15. Fig. 5-25 (b) shows t hat there is a significant increase in structure density. This can be explained through Fig. 5-9 (d) that the new phase has a shorter nearest C-C neighbor radius of 0.26nm t han that of aragonite (0.30 nm). Thereafter, the structure fails fi nally through an amorphous phase transition and propagation along {110} slip planes, as illustrat ed in Figure 5-24 (b). This result proves that the propagation of amor phous phase prefers to occur al ong {110} slip planes. 5.3 Conclusions In summary, ro om temperature molecular dynamics simulations have been carried out with an attempt of studying the mechani cal properties and dynamic behaviors of single crystalline aragonite under indentatio n, tension and compression. The measured elastic modulus and hardness of single crystal line aragonite in our simulations are well consistent with experimental measurement. Some observations that reported by previous experimental studies of aragoni te crystals have been reproduced in our simulations, including the load plateau in the force-displacement curves and the presence of pileup zones when being indented along c -axes. Through MD simulations we have found that when indented along different crystallographic orientations aragonite has different deforma tion patterns, different loaddisplacement curves, very different elas tic modulus, strength, and hardness. The simulations have revealed that those differ ences resulted from different deformation mechanisms, i.e., amorphous phase formation under indentation along c -axes and a


85 new crystalline phase transfo rmation under indentation along a -axes. We have also found that the material behaves differently under different loading conditions. Under uniaxial tension the plastic deformation is induced by both phase transformation and dislocations, while under compression along c -axes, the dominant plastic deformation mechanism is the phase transformation. Ho wever, in compression simulation along aaxes, we have not only observed phase tr ansformation, dislocation nucleation and migration, but also twinning. As a result of the different deformation mechanisms, the yield strength and fracture toughness of aragonite along c -axes are significantly higher than those along a -axes. The loading type and crysta llographic orientation dependent deformation mechanisms are summarized in table 5-5. This work is an attempt to identify the deformati on mechanisms in single crystalline aragonite and to establish the relati onship between the dominant deformation mechanisms and the crystallogra phic orientation and loading conditions, so as provide some insights on the formation and properties of nacre tablets. Simulation of a nacre tablet that consists of bot h the aragonite crystals and the or ganic proteins is our ongoing work, through which the dynamic behavior of single crystalline aragonite will be further investigated.


86 Table 5-1. A summary of t he potential parameters of diffe rent models for aragonite. References Pavese et al. (1992) RIM Dove et al. (1992) RIM Jackson et al. (1992) RIM Pavese et al. (1996) SM Braybrook et al. (2002) RIM Ca-O Buck. A/eV 2043.19 3943.59778839.31550.0 8839.3 Buck. / 0.2886 0.251570 0.238130.2970 0.23813 O-O Buck. A/eV 1563461 2879.126236010.816372.0 36010.8 Buck. / 0.1366 0.252525 0.197560.2130 0.19756 Buck. C/eV 6 3.47 0.0 C-O Buck. A/eV 14460.951 1.741110 3088.4----Buck. / 0.0458 0.038730.12635----Morse D/eV --------4.71 --Morse / 1 --------3.80 --Morse r 0/ --------1.18 --Harmonic k/eV ----------400.0 Harmonic r 0/ ----------1.29 Ion charges qCa/|e| +2.000 +1.64203+2.000+2.000 +2.000 qC/|e| +0.817 +1.04085+0.99805+1.134 +0.99805 q O / | e | -0.939 -0.894293-0.99935-1.045 -0.99935 qOs /|e| ---------1.632 --spring constants kb ( O-C-O ) /eV 4.0397 3.694419.31791.69 9.3179 kt/eV 0.1562 0.1251251. 13920.1129 1.1392 kcs ( O ) /eV 2 --------507.4 --Table 5-2. A summary of the co mputer models of nanoindentation. Samples LxLyLz (nm) Number of atoms Indentation direction 1,600,000 c -axes 2,016,000 c -axes 3,096,640 a -axes


87 Table 5-3. Aragonite structure of CaCO3. Parameters Experiment (Dickens and Bowen, 1971) In this study a() 4.9598 4.96 b() 7.9641 7.97 c() 5.7379 5.74 V( 3 ) 226.65 226.9 Bond length, Ca-O1=2.414 Ca-O2=2.653 C-O=1.288 Ca-Ca=3.9 Ca-O1=2.47 Ca-O2=2.62 C-O=1.27 Ca-Ca=3.89 Angles = = =90 0 = = =90 0 Space group pmcn pmcn Table 5-4. Post-aragonite X structure of CaCO3 at a pressure of 10GPa. Parameters In this study a() 4.43 b() 8.72 c() 5.98 V( 3 ) 231.78 Bond length, Ca-O1=2.41 Ca-O2=2.44 C-O=1.28 Ca-Ca=3.33 Angles =76.98 0 = =90 0 Space group pmmn Table 5-5. A summary of deformation mechanisms under indentat ion, tension and compression. Deformation mechanisms Amorphous phase formation New crystalline phase transformation Dislocation Crystal twinning Indentation along caxes Yes No No No Indentation along a axes No Yes No No Tension along a -axes No Yes Yes No Compression along caxes Yes Yes No No Compression along a axes No Yes Yes Yes


88 Figure 5-1. The orthorhombic unit cell of aragonite. Figure 5-2. An MD indentation model of aragonite.


89 Figure 5-3. Load-displacement (P-H) curves for sample 1 with finite size and the periodic boundary conditions, respectively. Figure 5-4. Load-displacement (P-H) curves of sample 1 with load ing rates of 0.1/ps and 0.3/ps, respectively. 0 0.5 1 1.5 2 2.5 3 3.5 0 100 200 300 400 500 600 Displacement H (nm)Load P (nN) Finite size Periodic boundary


90 Figure 5-5. Load-displacement (P -h) curves of indentation along a (sample 3) and c axes (sample 2). Figure 5-6. Deformed strucutr es at a displacement of 3. 5 nm for indentation along (a) c axes and (b) a -axes, respectively.


91 Figure 5-7. Side cross-sectional views of t he deformed structure in Fig. 5-6, indentation along (a) c -axes and (b) a -axes. Figure 5-8. Comparison of atomic structure diagram s, viewed along c -axes, of (a) aragonite and (b-d) transformed phases induced by indentation, tension and compression along a -axes, respectively.


92 Figure 5-9. Radial distribution functions of (a) calcium-carbon; (b) calcium-calcium; (c) calcium-oxygen; and (d) carbon-car bon for aragonite and transformed phase induced by indentation, tension and compression, respectively.


93 Figure 5-10. The load-displacement (P-H) cu rves for single crystalline aragonite under indentation along a-axes. The red and blue lines denote the loading and unloading curves, respectively. Figure 5-11. Side cross-sectional views of def ormed structure at (a ) indented depth of 3.8 nm and (b) after unloading. (a) (b)


94 Figure 5-12. Cross-sectional view s of unit cells of (a) aragonite and (b) post-aragonite X. Figure 5-13. Comparison of 3-D views of (a ) orthorhombic unit cell of aragonite and (b) monoclinic unit cell of post-aragonite X. Figure 5-14. Side cross-sectional view s of the transformed region induced by indentation along a -axes at the penetration depth of (a) 2.6 nm; (b) 3.0 nm and (c) 3.5 nm. The atoms are colo red by coordination number. Blue atoms are the original aragonite. Yellow and green atoms are the transformed ordered crystalline p hase and the amorphous phase, respectively.


