Dynamic Energy Dissipation Using Nanostructures: Mechanisms and Applications

Jun Xu

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY

2014

Dynamic Energy Dissipation Using Nanostructures: Mechanisms and Applications

Jun Xu

The emerging subject of mechanical impact protection at nanoscale where solids, fluids interact closely, has raised many multi-disciplinary and challenging questions which cannot be answered by the analogy from their macroscopic counterparts.

A series of counterintuitive phenomena have been observed without further profound theoretical explanations. It is pretty straightforward to take advantage of these novel properties for fascinating applications which cannot be achieved by traditional materials and structures. Among various exciting areas, one of the most promising and ever expanding topics is the impact protection at nanoscale.

Primarily inspired by the excellent mechanical properties of carbon nanotube

(CNT), a water-filled CNT system for impact protection is designed. The nanoconfined water molecules enhance the stiffness of the tube and also help to stabilize the tube such that the buckling force and the post-buckling plateau is higher than empty CNTs, indicating a much higher energy dissipation performance. Also, the energy dissipation performance is dependent on the aspect ratio which is similar in its bulk counterpart.

Additional support may come from adjacent tubes in CNT bundle and forests and the actual energy dissipation per unit volume/mass is improved. Unlike the tube or beam shape, once the single layer graphene is rolled into a spherical shell, it becomes buckyball whose mechanical properties are seldom studied.

Thus, firstly, the quasi-static and dynamic behavior of buckyball is investigated based on

MD simulation. Buckyball may be categorized according to the mechanical behavior. The force-displacement curve obey the continuum shell model prediction perfectly except for the slight difference in coefficient change due to the size effect. Interestingly, it is discovered that larger buckyball cannot recover to its original shape after unloading while the smaller buckyball can. Stronger van der Waals interaction between the buckled layer and the bottom layer may be the responsible reason for the non-recovery phenomenon.

The buckled shape should have higher strain energy such that more mechanical energy is dissipated.

Motivated by the novel behavior of buckyball, the various stacking forms of buckyball are investigated. By analogy for the 1D granular energy dissipation system, a

1D long chain buckyball system is designed and studied. With relatively small elastic deformations of C60 buckyballs during impact, a modified Hertz contact model is proposed, with critical parameters calibrated via MD simulations for given impact loading conditions. The major energy dissipation mechanism for the buckyball chain is the wave reflection among the deformation layers, covalent potential energy, van der

Waals interactions as well as the atomistic kinetic energy. For nonrecovery buckyballs such as C720, energy mitigation effect is more obvious. Over 99% and 90% of impact energy for C720 and C60 chain systems could be mitigated under particular impact conditions. Moreover, protective system based on short 1D vertical and horizontal alignments and various pseudo 3D stacking forms with different packing densities are also studied. It is found that stacking form with higher occupation density yields higher energy absorption and proves the available buckyball in bulk is ready for impact protection.

In addition, to quantify the material behavior, prove the recently suggested new theories and discover new phenomenon, desktop experiments serves as an important part of this thesis research. The governing factors, i.e. pre-treatment temperatures, solid-to-liquid mass ratio, particle size and electrolyte concentration are parametrically studied. Experiments show that the optimum processing pretreatment temperature is about 1000 ℃ with higher zeolite mass ratio. Also, the dynamic behavior of zeolite

β/water system is investigated and the system has a better dynamic performance than quasi-static since the infiltration pressure increases due to the water molecule inertia effect.

To conclude, impact dynamics and energy dissipation/mitigation at nanoscale is a lasting topic in mechanics related research area whose knowledge is highly desire in engineering application with the advancement of material science, physics and chemistry. Table of Contents

List of Figures ...... ii List of Tables ...... vii Acknowledgements ...... viii Chapter 1 Introduction and Motivation ...... 1 1.1 Challenge in Impact Safety ...... 1 1.2 Handling Impact Protection at Macro and Meso Scale ...... 2 1.3 Opportunity for Nanomaterials and Nanostructures ...... 7 1.3.1 Mechanical properties of major nanomaterials and nanostrcutures ...... 7 1.3.2 Opportunity of nanofluidics ...... 10 1.4 Current Research Progress of Impact Protection at Nanoscale ...... 16 1.5 Innovation of Current Research ...... 24 1.6 Methodology ...... 25 1.6.1 Basis of MD simulation ...... 26 1.6.1.1 MD force field ...... 26 1.6.1.2 Non-bonded atom forces ...... 26 1.6.1.3 Inter-molecule forces ...... 27 1.6.1.4 Thermostats and barostats ...... 28 1.6.2 Water molecules and carbon nanotubes ...... 28 1.6.2.1 Water molecular models ...... 28 1.6.2.2 Carbon nanotube and buckyball models ...... 29 1.6.2.3 Carbon-water interactions ...... 30 1.7 Outline of Dissertation ...... 31 Chapter 2 CNT Based Protection System ...... 34 2.1 Computational Model and Method ...... 34 2.2 Results and Discussions ...... 35 2.2.1 Typical buckling responses of hollow and water-filled CNTs ...... 35 2.2.2 Typical buckling responses of hollow and water-filled CNTs ...... 38 2.2.3 Effect of impact velocity on energy absorption ...... 40 2.2.4 Effect of impact velocity on energy absorption ...... 41 2.2.5 Energy absorption of nanotube forest ...... 44

2.3 Concluding Remarks ...... 45 Chapter 3 Mechanical Behavior of Buckyball ...... 47 3.1 Computational Model and Method ...... 47 3.2 Results and Discussion ...... 50 3.2.1 Buckling characteristics of buckyball ...... 50 3.2.2 Mitigation of transmitted impulse force of buckyball ...... 52 3.2.3 Impact energy dissipation of fullerenes ...... 53 3.2.4 Effect of varying impact energy ...... 55 3.2.5 Atomic simulation results for large buckyball ...... 56 3.2.6 Phenomenological mechanical models ...... 58 3.2.6.1 Three-phase model for low-speed crushing ...... 58 3.2.6.2 Two-phase model for impact ...... 62 3.3 Concluding Remarks ...... 64 Chapter 4 Impact Protection of Buckyball System ...... 66 4.1 Computational Model and Method ...... 66 4.2 Representative Impact Behavior For 1D Long Chain Buckyball ...... 68

4.2.1 Dynamic response of C60 chain system ...... 69 4.2.1.1 Hertzian model ...... 69

4.2.1.2 MD simulation of one-dimensional C60 long chain ...... 70 4.2.1.3 Dissipative Hertzian model ...... 72

4.2.2 Dynamic response of C720 chain system ...... 73 4.3 Parametric Study and Discussions ...... 75

4.3.1 Effects of initial impact speed and mass on C60 chain ...... 76 4.3.1.1 Force attenuation ...... 76 4.3.1.2 System equivalent Young’s modulus ...... 78

4.3.2 Effect of initial impact speed and mass on C720 chain ...... 79 4.3.2.1 Force attenuation ...... 79 4.3.2.2 System equivalent Young’s modulus ...... 80 4.3.3 Effect of buckyball size ...... 81 4.3.4 Effect of buckyball number ...... 82 4.4 Buckyball Assembly ...... 83 4.4.1 Short 1-D alignment buckyball system ...... 84 4.4.2 Pseudo 3D alignment buckyball system ...... 87 4.5 Concluding Remarks ...... 91

Chapter 5 Governing Factors in Impact Protection Based on Nanofluidics System . 93 5.1 Experimental Setup ...... 93 5.1.1 Material preparation ...... 93 5.1.2 Experimental device and setups ...... 96 5.2 Results and Discussions ...... 97 5.2.1 Typical loading and unloading behavior of ZSM-5/ water mixture ...... 97 5.2.2 Energy dissipation mechanism ...... 99 5.2.3 Effect of pretreatment temperature ...... 101 5.2.4 Variation in mass ratio of zeolite to water ...... 104 5.2.5 Variation in particle size ...... 108 5.3 Typical Sorption Isotherm for Sodium Chloride System ...... 110

5.3.1 Effect on infiltration pressure Pin ...... 112

5.3.2 Effect on defiltration pressure Pde ...... 117

5.3.3 Effect on pressure hysteresis Phys ...... 119 5.4 Dynamic Effect of Zeolite β/Water System ...... 121 5.4.1 Basic material properties and preparation ...... 121 5.4.2 Dynamic test platform ...... 122 5.4.3 Dynamic test results and discussions ...... 122 5.4.3.1 Cushioning effect ...... 122 5.4.3.2 Impact protection behavior ...... 127 5.5 Concluding Remarks ...... 130 Chapter 6 Conclusions and Future Work ...... 132 6.1 Concluding Remarks ...... 132 6.2 Recommendations for Future Work ...... 136 6.2.1 Nanomaterial behaviors in multi-physical fields ...... 137 6.2.2 Hierarchical impact protection system ...... 138 Bibliography ...... 141 Publications Related to This Thesis ...... 155

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List of Figures

Figure 1.3 (a) CNT forest before impact and (b) experimental setup for the drop ball impact test. [86] ...... 16

Figure 1.4 An in situ study of the mechanical behavior of vertically aligned CNT bundles at high strain rate. [92] ...... 18

Figure 1.5 Experiment evidence of volume-memory liquid (a) at -5℃ and (b) at 40℃. The arrows indicate the liquid surface. [103] ...... 20

Figure 1.6 Photos of (a) a buckled empty cell and (b) a buckled NMF liquid enhanced cell. The initial outer diameter of the cell is 6.86mm. [109] ...... 21

Figure 1.7 Schematics of nanoporous energy absorption system: (a) NEAS and (b) nanopore. [111] ...... 22

Figure 1.8 The radial distribution function (RDF) of the infiltrated water molecules at infiltration stage (displaced as dashed lines) and wave reflecting stage (displaced as solid lines) of the energy absorption procedure for (a) (10,10) tube and (b) (20,20) tube. The peak value of RDFs increases with the decrease of the impact velocity (v) for both stages. [112] ...... 23

Figure 1.9 Illustration of basic idea of ideal impact mitigation system working mechanism ...... 25

Figure 2.1 The schematic of the computational cells: hollow and water-filled single CNTs. Both the section-view and side-view are provided. In this example, L/R=18.14 and

R/t0=2.39, where t0 is a characteristic thickness (taken to be 0.34 nm, the van der Waals distance of carbon)...... 35

Figure 2.3 Critical buckling forces for both hollow and water-filled CNTs with various aspect ratios subject to crushing speed of v = 10 m/s. Typical buckling configurations for hollow CNTs are shown at corresponding data points...... 37

Figure 2.4 (a) Mass and (b) volume densities of energy absorption, for both hollow and water-filled CNTs with various L/R and R/t0, for v = 10 m/s, 5 m/s and 1 m/s respectively. Note that any color in straight line, 2-point line and 3-point line refer to v = 10 m/s, 5 m/s and 1 m/s respectively...... 39

Figure 2.5 Enhancement of mass and volume densities of energy absorption (water-filled vs. hollow single tube) with various L/R and R/t0, and for v = 10 m/s...... 40

Figure 2.6 CNT bundle: computational cell for (a) hollow and (b) water-filled tubes; buckling configurations of (c) hollow and (d) water-filled at crushing strain of   25% for water-filled CNT bundle...... 42

Figure 2.7 Enhancement of mass and volume densities of energy absorption (water-filled vs. hollow single tube) with various L/R and R/t0, and for v = 10 m/s...... 43

Figure 2.8 Mass and volume densities of energy absorption of water-filled single, bundle and forest of CNTs. L/R = 9.07, R/t0 = 3.19, and v = 10 m/s...... 43

Figure 2.9 CNT forest: computational cell for (a) hollow and (b) water-filled tubes; buckling configurations of (c) hollow and (d) water-filled at crushing strain of   25% ...... 44

Figure 3.1 Computational cell and the three categories based on buckling/deformation characteristics upon impact...... 49

Figure 3.2 Computational cell and the three categories based on buckling/deformation characteristics upon impact...... 52

Figure 3.3 History of transmitted impulse force for C60 and C720; the reference systems are also shown. The impact energies are 6.5 eV and 176.8 eV respectively (such that the 3 impact energy per unit fullerene volume is the same, volume 4753.43J cm )...... 53

Figure 3.4 Percentage of impact energy dissipation, ( Eimpactor - Eimpactor )/ , for 3 C60~C720 under the same impact energy per unit fullerene mass ( mass 1741.67J cm ),

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3 or under the same impact energy per unit fullerene volume ( volume 4753.43J cm ) .. 54

Figure 3.5 The dissipated impact energy ( Eimpactor - Eimpactor )/ is in part converted into heat and in part to excessive potential energy of the fullerene system. The impact condition is ...... 55 Figure 3.6 Percentage of impact energy dissipation as a function of impact energy, for three representative buckyballs...... 56

Figure 3.7 Normalized force displacement curves at both low-speed crushing and impact loading. The entire process from the beginning of loading to the bowl-forming morphology can be divided into four phases. Morphologies of C720 are shown at the corresponding normalized displacements...... 57

Figure 3.9 Comparison between computational results and analytical model at low-speed crushing of 0.01 m/s...... 62

Figure 3.10 Comparison between computational results and analytical model at impact loading under various impact speeds from 40 m/s – 90 m/s...... 64

Figure 4.1 Illustration of one-dimensional buckyball chain setup as an impact protector...... 67

Figure 4.2 Normalized force time history and impactor velocity history of C60 chain containing 100 buckyballs, when the impact energy is 6.49 eV and impact speed is 500 m/s...... 71

Figure 4.3 The normalized force distribution on selected buckyballs in C60 and C720 chain systems...... 73

Figure 4.4 Normalized force history and impactor velocity history of C720 chain containing 100 buckyballs, when the impact energy is 6.49 eV and impact speed is 500 m/s...... 74

Figure 4.5 Force reduction ratio FFri and normalized wave propagation speed  under various impact speeds ( 0.080 0.80 ) with fixed impact mass ( 1.73), as well as various impact masses (1.73 13.87 ) with fixed impact speed (  0.40) for

C60 chain system containing 100 buckyballs. Nonlinear models are suggested to fit the computational data...... 76

Figure 4.6 Force reduction ratio FFri and normalized wave propagation speed  under various impact speeds ( 0.196 1.96) with fixed impact mass ( 1.73), as well as various impact masses (1.73 13.87 ) with fixed impact speed (  0.98) for

C720 chain system containing 100 buckyballs. Nonlinear models are suggested to fit the computational data...... 77

Figure 4.7 Normalized force history and impactor velocity history of C720 chain containing 100 The impulse duration ratios 12 between the impactor and receiver for various buckyballs including C60, C180, C240, C320, C540 and C720 by normalized buckyball radii  at the impact speed of 500 m/s with the same  value in each buckyball...... 82

Figure 4.8 Relations between energy absorption rate and buckyball number for both C60 and C720 systems at the impact speed   0.40 for C60 chain system and   0.98 for

C720 chain system, and the impact mass of  1.73 for both systems...... 83

Figure 4.9 Various alignments of buckyball system as a protector...... 84

Figure 4.10 The characteristic normalized force-displacement curve of 1-D buckyball system with 5 vertically lined C720’s at impact speed of 50 m/s...... 85

Figure 4.11 The characteristic normalized force-displacement curve of 1-D buckyball system with various numbers of horizontally lined C720’s at impact speed of 50 m/s...... 86

Figure 4.12 UME and UVE values of both vertical and horizontal buckyball systems with various buckyball numbers at impact speed of 50 m/s...... 86

Figure 4.13 UME and maximum contact force at constant impact speed (50 m/s) with various impact mass (from 8.7×10-19 g to 7.1×10-17g), and constant impact mass (2.8×10-18 g) with various impact speeds (from 10 m/s to 90 m/s), for five-buckyball systems...... 87

Figure 4.14 Typical normalized force-displacement curves for SC, BCC, FCC and HCP packing of C720 at impact speed of 50 m/s, and the impact energy per buckyball is 1.83 eV...... 89

Figure 5.1 Schematic illustration of experimental setup. The system includes a rigid piston, chamber cover with two pairs of sealing rings and a chamber base...... 96

Figure 5.2 The pressure history curve during the pressure holding test at 127 MPa for 300 seconds...... 97

Figure 5.4 P-ΔV curves under cyclic loads (one, two and three cycles respectively) particle size; other experimental conditions are same as that in Figure 5.3...... 99

Figure 5.5 P-ΔV curves under quasi-static compression with zeolite average particle size of 9.557 μm, pretreatment temperature of 1000℃, particle size at various pretreatment temperatures of 800℃, 900℃, 1000℃, and 1100℃, respectively...... 101

Figure 5.6 Al MAS NMR spectroscopy for coarse particled ZSM-5 (particle size: 9.557 μm) without pretreatment, and that after pretreatment at 600℃- 1100℃...... 103

Figure 5.7 P-ΔV curves under quasi-static compression with zeolite average particle size of 9.557 μm and pretreatment temperature and 1000℃, at various mass ratios of zeolite to water, from 1:0-6:5...... 105

Figure 5.8 P-ΔV curves for fine particled (average particle size: 6.104 μm) and coarse particled ZSM-5 (average particle size: 9.557 μm) at pretreatment temperature of 800℃ and 1000℃...... 109

Figure 5.9 SEM photos for (a) coarse particled ZSM-5 (particle size: 5.251 μm, without pretreatment), (b) coarse particled ZSM-5 (particle size: 9.557 μm, pretreatment temperature: 1000℃), (c) fine particled ZSM-5 (particle size: 2.145 μm, without pretreatment), (d) fine particled ZSM-5 (particle size: 6.104 μm, pretreatment temperature: 1000℃)...... 110

Figure 5.10 (a) A typical sorption isotherm (P-ΔV) curve under quasi-static compression test, with pretreatment temperature of 1100 ℃ and no NaCl added; (b) An ideal isotherm...... 112

Figure 5.11 P-ΔV curves under quasi-static compression with pretreatment temperature of 600 ℃ and NaCl concentrations of 0-2 mol kg-1 water. (The unloading curves for 0.5-2 mol kg-1 water are omitted.) ...... 113

Figure 5.12 (a) Pin as a function of CNaCl at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively; (b) Al MAS NMR spectroscopy for ZSM-5

vi after pretreatment at 600 ℃ - 1100 ℃; (c) a and r as a function of CNaCl at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively...... 115

Figure 5.13 (a) Vpla as a function of CNaCl at pretreatment temperature of 600 ℃,

800 ℃, 1000 ℃, and 1100 ℃, respectively; (b) Pde as a function of at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively...... 118

Figure 5.14 hys as a function of at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively...... 120

Figure 5.15 as a function of at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively...... 123

Figure 5.16 F-t curves of zeolite β/water system under a drop hammer impact of 200 kg,

0.2 m height. (a) F-t curves upon pretreatment temperatures of RT and 1000 ℃, rM=1:1,

CNaCl=0, along with a curve of pure water as a reference. (b) F-t curves with NaCl added

(CNaCl=0, 2, 4, 6 mol·kg), RT, rM=1:1. (c) F-t curves at various mass ratios of zeolites to water (rM=1:1, 1:2, 1:4, 0), RT, CNaCl=0...... 124

List of Tables

Table 1.1 Water models parameters four models ...... 29

Table 3.1 Physical parameters of C60~C720 molecules ...... 48

Table 5.1 Physical parameters of ZSM-5 ...... 95

Table 5.2 Experiment results with different pre-compression cycles for three samples. . 95

Table 5.3 Selected results from quasi-static compression tests...... 106

Table 5.4 Quasi-static compression results at mass ratio of 1:5-6:5...... 107

Table 5.5 (a) Systems composed of zeolite β upon various pretreatment temperatures (RT,

1000 ℃), rM=1:1, CNaCl=0...... 125

Table 5.5 (b) Systems with NaCl added (CNaCl=0, 2, 4, 6 mol•kg-1 H2O), RT, rM=1:1 125

Table 5.5 (c) Systems at various mass ratios of zeolite β to water (rM=1:1, 1:2, 1:4), RT,

CNaCl=0...... 125

vii

Acknowledgements

First of all, I would like to express my sincere thanks to my advisor, Prof. Xi

Chen for his insightful academic guidance, precious suggestions, ultra-strong support and ubiquitous encouragement for my research work. His passion, rigorousness and innovation to scientific research have set an adorable and perfect example for my future research life. I would also be grateful for his providing us a balanced and joyful life, i.e. hardworking research life with the combination of colorful life with group members, which is critical for a foreign Ph.D. student in U.S.

Secondly, I would like to thank my collaborator Prof. Yibing Li and his entire research group at Tsinghua University, particularly Mr. Yueting Sun, Ms. Jingjing Chen and Mr. Xiaoqing Xu. Their intelligence and diligence for the nice experiment validation for my research lay a strong foundation for my thesis work.

My thanks also go to Prof. Gautam Dasgupta, Prof. Tuncel M. Yegulalp, Prof.

Ah-Hyung (Alissa) Prof. Elon Terrell and Prof. Xi Chen for their generosity and willingness to be my defense committee, review this dissertation, and attend the defense.

Special thanks should give to our group members, in particular Dr. Baoxing Xu,

Dr. Yilun Liu, Mr. Junfeng Xiao, Mr. Hang Xiao, Mr. Xiaoyang Shi and Prof. Akio

Yonezu for their constant helps and friendship throughout my stay at Columbia.

I would like to thank the Fu Foundation School of Engineering and Applied

Science, Columbia University for generously providing me the Distinguished Presidential

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Fellowship for my entire Ph.D. study.

Last but not the least, I would like to my appreciation to my beloved wife

Tingting Li and little baby Lilliana Y. Xu. They’ve brought me so much joy and happiness and provided me so many conveniences and comforts and without whom, this thesis can never be possible. My parents, Mr. Bin Xu and Ms. Pingping Ma are also greatly appreciated for their continuing supports and encouragement. They are always my strongest supporters.

Dedicated to my family

Chapter 1 Introduction and Motivation

1.1 Challenge in Impact Safety

Impact safety has long been a serious technical concern in our industry and society. From as huge as space shuttle, aircraft carrier, high-speed trains and vehicles, to as small as cell phones, flash disks and micro-chips, from as simple as package cushion to as complicated as the crashworthiness of the electric vehicle battery which involves electric, chemical reaction, fluid and solid mechanical fields together, from civil structure to military equipment and weapons, it is always a priority to solve the impact safety problem by providing energy absorption/mitigation materials and structures.

Take the automotive industry for example. Thanks to the highly developed and well organized highway network in U.S., Americans greatly rely on various vehicles and the number of vehicles has been continuously increasing. According to the statistics from

Department of Transportation, U.S., the registered vehicles in 2011 has reached to the number of 253,108,389 [1], indicating that every single person have about 0.8 vehicle on average. Although advances in technology have led not only to the increasing of vehicles, but also to higher quality, i.e. safety and reliability, and performance, i.e. speed and maneuverability, it remains inevitable to have vehicle related fatalities and injuries. In

2012, there are 5,615,000 police-reported crashes with 33,561 fatalities and 2,362,000 injured with 4.35% increase compared to its counterpart in the previous year, meaning

1 that 3.8 persons are died and 269.6 persons are injured every hour in U.S. due to the traffic accidents [2]. The rest of the world is facing the similar challenge. Road traffic injuries was the 9th global injury/death burden in 2004 [3], and now ranks at 5th [4], and is further anticipated to be the 3rd injury/death burden worldwide [4].

The major problem for impact protection during vehicle crashes is how to manage such a huge kinetic energy at the magnitude of 105~106 J in such a short time as the value of 102 ms. Likewise, during all impact events, an average force F which prevails over time t along the contact interface is generated in order to handle the momentum mv which could be expressed as F mv t . The larger momentum with shorter time could result a remarkable intense force which leads to a huge acceleration to the objects that we need to protect. Generally, the major ways to achieve the protection subject to the impact loading are energy absorption and dissipation, force mitigation and delay. Such requirements may need to fully utilize the mechanical properties of the material as well as the matching structure design.

1.2 Handling Impact Protection at Macro and Meso Scale

Upon the dynamic loading, the suddenly created stress would propagate away from the contact surface in the form of stress wave. If the normal stress applied is smaller than the yield stress of the impacted material, then the stress wave is defined as elastic

and the propagation speed CL is

E (1.1) C  L 

2 where E and  are the Young’s modulus and density of the material respectively. Also, it is fundamental to derive the relation between the stress  and particle velocity v as

E (1.2) E  v   CL v  v CL where  v is defined as stress wave impedance. Therefore a yield velocity can be defined as a material’s property as follows

YYY (1.3) vCyL   E CEL

Under circumstances that the particle velocity generated from the dynamic loading is below the yield velocity will the stress wave be purely elastic. In the cases where particle velocity exceeds far beyond

the yield velocity, in addition to the elastic wave propagating with velocity CL , a plastic wave will be initiated and propagated away from the loading region. More details should be referred to Johnson’s book [5] and only the major points are summarized here.

(1) If the material mechanical behavior is linear strain-hardening then the plastic wave would

propagate at the speed of CP

E (1.4) C  P P 

where EP is the strain-hardening modulus of the material. Generally, for typical engineering metals, typically is usually 2 or 3 orders smaller than E, indicating that the plastic wave is about an order slower than the elastic wave.

(2) If the material mechanical behavior exhibits the non-linear strain-hardening and obeys a

stress-strain relation     in the plastic range, the plastic wave propagation speed

could be expressed as

dd (1.5) C  P  where dd represents the tangential modulus of the material.

During impact, there are two dominant effects which makes the dynamic impact a much more complicated case than quasi-static case: one is the inertia effect and the other one is the strain-rate effect. The former one is caused due to the movement of structure during the dynamical deformation which is more structure related and the latter one refers to the dynamical deformation in structure as well as the strain rate dependent effect in material itself.

(1) Restricted and constant reactive force. The peak reaction force on the

structure/material should keep below the the required threshold or the object could go

under severe damage/injury. Besides, the reaction force should remain constant such

that maximum energy could be absorbed/dissipated.

(2) The reaction time/displacement is long. Long stroke may help gain the maximum

energy along with the abovementioned constant reaction force.

(3) Lightweight and high specific energy mitigation capacity. The protection component

should be light itself such as to gain a high specific energy absorption/dissipation

capacity which is vital for implementation of impact protection device.

It is evident that evaluating the impact protection ability of certain material and structure should also take the protection object requirement into account such that the

4 structure design and material selection may vary from one case to another. However, there are some fundamental principles that one should follow to achieve a decent impact protection goal, especially in the real-world engineering application.

Therefore, by taking advantage of the modern material technology, there are two ways to handle the impact protection problem, one is enhance the material mechanical properties and the other one is to design new structure geometrically.

Scientists and engineers have made significant progress and pioneering work towards the impact protection goal which is briefly summarized as follows.

From the material point of view, by taking the advantages of various material, composite materials become increasingly popular as ideal energy absorber candidates [6].

Laminated material by employing soft polymer sandwiched by metallic or glass sheets have been proved to significantly improve the protective effect [7-9] since the compliant interlay serves as the agents of stress containment [10]. Woven fabric composites [11-14] are recommended to mitigate the impact force since they have ultrahigh tensile strength and impact resistance. Similar force mitigation mechanism may be found in fiber/particle reinforced materials [15-17]. With the relatively high yield strength at low density and the large nominal strain, honeycomb and metal foams also receive wide attentions as excellent energy absorption materials [18-22].

Thin walled structures are now widely accepted for energy absorption structures and package. Two dimensionally, a thin walled tube could be regarded as a ring

5 structure when it is subject to a global loading while the tube should be analyzed three dimensionally during the local loading [23]. Thin walled structure also has outstanding mechanical performance under the axial loading via progressive buckling by utilizing the deformation of entire wall. Axial splitting of circular metallic tube is another way to dissipate the impact energy by plastic bending/stretching and tearing [24]. Further, more sophisticated structures are suggested and assembled to achieve the energy absorption goal. For example, a functionally graded syntactic foam material structure by stacking of tubes in layers is verified to have the large strain up to 75% without losing the strength

[25]. Micro-truss topology has generated significant interest from researchers in relevant areas which might offer strengths comparable to honeycombs [22] while simultaneously facilitating the other functionalities of open cell metal foams [26-28]. Besides, granular material arranging in a chain-like structure [29, 30] is attractive for force attenuation, and such a discrete system effectively responds to impact loading via stress wave propagation across various interfaces to reduce the transmitted force. Pioneering work on the characteristics of the solitary wave propagation in a homogeneous chain of metallic spheres based on the Hertz contact law was established by Nesterenko [31]. Since then, many contributions have been put forward to refine the chain system for outstanding energy damping ability, including the material and geometrical parameters [32, 33], arrangements [34, 35], and model parameterizations of different granular materials

[36-38].

1.3 Opportunity for Nanomaterials and Nanostructures

1.3.1 Mechanical properties of major nanomaterials and nanostrcutures

With the discovery of the carbon nanotube (CNT), buckyball and graphene and the advancement in material manufacturing and characterization, we are able to manipulate materials and structures at nanoscale driven by functionalities. The mechanical properties dominate the performance of energy absorption, dissipation and mitigation during impact. Naturally, nanomaterials and structures are in the center of the focus.

CNT is a long cylinder of carbon atoms, first discovered by Sumio Iijima [39] of

NEC Corporation’s Fundamental Research Laboratory in 1991. Depending on the chirality, CNT may be either metallic or semiconducting. Back to the beginning of 21st century before the discovery of graphene, CNT was known as the strongest or stiffest element in nanoscale device or composite material. Experimentally, the amplitude of the

CNT oscillations are defined through careful transmission electron microscopy (TEM) observations. By employing the basic idea of measuring free-standing vibrations in a

TEM to consider the limit of small vibration amplitudes in the cantilever governed by the well-known fourth-order wave equation, the average value of the CNTs Young’s modulus was obtained as 1.8 TPa [40]. Later, it was also found a smaller average value of

1.25-0.35/+0.45 TPa on a larger sample of nanotubes by the same technique [41]. Using the tip of an atomic force microscope (AFM) to bend anchored CNT is another effective

7 way to probe the Young’s modulus of CNT and it was measured as 1.28  0.5 TPa [42].

Although there are other experimental data available and the data on Young’s modulus are rather scattered from 0.4 TPa~4.5 TPa, the overall widely accepted values are

E 1.0 ~1.3 TPa . It still remains a challenge to measure the strength of carbon nanotube accurately since a nanotube is too small to be pulled apart with standard tension machines and yet too tough for small optical tips. Falvo et al. [43] estimates the maximum sustained tensile strain of a single-wall CNT could be as large as 16%. Considering the commonly accepted values of the Young’s modulus discussed above, the failure strength under tensile loading is about 100-150 GPa. Their axial buckling behaviors are essential for energy absorption. Yakobson et al. [44] pioneered the study of quasi-static buckling of

CNTs using molecular dynamics (MD) simulations and continuum mechanics models.

Quite a few continuum modeling efforts have been carried out, extending the conventional shell [45], beam [46], or space frame [47] theories and focusing on the quasi-static buckling modes and mechanisms. The continuum models may be improved by incorporating atomic potentials [48], such that the effects of chirality and defects may be accounted for. Meanwhile, MD simulations still provide arguably more reliable analysis for the mechanical instability, since it can account for thermal fluctuation, non-bond interaction and various types of defects quite accurately (depending on the forcefield), and it has been employed to study various buckling properties of CNTs

[49-51].

Buckyball is composed entirely of carbon atoms in a hollow spherical shape.

With the number of carbon atoms growing, the size of the buckyball increases. A typical representative of buckyball family is C60, also called buckminsterfullerene which is composed of 60 carbon atoms. On the basis of a simple composite model, it is calculated that a single densest-packed C60 crystals of C60 may attain a bulk modulus of 0.810~0.972

GPa [52]. By analogy to continuum mechanics, the bulk modulus can be calculated by

VEV22   0.86 TPa directly where the V and E are the volume and strain energy of the shell of C60, which agrees the previous value [53]. Such a high bulk modulus makes that C60 is probably the most incompressible material known. The buckyball is mainly treated as a shell structure at nanoscale in mechanical analysis such that the so-called

“Young’s modulus” and “tensile/compression strength” are not available in references.

Graphene is a two dimensional plan crystalline allotrope of carbon. It may be regarded as a monolayer of graphite and the basic structural element for CNTs and buckyballs. Back to 1970, experiments carried out by Seldin and Nezbeda proved that the in-plane Young’s modulus of bulk graphite is 1.02 0.03 TPa . Tensile tests listed above about the Young’s modulus and stiffness value could be projected here. Mechanical tests performed on suspended graphene films by nanoindentation has been used to measure their bending stiffness [54] and the Young’s modulus [55]. Lee et al. [56]measured the elastic properties and intrinsic strength of monolayer graphene also by nanoindentation in an AFM and showed that the graphene as the strongest material ever measured with

Young’s modulus of 1 TPa and intrinsic strength of 130 GPa. Ab initio calculation of the strength of graphene under tension also proofed to be 118 to 121 GPa [57]. However, due to the thermal and quantum fluctuations, the Mermin-Wagner theorem proves that the amplitude of the long-wave fluctuations grows logarithmically with the scale of 2D structure, indicating that if the graphene, being the strongest material in the world known, is in a sufficiently large size, the 2D structure would bend and crumple into 3D structure without any lateral force. This is an interesting phenomenon but it is beyond the discussion of this thesis.

1.3.2 Opportunity of nanofluidics

Nanofluidics is defined as the study of the behavior and mechanisms of fluids residing inside the structures of nanometer, typically within 1-100 nm in the length scale

[58]. The ratio of surface-to-volume increases largely leading to new physical and chemical properties. Nanofluidics is an emerging and multidisciplinary study where physics of fluids, thermodynamics, colloid chemistry and engineering meets.

Electrokinetic effects [59, 60], phenomena at the micro/nanochannel interface [61, 62], macromolecule separation mechanisms using nanoscale structures [63, 64] and nanopores and nanowires for label-free biomolecule detections [65, 66] are now heated research frontiers of nanofluidics.

One of the classic physical models is the water infiltration into the nanopore problem. A water molecule loses some hydrogen bonds during its entering the pores and

10 the van der Waals attraction of the hydrophobic pore-wall cannot compensate the loss

[67], indicating that water molecules cannot intrude into the small nanopores (e.g. CNT in

(5,5)). Interestingly, both MD simulation and experiments at the nanoscale show that water may transport spontaneously into smaller nanotubes. Essentially, the entrance of the first few water molecules is thermodynamically disadvantaged while the filling of the entire nanotube is favorable. Seminal work finished by Hummer et al. reported a spontaneous and continuous filling of a hydrophobic carbon nanotube with a 1D ordered chain of water molecules, shown in Figure 1.1.

Figure 1.1 Water residence in the CNT. Number N of water molecules inside the nanotube as a function of time with (a) normal and (b) reduced carbon-water interactions. (c), structure of the remaining water chain inside the CNT. [68] They also discovered that the small change of the interactions between the tube wall and water may dramatically affect the pore hydration. Despite its strongly hydrophobic proper, the empty CNT is rapidly filled by water from the surrounding reservoir and several water molecules remain inside the tube even after about 66 ns [68].

These innovative findings suggested the CNT might be utilized as a molecular channel for water molecules and other protons and the CNT occupancy and conductivity could be

11 broadly tuned via the changing in the local pore polarity and solvent conditions.

In traditional fluid mechanics definition, the liquid should be modeled as a continuum system where the behavior of a liquid can be described in terms of infinitesimal volumetric elements [69]. However, in a system where the size of a liquid molecule is comparable to the size of nanopore, the liquid should no long be regarded as a continuum system, rather, a “subcontinuum” one where the representative volumetric element is no longer valid. Thus, Thomas and McGaughey [70] using MD simulation to investigate the structure and flow of water within CNTs with various diameters from 0.83 to 1.66 nm. It was found that different water structures may form at different CNT diameters accordingly: single-file molecule chains, tilted pentagonal rings, stacked pentagonal rings, stacked hexagonal rings and disordered bulk-like water, shown in

Figure 1.2. These structures were also found in Ref. [67, 71]. From the water molecule structure, one may easily found that the molecules become less coupled in smaller-sized tubes [72] which may reduce flow friction and thus leads to higher flow rate.