95 Figure 5-15. Side cross-sectional views of transformed region at the penetration depth of (a) 3.8nm and (b) after unloading. The atoms are colored by coordination number. Blue atoms are the original aragonite. Green atoms are the transformed ordered crystalline phase. The other colors denote the amorphous phase. Figure 5-16. The MD comput er model of aragonite for uni axial tension simulation. (a) (b)


96 Figure 5-17. Stress-strain relation for si ngle crystalline aragonite under tensile loading along a -axes. Figure 5-18. Side cross-sectional views of aragonite under uniaxial tensile loading along a -axes at the strain of (a) 0. 052; (b) 0.056. The black arrows indicate the voids formed during dislocation propagation.


97 Figure 5-19. A schematic of dislocation nuc leation and migration pr ocess. (a) Initial perfect aragonite structure; (b) At oms moving one Burgers vector along [110] slip plane; (c) Atomic arrangement s after the dislocation move out to sample surface. Figure 5-20. The 3-D MD model for singl e crystalline aragonite under compression.


98 Figure 5-21. Stress-strain curves for single crystalline aragonite under uniaxial compression along a -axes and c -axes, respectively. Figure 5-22. Snapshots of aragonite under compression along a -axes at different strain stages: (a) =0.03; (b) =0.06; (c) =0.1. The black arrows label the voids formed due to dislocation propagation.


99 Figure 5-23. Cross sectional view of at omic arrangement (a) before and (b) after compression along a -axes at a strain of 0.12. The atoms in (b) are colored by coordinate number. (c) shows the twinned structure after comp ression, whose region before compression is squared in (a). Figure 5-24. Side cross sectional views of def ormed structure at st rains of (a) 0.12 and (b) 0.17 when compressed along c -axes.

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100 Figure 5-25. Comparison of (a) Initial ar agonite structure and (b) Compressed structure that squared in Fig. 5-24 (a).

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101 CHAPTER 6 MOLECULAR ORIGIN OF THE SAWTOOTH BEHAVIOR AND THE TOUGHNESS OF NACRE Abalone shell nacre is a remarkabl e biogenic composite mate rial. It is composed of 95-99% (by weight) calcium carbonate. Combi ned with small portion (< 5%) of organic matrix (Weiner, 1986), it becomes much stro nger and significantly much tougher than calcium carbonate crystals, an improvement in properties that current composite techniques cannot replicate. Also, it exhibits simultaneo usly high toughness, strength and stiffness (Jackson et al., 1988; Sarikaya, et al., 1990), a combination rarely seen in man-made materials. At the microscale, it is found that nacre has a layered tabletandmortar structure. At the nanoscale, each tablet is further com posed of aragonite crystals, a crystal form of calcium carbonate, separated by continuous organic bio-polymers in the grain boundaries (Rousseau, et al., 2005). The nanoscale organic matrixes not only nucleate and direct the growth of the aragoni te crystals, but also act as glue between the single crystalline grains and hold the cr ystalline grains together (Weiss et al., 2000). Numerous studies have been performed over the past decades through experimental, theoretical and comput ational approaches to understand how the microstructural features of nacre gov ern its mechanical performance. Various deformation mechanisms have been proposed with t he attempt to explai n the origins of the exceptional mechanical pr operties, particularly the high toughness of nacre (Weiner, 1986; Smith et al., 1999; Wang et al., 2001; Song et al., 2001; Li et al., 2004; Bruet et al., 2005; Katti et al., 2005; Li et al., 2005; Fratzl and Weinkamer, 2007; Barthelat, 2007; Ortiz and Boyce, 2008; Sumitomo et al., 2008; Espinosa et al., 2009). Facilitated by atomic force microscopy (AFM), many pr ogresses have been achieved in understanding

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102 of the role of the proteins and of the interaction between the proteins and the mineral (Smith et al., 1999). Sawtooth behavior has been observed in the force-extension curves when pulling a protein out of a tablet, which explains the high energy dissipation and hence high fracture toughness of nacre (Smith et al., 1999). Hypothesis of mechanisms, such as “modular” elongation (S mith et al., 1999), sacrificial bonds and hidden length (Fantner et al., 2006), were proposed that suggest protein chain unfolding may give rise to the saw-tooth behavior and hence contribute towards the high fracture toughness. Although a great amount of expe rimental and theoretical works have been performed, the relation between protein unfolding and sawtooth behavior in forceextension curves have still been a speculation (Hui and Klaus, 1999; Oberhauser et al., 2001; Li et al., 2005). In addition, through deta iled experimental study it was found that high toughness of nacre was measured mainly in hydrated state (Bart helat et al., 2007). This indicates that water molecules may also play a significant role in increase the toughness of nacre. Although advanced experi mental tools could measure the mechanical behavior of nacre accurately, the state of the art exper imental techniques cannot elucidate the deformation mechanism at fine scales. Atomic-level molecular dynamics (MD) simulations are thus ideal ly suited for this purpose and have the promise to provide the missing information on the fundamental mechanisms (Best et al., 2001; Marszalek et al., 1999; Bryant et al., 2000; Shen et al., 2002). The goal of the study in this chapter is to identify the mechanisms that give rise to the saw-tooth behavior in load-displacement relation of nacre and to study the water effect on protein-mineral interaction. A fter the introduction, the computer model, simulation setup and method employed will be introduced in section 6.1; simulation

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103 results will be presented and discussed in se ction 6.2; a summary will be given in section 6.3. 6.1 Model and Method The nacre tablet model is a 3-dimensional pol ycrystalline aragonite plate with a very thin organic layer intercalated betw een crystalline grain boun daries. Compared to ordered crystalline solids, proteins are r andomly arranged materials. Therefore, the challenge in building a comput er model is to determine t he arrangements of protein chains relative to the mineral crystals. In this study, we use steered molecule dynamics (SMD) method to simulate the process of dragging a protein chain into the grain boundaries to construct the structural model of the mineral-protein composite, and then to simulate the process of stretching it out of the grain boundaries to mimic the AFM experiments. In the SMD simula tions, we apply an external force to a protein in order to reveal the resulting structural changes at the atomic level. The pulling velocity is held constant during our simulations. Figure 6-1 pres ents our method of generating a co mputer model to mimic the composite structure of a nacre tablet. Firs t, the protein chains are dragged toward the predefined reference points in the grain boundaries using steered molecule dynamics (SMD); then, the system is allowed to equ ilibrate for a period of 100 picoseconds to reach its energy minimum; the pot ential energy vs. time is show n in Fig. 2; after that the energy minimized configuration is used as t he initial structure fo r protein stretching simulations. Four experimentally identified nacre proteins: lust rin A, perlucin, perlustrin and perlwapin, as listed in table 6-1, were se lected to represent the thin organic layer

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104 intercalated between grain boundaries in this study. All of these proteins are isolated from the nacreous layer of t he shell of abalone, among which lustrin A is the first large multidomain protein isolated from abal one nacre and characterized by sequence analysis, and is the most “popular” one (Shen et al., 1997) of all the molluscan proteins. It is the single protein that established a clear link betw een a primary structure and the overall mechanical properties of nacre (Ma rin et al., 2008) and is believed to be a component of the adhesive between mineral tablets (Smith et al., 1999). Analysis of its modular structure reveals that lustrin A contains 10 highly conserved cysteine-rich domains (C1-C10) with 8 proline-rich domai ns (P1-P8) interspersed between each of cysteine-rich domains. A glycineand seri ne-rich domain (GS) lies between two cysteine-rich domains (C9 and C10) near t he C-terminus (Shen et al., 1997). Because the function of each domain on overall mech anical behavior of nac re tablets is not known, in this study we have chosen two representative domains, C1-P1-C2-P2 and GS, to study the interaction betw een lustrin A and the mineral. Perlucin is a C-type lectin protei n isolated from abalone nacre (Weiss et al., 2000). It consists of 155 amino acids, the first 130 of which show a high similarity to the C-type (Ca2+ dependent) lectin-like domains (CTLD) (Mann et al., 2000). It was found that perlucin promotes the nucl eation and growth of CaCO3 (Mann et al., 2000). This suggested that this type of pr otein performs an important f unction in biomineralization. We believe it may also have a strong infl uence on the mechanica l properties of the biominerals. Recently, two other water-soluble proteins, perlustrin and perlwapin, were isolated from the aragonite layer of the abalone shell. Perlustrin has an “insulin-like growth factor

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105 binding N-terminal domain”, which may be bi ologically relevant (Weiss et al., 2001). Perlwapin consists of 134 ami no acids, in which there are “three whey acidic protein (WAP) domains” (Treccani et al., 2006).This i ndicated that perlwapin may be involved in the regulation of growth and could also pl ay a role in the polymorph transition and mechanical functions. Since the complete amino acid sequences of the four proteins have been well characterized, random stru ctures can be gener ated based on their primary sequences. Fig. 6-3 presents their molecula r structures. Fig. 6-4 present s four distinct models for the simulations. The model shown in Fig. 64 (a) is to mimic the stretch of a single perlucin chain so as to measure the force re quired during protein self -unfolding. Fig. 6-4 (b) presents a model in which protein chains ar e tangled together. This model is used to investigate the interaction between proteins. In Fig. 6-4 (c) one protein chain is inserted into the grain boundary of tablet nano-crystalline structur e to study the protein-mineral interaction. Then, a TIP3P water box is appli ed to the model in Fig. 6-4 (c) to study the effect of water (Fig. 6-4 (d)) on protei n-mineral interaction. The corresponding simulations are denoted as SMD-(single-chai n), SMD-(multiple-ch ain), SMD-(proteinmineral) and SMD-(wat-protein-mineral). Having obtained the energy-minimized structure of the nacre tablet models, SMD simulations are then performed using t he general MD program AMBER with the classical AMBER ff99 force field (Cornell et al ., 1995). The integration time step is set to 1 fs, and the cutoff of Coulomb forces is 10 The dimensions of the computer model are 300.0 300.0 60.0

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106 To mo del the tip of the AFM in the experiment s, an external force is applied to the head of the protein to pull the protein towards a predefined refe rence point at a constant velocity. The external force exer ted on the system is given as, Fkvtx (6-1) where k denotes the stiffness of restraint, x is the displacement of the dragged atom from its original position, vis the dragging speed. In our simu lations, we select a spring constant of SMD as 10 k kcal/mol/2 and the temperature of the system as T=300 K. Here, to simulate the mechanical unfolding, one end of the protein in SMD-(single-chain) is fixed and the other end is applied an extern al force to stretch the protein to a fully extended structure. In SMD-(mu ltiple-chain), once a specific protein is selected, the “tails” of other protein chains are fixed. T hen, an external force stretches the “head” of the selected protein out of the protein “rope”. For SMD-(p rotein-mineral) and SMD-(watprotein-mineral), pulling of proteins is acco mplished by applying an external force at the “head” of protein so that to stre tch it out of the grain boundary. 6.2 Results and Discussions 6.2.1 Protein Pulling Simulations In order to mi mic the AFM experiment and to derive insights from existing AFM observations, we have performed protein-pul ling simulations on SMD-(single-chain), SMD-(multiple-chain) and SMD-(protein-mineral ), respectively. For SMD-(proteinmineral) case, we have modeled four differe nt proteins, including CPCP and GS domains of lustrin A, perlucin, perlust rin and perlwapin, respectively. The obtained force-extension curves for different models are compared in Fig. 6-5.

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107 It is noted that the curves m easured from the simulations that involve proteinmineral interaction, especially the GS-dom ain stretching simulation, are qualitatively similar to the AFM experiment al results reported by Smith et al. (1999), i.e., they all exhibit a sawtooth like feature, and this sa wtooth behavior is a characteristic feature observed when pulling protein fr om a nacre tablet. In cont rast, the curve obtained from the simulation of single chain unfolding is much smoother and the magnitude is much smaller. This indicates that the well-kn own protein self-unfolding explanation to sawtooth behavior in force-extension curves may not valid; since this work shows protein self-unfolding make s insignificant contributi on to the sawtooth phenomena and the force magnitude. In addition, the obtained force-extension curve for simulation of a perlucin chain stretching out of multiple proteins “rope” shows similarity to the curve of single chain unfolding simulation. This result excludes the possibili ty that interaction between proteins is an orig in of sawtooth behavior. To further explore the major source of sawt ooth behavior, we have also monitored the atomic trajectories around the force peaks plotted in Fig. 6-5. It is interesting to note that at the extension of maximum force, a bunch of ionic bonds between protein and mineral break concurrently. The force peak s quared in Fig. 6-5 is selected to elucidate the molecular origin of sawtooth behavior in detail. Fig. 6-6 pres ents snapshots of the atomic arrangements near the protein-mineral interface at the extensions immediately before and after the squared force peak of perlwapin pulling out simulation. It is observed that a sharp force increase occurs from 10.0 to15.0 which corresponds to the stretching of a bunch of ionic bonds betw een protein and mineral, as illustrated in Fig. 6-6 (a). One can recognize that the acidic (red) and basic (blue) amino acids have

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108 an obvious tendency to adhere to calcium car bonate. The highest force peak of 40 nN is reached at the extension of 15.0 nm when the ionic bonds are stretched to a critical length. With further stretching, the ionic bon ds cannot resist further loading and break simultaneously, which accounts for the sudden force drop that reaches 25 nN at 15.1 nm, as shown in Fig. 6-6 (b). Thereafter, the domains begin to extend rapidly and new ionic bonds reform between protein and mi neral. The newly reformed ionic bonds together with the initial ioni c bonds are stretched to sust ain the upcoming loading, producing the subsequent force peak. Since the ionic bonds between protein and mineral can only form between acidic ions (COO-) and Ca2+ or between basic ions (NH3 +) and CO3 2, to further explore the relationship between sawtooth behavior and prot ein-mineral ionic bonds, we count the number of acidic and basic amino acids for each protein domain. Here, we define the ratio of the number of acidic/ basic amino acids to total resi due number of protein as the density of ionic bonds formed on the grain boundaries and list t he densities in Table 6-2. Comparing table 6-2 and Fig. 6-5, we find that the magnitude and intensity of force sawtooth behavior clearly have a strong dependence on the density of ionic bonds. The larger the ionic bond density on grain boun dary, the higher the magnitude and the intensity of force peaks are observed. Accord ingly, although the number of acidic/basic residues in perlwapin is smaller than that of CPCP-domain, the ma gnitude and intensity of force peaks in perlwapin simulation are significantly higher t han those of CPCPdomain pulling simulation. This, we believe, is due to the higher ionic bonds density of perlwapin chain on grain boundaries. In com parison, the magnitude of force peaks in GS-domain pulling simulation is the lowest due to the lowest ionic bond density.