It also arouses researchers’ interests that it is argued 4 to 5 orders of magnitude enhancement in water molecule transportation than its counterpart in bulk materials both in experiments [73-75]. On the other hand, some more recent experiments on individual long CNTs reported water flow increase rates below 1000 [76] and also several MD simulations demonstrated that the enhancement rate are 2-3 orders of magnitude [72, 77,

78]. Walther et al. [79] clarified the argument with large scale of MD simulation (at the

12 experimental length scale) and concluded that the water transport enhancement rates are length dependent but asymptote to 2 orders of magnitude over its continuum counterpart.

Figure 1.2 (a) Water structure and formation inside the CNT at CNT diameters varying from 0.83 nm to 1.66 nm. (b) Axial distribution function and the structure relaxation time for each CNT. (c) The probability that n molecules cross the system mid-plane over the characteristic flow time. [70] In the meantime, the cutting edge theories about nanofluidics are constantly pushed forward. The most heated area is the discussion of nanofluidics mechanics based on classical continuum fluidic and microfluidic theories. The average water flow velocity

v of the slow flowing liquid whose Reynolds number is much less than one inside a

13 tube with a uniform radius is estimated by the Darcy law [80]

P (1.6) v    L where P is the pressure difference across the tube, L is the total length of the tube, and

 is the hydraulic conductivity which could be derived directly from the non-slip

2 Poiseuille relation, non-slip  D 32  where D is the diameter of the tube and  is the liquid viscosity [72]. If the water molecule slip is considered, then the velocity is expressed as [72]

2 2 D 2 rPLs  (1.7) ur  1 2  42 D 2 Dl where Ls is the slip length at the liquid/solid boundary. The slip length is defined as [72,

81]

ur  (1.8) L  s ddur rR

Such that the corresponding volumetric flow rate Qs with slip is then given by [72]

43  DDL2  4 2 s P (1.8) Q   s 8 l

Thus, the water transport enhancement  discussed and reported above from previous references is defined as the ratio of the measured flow rate to QN. By adopting Equation

1.8, the enhancement could be

Qs Lds    (1.9)   18   QN  D  d 

Let us take one step back to the very beginning of water filling and focus on the

14 pressure-driven infiltration phenomenon. When the water molecule start to infiltrate the nanopore, capillary effects dominate the process and it can be described well by using the

Laplace-Young’s equation as [82] 4 P  (1.10) in d where Pin is the pressure difference across the liquid-gas interface, and used to overcome the initial energy barrier,  is the excess solid-liquid interfacial tension, and d is the diameter of macro/microchannel. Once the scale size enters the liquid molecular size level, the continuum theory may break down. In the study of Qiao et al. [83], they investigated the pressure-driven infiltration behavior in a hydrophobic MFI zeolite/water system. In the meantime, they used MD simulation to validate the experiment observation and studied in detail about the water molecule infiltration behavior. Based on MD simulations and experiments, they suggested that an additional pressure P should be added with the following expression as [83] 4L P (1.11) d where L is the infiltrated length and  is the resistance per unit lateral surface area. Therefore, at the nanoscale, by combing the infiltration pressure and the the extra pressure, the pressure gradient of should be written as [83]

4L   (1.12) P  d

As it is shown in Equation 1.12, the pressure-driven infiltration may generate a pressure plateau, very similar as the idealized energy-absorption material behavior thus inspire us

15 to further utilize the nanoporous/water system for impact protection.

1.4 Current Research Progress of Impact Protection at Nanoscale

With their high stiffness and strength to weight ratios, carbon nanotubes (CNTs)

[84] have emerged as candidates for advanced mechanical systems [85]. Dario et al. presented a simple experimental method to determine the high-strain rate behavior of a forest of vertically aligned CNTs [86], shown in Figure 1.3. During the experiment, the authors were able to extract force-displacement curves and further estimate the dissipated energy the CNT forest. The force-displacement curve showed to be strong nonlinear dependent which was fundamentally different from Hertz law. The energy dissipate capacity was about 230 J/cm3 which far exceeded current engineering materials. Further,

Dario et al. [87] showed that there was no trace of plastic deformation and full recovery of the foamlike layer of coiled CNTs under various impact velocities by employing the same experimental device, indicating a good candidate for localized impact protection.

Figure 1.3 (a) CNT forest before impact and (b) experimental setup for the drop ball impact test. [86]

Mantena et al. [88] examined the dynamic mechanical behavior and high-strain rate response of a functionally graded material consisting of vertically aligned CNTs gown on silicon wafer substrate. The results show that the energy dissipation capacity of CNT forests was about 50 J/g, which was about 5 times as high-strength steel. A more promising experiment result about CNT being as an energy storage media was reported by Zhang et al. The authors experimentally demonstrated that the defect-free CNTs with length over 10 cm, may have the failure strain up to 17.5% and tensile strength up to 200

GPa and Young’s modulus up to 1.34 TPa. These ultralong CNTs may endure a continuously repeated mechanical compressive loading for over 1.8108 times. Besides, these CNTs have the energy density nearly 3 times of that of Carbon T1000 flywheels,

5-8 times that of Li-ion batteries and 25,000 times that of steel springs [89]. Yang et al.

[90] used coarse-grained MD simulation to show that the entangled networks of CNT with temperature and frequency-invariant dissipative behavior under cyclic compressive loadings can be attributed to the unstable attachments/detachments between adjacent

CNTs induced by van der Waals interactions. Further, they employed a mesoscale bead-spring model to demonstrate that the complicated deformation behaviors of CNTs could be explained from competing elastic and adhesive interactions at the micro scale

[91]. Recently, Pathak et al. [92] reported that the mechanical behavior of vertically aligned CNT bundles would perform much better (shown in Figure 1.4), i.e. 6-fold increase in elastic modulus and gradual decrease in recoverability under high strain rate

17 loadings, positioning CNT bundles in the “unattained-as-of-to-date-space” in the material property landscape.

Figure 1.4 An in situ study of the mechanical behavior of vertically aligned CNT bundles at high strain rate. [92] Naturally, another branch of fullerene family with a spherical shape, i.e. buckyballs, also possess excellent mechanical properties similar to CNTs. Man et al. [93] examined a C60 in collision with a graphite surface and found that the C60 would first deform into a disc-like structure and then recover to its original shape. It is also known that C60 has decent damping ability by transferring impact energy to internal energy [94,

95]. This large deformation ability under compressive strain of C60 was also verified by

Kaur et al. [96]. For higher impact energy, Zhang [97] employed C60/C320 to collide with mono/double layer graphene, and the penetration of graphene and the dissociation of buckyball was observed. Further, Wang and Lee [98] observed a novel phenomenon of heat wave propagation driven by impact loading between C60 and graphene which is responsible for the mechanical deformation of the buckyball. Meanwhile, giant buckyballs, such as C720, have smaller system rigidity as well as non-recoverable

18 morphology upon impact, and thus they are expected to having higher capabilities for energy dissipation. However, to the best knowledge of authors, currently only few studies about the mechanical behavior of giant buckyball are available [99-101].

The pioneering work about utilizing the nanofluidics system for mechanical energy absorption mainly focused on quasi-static which serves as a very first and fundamental step towards the impact protection. Punyamurtula et al. [102] experimentally investigated on a nanoporous carbon functionalized and they found that during the compression process, the pressure was increased to a critical value such to lead to a considerable increase in solid-liquid interfacial energy. Due to the hysteresis characteristic in the loading-unloading process, the mechanical energy was absorbed and the energy absorption level was about 15 J/g. Han et al. [103] adopted the similar idea by dispersing nanoporous particles in an electrolyte solution to form a suspension and found that the hydrophobicity of the nanopore could be greatly tuned via the temperature, evidenced in Figure 1.5. It was also found that due to the large surface area, the energy density was much higher than that of conventional shap-memory solids. Another type of the system consisting of a polyacrylic acid gel matrix composite material functionalized by hydrophobic nanoporosu silica particulates was developed by Surani and Qiao [103].

They proved that the infiltrated water stayed within the nanopore even after defiltration, indicating the system energy absorption capacity could be 14 J/g [104]. Further, Han and

Qiao [105] proposed an idea of changing the interfacial tension by varying the ion density

19 at the solid-liquid interface which was validated by the results of a controlled-temperature infiltration of a hydrophobic zeolite/saturated aqueous solution of sodium acetate. As mentioned above, the infiltration pressure is one of the key parameters to demonstrate the energy absorption/mitigation capacity of the nanofluidics system and thus Han and Qiao

[106] investigated the possible way to change the infiltration pressure by modifying the electrolyte. The thermally aided cation exchange in nanopores may contribute to the result of increasing sodium chloride concentration to help reduce the small extent of hysteresis of sorption isotherm. In addition, a selective energy absorption nanoporous system was develop to make a functionalized system [107].

Figure 1.5 Experiment evidence of volume-memory liquid (a) at -5℃ and (b) at 40℃. The arrows indicate the liquid surface. [103] By taking one step further, Surani et al. [108] analyzed the energy absorption behaviors of a nanoporosu system subject to dynamic loadings through a SHPB. The energy absorption capacity was found to be about 41 J/g, three times higher than the quasi-static value. The internal friction of the liquid may be responsible for this result, indicting the system could be designed for impact situation by better performance.

Aiming at the engineering application, the nanofluidics system need a certain package.

The intuitive idea is to put the nanofluidics system into a hollow steel tube (shown in

Figure 1.6) such that the work generated by the compressive load along the axial direction may be dissipated both the ordinary thin-wall structure buckling and pressure-driven infiltration [109]. About 3-fold of the increase in energy absorption capacity was gained. Thus, next question should be the energy density of nanoporous materials functionalized liquid. The energy density, is a direct indicator for the upper limit of energy absorption capacity. Han et al. [110] reported an experimental result of energy dissipation of a mobil crystalline material 41 with a great portion of nanopore surface in mercury. This system represented the maximum values of specific nanopore surface area and the solid-liquid interfacial tension that could be achieved by the current material processing technology. The energy absorption value was reported to be 140 J/g, ten times as large as the above mentioned system and is also 1 to 2 orders higher than current engineering materials.

Figure 1.6 Photos of (a) a buckled empty cell and (b) a buckled NMF liquid enhanced cell. The initial outer diameter of the cell is 6.86mm. [109] These experiment work proposed and validated the possibility of the nanofluidics system to an energy absorption/mitigation system with reasonable

21 mechanism explanation. As a more detail investigation into the working mechanism of the energy dissipation behavior, Cao [111] employed the MD simulation method by modeling a rigid CNT as a nanopore channel for water molecule infiltration (shown in

Figure 1.7) to study the system by monitoring the molecules behaviors. It was found that the presented model system may dissipate the impact energy into water molecules potential change due to the nanoconfinement, solid-liquid interaction energy and the heat dissipated by the surface friction and the third part provided the main contribution to the overall energy absorption during the impact. This underlies the fundamental guidance for the future engineering design of such a system. Based on this finding, Liu and Cao [112] together studied the interaction between mechanical wave imitated by the impact loading within the nanopore. The reflected mechanical wave for water molecules interaction with nanopore may also dissipate a good quantity of energy. The detailed water molecules distribution was studied and revealed the fundamental understanding of how the system handling the stress wave, shown in Figure 1.8.

Figure 1.7 Schematics of nanoporous energy absorption system: (a) NEAS and (b) nanopore. [111]

1.5 Innovation of Current Research

Aforementioned research work contributed significantly to improve the impact safety from traditional engineering material to nanoscale material; however, for bulk engineering material and structures, the energy mitigation capacity and capability are limited to 1 J/g ~ 10 J/g while for carbon nanotube and nanofluidics system, the profound energy mitigation mechanism and the possible types are only scratched and an effective comprehensive study and system design are still lacking. For example, buckyball has proven to have exceptional mechanical properties but few research has been conducted on the mechanical behavior under both quasi-static and dynamic loadings. A clear understanding of the mechanical behavior of single buckyball and its various stacking forms would greatly benefit the impact protection utilization based on buckyball system.

For another example, a few experiments and theoretical efforts have been made to understand the energy absorption mechanism of nanofluidics system but the real obstacles for engineering application still remains, e.g. the pre-treatment temperature and the ratio between nanoporous material and the liquid.

For energy-absorption wise, the structure should be “plastic” such that the impact energy could be consumed via the system deformation work. However, facing the high energy density impact scenarios such as high impact speed and explosion,

“absorption” of energy becomes an impossible task. Thus, objects can be protected only if the stress wave could be trapped within the protection layer by mitigating the stress

24 wave peak value and extending the reaction time. The basic idea is illustrated in Figure

1.9. To achieve high energy mitigation performance, the momentum generated by the impact wave should be trapped, transferred and consumed.

Figure 1.9 Illustration of basic idea of ideal impact mitigation system working mechanism Therefore, this thesis tries to presents several types of energy absorption system at nanoscale with the discovery of the unique working mechanism and parametric system tuning guidance for engineering design.

1.6 Methodology

In nanoscale, due to the large surface-to-volume ratio, new physical behaviors emerge which breaks the classical mechanics theories down. Besides, manipulation and characterization become difficult at such a small length scale which is one of the major responsible reason for the undermined knowledge. In this case, numerical simulation becomes a priority to virtually study the material and structure behaviors according to established molecular dynamics. MD simulation now becomes the predominant research method in nanoscale phenomenon with relative high accuracy and low computational

25 resource [113-116]. In addition to the MD simulation, desktop experiments are also carefully designed and conducted to enrich the relevant mechanisms. In this section, major focus is put on the fundamental principles of MD simulation.

1.6.1 Basis of MD simulation

MD is a form of investigation where the motion and the corresponding interaction of a certain number of atoms and molecules are studied. The origins of MD are fully rooted in the atomism of antiquity. The simplest form of MD, that of structureless and discrete particles involves little more than Newton’s second law.

1.6.1.1 MD force field

In classical MD simulations atoms move according to the Newtonian equation of motion [67]

2r  (1.13) mi   U r, r , , r , i  1,2, , N iNtr2 tot 1 2

where mi is the mass of atom i, ri is the position and U tot is the total potential energy depending on all atomic positions. The potential energy is described by the forcefield and the most widely known MD software are based on various forcefield packages.

Conceptually, the forces acting on atoms are divided into atomic and intramolecular atomic forces [67].

1.6.1.2 Non-bonded atom forces

The Lennard-Jones potential [117], referred as L-J potential, is a simple but widely accepted forcefield with satisfied accuracy. The potential could be expressed as

12 6     (1.14) i,, j i j UrvdW i , j 4 i , j     rr    i,, j   i j  where  is the depth of the potential wall and  is the (finite) distance where the potential is zero. i and j denote the i-th and j-th atomic species, respectively. As one may see that the L-J potential usually converges pretty fast such that the trcuncation of the

potential at a certain distance rc is allowed. Two critical L-J parameters, and are determined based on experimental work or theoretical quantum computation results. For any atom interactions without any experimental or theoretical evidence,

Leroentz-Berthelot mixing rules are adopted [118]:

ij  ii  jj (1.15) 1 ij  ii  jj  (1.16) 2 and the method has been verified to be effective [119].

The electrostatic potential follows the known Coulomb law as

qqij (1.17) Urcolumb ij ,   4 0,rij

where qi and q j are the electrostatic charges of atom i and j, rij, is the distance

between them and  0 is the dielectric constant.

1.6.1.3 Inter-molecule forces

The intramolecular force description is made via the intramolecular energy based on the following approximation [67]

UUUUintramolecular stretch  angle  dihedral (1.18)

27 and each contribution to Uintramolecular can be further modeled by the following [120]

2 Ustretch k bond r r 0  (1.19)

2 Ukangle angle 0  (1.20)

2 Udihedral k dihedral1  cos n  0  (1.21)

In Equations (1.19)-(1.21), k is the constant for various energies and letter with subscript

“0” represent for the balanced values, e.g. balanced positions and angles. Usually, values of these parameters are determined from quantum chemistry calculations.

1.6.1.4 Thermostats and barostats

In the canonical (NVT) or the isothermal-isobaric (NPT) ensemble, the system may be coupled to a thermostat such to ensure the maintenance of the average temperature or to a barostat to the size and shape of the simulation cell adjustment to a desired pressure during the simulation process. Thus, many methods were suggested to overcome the problem such as the Berendsen [121] and Parrinello-Rahman [122] barostats, and Nose-Hoover [123, 124] thermostats. In some specific cases, the wise choice on the thermostats and barostats is a headache but generally, the results won’t differ too much.

1.6.2 Water molecules and carbon nanotubes

1.6.2.1 Water molecular models

A large quantity of “hypothetical” models for water have been proposed over the years [67] and generally, each model aims to depict one specific physical

28 characteristic of water. There are now over 50 molecular water models available [125] which may offer more options over the model decision while indicates none of the model may perfectly describe the real water molecule behavior under all circumstances. Thus, the best shot we can take for classic MD simulations of water in CNTs is probably to compare the results by using various models [126]. The most frequently used water models for MD in CNT are listed in Table 1.1.

Table 1.1 Water models parameters four models

Model  OO (Å ) OO (kJ/mol) r0 (Å ) q1 (e) q0 (e) 0 (kJ/mol)

SPC [127] 3.166 0.650 1.0 +0.41 -0.82 109.47

SPC/E [128] 3.166 0.650 1.0 +0.4238 -0.8476 109.47

TIP3P [129] 3.15061 0.6364 0.9572 +0.4170 -0.8340 104.52

TIP4P [130] 3.15365 0.6480 0.9572 +0.52 -1.04 104.52

1.6.2.2 Carbon nanotube and buckyball models

For an empty carbon nanotube, the harmonic approximation of the intramolecular potential is acceptable where no large deformation of the bond is observed.

If more extreme conditions are considered, other functions must be used. The combination of Tersoff [131] empirical potential and Brenner [132] carbon parameters has been widely accepted [133]. A systematic study comparing the results of using different C-C intramolecular potentials in water-CNT simulations showed that the C-C bond deformation was small and the water properties were similar [126]. The widely used

L-J potentials for carbon nanotube is  CC  3.851A , CC  0.4396kJ mol , rC 1.418A ,

 120.00 , K  478.9 kJ molA2 , K  562.2 kJ mol , K  25.12kJ mol and C Cr C C

  2.1867A1 . K , r and  are the Morse potential; K and  are the angle Cr C C C parameters and K is the torsion parameter. C

Much less focus has been put on the mechanical behavior of buckyball.

Girifalco et al. [134, 135] gave out an important guidance for a universal graphitic potential for carbon nanotubes, buckyballs and ropes. L-J parameters for the carbon

atoms of the buckyball is  CC  3.47A and CC  0.27647 kJ mol .

1.6.2.3 Carbon-water interactions

It is the most crucial choice of carbon-oxygen parameters for the MD simulation of carbon-water system, especially for confined water. Given the atom interactions in water and carbon respectively, often, the values of the C-O interactions are determined by the Lorentz-Berthelot rule (i.e. Equations (1.15) and (1.16)). In this case, various types of matches could be suggested. Alternatively, Werder et al. [136] discussed the influences of the C-O interaction through the contact angle of a water droplet on graphite. A new pair of L-J potentials were suggested to reproduce the real-world

macroscopic water contact angles for  CC  3.19A and CC  0.3920kJ mol . On the other hand, Wang et al. [137] argued that those values may only be suitable for very large

CNTs. Thus, the discussion may not be fully solved until a larger amount of ab initio simulation results are available.

1.7 Outline of Dissertation

Nanomaterials and nanostructures open a promising door for us to solve numerous issues and greatly advance the relevant technologies. One of the most interesting and important problems is the impact safety, which still remains a big hurdle at macroscopic world. Through the present dissertation, several types of nanomaterial and nanostructures are proposed with new impact protection working mechanisms. Also, comprehensive desktop experiments are provided to support the numerical studies.

In Chapter 1, an introduction of mechanical impact challenge over industries by taking examples of automotive industry is provided. In the meantime, a brief overview of science of nanomaterials including CNT, buckyball, nanofluidics and their possible application in impact protection is given by pointing out their unique nanoscale phenomenon, working mechanism and widely accepted methods.

In Chapter 2, a water-filled CNT system is suggested and studied via MD simulation. This system takes advantage of previous known CNT system for their possible excellent impact protection performance and results reveal a good energy dissipation capacity of the system. Several key factors such impact speed and system stacking type are parametrically studied to explain the working mechanism.

In Chapter 3, the quasi-static and dynamic mechanical behaviors of buckyball are investigated to fill the current research blank and provide a better understanding of the understanding of the nanomechanics for nano-shell shape and lay a strong foundation

31 for further study of the impact protection performance of buckyball based system.

In Chapter 4, based on Chapter 3, the energy mitigation and dissipation performance of 0D, 1D, 2D and pseudo 3D stacking forms are examined. Theoretical analysis combined with MD simulation unravels the working mechanisms of buckyball impact protection which creates a new road towards impact protection system design at the nanoscale.

For each nanoscale impact protection system studied in the thesis (such as

Chapter 2 and Chapter 4), a synergy is pursued among modeling and simulation to fill the blank of the cutting-edge nanoscale research. Generally, a molecular model describing the physical properties with promising impact protection performance is established firstly.

Then, proper force-field is selected for further MD simulation. By varying key factors of both material and system, all-atomic simulation based on MD are conducted to fully explore the system output and evaluate the mechanical performance. By the combination of frontier theories, the fundamental working mechanism are clarified, shedding lights on the next generation impact protection system design and process.

In Chapter 5, by aiming at the engineering application of the nanofluidics system, dominant factors during manufacturing, including pre-treatment temperature, concentration of the electrolyte and the loading rate to the impact protection performance are parametrically investigated by experiments. The strain rate effect on the infiltration and defiltration behavior in a nanoconfined environment is also clarified, laying a strong

32 foundation for process and application of nanofluidics system in the near future. The desktop experiments were conducted in the Sate Key Laboratory of Automotive Safety and Energy at Tsinghua University, Beijing, China. The major collaborators were Prof.

Yibing Li and Mr. Yueting Sun. The collaboration work was finally supported by the

International Research Project at Tsinghua University PI’ed by Pro. Yibing Li and Prof.

Xi Chen (No. 20121080050).

In Chapter 6, the major results and findings are summarized and the some concluding remarks are given on the future work.

Chapter 2 CNT Based Protection System

It is considered that nanoparticles and carbon nanotubes have far better mechanical properties over traditional engineering materials thus scientists and engineers intuitively try to add nanofillers into the current material as reinforcements [6]. Likewise, since CNT has been verified to have promising energy absorption performance, it is naturally to move one step further to develop a CNT based system for impact protection.

In this chapter, a water-filled-in CNT system is suggested. By studying the mechanical behavior of the system, impact protection performance is thus revealed.

2.1 Computational Model and Method

A computational cell is sketched in Figure 2.1, contrasting a hollow and a water-filled model (12,12) SWCNT (with diameter 1.627 nm). The diameter, D, and length, L, are varied in this study, from 1.085nm to 2.17nm, and from 9.38nm to 19.68nm, respectively. For the filled tube, the density of water molecules inside the occupied

3 volume of CNTs is close to that of bulk water, o =998.0 kg/m , at 300 K and 0.1 MPa.

[70, 138]. The left end of the tube is fixed, and the right end is being compressed with a constant velocity v in the axial direction: this qualitatively mimics a large mass colliding with the right end of the tube (and the impactor’s velocity is unchanged during crushing). The right end is assumed to remain normal to the impactor (i.e. stick with the impactor upon contact) such that any liquid confined inside does not leak in the due

34 course of deformation. The compressive force-displacement history is recorded to indicate the buckling characteristic and energy absorption.

Figure 2.1 The schematic of the computational cells: hollow and water-filled single CNTs. Both the section-view and side-view are provided. In this example, L/R=18.14 and R/t0=2.39, where t0 is a characteristic thickness (taken to be 0.34 nm, the van der Waals distance of carbon). MD simulation is performed using LAMMPS (large-scale atomic/molecular massively parallel simulator), with the NVT ensemble at an ambient temperature of 300

K [138-140]. The non-bond interaction is described by the 12-6 Lennard-Jones (LJ) empirical forcefield. Water molecules are modeled with the extended simple point charge potential (SPC/E) [128]. The particle-particle particle-mesh (PPPM) technique with a root-mean-square accuracy of 10-4 is employed to handle the long-range Coulomb interactions. The forcefield parameters are taken from ref. [68].

2.2 Results and Discussions

2.2.1 Typical buckling responses of hollow and water-filled CNTs

A representative case with nanotube dimension D=1.627 nm, L=14.757 nm, and crushing speed v =10m/s is given in Figure 2.2, comparing the dimensionless

35 force-nominal strain  curves of the hollow and water-filled CNTs. Here the dimensionless force is the compressive force P normalized by  EtD , where Et =0.34

TPa nm is the effective tensile stiffness of the hollow CNT commonly used in literature

[85], and the nominal strain is the compressive displacement divided by L.

Figure 2.2 Typical normalized force-nominal strain curves of hollow and water-filled single CNTs with L/R=13.60 and R/t0 = 3.19, subject to crushing speed of 10 m/s. The corresponding buckling morphologies are shown. As the crushing proceeds, the initial linear response is similar for the hollow and water-filled tubes, since the bulk modulus of water is much smaller than that of CNT.

Meanwhile, the arise internal pressure from the water help to stabilize the CNT, making its critical buckling force much higher than that of the hollow counterpart. The post-buckling stress of the water-filled CNT is also considerably larger due to the same strengthening mechanism, although its reduction is quicker than the hollow one (since

36 water cannot sustain shear).

By varying the CNT size and length, the critical buckling force Pcr is plotted

in Figure 2.3 as a function of L/R (R=D/2) and for various R/t0 (where t0 =0.34 nm is a characteristic thickness), for v=10m/s. Note that for the slender members (with smaller

R/t0 and larger L/R), decreases nonlinearly with the increase of length L/R, like that for beams; whereas for the stubby systems (with larger R/t0 and smaller L/R), remains almost invariant with length for the range of parameters considered in this study,

similar to that in shells [141, 142]. The buckling force in water filled system, Pcr-water-filled ,

is significantly higher than that in the hollow CNT Pcr-hollow -- and the strengthening effect is stronger in the more stubby, shell-like members.

2.2.2 Typical buckling responses of hollow and water-filled CNTs

The energy absorbed during crushing ( Etotal ) can be evaluated from the area below the force-displacement curve (for up to a nominal axial strain of 25% which is close to the failure strain of CNT [143]). The mass and volume energy absorption densities are deduced by dividing with the mass and the effective volume of the nanotube, respectively. For water-filled tube, the mass also includes the confined water molecules. The effective volume of the nanotube is counted as the average space occupied by a CNT within a bundle or forest (where the van der Waals equilibrium distance for carbon is taken into account), so that the performance index can be compared with that of the CNT bundle and forest later in this paper.

Take v = 10m/s for example, Figure 2.4(a) shows that for both hollow and water-filled CNTs, the mass densities of energy absorption of hollow and water-filled

tubes, Eum-hollow and Eum-water-filled , increase as L/R reduces; that is, the transition from beam-like buckle to shell-like buckle can enhance and . At the

same aspect ratio (L/R), increases with the reduction of Rt/ 0 , in part owing to the higher buckling force. Similar behaviors can be observed for the volume density of

energy absorption, Euv-hollow and Euv-water-filled (Figure 2.4(b)). For water-filled CNTs and for the current range of parameters explored in this study, the energy absorption densities have power-law dependencies on LR and , which can be fitted as:

0.76 0.90 Eum-water-filled E um0 4.294 L R  R t 0  (2.1)

0.74 1.65 Euv-water-filled E uv0 5.084 L R  R t 0  (2.2)

3 where Euv0 =618.75 J/g and Eum0 =618.75 J/cm are reference strain energy (per volume or mass) of bulk water under hydrostatic pressure with strain of 0.25.

(a) Unit mass energy absorption for both water-filled and hollow CNTs

(b) Unit volume energy absorption for both water-filled and hollow CNTs Figure 2.4 (a) Mass and (b) volume densities of energy absorption, for both hollow and 39 water-filled CNTs with various L/R and R/t0, for v = 10 m/s, 5 m/s and 1 m/s respectively. Note that any color in straight line, 2-point line and 3-point line refer to v = 10 m/s, 5 m/s and 1 m/s respectively. The enhancement of water filling (versus that of hollow tube) can be deduced

from the ratios, umEEE um-water-filled um-hollow um-hollow and

uvEEE uv-water-filled uv-hollow uv-hollow , given in Figure 2.5. In general, the volume density of energy absorption can be improved over 100% with water filling, whereas the gain for

mass density is above 50% or so. For the examples in Figure 2.5, um and uv are the

highest for the stubby systems (with larger Rt/ 0 ) if L/R is relatively low, whereas the largest gains of water filling are for the slender systems (with smaller ) if L/R is high.

Figure 2.5 Enhancement of mass and volume densities of energy absorption (water-filled vs. hollow single tube) with various L/R and R/t0, and for v = 10 m/s. 2.2.3 Effect of impact velocity on energy absorption

Simulations are carried out for a spectrum of low-crushing speeds, 1 m/s ~ 10

40 m/s. And the resulting mass and volume densities of energy absorption are given in

Figures 2.4(a) and (b), respectively. The effect of crushing speed is rather small, although the inertia effect makes the system slightly stiffer at higher speed. The energy absorption is more sensitive to buckling mode, which is more robust for the longer tubes, hence in the members with larger LR, the effect of crushing speed is even smaller.

2.2.4 Effect of impact velocity on energy absorption

When CNTs form a bundle (where the tubes are aligned in parallel to each other

before deformation), the critical buckling force Pcr increases owing to the enhancement

of bending stiffness [144, 145]. CNTs with Rt0  3.19 are chosen as illustrative examples. The computational cell containing the initial configurations of hollow and water-filled CNT bundles (with 7 nanotubes) are illustrated in Figure 2.6(a) and (b), respectively, where the spacing between tubes is set to be the equilibrium distance

0.34nm [144, 146]. The respective buckled morphologies at maximum crush strain of

25% are shown in Figure 2.6(c) and (d).

The averaged normalized force-nominal strain curve of a constituent tube in the bundle is given in Figure 2.7, for both the hollow and water-filled cases. Both the critical buckling force and post-buckling force are enhanced (with respect to the case of isolated tube in previous sections), and the increment is more prominent for the water-filled ones.

The bundle also exhibits larger stiffness (and hence smaller buckling strain) owing to the van der Waals “tie” between the tubes.

(a) Initial computational cell setup for (b) Initial computational cell setup for hollow CNT bundle water-filled CNT bundle (after initial equilibrium)

(c) Top view of the compression (d) Top view of the compression morphology at   25% for hollow morphology at   25% for water-filled CNT bundle CNT bundle Figure 2.6 CNT bundle: computational cell for (a) hollow and (b) water-filled tubes; buckling configurations of (c) hollow and (d) water-filled at crushing strain of for water-filled CNT bundle.

The mass and volume densities of energy absorption, Eum and Euv , are shown in Figure 2.8. Compare with the isolate tube counterpart, and of the bundle increase by 8.07% and 10.91% respectively, due to the higher buckling and post-buckling stresses.

Figure 2.7 Enhancement of mass and volume densities of energy absorption (water-filled vs. hollow single tube) with various L/R and R/t0, and for v = 10 m/s.

Figure 2.8 Mass and volume densities of energy absorption of water-filled single, bundle and forest of CNTs. L/R = 9.07, R/t0 = 3.19, and v = 10 m/s.

2.2.5 Energy absorption of nanotube forest

When the CNT bundle extends infinitely, a forest is formed where a representative periodic unit cell is shown in Figure 2.9(a) and (b), and the buckling morphologies for hollow and water-filled CNT forests are given in Figure 2.9(c) and (d).

(a) Initial computational cell setup for (b) Initial computational cell setup for hollow CNT forest water-filled CNT forest (after initial equilibrium)

(c) Top view of the compression (d) Top view of the compression morphology at   25% for hollow morphology at   25% for water-filled CNT forest CNT forest Figure 2.9 CNT forest: computational cell for (a) hollow and (b) water-filled tubes; buckling configurations of (c) hollow and (d) water-filled at crushing strain of   25%.

The averaged normalized force-nominal strain curve of a constituent tube in the forest is compared with that of the bundle and single tube in Figure 2.7, for both the

hollow and water-filled cases. The average Pcr of forest is significantly higher due to the 44 constraint of surrounding tubes. Meanwhile, the buckling strain  cr is smaller since the effective stiffness of the forest is rather large.

According to Figure 2.8, values of Eum and Euv of the forest are also higher than that of the bundle and isolated tube. Since in practice CNTs are available in bundle form, the prospect of its energy dissipation performance (especially with filled liquid) is worth considering.

2.3 Concluding Remarks

In this chapter, the energy absorption capabilities of hollow and water-filled

CNTs, in either isolate, bundle, or forest configuration, are studied via parametric MD simulations. The nanotube length, radius, and crush speed are varied. The filament of water can significantly enhance the volume and mass energy absorption densities, through the strengthening effect which elevates the critical buckle load and post-buckling stress. The strengthening effect strongly depends on the aspect ratio, and it is more prominent in the slender members. The configuration in bundle or forest may further solidify the system (owing to the constraint of neighbor tubes), leading to higher energy density that can be close to 1000 J/g for the stubby water-filled CNT forests.

There are additional advantages of employing CNTs as tunable energy absorption devices. For example, if an appropriate electric field is applied, the buckling strength of CNT could be adjusted [147], moreover, water may flow in or out of tubes

[138, 148] and the system performance can be well controlled. Note that the present study

45 assumes no leakage will take place upon crushing of tubes filled with water, and the effect of leakage will be explored elsewhere (which depends strongly on the load application mode and boundary condition). The present study may provide some insight on the potential application of employing CNTs as advanced energy absorption materials.

Chapter 3 Mechanical Behavior of Buckyball

As originated from the same carbon-family as CNT, buckyball can also be regarded as the rolling of a single layer graphene into a sphere. It is also expected that buckyball also has exceptional mechanical properties. The major contribution of this chapter is to investigate the mechanical behavior of buckyball under both quasi-static and dynamic loadings by using MD simulation with the suggestion of mechanical models based on shell model in continuum mechanics. Also the impact protection of the single buckyball is revealed.

3.1 Computational Model and Method

Six spherical fullerene molecules with varying diameter D are selected in this study, whose physical properties are listed in Table 3.1 (where the van der Waals equilibrium distance is accounted for in the radius). A computational cell is sketched in

Figure 3.1, where a buckyball subjects to the impact of a rigid plate with incident energy

Eimpactor. The fullerene sits on a rigid and fixed bottom plate during the impact process, and the bottom plate also functions as a receiver -- the force history on the receiver

(which may be regarded as the material/system to be protected) indicates the energy mitigation capability of the buckyball buffer. The computational box size is set to be much larger than the fullerene molecule, so as to study focus on the impact on a single buckyball. For comparison, a reference system is also built with similar setup except the

47 buckyball is rigid and non-deformable.

Table 3.1 Physical parameters of C60~C720 molecules

Diameter, D (Å) Volume, V (nm3) Mass, M (g)

C60 ≈7.5 ≈0.22 ≈1.20e-21

C180 ≈12.1 ≈0.93 ≈3.61e-21

C240 ≈14.2 ≈1.50 ≈4.82e-21

C320 ≈16.48 ≈2.34 ≈6.42e-21

C540 ≈21.64 ≈5.31 ≈1.08e-20

C720 ≈24.12 ≈7.35 ≈1.45e-20

Buckling stage Final stage

R/h ratio C540~ C720 Non-recovery Obvious buckling 18.28

v0 16.39

C ~ C b 180 320 Full-recovery 12.48 Obvious buckling

Buckyball 10.76

Receiver 9.17 a Full-recovery C60 No obvious buckling 5.68

dh 2.5 Compression time, T

Figure 3.1 Computational cell and the three categories based on buckling/deformation characteristics upon impact.

C720 is a spherical buckyball with diameter of 2.708 nm (where the van der

Waals equilibrium distance is considered), volume of 7.35 nm3 and mass of 1.45 1020 g. C720 with varying numbers and packing directions (both vertical and horizontal) are selected in this study. Computational cells from single buckyball to 3-D buckyball stacking system are illustrated in selected examples in Figure 1. In the scenario of impact, the buckyball system subjects to the impact of a top rigid plate with incident energy

Eimpactor and the initial impact speed is below 100 m/s; in the scenario of crushing, the top rigid plate compresses the buckyball system at a constant speed below 100 m/s. The bottom plate, which is rigid and fixed, serves as a receiver and the force history it

49 experiences could indicate the energy mitigation capability of the protective buckyball system.