PAGE 109

109 Thus, we believe it is the low density of ionic bonds in GS-domain that explains why no significant sawtooth behavior was observed in the previous computer simulations of GS-domain pulling on aragonite su rface (Ghosh et al., 2007; Ghosh et al., 2008). In addition, the force peaks observed in force-extension curves in nacre were argued to be caused by non-bonded secondary interactions such as hydrogen bonds and van der Waals interactions. However, it is well known that the ionic bond (700 to 1000 kJ/mole) is more than twenty times st ronger than hydrogen bond (5 to 30 kJ/mole) or van der Waals interaction (Yariv and Yeh, et al., 1984). Therefore, we believe that these outstanding force peaks observed in our simulations are induced by the breaking of high density ionic bonds between protein and mineral interface. 6.2.2 Water Effect on Protein-mineral Interaction To investigate t he effect of water on protein-miner al interactions, simulations of perlucin pulling with and without water mole cules presented in the grain boundaries are performed, respectively. The obtained force-ext ension curves are compared in Fig. 6-7. Both curves display sawtooth characteristic However, with the presence of water, the force peaks become much broader, and the mean force magnitude is slightly smaller than that in simulations without water. As seen in Fig. 6-7, at the extension from 28.0 to 38.0 two sharp force peaks can be obs erved in the perlucin pulling simulation, while with the presence of water t he forces reach a plateau region. To identify t he underlying deformation mechanism s that lead to the different pattern of force-extension curves, again we have tracked the atomic trajectories at extensions before and after the force peak and force plateau squared in Fig. 6-7. As stated above, when the protein is pulled, a bunch of ionic bonds between protein and

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110 mineral are forced to stretch to gener ate the force peak, and then they break concurrently, resulting in the sudden force dr op; in the following cycle, the prior broken ionic bonds reform between protein and mineral at specific sites, making a contribution to the next force peak formation. However, with the presence of water molecules, a water layer is formed to cover the mi neral surface and abundant hydrogen bonds are brought in as illustrated in Fig. 6-8. It is noted that before the pl ateau region all acidic and basic residues of perlucin adhere to mineral surface, as circled in Fig. 6-8 (a); once the perlucin chain is stretched, the acidic and basic residues of perlucin are forced to deviate from their original positions. This isolated water layer thus prevents new ionic bonds reforming between protein and mineral, as squared in Fig. 6-8 (b-c). This means that only the initially formed ionic bonds between protein and mineral and the hydrogen bonds formed due to the addition of water will be stretched to make a contribution in generating the new force peak. Therefore, the magnitudes of force peaks are smaller and the peaks become much broader. 6.3 Summary Sawtooth behavior is a phenomena obse rved in the force-extension curves in AFM experiments when pulling a protein out of nacre (Smith et al., 1999) and bone (Thompson et al., 2001; Sanghvi et al., 2005). Protein unfold ing has been widely believed to be the mechanistic origin of the sawtooth behavior and hence the high toughness of tough biological materials (Fantner et al., 2006). In this study, we present a method to build computer models that mimi c the mineral-protein composite structure of a nacre tablet. Steered molecular dynami cs (SMD) have been perf ormed to simulate the AFM experiments of pulling protein chains out of nacr e tablets. The interaction

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111 between protein and mineral has been invest igated and the sawtooth force-extension curves have been observed in simulations in good agreement with existing AFM experiment measurements and observations. Di fferent from the widely believed protein self-unfolding mechanism for sawtooth behavio r, we have found the ionic interactions (electrostatic interactions) between protein and mineral are responsible for the sawtooth behavior. Also, we find the hydrogen-bonds inte ractions that mostly induced by water molecules has contributed significantly to the passivation of force peaks in forceextension curves. It should be noted that currently SMD simulations can only be performed for nanoseconds, which require forces one order stronger than those in AFM experiment. Nevertheless, our simulation re sults obtained in this study are in a qualitative agreement with AFM observations, and have provided some insights on the origin of the high energy required to break nacre, i.e., the high toughness of nacre.

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112 Table 6-1. The nacreous proteins used in this study. Protein Name Species Molecular Weight (kDa) p I References Lustrin A Haliotis rufescens /Nacre 140.08.13 Shen et al., 1997 Perlucin Haliotis laevigata /Nacre 18.27.15 Mann et al., 2000 Perlustrin Haliotis laevigata /Nacre 9.38.02 Weiss et al., 2001 Perlwapin Haliotis laevigata /Nacre 14.58.62 Treccani et al., 2006 Table 6-2. A summary of the pr operties of the four proteins. Protein No. of acidic amino acids No. of basic amino acids Total No. of acidic /basic residues Total No. of residues Density (%) Aspartic acid Glutamic acid Lysine Arginine Histidine Perlucin 7 10 413640 15525.8% GS-domain 2 0 0002 2240.9% CPCPdomain 9 6 415135 21716.1% Perlustrin 3 4 54117 8420.2% Perlwapin 7 4 1010132 13423.8%

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113 Figure 6-1. Schematic repres entation of the initial comput er model, in which predefined reference points along grain boundar ies are marked as 1, 2,Â…6. Figure 6-2. Potential energy vers us time during ener gy minimization. 0 20 40 60 80 100 -4 -3 -2 -1 0 1 x 105 time (ps)potential energy (kcal)

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114 Figure 6-3. Molecular struct ures of (a) perlwapin (b) perlu cin (c) perlustrin (d) CPCP domain of lustrin A and (e) GS domain of lustrin A. Figure 6-4. Top views of computer models of (a) a single protein chain; (b) multiple tangled proteins including lustrin A, perlucin, perlustrin and perlwapin, respectively; (c) polycrystalline aragonite with one protein chain inserted in the grain boundary; (d) model c with the presence of water molecules on grain boundaries.