MD simulation is performed based on LAMMPS (large-scale atomic/molecular massively parallel simulator) platform with the NVE ensemble (micro-canonical ensembles) [149]. A pairwise Lennard-Jones potential term is added to the buckyball potential to account for the steric and van der Waals carbon–carbon interaction

12 6 (3.1)     CC CC Ur ij 4 CC     rr    ij   ij  where CC is the depth of the potential well between carbon-carbon atoms,  CC is the finite distance where the carbon-carbon potential is zero, rij is the distance between the two carbon atoms. Here, L-J parameters for the carbon atoms of the buckyball

CC  3.47A and CC  0.27647 kJ/mol as used in the original parametrization of Girifalco [135]. The particle-particle particle-mesh (PPPM) technique with a root-mean-square accuracy of 10-4 is employed to handle the long-range Coulomb interactions.

3.2 Results and Discussion

3.2.1 Buckling characteristics of buckyball

We first let the buckyball undergo the same impact energy per unit fullerene

3 volume ( volume 4753.43J cm ), and explore the configurations of the buckyballs at the critical buckling stage and the final stage (after ricochet of impactor). For convenience, denote R as the fullerene radius, h as the effective thickness (h=0.066 nm [85]), and d as the penetration depth of the impactor (which takes into account the van der Waals

50 equilibrium distance between the impactor and buckyball). The morphological characteristics may be divided into three categories under the present impact condition.

Type I applies to the smallest C60 which does not experience obvious buckle (and it only subjects to compressive deformation); Type II includes C180~C320 which buckles into an

inverted cap upon a critical dcr , however the deformation is fully recovered after unloading; Type III applies C540~C720 whose buckled morphology remains after ricochet; the stabilization of such a buckled morphology is owing to the van der Waals attraction

(“sticking”) between the atomic layers of the inverted cap, which leads to a lower system potential energy in the buckled configuration.

Some useful insights may be obtained from macroscopic continuum spherical shells under a point load. Except C60, all buckyballs experience initial buckle under a

critical dhcr  2.5 , which is qualitatively consistent with their continuum counterparts

[150-152]. The critical buckling force of a continuum spherical shell scales with

Pcr h dcr 2 ~  [153] which agrees with the trend of MD simulation, see Figure 3.2. Eh Rh

Moreover, for continuum shells with larger R/h, they tend to maintain their inverted cap morphology after unloading [154].

Figure 3.2 Computational cell and the three categories based on buckling/deformation characteristics upon impact. 3.2.2 Mitigation of transmitted impulse force of buckyball

The fullerene acts as a protective “buffer”. If the buckyball is rigid (reference

3 system), upon impact energy per unit fullerene volume volume 4753.43J cm , the impulse force histories on the receiver are given as open and solid squares for C60 and

C720, respectively. Meanwhile, with the deformable fullerene buffer, the impulse force history counterparts are presented as open and solid circles in Figure 3.3 – the great reduction of the transmitted peak impulse force (on receiver) as well as the significant elongation of the transmitted impulse history demonstrate the high impulse mitigation of the fullerene buffer. Under the present impact condition, the reduction of the transmitted

52 peak impulse force is about 92.52% and 90.12% for C60 and C720 respectively; whereas the reduction of the transmitted impulse energy is about 92.54% and 84.65% for C60 and

C720 respectively.

Figure 3.3 History of transmitted impulse force for C60 and C720; the reference systems are also shown. The impact energies are 6.5 eV and 176.8 eV respectively (such 3 that the impact energy per unit fullerene volume is the same, volume 4753.43J cm ).

3.2.3 Impact energy dissipation of fullerenes

For different buckyballs, the impact energy is varied such that either the impact

energy per unit fullerene mass mass 1741.67J g , or the impact energy per unit

3 fullerene volume volume 4753.43J cm , is kept a constant. Figure 3.4 illustrates the

53 percentage of energy dissipated per unit mass Wmass or per unit volume Wvolume for corresponding scenarios, as the buckyball size is varied. The energy dissipation is computed from the difference between the impactor’s initial kinetic energy and that after ricochet. In general, a larger proportion of incident energy is dissipated when a larger buckyball is employed, and the energy dissipation is significantly enhanced when the non-recoverable deformation occurs (Type III).

Figure 3.4 Percentage of impact energy dissipation, ( Eimpactor - Eimpactor )/ , for 3 C60~C720 under the same impact energy per unit fullerene mass ( mass 1741.67J cm ), 3 or under the same impact energy per unit fullerene volume ( volume 4753.43J cm )

The initial incident kinetic energy is denoted as Eimpactor . Upon impact, part of

it is transformed to the buckyball’s excessive potential energy, Epotential , part becomes

the buckyball atoms’ kinetic energy ( Ekinetic , and largely converted into heat), and the

54 remaining part is the residual kinetic energy of the ricochet, Eimpactor . In Figure 3.5, the

y-axis represents the percentage of energy dissipation ( Eimpactor - )/ , and the

proportions of Epotential / and Ekinetic / are deduced at the end of impact process. Indeed, the fullerene strain energy is significant only in the non-recoverable configurations, Type III; whereas for other two types of recoverable deformation the energy is dissipated mainly into heat. This makes the non-recoverable buckyballs as better candidates of energy absorption material.

60 Kinetic energy Potential energy 50 Total energy Potential energy Kinetic energy 40

Percentageenergy of dissipation (%)

0 CC60 C180C C240C C320C C540C C720C 60 180 240 320 540 720 Type

Figure 3.5 The dissipated impact energy ( Eimpactor - Eimpactor )/ is in part converted into heat and in part to excessive potential energy of the fullerene system. The impact condition is 4753.43J cm3 volume . 3.2.4 Effect of varying impact energy

Three representative buckyballs from Types I, II, and III, C60, C240 and C720 are chosen under various impact energies, and the total energy dissipation performance is 55 illustrated in Figure 3.6. With the increasing impact energy, the percentage of dissipated

energy, ( Eimpactor - Eimpactor )/ , also increases. For larger buckyball when the impact energy is significant enough to cause the non-recoverable buckle deformation, a large increase of the energy dissipation is observed.

70 Energy dissipation of C60 Energy dissipation of C 60 240 Energy dissipation of C720

50 fully-recovery regime

40 non-recovery regime

Percentageenergyof dissipation (%)

0 50 100 150 200 250 Impact energy (eV) Figure 3.6 Percentage of impact energy dissipation as a function of impact energy, for three representative buckyballs. 3.2.5 Atomic simulation results for large buckyball

The distinctive mechanical behavior of a single buckyball should underpin the overall energy absorption ability of a buckyball assembly. The force-displacement response under both quasi-static and a representative dynamic impact loading (with impact speed of 50 m/s and energy of 1.83 eV) are studied, shown in Figure 3.7. The force F and displacement W are normalized as FR Eh3 and W/D, respectively, where R,

56 h, D, and E are the radius, effective thickness h  0.66 nm [85], diameter and effective

Young’s modulus E  5 TPa [85] of the buckyball, respectively. Here, a crushing speed at 0.01 m/s is employed to mimic quasi-static loading because the normalized force-displacement curves are verified to be the same at various loading rates from 0.1 m/s to 0.001 m/s in trial simulations. Two obvious force-drops could be observed in low-speed crushing while only one prominent force-drop exists in dynamic loading which is related to the less evident snap-through deformation shape.

Figure 3.7 Normalized force displacement curves at both low-speed crushing and impact loading. The entire process from the beginning of loading to the bowl-forming

morphology can be divided into four phases. Morphologies of C720 are shown at the corresponding normalized displacements. The entire compression process could be divided into four phases according to the FR Eh3 ~ W/D curve, i.e. buckling (W/D<10%), post-buckling (10%≤W/D<30%),

57 densification (30%≤W/D<40%) and inverted-cap-forming phase (W/D>40%). Upon the ricochet of the plate, the deformation remains as a bowl shape with great volume shrinkage thus a large portion of external energy could be absorbed and stored within the system without any future energy release. The derivative of curve undergoes a sudden change at the same W/D value and at two completely different loading rates, suggesting that the sudden force-drop points are dependent on the buckyball deformation. And theoretical insights may be obtained from the four-phase deformation. Note that due to the property of FR Eh3 ~ W/D curve under impact loading, Phase III is a force-drop process which can be ignored for simplicity.

3.2.6 Phenomenological mechanical models

Among the phases of compression process, those with significant reduction of force (Figure 3.7) are relatively unimportant for energy absorption and not included in the modeling effort. A three-phase model for low-speed crushing and a two-phase model for impact loading are proposed separately in the following sections.

3.2.6.1 Three-phase model for low-speed crushing

(1) Phase I: Buckling phase

In the range of small deformation, the model describing thin-shell deformation under a point force is applicable [155, 156]. Considering a buckyball with wall thickness h=0.066 nm is compressed by F with deformation of δ, with the subscript number denoting the phase number sketched in Figure 3.8), the force-deflection relation should

58 be expressed as [157] 8D F 0      (3.2) 1Rc 1 1 b1 where the bending stiffness D Ehc2 ; the reduced wall thickness ch12 1  2  and  is the Poisson’s ratio. The linear deformation behavior continues until it reaches

the critical normalized strain b1 . Experimental results for bulk thin spherical shell show that the transition from the flattened to the buckled configuration occurs at a deformation

close to twice the thickness of the shell [151]. Thus, b1 is about 2t which agrees well with the simulation.

Due to the van der Waals interactions, the nanostructure has higher resistance to buckle and based on the fitting of MD simulation, a coefficient f   2.95 should be expanded to Eq. (3.2), as

8D  Ff1 1   0   1   b1  (3.3) Rc

It is reminded that this equation is only valid for C720 under low-speed ( or quasi-static) crushing.

(2) Phase II: Post-buckling phase

Once the compressive strain reaches , the flattened area becomes unstable and within a small region, the buckyball snaps through to a new configuration in order to minimize the strain energy of the deformation, shown in Figure 3.8. The ratio between the radius and thickness of buckyball is quite large, i.e. Rh 36.5, and only a small portion of volume is involved thus the stretching energy is of secondary order

59 contribution to the total strain energy. Hubbard and Stronge [153] developed a model to describe the post-buckling behavior of a thin spherical shell under compression based on

Steele’s [158] model

2 h 16D (3.4) F 2       2K Rc b1 2 b2

22 58    2 where K     31   . This nonlinear deformation behavior extends until it 43   

reaches the densification critical normalized strain b2 . The value of b2 could be fitted

from the simulation data for C720 where b2  6h .

Figure 3.8 Illustration of deformation phases during compression for C720. Dynamic loading and low-speed crushing share the same morphologies in Phase I while they are different in Phase II. Analytical models are based on the phases indicated above and below the dash line for low-speed crushing and impact loading, respectively. The first force-drop phenomenon is obvious once the buckling occurs where the loading drops to nearly zero. Therefore, Eq. (3.4) maybe further modified as

2hD 16  (3.5) Ff2 2   b2     b1   2   b2  K Rc  

(3) Phase III: Densification phase

When the crushing displacement is much larger than the thickness, the force-displacement relation becomes nonlinear [158]. The buckled buckyball is densified during this process. Therefore, a nonlinear spring model could be adopted as

n F33  (3.6) where  is a coefficient and n is fitted as n≈1.16.

Considering the relationship [153, 158]

n 2 F (3.7) 3  K b h 2 and FRc F  3 (3.8) b 8Dh we may come to the following equation

n 16Dh  2 n (3.9) F3 3  b2  3  Rc Kh

Once the force reaches the value when first buckling happens, the buckyball enters this deformation phase. Thus, by considering the continuity condition to connect two curves in adjacent phases, we may rewrite the Eq. (3.9) as

n 16Dh  2 (3.10) Fnn    F   f *    3 3bb 2 2 2    b2 3  Rc Kh

Figure 3.9 shows the simulation data at low-speed crushing compared with the

61 model calculation. A good agreement between two results is observed which validates the effectiveness of the model.

Figure 3.9 Comparison between computational results and analytical model at low-speed crushing of 0.01 m/s. 3.2.6.2 Two-phase model for impact

The mechanical behaviors of buckyball during the first phase at both low-speed crushing and impact loadings are similar. Thus, Eq. (3.2) is still adopted in phase I with a different f   4.30 . The characteristic buckling time is much longer than the wave traveling time, and thus the enhancement of f  should be caused by the inertia effect

[23].

As indicated before, the buckyball behaves differently during the post-buckling phase if it is loaded dynamically, i.e. no obvious snap through would be observed at the buckling point such that the thin spherical structure is able to sustain load by bending its

62 wall. Therefore, a simple shell bending model is employed here to describe its behavior as shown in Figure 3.3: the top and bottom flattened wall with length of L experiences little stretching strain, whereas the side wall bends with finite deformation, governing the total system strain energy

1 M 2 (3.11) EA d system 2 A EI

Eh3 where the bending rigidity EI  and M is the bending moment. A denotes the 12 1 2  integration area. h is the “enlarged” thickness, the result of smaller snap-through phenomenon. Here, hh 1.40 via data fitting. Substituting geometrical constraints and taking the derivative, the force-displacement relation becomes (for C720 under 50 m/s impact)

11 F EI2 R (3.12) 2 4 2 R 2 2

When the impact speed is varied, the corresponding force is modified by a factor  owing to strain rate effect [159-161]. With the subscript representing the

impact speed (in units of m/s), the correction factor α  40,,,,,  50  60  70  80  90 

 0.83,1.00,1.12,1.14,1.17. Figure 3.10 illustrates the comparison between atomistic simulation and model (for impact speeds of 40 m/s to 90 m/s), with good agreements.

Figure 3.10 Comparison between computational results and analytical model at impact loading under various impact speeds from 40 m/s – 90 m/s. 3.3 Concluding Remarks

In this chapter, the impact responses of a series of buckyballs are investigated using MD simulations. From the initial and post-buckling behaviors, the fullerenes may be divided into three categories, with the third type (with non-recoverable buckling deformation after ricochet) capable of mitigating most impulse force/energy and dissipating most impact energy. C720 as a representative giant buckyball has the distinctive property of non-recovery deformation after crushing or impact, which makes it capable of absorbing a large amount of energy. The mechanical behaviors of a single C720 under low-speed crushing and dynamic impact are investigated via simulation and analytical modeling. For smaller buckyballs, the dissipated energy is converted into

64 thermal energy; whereas for the larger buckyballs, the potential energy of the non-recoverable buckled configuration (inverted cap shape) is the major source of energy absorption. The proportion of energy dissipation also increases with impact energy. The present study may serve as a first step of evaluating the potential of employing fullerenes as advanced energy absorption materials, and the future studies may include fullerene cluster as well as the effect of defects, which may further fulfill the mechanical promise of buckyballs.

Chapter 4 Impact Protection of Buckyball System

Based on the mechanical behavior analysis in Chapter 3, the impact protection ability of buckyball system with various stacking forms are studied in this chapter, namely, short 1D alignment, 1D chain-like alignment, 2-D stacking form and pseudo 3D stacking forms by analogy to cubic-centered, face-centered and hexagonal-centered package ways.

4.1 Computational Model and Method

The first investigated stacking form is the 1D long chain. Small and large buckyballs behave differently upon impact: the smaller ones are often resilient while the larger ones exhibit non-recovery phenomenon after unloading [162]. In this study, C60 and C720 are selected to represent “recoverable buckyball” and “non-recoverable buckyball” respectively. In continuum modeling, buckyballs are assumed to share the same effective Young’s modulus E=5 TPa and nominal wall thickness t=0.66 nm [162].

3 3 The densities of C720 and C60 are  1.975 kg/m and   5.455 kg/m C720 C60 respectively. The other basic physical parameters of C720 and C60 are listed in Ref. [163].

To simulate a granular system, we assume the identical buckyballs are packed in a simple cubic manner such that the stress wave would be confined within one dimension (effects caused by different packaging arrangements have been discussed in

Ref [162]). We have shown that the system deformation mode and the energy

66 absorption/mitigation ability are independent of the arrangement number in both vertical and horizontal lineups in previous work [162]. In addition, preliminary simulation also reveals that system with multi-column stacking has no obvious difference in deformation behavior and unit energy absorption rate. Thus, by taking advantage of symmetry, a long chain of buckyball system is simulated. The “long chain” is set to be at least 20 times in length than its width, and a typical system contains 100 buckyballs. The computational cell is illustrated in Figure 4.1, where the buckyball system is subject to the impact of a rigid left plate with incident energy Eimpactor and the impact speed is varied from 100 m/s to 1000 m/s which is conventionally considered as high impact speed domain, mainly aiming at the ballistic impact related problem.

Figure 4.1 Illustration of one-dimensional buckyball chain setup as an impact protector.

Mass changing falls into the domain where the maximum strain is large enough while the temperature rising of the buckyball caused by the kinetic energy is below 800 K where buckyball may remain stable. A rigid and fixed right plate serves as a receiver which would indicate the energy mitigation capability of the protective system (the buckyball chain is sandwiched between the plates). Force histories on the left and right plates are recorded.

A fully atomistic description of the buckyball is used. MD simulation is performed based on LAMMPS (large-scale atomic/molecular massively parallel simulator) platform with the NVE ensemble (micro-canonical ensembles) [164] after running initial equilibrium. A pairwise Lennard-Jones (L-J) potential term is added to the buckyball potential to account for the steric and van der Waals carbon–carbon

12 6 interactions U r4  r  r where  is the depth of the  ij CC CC ij  CC ij  CC potential well between carbon-carbon atoms,  CC is the finite distance where the

carbon-carbon potential is zero, rij is the distance between the two carbon atoms. Here,

L-J parameters for the carbon atoms of the buckyball CC  3.47A and

CC  0.27647 kJ/mol as used in the original parameterization of Girifalco [135] and Van der Waals interactions governs in the plate-buckyball interaction. Carbon atoms are employed to make both the impactor and receiver plates with varying masses in the following simulation to set various loading conditions (varying impactor mass) while the interactions between the plates and buckyballs remain as carbon-carbon ones. Details of the simulation methods are described elsewhere [162]. To simulate the long one dimensional chain, four L-J walls with the same parameters are set as four sides of the simulation box to provide necessary lateral constraints from simple cubic packing. A time integration step of 1 fs is used and periodical boundary conditions are applied in the x,y plane to eliminated the boundary effect.

4.2 Representative Impact Behavior For 1D Long Chain Buckyball

4.2.1 Dynamic response of C60 chain system

4.2.1.1 Hertzian model

Interactions between particles in the one-dimensional chain system subject to contact loading may be treated based on the Hertz law [31]. Similar to granular particles, each C60 molecule in the chain system undergoes relatively small deformation without any buckling or bifurcation. In addition, the characteristic time  101 ~

0 5 10 ns > T2.5 R c  5.71  10 ns where R is the radius of C60 and C160 C60

cE  is the wave speed [31]. Therefore, the Hertz contact law still 1C60

approximately holds for the dynamic response of C60 chain system.

Consider a one dimensional chain of N same C60 each of mass m , radius C60

and Young’s modulus E and Poisson’s ratio  in contact without any precompression. The Hertzian contact law between neighboring buckyballs and could be expressed as [165]

3 4 3 (4.1) 2  2 F kc  E R 2 R  x21  x  3

where F is the contact force, kc referring the elastic coefficient,  is deformation, x2,

 2 x1 are coordinates of two neighboring buckyball centers ( xx21 ); EE21   , and

RR  2 are the effective Young’s modulus and effective radius respectively. By C60

replacing the coordinate xi by the displacement ui of the ith buckyball from its equilibrium position in the chain, the equation of motion for each buckyball may be further written as

3 33 2 22 (4.2) ui u i11  u i  u i  u i  This is widely used for granular materials.

4.2.1.2 MD simulation of one-dimensional C60 long chain

The forces on both impactor and receiver plates are normalized as FR Eh3 , C60 and the representative impact force attenuation for 100 C60 particles is shown in Figure 2

(where the positive value stands for compression force along the impact velocity direction). A sharp and narrow impact pulse is initiated once the top plate collides with

the buckyball system and it drops to nearly zero at about 0.02 ns ( 1 0.02 ns ), indicating that the compressive stress wave is traveling towards the receiver. The receiver

does not experience any force until the stress wave arrives at tt 1 (shown in Figure 4.2); from which the average traveling speed of the stress wave is estimated as

u L t 1252 m s and thus the system equivalent modulus is Eu2 3.10 GPa 01 0C60 for the specific impact loading condition (impact energy of 6.49 eV and impact speed of

500 m/s). Once the stress wave reaches the receiver, it reflects back and if it successfully

travels back to the impactor, a secondary impact impulse would form at tt 2 (shown in

Figure 4.2) and thus causes the speed of the ricochet impactor increase again. The peak transmitted force on the receiver is about 42.27% of the original peak force on the impactor, after force attention of 100 C60 buckyballs. About 93.75% of the impactor kinetic energy (i.e. impact energy) is dissipated by the system, therefore, one may define the energy mitigation rate as   0.9375. The effect of buckyball number on the energy mitigation rate is discussed later.

Figure 4.2 Normalized force time history and impactor velocity history of C60 chain containing 100 buckyballs, when the impact energy is 6.49 eV and impact speed is 500 m/s. According to the force equilibrium and mass continuity, the stress of a particular mass point during the wave propagation is  vE [23], and the relation C60

between stress  b and  r (at the interface of buckyball and the rigid plate respectively) may be expressed as [23]

 cc r  r r b b (4.3) b  rcc r  b b

where r and b are densities and cb and cr are wave speeds of the material on the two sides of the interface respectively. Similarly, the stress wave speed may be written as

[23]

v cc r  b b r r (4.4) vb b c b r c r

Since the receiver is fixed as a rigid body in this study, rrc , such that rb1

and vvrb1 which means that the stress wave propagates back to impactor at the same speed. After the reflective wave travels through 100 C60 buckyballs, the magnitude of force on impactor reduces to 21.95% of the original force. On the other hand, the transmitted force pulse duration is about 5.4 times of that on the impactor, i.e.

12   0.185, showing a prominent stress wave mitigation effect. The major energy mitigation effect results from the stress wave attenuation caused by the reflections among buckyball walls, similar as that found in previous research in granular system [29, 32, 36,

37, 166], as well as the van der Waals interactions between buckled layers and similar energy absorption mechanism revealed in carbon nanotubes in Ref. [90, 91, 167]. In addition, about 1.5% of the impact energy may be converted to the kinetic energy of the atoms within C60.

4.2.1.3 Dissipative Hertzian model

As the method adopted in Ref [168] to include the dissipation term to Eq. (2), from MD simulation, the following relationship can be fitted

33 6 (4.5) 22 iA   i   i11    i   i   where A E3 1  2 m  2 R , the second term implies dissipation which is   buckyball C60 fitted based on the force-displacement curve at large deformation in our previous study

[162, 163] and its coefficient   61.32 ms52 . This relationship is valid for systems with large number of C60 buckyballs at all loading conditions as long as the Hertzian

72 contact law holds. Figure 4.3 shows the maximum force on the ith ball, Fti,max   , of the dissipative model (Eq. (4.5)), which is consistent with the MD results of C60 chains.

Figure 4.3 The normalized force distribution on selected buckyballs in C60 and C720 chain systems.

4.2.2 Dynamic response of C720 chain system

The large non-recoverable deformation of C720 makes the Hertzian contact law invalid. The energy mitigation behaviors are investigated using MD simulations. Typical normalized force history curves of the impactor and receiver are shown in Figure 4.4, where 100 C720 are studied. In terms of stress wave traveling, its average speed is

u01 L t 509.8 m s , and thus the system equivalent Young’s modulus is

2 Eu 0.536 GPa , which means the C720 chain system is more “compliant” than 0C720

C60. In our previous work, the “non-recovery” phenomenon is proven to be only strain determined, regardless of the impact mass and velocity [162] and during preliminary

73 simulations, we also confirm that the “non-recovery” phenomenon in C540 is impact-condition-independent.

Figure 4.4 Normalized force history and impactor velocity history of C720 chain containing 100 buckyballs, when the impact energy is 6.49 eV and impact speed is 500 m/s. From energy mitigation perspective, a very sharp initial impulse is attenuated to a much milder and longer impulse. The ratio of the peak magnitude and duration between

the original and transmitted impulses are FFri13.2% (where the subscript r and i

refer to the receiver and impactor respectively) and 12   0.0290 . The force reduction and duration elongation are much higher than that in C60 chain system due to the buckled-through shape of C720 during impact. Therefore, van der Waals interactions between buckled and “stickered” layers may contribute more energy dissipation compared to its counterpart in C60 system due to the un-recoverable deformation. Also,

74 with the buckled morphorlogy of C720, the covalent potential energy also increase via the consumption of external impact energy. Moreover, about 12% of the impact energy could be mitigated in the form of atom kinetic energy which also contributes the superiority of energy dissipation for C720 system. The power-law-like dissipative model for contact

force attenuation Fti,max   at various buckyballs still applies, see Fig. 4.3, indicating a fast force decay along the wave propagation direction. In the meantime, over 99% of the impact energy is mitigated to the kinetic energy and strain energy of buckyballs.

4.3 Parametric Study and Discussions

A parametric study is carried out where the impact speed is varied from v0 

100 m/s to 1000 m/s, and the impact mass per carbon atom is varied at

  mmimpactor buckyball =1.73 to 13.87 for both the C60 and C720 chains containing 100

buckyballs. The initial impact speed is normalized as   vu00 (where u0 1252 m s

and u0  509.8m s are used for C60 and C720 chains respectively); the stress wave propagation speed (calculated based on the time when the wave transmits through the

chain, which is dependent on the number of buckyballs) is normalized as   uu0 . The corresponding fitting curves of the suggested models are also shown in Figures 4.5 and

4.6.

C60 chain system containing 100 buckyballs. Nonlinear models are suggested to fit the computational data.

4.3.1 Effects of initial impact speed and mass on C60 chain

4.3.1.1 Force attenuation

The force reduction ratio FFri and normalized wave propagation speed  are two indices employed to evaluate the mitigation properties, shown in Figure 5.

Following Reid and Peng [169], the enhanced dynamic stress  * can be expressed as

2 * buckyballv (4.6) cr  D

where  cr is the crushing strength of buckyball and the  D is the material strain attained behind the wave front. v is the particle velocity at a certain time t. By keeping the

76 impact mass constant, the particle velocity, vv 0 [169]. Assuming the contact area

** keeps a constant as A0 , one may come to FFr i r i . Thus, the force reduction ratio under a fixed impact mass (but different impact velocities) is

Fr  cr 1 (4.7) 22 Fi buckyballvv 0 buckyball 0  cr kk1 D  cr  D where k is the linear coefficient between v and v0 .

C720 chain system containing 100 buckyballs. Nonlinear models are suggested to fit the computational data. Alternatively, under this condition, we may fit the equation in the form of

Fr 1 (4.8)  2 Fai 1  where a is material-related parameter and from Figure 5 it yields a  24.05 for the present system.

One may also regard the buckyball system as a non-linear spring damping system whose stiffness is only slightly affected by the mass of the impactor. Such a damping system reduces the force in the receiver by extending the functioning time over a longer time period. When the impact speed remains the same but impact mass is different, the following form is fitted to describe the force attenuation

Fr  (4.9) 1 1  ln 1  Fi  1 where   39.6 and   0.247 for the present system.

Eqs. (8) and (9) in together reveal that the one-dimensional C60 chain system has a better mitigation performance under the condition of higher impact speed with smaller mass, in terms of the force attenuation to alleviate the transmitted load on objects to be protected.

4.3.1.2 System equivalent Young’s modulus

The system equivalent Young’s modulus may be characterized via the elongation of wave propagation speed. The mitigation behavior is still dominated by impact energy, which means that changing the impactor mass or speed may vary the

mitigation performance. The ratio between dynamic stress  dynamic and static stress

 static for rate-sensitive material may be expressed as [170]

1 q  dynamic  (4.10) 1   static D where  is the strain rate, D and q are constants for a particular material. With the relation between stress and Young’s modulus as well as the strain rate and velocity, one may fit the normalized wave propagation speed with various impact speed  (yet same impact mass) in the form of

1 q  (4.11)    D where D  0.937 and q  9.835 . Combining the two equations above yields the relationship under various impact mass (but same impact speed)

1 p A 2 1 (4.12)     B where A 1.41, B  8.97 and p 18.8 through the best fitting.

Note that when the number of buckyballs in the system increases, the effective system rigidity becomes smaller due to the longer stress wave transmission. Therefore, the fitted formula for calculating the stress wave speed and the corresponding equivalent rigidity are only valid for this specific system under subscribed loading conditions.

However, these parametric values may become stable under certain impact mass once the number of buckyball reaches the threshold value which is discussed later.

4.3.2 Effect of initial impact speed and mass on C720 chain

4.3.2.1 Force attenuation

To evaluate the energy mitigation performance of C720 chain, the force

reduction ratio FFri and normalized wave propagation speed  are employed in

Figure 6. The value reduces sharply in the relatively low impact speed domain and becomes stable once the impact speed exceeds over 500 m/s. Eq. (8) still applies with

a 15.77 via best fitting.

Due to the non-recoverable deformation of C720, the impact mass poses more influence over the force reduction ratio because the larger mass makes the first few buckyballs easier to buckle. With the impactor mass increasing, the force reduction is also more prominent than that in C60 chain system. Similarly, Eq. (10) may be applied with

 119 and   0.486.

4.3.2.2 System equivalent Young’s modulus

Similarly, we may also take the form of Eqs. (11) and (12) to describe the system equivalent rigidity based on stress wave propagation speed. With the impact speed increases, the average wave propagation speed also increases, leading to a much stiffer system in terms of rigidity. In Eq. (11), the fitting parameters are D  2.12 and

q 12.0 for the C720 buckyball system. By taking the derivative of Eq. (11), the variation

rate in C60 is more prominent than that of C720, indicating that C60 exhibit even higher effective stiffness than C720 under very high impact speed situations. The fitting of Eq.

(12) yields A 1.20, B  9.49 and p  23.3 for the C720 chain system, indicating that

the effect of impactor mass is less on C720 than that on C60 chain. Again, these fitted

80 equations are only valid for the protective system with particular number of buckyball under the specific loading conditions. System rigidity would also alter accordingly if any of the corresponding factors change.

4.3.3 Effect of buckyball size

The ratio between the initial and transmitted impulse duration, 12, is also an important indicator for energy mitigation. The buckling forces for larger size buckyballs are smaller, owing to the buckling phenomenon. Figure 4.7 shows the relation between and normalized buckyball diameter RR at the impact buckyball C60 speed of 500 m/s with the same impactor mass per carbon atom. The sizes of all buckyball involved here are labeled in Figure 4.7. The values decay in a power-law manner as the buckyball size increases. More importantly, a sudden drop is observed between C320 and C540 where the non-recovery phenomenon starts to appear.

Once the buckyballs stay in a buckled morphology, the layered and densified structure would create more barriers to transmit the stress waves and the waves are attenuated through the wave reflection among interfaces of buckled shapes. The numerical results may be fitted as

  0.184 0.576 , 1    2.20 (4.13)  12 12  0.0660  0.0115  , 2.89    3.22

Figure 4.7 Normalized force history and impactor velocity history of C720 chain

containing 100 The impulse duration ratios 12 between the impactor and receiver for various buckyballs including C60, C180, C240, C320, C540 and C720 by normalized buckyball radii  at the impact speed of 500 m/s with the same  value in each buckyball. 4.3.4 Effect of buckyball number

As aforementioned, with the change of buckyball number within the protective system, stress wave propagation characteristics as well as the equivalent system rigidity alters, which may influence the energy mitigation ability of the system for both C60 and

C720 systems. The energy mitigation rate  is calculated for systems with buckyball numbers varying from 1 to 200 under the specific impact condition. In Figure 4.8, one may clearly observe that nonlinear increase on with the buckyball number for both systems. The increasing rate becomes much milder in longer buckyball chains, indicating that there may be a certain length threshold beyond which the system acquires high-efficiency impact wave mitigation. In addition, to reach the same mitigation ability, 82 fewer buckyballs are needed to for larger particles; for example, the system with about 20

C720 buckyballs may mitigate over 99% of the impactor kinetic energy (i.e.   99% ), whereas it would take about 80 C60 buckyballs to reach   90% , showing another

superiority of C720 system without the system mass and volume constrain in application.

Figure 4.8 Relations between energy absorption rate and buckyball number for both C60

and C720 systems at the impact speed   0.40 for C60 chain system and   0.98 for

C720 chain system, and the impact mass of  1.73 for both systems. From systematic simulations, one may also summarize an empirical law at the impact speed for C60 chain system and   0.98 for C720 chain system, and the impact mass of for both systems to describe the relation between buckyball number N (N > 0) and  as

 N  0.9519  0.4872  0.9628 , for C60 system (4.14)   0.8711  0.12921  N 1.182 , for C system    720 and Eq. (14) may serve as a guidance for engineering design.

4.4 Buckyball Assembly 83

In practice, large buckyballs need to be assembled (shown in Figure 4.9) so as to protect materials/devices. Various stacking arrays are investigated as follows.

(a) Single C720 buckyball energy absorption system; (b) Short 1D alignment C720 buckyball energy absorption system with 3 buckyballs included (c) Pseudo 3D C720 buckyball energy absorption system with 6 buckyballs included Figure 4.9 Various alignments of buckyball system as a protector. 4.4.1 Short 1-D alignment buckyball system

The C720 can be arranged both vertically and horizontally in a 1-D chain-like alignment. Figure 4.10 shows the mechanical behavior of a five-buckyball array subjecting to a rigid plate impact with impact energy and speed of 9.16 eV and 50 m/s respectively. Progressive buckling and bowl-shape forming behavior takes the full advantage of single buckyball energy absorption ability one by one, and controls the force on the receiver within a relatively low value during first section of deformation (within

WD1.5 ) which provides cushion protections.

Figure 4.10 The characteristic normalized force-displacement curve of 1-D buckyball

system with 5 vertically lined C720’s at impact speed of 50 m/s. Another 1-D arrangement direction is normal to a plate impact. Unlike the progressive buckling behavior in the vertical system, all buckyballs buckle simultaneously in the horizontal array. Figure 4.11 shows the scenario with impact energy of 1.83 eV per buckyball and impact speed of 50 m/s, where the total reaction force scales with the number of buckyballs. Systems with different buckyball numbers show almost uniform deformation characteristics of individual buckyballs.

The energy absorption per unit mass (UME, J/g) and unit volume (UVE, J/cm3) are given in Figure 4.12, which shows that the UME and UVE are almost invariant regardless of buckyball number or arrangement. In Figure 4.12 the impact energy per buckyball is fixed as 1.83 eV, if the impact energy or speed changes, the value of UME or

UVE will change, however the result is still insensitive to buckyball number or

85 arrangement. The major reason is that the energy absorption ability of the system stems from the non-recoverable deformation of individual buckyball which is almost uniform.

Figure 4.11 The characteristic normalized force-displacement curve of 1-D buckyball

system with various numbers of horizontally lined C720’s at impact speed of 50 m/s.

Figure 4.12 UME and UVE values of both vertical and horizontal buckyball systems with various buckyball numbers at impact speed of 50 m/s.

By fixing either the impact speed or mass and varying the other parameter, the impact energy per buckyball can be varied. It imposes a nonlinear influence on the UME and the maximum force on the receiver, shown in Figure 4.13 for the vertical alignment of five-buckyball system. No matter how the impact speed or mass varies, it is the impact energy per buckyball that dominates the values of UME and maximum transmitted force.

The behaviors of the 2D systems may be directly conjectured from the 1D cases and they are not often applied in practice. Considering the computation resources available, the real 3D cases are not computable right now so the pseudo 3D cases, i.e. the size of the computational cell is restricted.