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115 Figure 6-5. Force-extension curves measur ed in the simulations during the processes of pulling the protein, including CPCP a nd GS domains of lustrin A, perlucin, perlustrin, and perlwapin, out of grain boundaries. Force-extension curves during protein-unfolding and being stretched out of t he multiple proteins “rope” are also plotted. The pulling ve locity is controlled at 0.6/ps. 0 10 20 30 40 50 0 10 20 30 40 50 Extension (nm)Force (nN)GS-domain CPCP-domain Perlucin Perlwapin Perlustrin Proteins-unfolding Multiple-proteins

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116 Figure 6-6. Snapshots of the atomic trajectory during pulli ng out process of perlwapin molecules (top views): (a) before the fo rce peak at the extension of 14.8, (b) after the force peak at the extensi on of 15.1. The colors of molecules represent different residue types, w here the red and blue ones denote the acidic and basic amino acids, and t he green and white residues represent the polar and non-polar amino acids, respectively. The cyan atoms denote the ionic molecules – calcium carbonate, and the circles highlight the ionic bonds formed between protein and mineral.

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117 Figure 6-7. Comparison of the force-extension curves of perlucin pulling simulations with and without the presence of water molecules in the grain boundaries. The pulling velocity is controlled at 0.6/ps. 0 10 20 30 40 50 60 0 5 10 15 20 25 30 35 40 45 Extension (nm)Force (nN) Perlucin Perlucin-water

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118 Figure 6-8. Snapshots of the atomic arrangements (a) before, (b) at and (c) after the plateau region in the force-extension cu rve, the squared regi on in Fig. 6-7. Pink dotted lines represent the hydrogen bonds formed among water, protein and mineral. Red and blue atoms denote the acidic and basic amino acids, respectively.

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119 CHAPTER 7 A NEW INSIGHT INTO TOUGHENING ME CHANISM OF MIMIC NACRE TABLET: MINERAL-PROTEIN COMPOSITE In this chapter, room temperature MD simulations were conducted to investigate the critical role that protein plays in impr oving the mechanical properties, particularly the toughness, of nacre. Three sample conf igurations: single crystalline aragonite, polycrystalline aragonite and mineral-protein co mposite, are employed in the uniaxial tension simulations. 7.1 Simulation Details In the current inve stigation, there are three kinds of sample models, i.e., single crystalline aragonite, polycrystal line aragonite and protein-miner al composite, which is simulated as polycrystalline aragonite with prot eins intercalated in grain boundaries. Four experimentally identified nacre proteins: lu strin A, perlucin, perlustrin and perwapin, as detailed discussed in the prev ious work (Zhang and Chen, 2012), tangled together to represent the thin organic layer intercalated between grain boundaries in this study. All of these proteins ar e isolated from the inner layer of abalone. Lustrin A is the first found large multi-domain protein that isolated from the inner layer of abalone (Shen et al., 1997). It is also the mo st complex in its primary st ructure and the most “popular” one of all the molluscan proteins. Lustrin A has an established link between a primary structure and the overall mec hanical property of nacre. Bec ause the full-length of lustrin A is so long (4,439 bp), two typical dom ains, C1-P1-C2-P2 and GS, are chosen to represent the structure of lustrin A. Perlucin is an N-glycosylated protein with a character of calcium-dependent lectin (C-type) (Weiss et al., 2000). Perlucin is reported to have a significant influence on biominer alization (Mann et al., 2000), consequently

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120 may have a strong influence on the mechanical pr operties of biominerals. Perlustrin is a small protein with “an insuli n-like growth factor binding N-terminal domain”, which may be biologically related (Weiss et al., 2001). Pe rlwapin contains 3 repeats of 40 amino acid residues with similarity to the whey ac idic proteins (WAP) (Treccani et al., 2006). It is suggested that perlwapin inhibits the grow th of certain crystallographic planes and could also play a role in the polym orph transition and mec hanical functions. The crystal structur e of aragonite that was used to bui ld the computer model in this study has been fully depicted in the previ ous work (Zhang and Chen, 2013). Fig. 7-1(a) and (b) present the initial computer model s of single crystalline and polycrystalline aragonite, which have the same syst em size of 43.543.510.5 nm3 and include 1,839,200 and 1,487,250 atoms, respectively. The geomet ric construction of mineral-protein co mposite is a little bit challenging. We used steered molecular dynamics (SMD) method to simulate the process of dragging protein chains into grain boundaries of polycrystalline aragonite to construct the structural model of mineral-protein com posite. SMD is an increasingly popular tool for accelerating conformational changes in biomolecular systems through the application of external forces. Fig. 7-2 presents our implementation of dragging one protein chain into grain boundary. First, pairs of reference points are predefined on grain boundaries and protein chain as schematically A-A’, B-B’…, F-F’. It should be mentioned that ther e are lots of pairs of referenc e points between grain boundaries and protein chain. For simplicity, the schematic in Fig. 7-2 only presents atoms on grain boundaries of polycrystalline aragonite and only six pairs of reference points are shown. By control the dragging velocity at a consta nt value, SMD simulations were conducted

PAGE 121

121 by fixing the reference atoms, i.e., A, B Â…, F, of polycrystalline aragonite, and by applying external force to the atoms, i.e. AÂ’, BÂ’Â…FÂ’, of the protein chain. Take one pair of reference points (A-AÂ’) for instance, the ex ternal force were carried out by restraining the A atom of aragonite harmoni cally to the restraint atom AÂ’ of protein. And then the restraint point AÂ’ is dragged at a constant speed v along the defined direction. This procedure is very similar to attach one end of a spring on an aragonite atom (A) and then drag the other end. This simulation is equivalent to dragging a protein out of a tablet in AFM experiment (Smi th et al., 1999). The difference is that the dragging speed in SMD simulations is approxim ately six orders larger than that in AFM experiment. The forces on the dragging atom are Fkvtx (7-1) In equation 7-1, k denotes the spring constant, x denotes the displacement of the dragged atom from its original location, vdenotes the dragging speed, which is controlled at 1.0 /ps in our simulations, then vt will be the location of the restrained point. The vector from atom AÂ’ on protein chain to atom A on polycrystalline aragonite will be the dragging direction. The sp ring constant is controlled at 10 BkT/2. To make sure the dragging velocity of restraint point AÂ’ is constant, the location of AÂ’ is updated every 10 fs. After all protein chains were dragged into grain boundar ies, the system is allowed to equilibrate for a period of 1ns to reach its energy minimum. The top view of resulting configuration is shown in Fig. 7-3 (a). In experiments, it is repor ted that the tensile strength for dry and wet nacre sample is 170 MPa and 140 MPa, respectively (Jackson et al., 1988). Associated with the permanent plastic deformation, wet nacre show s very high toughness. This indicate that