The packing density of a pseudo 3D system can be different than that of the 1D system, and thus the performance is expected to vary. four types of pseudo 3D stacking forms are investigated, i.e. simple cubic (SC), body-centered cubic (BCC), face-centered cubic (FCC) (a basic crystal structure of buckyball [171]), hexagonal-closed packing

(HCP). The occupation density SC 6 0.52, BCC 3 8 0.68,

FCC  HCP   3 2  0.74 [172] for SC, BCC, FCC and HCP respectively.

Figure 4.14 illustrates the normalized force-displacement curves for SC, BCC,

FCC and HCP units under the same impact energy per buckyball (1.83 eV). As expected, the mechanical behaviors of FCC and HCP are similar, while the BCC and SC units (with lower  ) have more space for system to comply and hence the impact force is smaller yet the displacement is larger. Consequently, FCC and HCP have the same energy absorption ability and that of BCC and SC are inferior.

Energy absorption performances of the three basic units are studied at various impact speeds, i.e. from 10 m/s-90 m/s while the impact mass is kept a constant, shown in

Figure 4.15. With the impact speed increases, more mechanical energy is absorbed but the increasing trend becomes slighter at higher impact speed when the buckyball system reaches its mitigation limit. The improvement is greater in terms of UVE than UME with higher .

Figure 4.14 Typical normalized force-displacement curves for SC, BCC, FCC and HCP packing of C720 at impact speed of 50 m/s, and the impact energy per buckyball is 1.83 eV.

(a)

(b) Figure 4.14 (a) UME and (b) UVE values of SC, BCC, FCC and HCP packing of C720 at impact speeds from 10 m/s to 90 m/s. Fitting surfaces based on the empirical equations are also compared with the simulation.

By normalizing the UME and UVE as m UME Emimpactor  and

v UVE EVimpactor volume  where Vvolume is the volume of the buckyball, as well as impact speed as V v B  where B = 34 GPa [52] is the bulk modulus of graphite.

An empirical equation could be fitted as

C m A  BV  DV  (4.15) where A=5.50, B=-0.25, C=0.21 and D=25.0 with fitting correlation coefficient of 0.96, and

C v A  BV  DV  (4.16) where A=0.46, B=-1.94, C=0.21 and D=187.9 with fitting correlation coefficient of 0.96.

These equations are valid for low speed impact speed (below 100 m/s) on stacked C720

90 buckyballs. When the impact speed is fixed, the unit energy absorption linearly increases with the occupation density; under a particular spatial arrangement, the energy absorption ability increases nonlinearly with the impact speed.

4.5 Concluding Remarks

In this paper, the impact mitigation characteristics of a long one dimensional buckyball chain are investigated, which can be extended to granular buckyballs of simple cubic packing. Representative small and large buckyballs, i.e. C60 and C720 under high speed impact loadings are studied. The impact energy, size and number of buckyballs, are varied in a systematic manner. With relatively small elastic deformations of C60 buckyballs during impact, a mechanical model based on Hertz contact law is proposed, with critical parameters calibrated via MD simulations for given impact loading conditions. Energy mitigation is illustrated through force impulse history difference between the impact and receiver. The stress wave propagation speed, the reduction of peak impulse force, and the impulse duration ratio are studied to reveal the dynamic response of the system. The major energy dissipation mechanism for the buckyball chain is the wave reflection among the deformation layers, covalent potential energy, van der

Waals interactions as well as the atomistic kinetic energy. These terms may have higher contribution to energy dissipation in C720 system with non-recoverable morphologies.

Moreover, Buckyball systems are investigated under various impact speeds and various impact masses. The smaller mass and higher impact speed results in a higher impulse

91 force attenuation effect, as well as higher system stiffness and shorter wave propagation time. Over 99% and 90% of impact energy for C720 and C60 chain systems could be mitigated under particular impact conditions respectively and thus a promising buckyball based stress wave mitigation system is suggested.

By understanding the mechanism of mechanical behavior of individual C720, the energy absorption ability of a 1D array of buckyball system is studied. It is found that regardless of the direction of alignment and number of buckyballs, the unit energy absorption density is almost the same for low speed impact and crushing. Further, the study is extended to pseudo 3D buckyball stacking at dynamic loadings with impact speed from 10 m/s to 90 m/s. The energy absorption increases nonlinearly with the impact speed until the system energy capability saturates. In addition, different pseudo

3D stacking forms may directly influence the energy absorption rate, which is proportional to the packing density.

The results may shed lights on the research and development of novel impact/blast protection system.

Chapter 5 Governing Factors in Impact Protection Based on Nanofluidics System

As mentioned in Chapter 1, quite a few research results regarding the nanofluidics system for energy absorption have been presented since the raise of the fundamental idea by converting mechanical energy into the excessive solid-fluid interfacial energy through liquid infiltration into the nanochannels. To make the system more engineering applicable, further under the working mechanisms and underpin the science of nanofluidics, in this chapter, the focus is put on the experimental study of governing factors for the nanofluidics system in terms of the impact protection. The pre-treatment temperature, concentration of sodium chloride, solid-liquid mass ratio, particle size and loading rate are investigated to fully explain the system working behavior.

5.1 Experimental Setup

5.1.1 Material preparation

+ [19] Zeolite ZSM-5 (|Na n (H2O)16| [AlnSi96-n O192], n<27) is chosen to be the experimental material. Its particle size ranges from 3-10 μm and it is widely used in chemical engineering. The MFI (Zeolite Socony Mobil – five) framework of ZSM-5 consists of two intersecting tubular channels defined by 10-member rings of SiO4/AlO4 tetrahedra. The pore size for both the linear (parallel to the [010] direction) and the zigzag

(parallel to the [100] direction) is approximately 5 Å. [19] The encapsulated water molecules may only retain a single-file, which indicates that the infiltration of liquid consumes a great amount of external energy.

By using a Quantachrome Autosorb-iQ-MP gas sorption analyzer, ZSM-5 used in this paper has the average pore size 4.523 Å ; its specific surface area is higher than

300 m2g and its specific nanopore volume is higher than 0.13 cm3/g (listed in Table 5.1).

By using a MasterSizer 2000 particle size analyzer, the mean particle sizes of two samples in this paper were 2.145 μm (6.104 μm after heated) and 5.251 μm (9.557 μm after heated) respectively. The silica-to alumina ratio is 36.

Pretreatment is essential because the raw materials may have impurities. This pretreatment process aims at improving the purity and changing the Si-Al ratio of the sample material, thereby adjusting hydrophobicity. We heat ZSM-5 in a tube furnace at a fixed temperature for 3 hours. Similar procedures are elaborated in Ref. [20, 21] while in this paper we also vary the pretreatment temperature. The pretreated zeolite (whose ranges of parameters are listed in Table 5.1) is then mixed with distilled water at a certain mass ratio and then placed in the experimental chamber.

Table 5.1 Physical parameters of ZSM-5

Particle size [μm] Pretreatment temperature [℃] BET [m2/g] Pore volume [cm3/g] Pore size [nm]

800 373.6 0.1526 0.4523

5.251 (before heated) 900 368.0 0.1469 0.4523

9.557 (after heated) 1000 359.9 0.1416 0.4523

1100 315.1 0.1332 0.4523

95 2.145 (before heated) 800 380.2 0.1561 0.4523

6.104 (after heated) 1000 338.1 0.1346 0.4523

Table 5.2 Experiment results with different pre-compression cycles for three samples.

Displacement at the top Displacement Materials pressure [mm] (for 3 cycles) deviation Distilled water 5.530 5.512 5.485 0.33%

Fine particled zeolite water solution (particle size: 6.104 μm) 6.700 6.590 6.597 1.67%

Coarse particled zeolite water solution (particle size: 9.557 μm ) 7.250 7.058 7.090 2.72%

5.1.2 Experimental device and setups

The experimental system is comprised of a chamber and a type CSS-2220 material testing system with load capacity of 200 KN and velocity range of 0.5-500 mm/min. The chamber is made of stainless steel with yield strength   680MPa and y hardness=195HB/13Rc, [22] shown in Figure 5.1. The diameter of piston is 40 mm. The depth and volume of the chamber are 80.0 mm and 110.8 ml respectively. Two precisely-fit sealing rings ensures the integrity of the chamber, providing an upper limit of pressure of 145 MPa.

Figure 5.1 Schematic illustration of experimental setup. The system includes a rigid piston, chamber cover with two pairs of sealing rings and a chamber base. The pressure-holding ability of the chamber is verified by keeping the pressure at the maximum value of 127 MPa over a period of 5 minutes (300 seconds), and the pressure reduces by merely 3% during the entire holding period, Figure 5.2. On the other

96 hand, a complete loading and unloading process in experiment takes approximately 145 s, indicating that the pressure drop is insignificant during the experiment. Due to the initial flaws and gaps among particles, it is necessary to carry out pre-compression tests. After series of trials (Table 5.1), the pre-compression pressure is set to be 40 MPa, which could ensure robust testing data for the subsequent infiltration experiment, described below. In what follows, the loading and unloading rate is set to be 5 mm/min up to a maximum pressure of 127 MPa; the loading rate is verified to be sufficiently low so as to represent quasi-static condition.

Figure 5.2 The pressure history curve during the pressure holding test at 127 MPa for 300 seconds. 5.2 Results and Discussions

5.2.1 Typical loading and unloading behavior of ZSM-5/ water mixture

Figure 5.3 shows a typical pressure-volume change (P-ΔV) curve, where the

ZSM-5 particle size is 9.557 μm, pretreated at 1000℃, and the ZSM-5 water mass ratio is

3:5. The system compliance is deducted via the compression test of pure water.

Figure 5.3 A typical sorption isotherm ( PV ) curve under quasi-static compression test, with zeolite average particle size of 9.557 μm , pretreatment temperature of 1000℃, and zeolite:water mass ratio of 3:5. When the pressure is low, water resides outside the hydrophobic zeolite and the system compressive behavior is dominated by the bulk modulus of water (unless the zeolite mass ratio is too high). Indeed, after deducting the system compliance, the initial portion of P-ΔV curve in Figure 5.3 is almost vertical. Once the pressure rises beyond a critical value, Pin, the water molecules overcome capillary resistance and infiltration starts.

The small slope of the infiltration stage is mainly caused by friction between water molecules and nanopores. When nanopores are filled with water molecules, the system becomes rigid again. The total infiltration volume is approximately 0.051 cm3/g, smaller than the pore volume 0.142 cm3/g.

During the unloading process, the excessive liquid-solid interfacial energy drives water molecules out of the hydrophobic pore, which occurs when the pressure is 98 below a critical defiltration pressure, Pout. At the end of defiltration plateau, the P-ΔV curve will return to the original starting point. No variation in final volume is observed, indicating that all the water molecules flow out of the channels when external pressure is removed, and thus the system is expected reusable. Figure 5.4 further demonstrates the system response under three cyclic loads. Due to the small remnant deformation the system is a bit stiff in 2nd and 3rd cycles than the 1st cycle. This small remnant deformation lies in the fact that a small fraction of water molecules can be trapped within some channels due to the inevitable inconsistence in pore size and possible defects in framework structure. In general, the performance decay is relatively small and the system is envisioned to work well under cyclic/multiple loadings.

140

120 loading

100

(MPa) 80 unloading

Pressure, 1st cycle 20 2nd cycle 3rd cycle 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30

△ V Figure 5.4 P-ΔV curves under cyclic loads (one, two and three cycles respectively) particle size; other experimental conditions are same as that in Figure 5.3 5.2.2 Energy dissipation mechanism

In the perspective of energy, the infiltration process is accompanied by the

99 conversion from external mechanical energy W to the excessive liquid/solid 1

S D interfacial energy E1 and that overcomes flowing resistance E1 . Ideally,

SD WEE1   1   1 . Similarly, during the defiltration process, the liquid/solid interfacial

S energy E2 converts back to mechanical energy W2 and that overcomes flowing

D SD resistance E2 , i.e. EEW2   2   2 in the case of all water molecules defiltrate out of the pores.

In Figure 5.3, ES can be measured as EPVS , and in the present study, 1 1 in

S E1 174.587J for 70 ml liquid in total including 33.250 g zeolite and 55.417 g water.

The flowing resistance came from the shear stress for the encapsulated water molecules to overcome the lattice “friction”, represented by the slope of the infiltration plateau. [23]

The term equals to the area above P and below the loading curve, and in this in

D S specific example, E1 7.460J , which is much smaller than E1 and indicates a relatively smooth transport behavior inside the nanopores.

Quartieri et al. [24, 25] investigated the elastic behavior of H-ZSM-5 and

Na-ZSM-5 by in-situ synchrotron X-ray powder diffraction, under high pressure established by (16:3:1) methanol:ethanol:water. It’s proved that under the pressure up to

0.8 GPa, structural deformation is trivial and purely elastic. In our research, the maximum pressure is 127 MPa, thus the structural deformations of the channels upon infiltration of water are then to be expected extremely minor and completely reversible. Therefore, we

SS can have EE12   , and the recoverable infiltration-defiltration cycle (Figure 2)

100

DD indicates that WWEE1   2   1   2 . That is, the energy dissipated during the loading-unloading cycle equals to the frictional dissipation during infiltration and defiltration. Indeed, the pore size and gas phase trapped inside the pores have shown to play a dominant role in system reusability, [15] and in pores smaller than 2nm, the insolubility of gas molecules can be a critical driving force for defiltration, which echoes the findings in the present study.

5.2.3 Effect of pretreatment temperature

Heat treatment from 600℃ to 1100℃ is used to prepare the material, and its effect on the sorption isotherm is shown in Figure 5.5. With a relatively high pretreatment temperature, the Si-Al ratio is improved, the hydrophobicity of the ZSM-5 is enhanced and the critical pressure required for infiltration, Pin, is also higher; in addition, the transport resistance is smaller, leading to a more flat infiltration plateau.

140

120 P in ( 1100 ℃ ) 100

(MPa) 80 P P in ( 1000 ℃ ) 60 P in ( 900 ℃ ) P 40 in ( 800 ℃ ) 800 ℃

Pressure, 900 ℃ 20 1000 ℃ 1100 ℃ 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

△ V Figure 5.5 P-ΔV curves under quasi-static compression with zeolite average particle size of 9.557 μm, pretreatment temperature of 1000℃, particle size at various pretreatment temperatures of 800℃, 900℃, 1000℃, and 1100℃, respectively. 101

From a molecular point of view, the framework of ZSM-5 zeolite is composed of oxygen-silicon tetrahedron and oxygen-aluminum tetrahedron. The oxygen-silicon tetrahedron is nonpolar whereas the oxygen-aluminum tetrahedron is polar and shows certain hydrophilicity. [26] In this case, the higher the content of aluminum, the higher degree of hydrophilicity. [26-31] A series of Al MAS NMR (Magic Angle Spinning Nuclear

Magnetic Resonance) tests are conducted to verify the trend of variation of Al content in the ZSM-5 framework upon different pretreatment temperatures, and the results are shown in Figure 5.6. The framework (tetrahedrally coordinated) and non-framework

(octahedrally or pentahedrally coordinated) aluminum can be distinguished in the Al

MAS NMR spectra. [32] Under treatment of low temperature, the spectra contains a dominant resonance at 50 ppm assigned to tetrahedrally coordinated framework Al and a small amount of non-framework Al with octahedral coordination resulting in a resonance at 0 ppm. [33] With the increase of treatment temperature, the intensity of the signal at 50 ppm decreases, and the signal at 0 ppm increases and a broad signal at 25 ppm appears above 800℃ which is ascribed to the pentacoordinated non-framework Al. [34, 35] All these facts demonstrate the heat treatment leads to dealumination of the framework, in line with the report by Marturano et al.. [36] The dealumination is due to the fact that bond energy of Al-O is much weaker than that of Si-O, so Al will be released away from the framework under high temperature. [37, 38]

102

AlV (~ 25) VI AlIV (~ 50) Al (~ 0)

1100 ℃ 1000 ℃ 900 ℃ 800 ℃ 700 ℃ 600 ℃ RT

300 200 100 0 -100 -200 27 Al NMR Frequency (ppm) Figure 5.6 Al MAS NMR spectroscopy for coarse particled ZSM-5 (particle size: 9.557 μm) without pretreatment, and that after pretreatment at 600℃- 1100℃. Besides, Table 5.1 shows a decrease in BET (Brunauer-Emmertt-Teller surface absorption index) and pore volume with the increase of pretreatment temperature. Under high temperature, the position of Al may be substituted by Si or just left with a blank defect in the structure. Since the bond of Si-O is a little shorter than that of Al-O, [39] the

BET and pore volume may decrease. Under extremely high temperature above 1000℃,

Si-O may also be broken [32] which may be supported by the distinct decrease in BET and pore volume for 1100℃, shown in Table 5.1 .

With the increase of pretreatment temperature, the arise of hydrophobicity not only enhances the infiltration pressure, Pin, but also the water transport inside the pore is

easier, leading to a larger maximum displacement at the peak force, dmax , Table 5.3.

2 That is, the accessible pore volume Vmax is larger. dmax V max /() r , where r is the cross-sectional radius of the piston. The infiltration percentage in Table 3 depicts the

103 extent of ZSM-5 channel volume that has been occupied by water molecules. Some pores remain empty despite the high pressure, which may be caused by the defects and collapse of pore structure. The effective infiltration percentage is about 63%.

Due to high Pin and large dmax, the sample with 1000℃ heat treatment shows the highest energy dissipation density of 5.158 J/g in the present study. Pin for 1100℃ is the highest, but for the decrease in pore volume and dmax, its energy dissipation density is lower than that for 1000℃ . The study indicates that pretreatment temperature is a convenient way to adjust the energy dissipation performance, and depending on various working conditions (e.g. pedestrian protection vs. crash safety), the low and high working

(infiltration) pressure can be tuned for optimization.

5.2.4 Variation in mass ratio of zeolite to water

Intuitively, the content of zeolite should be one of the most influential factors affecting the system efficiency. Based on the previously determined effective 1000℃ preheat treatment, a series of experiments is conducted, where the mass ratio of zeolite to water varies as 1:5, 2:5, 3:5, 4:5, 5:5, and 6:5, respectively.

Figure 5.7 shows corresponding sorption isotherms under various mass ratios.

It is straightforward that the accessible (infiltrated) volume increases with the mass ratio, thereby enhancing energy absorption density (also see Table 5.4). The energy dissipation density reaches the highest of 5.551 J/g at a mass ratio of 6:5. On the other hand, the infiltration pressure, Pin, as well as the slope of the plateau, are insensitive to the zeolite

104 to water mass ratio since the solid/liquid interfacial characteristics do not change.