PAGE 122

122 water molecules may play a significant role in improving the me chanical behaviors of nacre. To simulate the hydrated nacre tabl et, the solvent was modeled by TIP3P water model (Jorgensen et al., 1983) to cover the su rfaces of proteins. Figure 7-3 (b) shows the top view of the initial dehydrated mi neral-protein composite model before MD simulation. It should be noted from Fig. 7-3 (a) and (b) that big spaces were left between protein and mineral after t he initial model generation. To ensure protein and mineral interact with each other intimately, prelim inary MD simulations were performed to squeeze the well-built model, i. e., Fig. 7-3 (b), to dimi nish the spaces on grain boundaries. The squeezing procedure is achieved by shrinking the volume of simulation box in specified dimensions, i.e., x and y direct ions, at a constant ra te until the shrunken distance along each direction reaches 1nm. Afte r that, the entire system is allowed to carry out structural relaxation for a period of 1ns to fulfill energy minimization. This cyclic procedure is repeated until the spacing on grain boundaries diminished enough to ensure protein and mineral contact intimately. Before carrying out MD simulations, it is important to ensure that the chosen potential function used gives reliable results. Construction of the simulations presented below requires reliable force fi eld for the mineral, the organi c layer, and interactions between the two. The potentia l of aragonite was taken from previous work (Zhang and Chen, 2013), in which calcium carbonate wa s modeled with the rigid-ion model (RIM) developed by Dove et al (1992). The Do ve potential functi on includes non-bonded and bonded parts. In bonded part, bond-bending of O-C-O are described by harmonic function, which takes the form

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123 2 01 () 2 Vk (7-2) where 0 denotes the equilibrium angle, k denotes the constant for bond bending, denotes the angle between the O-C-O atoms. An additional four-body term is used to model the planarity of the CO3 molecular ion. This tors ional term is of the form 1cos2tVk (7-3) where tk denotes force const ant due to out-of-plane, is the angle between two O-CO planes in a single molecular ion. For the non-bonded part, the Coulomb interaction is evaluated using Ewald sum, with a precision of 1106. The short-range interaction be tween Ca-O, O-O and C-O are treated using Born-Mayer repulsive potential, ()exp() VrAr (7-4) where A are parameters for differen t atoms interaction, and r denotes the distance between two atoms. The detailed information of these parameters is summarized in Tab 7-1. The organic layer was represented wit h the AMBER ff99 force fi eld (Cornell et al., 1995), consistent with previous simulations on this system (Zhang and Chen, 2012). Potentials for interaction between the mi neral and organic com ponents are somewhat more complicated. In the cu rrent context, organic-mineral is also modeled with the AMBER ff99 force field (Cornell et al., 1995), which takes the form

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124 22 00 2 0 1261cosb bondsangles dihedrals imp impropers ijijijijijij nonbijVrKbbK Kn K A rBrqqr (7-5) where is dihedral angle, is bond angle, is the improper torsion angle and bis bond length. K impK,bK and K denote the force constant of angle, improper dihedral angle, bond and dihedral angle. The equilibrium values ar e denoted by the subscript zero. ij A ij B are the minimum distances of Lennard-Jones potential, ijr denotes separation of atom i and atom j iq, jq are the atom charges. SMD simulations were conducted using the AMBER simulation package (Cornell et al., 1995). Constant volume and temperatur e (NVT) ensemble were used with the MD program LAMMPS (Plimpton, 1995). The Verl et-Leapfrog algorith m (Verlet, 1967; Gunsteren and Berendsen, 1990) is used. T he time step is 1fs. The Nos–Hoover thermostat (Woodcock and Singer, 1974; Nos 1984) method with relaxation constant of 0.1ps was used to control the temperature at a constant value (298K). a cut-off of 15.0 is chosen for the calculation of Coulomb and vdWs interactions. 7.2 Results and Discussion In analyzing the re sults, we first look at the overall deformation behavior and then elucidate the atomic mechanism in detail. Before applying strain, the computer models of single crystalline aragonite, polycrystalline aragonite and protei n-mineral composite as seen in Figure 7-1 (a-b) and

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125 Figure 7-3 (c) are fully relaxed. In applying strain, the uniaxial dimension is uniformly increased by 0.1% of the or iginal length every 50,000 st eps. The corresponding strain rate is 2107/s. The simulated stress-strain relations are summarized in Fig. 7-4, from which one can note that for single crystalline aragonite the stress first approximately linearly increases with strain before a sudden drop, whic h indicates yielding of aragonite plate. The YoungÂ’s modulus of about 150 GPa is obtained through measure the slope of the stress-strain curve near zero strain. This value is in agreement with the experiment measurement of 144 GPa (B arthelat and Espinosa, 2003). The maximum stress indicates the beginning of plastic flow. To reveal the underlying plastic deformation mechanism, in Fig. 7-5 we present the at omic configuration of single crystalline aragonite under 0.8% and 0.9% tensile strain. The atoms are colored according to coordinate number with green for original aragonite, blue for new phase and dislocation line. It is found that under continuous t ensile loading disloc ations nucleate and propagate along {110} slip plane. When the di slocation along [110] direction meets the one along [-110] direction, the atomic struct ure of the area ahead of the intersection is changed but still maintain a long-range crystalli ne order, which indicate the occurrence of phase transformation. Detailed plastic de formation analysis has been depicted in the previous work (Zhang and Chen, 2013). As for the case of uniaxial tension of polycrystalline aragonite, it can be observed from Fig. 7-4 that the stre ss-strain curve shows inelastic behavior from the initial part. To understand what controls the nonlinear tensil e behavior; we present the atomic structure of polycrystalline aragonite at stra in of 0.3% as shown in Fig. 7-6(a).

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126 Compared with the initial structur e in Fig. 7-1(b), it is noted that all grains have been stretched along the a-axis. Some grains even ro tate to resist furt her deformation, which is consistent with the prev ious report (Li et al., 2006) that “nanograin rotation and deformation are the two prominent mechanism s contributing to energy dissipation in nacre”. Void formation is observed along th e grain boundaries marked with black arrows in Fig. 7-6(a). In addition, as the grains are stretched to undergo tensile deformation, it is observed that the atomic arrangement in the grain that encircled with the dash box in Fig. 7-6(a) is changed but still maintain a lo ng-range crystalline order. Part of the crystal structures of circled grain bef ore and after applying tensile loading are plotted in Fig. 7-7. In this study, both radial distributi on function (RDF) and coordinate number are employed to identify the new phase. Struct ure analysis and RDF results indicate that the distance between nearest Ca-Ca neighbor s of the new transformed phase, the location of the first peak of red line as shown in Fig. 7-8, is 3.3 which is significantly smaller than that of aragonite (3.89 ). Theref ore, a cutoff radius of 3.5 which is between 3.3 and 3.89 is picked to calculat e the coordinate number of calcium ions. One can notice from Fig. 7-8 t hat for a specific calcium atom within a distance of 3.5 there are two atoms in the new phase while there are no atoms in the aragonite phase. Fig. 7-6 (b) and (c) present the cross sectional views of deformed structures at strain of 0.3% and 0.6%. The atoms are colored accord ing to the coordinate number of calcium atoms with blue represent aragonite phase, green and cyan represent the transformed regular new phase and amorphous phase, respectively. We believe that it is the combination of grain stretching deformati on, void formation an d phase transformation that leads to the inelastic deformation behav ior of polycrystalline aragonite as seen in

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127 Fig. 7-4. With the tensile strain in creases, three phenomena are observed through the comparison of Fig. 7-6 (b) and (c). Firstly, the area of new phase extends. Secondly, area of cyan color on grain boundaries increas e, which indicates the extension of amorphous phase formation. Finally, small vo ids grow up to big crack along grain boundaries, which eventually results in final failure of material. The area under stre ss-strain curve is defined as t he work-of-fracture. It can be observed from the comparison of Fig. 7-4 (a) and (b) that the pa ttern of deformation behavior from our simulation is in good agreem ent with that from experiment, in which the work-of-fracture of mineral -protein composite is signifi cantly larger than that of single crystalline aragonite. To reveal t he underlying mechanism of mineral-protein composite that gives rise to high work-offracture, we track the deformed structure under different strains. Fig. 7-9 (a) and (b) present the atomic a rrangement of mineralprotein composite under strain of 1% and 5%. It can be noted from the comparison of (a) and (b) that, as the tensile strain increases some deformation behaviors are observed. All grains are stretched to ex tend along tension direction. Meanwhile, the width of grain boundaries grows due to the applyi ng of tensile loading, whic h is consistent with the observation of polycrystalline aragonite under tension. Although ionic force between protein and mineral on grain boundaries is smaller than t hat within nanograins due to the high ionic bond density wit hin grains, the separation on grain boundaries is significantly larger than that within grain due to soft and ductile properties of proteins. Accordingly, energy release rate needed to make grain boundary fractures is much larger than that to make grains fracture, wh ich is reflected in computational model as fracture within grains are observed, as shown in Fig. 7-9 (c). Fig. 7-9 (c) presents the

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128 detailed atomic structure of the boxed region in Fig. 7-9 (b). Proteins on grain boundaries are colored according to residue types that red and blue ones represent acidic and basic amino acids, and green and white ones represent polar and non-polar amino acids. The circles and boxes highli ght the ionic bonds formed between protein and mineral. One can recognize that the acidic (red) and basic (blue) amino acids have an obvious tendency of stick to calcium carb onate ions. This failure mechanism is different from that of pol ycrystalline aragonite, in which the dominant failure phenomena is the fracture along grain boundaries. Sinc e the ionic bonds are more than twenty times stronger than hydrogen bonds due to the addition of water molecules or van der Waals interaction, we believe that the ionic inte raction between protein and minerals is the primary force to glue the grains together to prevent fracture along boundaries, which is reflected as high work-of-fracture in stress-strain relation in Fig. 7-4. Accordingly, as the tensile loading increase to a cr itical value, fracture alon g [-1 1 0] within grain are observed as illustrated in Fig. 7-9 (c). 7.3 Conclusions In summary, room temperature MD simulations have been performed on single crystalline aragonite, polycryst alline aragonite and mineral-p rotein composite, to investigate the plastic deformation mechani sm, especially the toughness mechanism, of mimic nacre tablet. Simulation results show that the pattern of stress-strain relation is in agreement with that of experi mental measurement. The work -of-fracture of mineralprotein composite is significantly larger than that of single crystalline or polycrystalline aragonite. The measured elastic modulus of single crystalline aragonite is consistent with the experimentally measured value.

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129 Different def ormation mechanisms have been observed for different computer models, as summarized in table 7-2. Under uniaxial tensile loadi ng, single crystalline aragonite fails through phase transformation, dislocation and fracture along {110} cleavage plane. While for polycrystalline aragonite phase transformation is observed within nano-grains. Voids form along grai n boundaries and conseq uently grow into a critical crack, which directly leads to the failure of material. Fo r the mineral-protein composite, it is surprisingly observed that the ionic interacti on between acidic/basic amino acids and calcium carbonate ions plays a vital role in gluing mineral grains together to resist continuous plastic deforma tion, which we believe is a significant source of high toughness of nacre tablet. T he soft and ductile proper ties of proteins make the energy release rate that needed to make the fracture along grain boundaries is significantly larger than that for fractu re within grains. Intra-granular fracture along {110} cleavage plane is observed.

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130 Table 7-1. Potential parameters for aragonite. Interaction A (eV) () Ca-O 3943.59770251570 O-O 2879.12620.252525 C-O 1.741130910 13 0.03873 Ca charge = +1.64203e k(O-C-O) = 3.69441 eV rad2 O charge = –0.894293e kt(O-C-O) = 0.125125 eV C charge = +1.04085e Table 7-2. A summary of deformation mec hanisms of different co mputer models under uniaxial tensile loading. Single crystalline aragonite Polycrystalline aragonite Mineral-protein composite Deformation mechanism (1) Phase transformation (2) Dislocation (3) Fracture (1) Phase transformation (2) Fracture along grain boundaries (1) Extension of grain boundaries (2) Intra-granular fracture

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131 Figure 7-1. Initial atomic c onfigurations of (a) single crystalline aragonite and (b) polycrystalline aragonite.

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132 Figure 7-2. Schematic represent ation of the initial computer model of protein-mineral composite, in which predefined refe rence points along grain boundaries and protein chain are marked as A, BÂ…, F and AÂ’, BÂ’Â…, FÂ’, respectively.

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133 Figure 7-3. Top views of mineral-protein composite model with proteins and water molecules intercalated in the grain boundaries are shown in (a) and (b), respectively. The top view of sh runken model is shown in (c).

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134 Figure 7-4. Stress-strain curves for single crystalline aragonite, pol ycrystalline aragonite and protein-mineral composite under uni axial tensile loading from (a) computer simulation. (b) stress-strai n relation of nacre measured from experiment (Sun and Bhushan, 2012).

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135 Figure 7-5. Snapshots of single crystalline ar agonite under uniaxial tension along a-axis at strain of (a) 0.8% and (b) 0.9%. The atoms are colored by coordinate number.

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136 Figure 7-6. Side cross-sectional views of deformed structur e of polycrystalline aragonite at strains of (a -b) 0.3% and (c) 0.6%. The atoms in (b) and (c) are colored by coordinate number.

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137 Figure 7-7. Comparison of atomic stru cture diagrams of (a) aragonite and (b) new phase. Figure 7-8. Radial distributi on function (RDF) of calcium-cal cium for aragonite and new phase. 0 0.1 0.2 0.3 0.4 0.5 0.6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 Radial Separation (nm)Radial DensityAragonite New Phase

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138 Figure 7-9. Top views of atom ic arrangement of mineral-prote in composite at strains of (a) 1% and (b) 5%. (c) Zoomed in atom ic configuration of the dash boxed region in (b).

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139 CHAPTER 8 DISCUSSION To understand how the microstructure of nacre governs its mechanical performance, numerous studies including expe rimental, theoretical and computational approaches have been performed over the past decades. It has been demonstrated that at the micro-scale, nacre has a layered tabl et-and-mortar structure; while at the nanoscale, each tablet is further composed of aragonite crystals enclosed by continuous organic bio-polymers. Various deformation me chanisms, such as asperities on tablet surface (Wang et al., 2001; Evans et al., 2001), mineral bridges (Song et al., 2003; Lin et al., 2007; Gries et al., 2009), tablets interl ocks (Katti et al., 2006), tablet surfaces waviness (Barthelat 2007), rotation and deforma tion of nanograins in tablet (Li et al., 2004) and hierarchical structur e (Gao et al., 2003; Fratzl et al., 2007), have been proposed with the attempt to explain the origins of t he exceptional mechanical properties of nacre. This work is an attempt to use molecular dynam ics (MD) method to identify the deformation mechanism of nacre in red abalone, so as to provide some insights on the origin of high toughness, str ength and stiffness of the nacre tablet. Aragonite, as the predominant component of nacre, is first inve stigated under various loading conditions – indentation, tension and compression. Simu lation results show that aragonite at different orientations has different deforma tion pattern, different load-displacement curve, different stress-strain relation and very different elastic modulus, strength and hardness. We have revealed that those di fferences are resulted from different deformation mechanisms, i.e., amorphous phas e formation, new regular crystal phase

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140 formation, dislocation nucleat ion and migration and crystal twinning. Some observations including the load plateau in force-displacem ent curves, presence of pileup zones and crystal twinning that reported by previous experimental studies have been reproduced in our simulations. Motivated by t he saw-tooth behavior that others observed in the force-extension curves in AFM experiments (Smith et al ., 1999), we use steered molecular dynamics (SMD) to simulate the AFM exper iments of pulling protein chains out of nacre tablets. In this study, four experimenta lly identified nacre protein: lustrin A (Shen et al., 1997), perlucin (Weiss et al., 2000), perlustin (Wei ss et al., 2000) and perlwapin (Treccani et al., 2006), have been selected to represent the thin organic layer intercalated between grain boundaries. One of the bi g challenges we have overcome is that we figured out a novel method to construct a mimic nacre tablet structure. The saw-tooth force-extension curves have been reproduced in our simulati ons, which is in a qualitative agreement with AFM observations. Differ ent from the widely believ ed protein self-unfolding mechanism for saw-tooth behavior, we have found that the ionic interactions between protein and mineral are responsib le for the saw-tooth behavior. To further invest igate the role that protein pl ays in improving the toughness of nacre, we built a computer model of mineral-p rotein composite to mimic a nacre tablet. Uniaxial tension simulation results show that different sample confi guration has different failure mechanism. Single crystalline arag onite fails through phase transformation, dislocation and fracture along {110} cleav age plane. Polycrystalline aragonite fails through phase transformation within nano-grai ns and crack propagation along grain boundaries. However, for mineral-protein co mposite, fracture within nanograins is

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141 observed. The soft and ductile properties of pr oteins make the energy release rate that needed to make the fracture along grain boundarie s is significantly larger than that for fracture within grains. Theref ore, we believe that we bel ieve that the electrostatic interaction between protein and mineral is a significant source of high toughness in nacre.

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156 PUBLICATIONS, CONFERENC ES, POSTERS AND AWARD Journal Papers: 1. Ning Zhang, Youping Chen, Nanoscale Pl astic Deformation Mechanism in Single Crystal Aragonite, Journal of Materials Science 2013 (48): 785-796. 2. Ning Zhang, Youping Chen, Molecular Or igin of the Sawt ooth Behavior and the Toughness of Nacre, Materials Science and Engineering C 2012 (32), 1542-1547. 3. Ning Zhang, Qian Deng, Yu Hong, Shi Li, Matthew Strasberg, Liming Xiong, Weiqi Yin, Yongjie Zhou, Cutis Taylor, Greg Sawyer, Youping Chen, Deformation Mechanisms in Silicon Nano-Particles, Journal of Applied Physics 2011 109(6), 063534(1-6). 4. Ning Zhang, Youping Chen, A new insight into toughness mechanism of nacre tablet. Ready to submit. 5. Ning Zhang, Youping Chen, Twinning bound ary effect on crack propagation of aragonite. In preparing. Conference papers and presentations: 1. Ning Zhang and Youping Chen, “Molecular origin of the sawtooth behavior and the toughness of nacre ”, Society of Engineering Scienc e 49th Annual Technical Meeting (SES) October 10-12, 2012, Georgia Tech, USA. 2. Ning Zhang and Youping Chen, “ Nanoscale plastic deforma tion mechanism in single crystal aragonite ”, Society of Engineering Scienc e 49th Annual Technical Meeting (SES) October 10-12, 2012, Georgia Tech, USA. 3. Ning Zhang and Youping Chen, “Dislocation behavior in single and polycrystalline aragonite by molecular dynamics simulation”, 16th US National Congress of

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157 Theoretical and Applied Mechanics (USNCTAM) Pennsylvania State University in University Park, PA on June 27 July 2, 2010. 4. Ning Zhang and Youping Chen, “Steered molecular dynamics studies on mechanical behavior at protein-mineral interfac e in biological nanocomposite”, 16th US National Congress of Theoretical and Applied Mechanics (USNCTAM) Pennsylvania State University in University Park, PA on June 27 July 2, 2010. 5. Ning Zhang and Youping Chen, “Phase tr ansformation in single and polycrystalline aragonite by molecular dynamics simulation”, 2009 ASME International Mechanical Engineering Congress Lake Buena Vista, FL on No vember 13 – November 19, 2009. Posters: 1. Ning Zhang and Youping Chen, “Molecular Origin of the Sawtooth Behavior and the Toughness of Nacre”, 2011 ASME International Mechanical Engineering Congress & Exposition Denver, CO on November 11-17, 2011. 2. Ning Zhang and Youping Chen, “St eered Molecular Dynamics Studies on Mechanical Behavior at Protein-mineral In terface in Biological Nanocomposite”, 2011 NSF-CMMI Research and Innovation Conference, Atlanta, GA on January 4-7, 2011. 3. Ning Zhang and Youping Chen, “Deformation Mechanisms in Silicon NanoParticles”, UF NSF Research Day Gainesville, FL on October 25, 2010. Awards & Honors 1. UF Engineering Outstanding International Student Award, 10/2012 2. NSF Student Travel Grant s for the ASME IMECE 2011 Mi cro/Nano Poster Forum,

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158 11/2011 3. Student Participation Gr ant from the 2011 NSF-CMMI Research and Innovation Conference, 01/2011 4. GSC travel grant, 04/2010

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159 BIOGRAPHICAL SKETCH Ning Zhang was born in Zouping, Shandong, P.R.China, in 1982. She earned her Bachelor of Science with a major in engine ering mechanics from Dalian University of Technology (DUT), Dalian, P.R.China, in 2006. S he was then recommended to Huazhong University of Science and Tech nology (HUST), Wuhan, P.R.China to continue her graduate study. In 2008, she obtai ned her Mater of Science in a major of Solid Mechanics from HUST. From summer 2008, she began to work as a teaching and research assistant with Dr. Youping Chen at Univ ersity of Florida. Her research goal is using Molecular Dynamics (MD) to reveal the underlying deformation mechanism of abalone nacre that give rise to the remarkable mechanical performances. During the past five years, s he has published 3 peer reviewed journal papers as first author and she has 5 oral presentations in national and international conferences including American Society of Mechanical Engineers (ASME), Society of Engineering Science (SES) and US National Congress on Theoretical and Applied Mechanics (USNCTAM). She also has 3 posters nation conferences including American Society of Mechanical Engineers (ASME) and Division of Civil, Mechanical and Manufacturing Innovation (CMMI). She got University of Florida (UF) Engineering Outstanding International Student Award in 2012 and ot her two National Science Foundation (NSF) Student Travel Grants in 2011.