140

120

100

(MPa) 80

P 60 zeolite-water mass ratio 1:0 40 1:5 4:5 Pressure, 2:5 5:5 20 3:5 6:5 0 0.0 0.5 1.0 1.5 2.0 2.5 3.0 Volume, V (ml) Figure 5.7 P-ΔV curves under quasi-static compression with zeolite average particle size of 9.557 μm and pretreatment temperature and 1000℃, at various mass ratios of zeolite to water, from 1:0-6:5. If the mass ratio of zeolite is too high, the mixture will saturate in the current experiment at a ratio of about 1.5-1.7, where the suspension liquid can hardly flow.

Figure 5.7 also depicts a P-ΔV curve for pure zeolite without water (mass ratio=1:0).

After initial compaction, the elastic deformation of zeolite nanostructures starts at about

50 MPa and the failure behavior is observed at 100 MPa where an abrupt derivative exists, consistent with a previous molecular dynamics simulation.

105

Table 5.3 Selected results from quasi-static compression tests.

Pretreatment Infiltration Energy dissipation Particle size [μm] P [Mpa] d [mm] temperature [℃] in max percentage density [J/g] 800 58.5 1.076 26.431% 3.492

5.251 (before heated) 900 68.5 1.150 29.586% 3.941

9.557 (after heated) 1000 95.5 1.344 35.869% 5.158

1100 97.5 1.208 34.279% 4.671

2.145 (before heated) 800 54.5 0.899 21.766% 2.783

6.104 (after heated) 1000 85.5 1.171 32.880% 4.264

Table 5.4 Quasi-static compression results at mass ratio of 1:5-6:5.

Energy dissipation Mass ratio Mass of zeolite (g) Mass of water (g) Infiltration percentage density (J/g) 1:5 12.731 63.639 33.868% 4.874

2:5 23.336 58.336 35.627% 5.089

3:5 33.250 55.417 35.869% 5.158

4:5 39.375 49.298 36.624% 5.343

5:5 45.500 45.500 38.307% 5.512

10 6:5 51.625 43.155 38.697% 5.551

5.2.5 Variation in particle size

The average particle sizes of ZSM-5 zeolite can vary. Table 1 lists the parameters of fine particled ZSM-5 and coarse particled ZSM-5 used in the present study, at pretreatment temperature of 800℃ and 1000℃. It can be seen that at pretreatment temperature of 800℃, samples of different particle sizes have similar BET surface and pore volume, whereas for preheat of 1000℃, the BET surface and pore volume of fine and coarse particles are quite different. This suggests that for smaller particle size, because of more Si and Al atoms appear on the particle surface, the framework structure of ZSM-5 may break more easily at a higher temperature. [32] In other words, for fine particled ZSM-5, heat treatment of 1000℃ may lead to both dealuminum and desilicification and may cause structural damage, whereas for coarse particled ZSM-5, dealuminum is dominant. Therefore, after treatment of 1000℃, the Si-Al ratio of coarse particled ZSM-5 should be higher than that of fine particled ZSM-5.

Figure 5.8 depicts the P-ΔV curve for fine and coarse particled ZSM-5 at pretreatment temperature of 800℃ and 1000℃, and some key results are listed in Table 3.

At 800℃, infiltration pressures of the two systems are similar; however, with the reasons stated above, at 1000℃, the infiltration pressure of coarse particled ZSM-5 is much higher than that of fine particled ZSM-5, and the accessible volume is also larger, leading to better energy dissipation.

108

140

120

100

(MPa) 80

40 fine particle at 800℃

Pressure, coarse particle at 800℃ 20 fine particle at 1000℃ coarse particle at 1000℃ 0 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40

△ V Figure 5.8 P-ΔV curves for fine particled (average particle size: 6.104 μm) and coarse particled ZSM-5 (average particle size: 9.557 μm) at pretreatment temperature of 800℃ and 1000℃. Note that the particle size may change upon heat treatment. For example, the average particle size will vary from 5.251 μm to 9.557 μm, and from 2.145 μm to 6.104

μm for coarse and fine particled ZSM-5, respectively, under 1000℃ heat treatment.

They’re measured by MasterSizer 2000 particle size analyzer, and the SEM images in

Figure 5.9 also provide a clear comparison. This can be regarded as an agglomeration phenomenon of particles under high temperature. The external thermal energy drives small particles to reunion and form large particles, which means a stable and low energy status. Thus, agglomeration phenomenon of fine particled ZSM-5 is more obvious than that of coarse particled ZSM-5, as we measured. Therefore, it is suggested that coarse particled ZSM-5 would have better performance under heat treatment in terms of energy dissipation ability.

109

(a) (b)

(c) (d) Figure 5.9 SEM photos for (a) coarse particled ZSM-5 (particle size: 5.251 μm, without pretreatment), (b) coarse particled ZSM-5 (particle size: 9.557 μm, pretreatment temperature: 1000℃), (c) fine particled ZSM-5 (particle size: 2.145 μm, without pretreatment), (d) fine particled ZSM-5 (particle size: 6.104 μm, pretreatment temperature: 1000℃). 5.3 Typical Sorption Isotherm for Sodium Chloride System

Figure 5.10(a) is a typical sorption isotherm ( PV- ) curve using ZSM-5 zeolite pretreated at 1100 ℃ with no NaCl added. The infiltration of water molecules does

not start until the applied pressure reaches the threshold Pin . The infiltration plateau starts at and ends at P , with a slope . and are taken here as the max Spla points with a gradient equivalent to 1.5Spla . Similarly, the defiltration of water

molecules starts at Pde and ends at Pend . Due to the hydrophobicity property of the 110 inwall of nanoproes within ZSM-5 zeolite, water molecules completely extrude from nanopores, evidenced by the fact that the unloading curve ends at the original starting point.

Figure 5.10(b) is a simplified ideal isotherm which excludes minor factors e.g., the elastic deformation of water (such that an inclined straight line is simplified as a

vertical straight line). Critical parameters, i.e., infiltration pressure Pin , defiltration pressure Pde , advancing capillary pressure Pa , receding capillary pressure Pr , pressure when infiltration ends Pmax , pressure hysteresis PPPPPhys= max - de = a - r , pressure span

Ppla and volume span Vpla of the plateau, with PVSpla=  pla  pla are clearly indicated and defined in Figure 2(b). All these parameters will be explained and analysed in following sections.

(a)

111

(b) Figure 5.10 (a) A typical sorption isotherm (P-ΔV) curve under quasi-static compression test, with pretreatment temperature of 1100 ℃ and no NaCl added; (b) An ideal isotherm.

Figure 5.11 depict the influence of NaCl concentration CNaCl (0, 0.5, 1, 1.5, 2

-1 mol kg water, i.e., moles of salt/kg of water) on the sorption isotherm curves. In general, the influence of T mainly lies in and , while mainly impacts Pin Spla and overall stiffness of the mixture, i.e., more NaCl results in smaller deformable volume of the mixture, with larger slope in the pressure rising stage in the beginning compression.

In the following sections, the results will be discussed in detail.

5.3.1 Effect on infiltration pressure

k According to Laplace-Washburn equation, PPcos ; in ar a k P  cos , where k is the pore shape factor which equals to 2 for approximate rrr cylindrical pore for ZSM-5 framework; r is the pore radius;  is the surface tension

112 of the liquid; a and r are advancing contact angle during infiltration and receding contact angle during defiltration respectively. Pa and Pr can be determined by

Laplace-Washburn equation due to the quasi-static loading condition [173], and the

hysteresis between and is considered to explain Phys which will be analyzed in detail shortly [174, 175].

Figure 5.12(a) shows Pin as a function of CNaCl at different T s. It is observed that when T is increased from 600 ℃ to 1100 ℃, increases by 20~25

MPa. The dealumination of the ZSM-5 framework under high temperature should be a major responsible reason [176]. The dealumination phenomenon can be further demonstrated by Al MAS NMR (Magic Angle Spinning Nuclear Magnetic Resonance) tests shown in Figure 5.11(b). Two resonances at 50 ppm and 0 ppm indicate the

113 tetrahedrally coordinated framework Al and octahedrally coordinated non-framework Al respectively. The intensity of the signal at 0 ppm increases with T , indicating the dealumination due to the breaking of Al-O bond whose energy is lower than that of Si-O.

The dealumination enhances the hydrophobicity of ZSM-5 framework, which results in weaker adherence of water molecules from the solid phase. Thus, the contact angle grows higher with . Naturally, according to the abovementioned Laplace-Washburn equation,

Pin increases.

(a)

114

(b)

Figure 5.12 (a) Pin as a function of CNaCl at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively; (b) Al MAS NMR spectroscopy for ZSM-5

after pretreatment at 600 ℃ - 1100 ℃; (c) a and r as a function of at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively. In the meantime, Figure 5.12(b) also shows that as is increased from 0

-1 to 2 mol kg water, increases by 10~15 MPa. It has been presented in open literatures

115 that the surface tension grows higher with increasing NaCl concentration [177, 178]. This effect is due to the fact that Na+ is a structure-making ion that can strengthen the hydrogen bonds between water molecules by compacting water molecules around themselves and orienting their hydrogen towards neighboring water molecules [179, 180].

Thus, the enhancing of may be treated as an explanation for the effect of on  CNaCl

Pin . Further, a closer quantitative observation reveals that the advancing contact angle

actually plays the most important role. a

In order to provide a deeper investigation, the contact angle and r in various combination of T and are calculated by Laplace-Washburn equation and plotted in Figure 5.12(c) , in which r=0.4523 nm (Table 5.1) ; k=2 ; the data of

are extracted from Ref. [177]. and increases with both and .

Further, It can be calculated that contributes to an 8~19% increase in at various

-1 pretreatment temperatures as is increased from 0 to 2 mol kg water, while can merely contribute to a 4% increase in . Thus, the contact angle is the major contributor for the increase in .

The reason why NaCl raises the contact angles needs to be clarified. The effect of NaCl on contact angle can be easily understood qualitatively. The contact angle is produced by the equilibrium between the relative force of the liquid, solid, and vapor molecular interaction. The structure-making effect of Na+ results in a stronger internal attractive force in bulk water, thus inter molecular bond between water molecule and the

116 solid framework becomes weak, indicated by a high contact angle. Conversely, where the internal force in water phase is low or the force from solid phase is strong, the water molecules tend to spread out on the surface, leading to a small contact angle. For the hydrophobic surfaces of ZSM-5 framework after high temperature pretreatment, the gap between the force from the liquid and that from the solid is already quite sharp, thus a further increase on the liquid side can contribute a limited variation on the contact angle.

-1 Figure 5.12(c) shows that a 2 mol kg water contributes to an increase of no more than 2.5° in contact angle, which is in line with the finding of Daub [181] and Sghaier[182].

5.3.2 Effect on defiltration pressure Pde

From Figure 5.10(b), it is straightforward to come to the equation

k as PPPVS=  = cos    . Thus, P is comprehensively impacted de r plar r pla pla de by several parameters, including  , r , Vpla and Spla .

Figure 5.13(a) shows that goes down with increasing , mainly Vpla CNaCl because Na+ and Cl- will occupy part of the room for water molecules inside the nanopores. The ionic radii of Na+ and Cl- are 0.095 nm and 0.181 nm respectively [183],

which is comparable to the pore size of ZSM-5. Meanwhile, Vpla also decreases with

T since heating process may produce certain areas inside the channel too hydrophobic and inaccessible for water molecules, and meanwhile a slight part (~15%) of the channel may be damaged by high temperature, which is indicated by the pore volume data in

Table 5.1.

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(a)

(b)

Figure 5.13 (a) Vpla as a function of CNaCl at pretreatment temperature of 600 ℃,

800 ℃, 1000 ℃, and 1100 ℃, respectively; (b) Pde as a function of at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively.

Spla is dominated by a nominal “energy barrier force” which resists water to flow deep into the nanopores so as to maintain a minimum energy potential of the zeolite framework system from being destroyed by infiltration. This energy barrier force is

118 determined by the wetting properties of solid and liquid phase, as well as the air gas molecules [184, 185]. The pretreatment will greatly alter the wetting properties of the solid framework while the concentration of NaCl cannot. Therefore, change in is Spla observed in Figure 5.13 (a) but not in Figure 5.13 (b), i.e., decreases with T and

has no correlation with CNaCl .

Figure 5.13(b) depicts as a function of at different s. As Pde CNaCl T

-1 is increased from 0 to 2 mol kg water, Pde increases by 10~15 MPa, which is similar with Pin and indicates that NaCl has an effect of defiltration promotion. However, no significant correlation can be observed between and since r increases with

but both V and decreases with . pla

5.3.3 Effect on pressure hysteresis Phys

Although water molecules flows out of the channels at the end of defiltration completely, a hysteresis can be observed between the loading curve and unloading curve.

k The hysteresis pressure is defined as PPPPP= - = - =（ cos  - cos  ）. In hys max de a rr a r essence, Phys dominates the water defiltration behavior: if is large, the defiltration will not happen; while is small, complete defiltration may occur [186].

Thus, the contact angle hysteresis hys=-  a  r has a major impact on , determining the system performance [174, 175, 187].

Surface roughness and chemical heterogeneous are two main reasons for

contact angle hysteresis hys [188-192], and other possible causes include liquid sorption

119 on the surface [193], molecular scale topography [194], etc. In this case, considering the comprising of both nonpolar oxygen-silicon tetrahedron and polar oxygen-aluminum tetrahedron, the framework of ZSM-5 zeolite is not completely chemically homogeneous

[176]. A contact angle is attributed to the energy balance at the solid-liquid-gas contact line [195], which tends to vary locally at the inner wall of the ZSM-5 framework. Thus, during its infiltration or defiltration, water will meet different local energy barriers, which

results in contact angle hysteresis. hys decreases with CNaCl since under high NaCl concentration and internal force inside bulk water, the energy barrier at the solid phase can hardly present significant effect. This is indicated by Figure 5.14 at pretreatment temperature of 800 ℃, and the same trend holds for other temperatures. With the

definition of Phys , all these effect on above contributes to the same trend in

, which is a key characteristic during defiltration process.

Figure 5.14 hys as a function of CNaCl at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively.

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5.4 Dynamic Effect of Zeolite β/Water System

5.4.1 Basic material properties and preparation

+ Zeolite β (|Na 7|[Al7Si57O128]) contains three-dimensional 12-ring channels with pore diameters of 6.6 Å×6.7 Å and 5.6 Å×5.6 Å [196]. It’s constructed by TO4 tetrahedra

(T=Al, Si), with apical oxygen atom shared between adjacent tetrahedral [197]. Zeolite β is recognized as an intergrowth of two end-members, polymorph A and polymorph B, which are built from different stacking of the same building layer [198]. Both polymorphs have three mutually intersecting channels, with two straight channels perpendicular to

[001] and a tortuous channel which snakes along the c crystallographic axis [199]. By using Quantachrome Autosorb-iQ-MP gas sorption analyzer, its specific surface area is determined to be 422.60 m2/g, and the specific micropore volume is 136.10 mm3/g. By using MasterSizer 2000 particle size analyzer, the average particle size is 9.11 μm. The specific mass density of zeolite β is measured to be 2.40 g/cm3. Note that zeolite β is known as a high mechanical strength material due to its dense crystalline backbone [200].

It is reported that zeolites usually have bulk modulus on the order of 10 GPa (about 5 times higher than that of pure water at 1 atm, room temperature), thus the deformation of its framework is negligible in this work. Zeolite  is immersed in deionized water and then sealed in a 316 stainless steel chamber shown in Figure 5.1(a) by precisely-fit sealing rings. Zeolite  can be homogeneously distributed in water (and NaCl solution), forming a stable gel-like liquid which is hard to be segregated.

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5.4.2 Dynamic test platform

The dynamic tests are conducted using a customized drop hammer testing platform depicted in Figure 5.15. A pair of slide rails and pulleys are used to guide the hammer. The maximum falling height and maximum mass of hammer is 7 m and 200 kg respectively. For current test, the mass is set at 200 kg and the falling height is 0.2 m, corresponding to an initial impact velocity of 1.98 m/s and strain rate of 27.50 s-1, so that an impact of high energy and relatively low strain rate is provided to help investigate its potential applications in marine and transportation industries. The dynamic responses of each specimen is measured as acceleration signal captured by the accelerometer (Model

7264C, ±500 g, Endevco) installed at the center of top hammer surface by screw joint.

The displacement of the hammer is recorded by a high speed cine camera (FASTCAM

SA1.1, Photron) at 5400 fps and 1024×1024 pixels. During post-processing, DIAdem

(National Instruments) is employed to analyze the acceleration signal with noise smoothing processing.

5.4.3 Dynamic test results and discussions

5.4.3.1 Cushioning effect

Figure 5.16 presents the force versus time response (F-t curve) of zeolite

β/water system under the 200 kg and 0.2 m height impact. The testing result of pure water is shown in Figure 5.14(a) as a reference system. Pure water has been verified to be an impact energy mitigation material under higher pressure since water molecules may

122 restructure their space distribution[201]. For a cushioning device, peak force Fmax and duration time t are two key evaluation indicators of performance. Table 5.5 listed the data in percentage value upon the results of pure water (Fmax= 139 kN, t=8.3 ms).

Figure 5.15 hys as a function of CNaCl at pretreatment temperature of 600 ℃, 800 ℃, 1000 ℃, and 1100 ℃, respectively.

(a)

123

(b)

0.2 m height. (a) F-t curves upon pretreatment temperatures of RT and 1000 ℃, rM=1:1,

CNaCl=0, along with a curve of pure water as a reference. (b) F-t curves with NaCl added

(CNaCl=0, 2, 4, 6 mol·kg), RT, rM=1:1. (c) F-t curves at various mass ratios of zeolites to water (rM=1:1, 1:2, 1:4, 0), RT, CNaCl=0.

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Table 5.5 (a) Systems composed of zeolite β upon various pretreatment temperatures (RT,

1000 ℃), rM=1:1, CNaCl=0.

3 T (℃) E (J/cm ) Fmax (%) t (%)

RT 3.24 42.82 79.16

1000 1.61 16.36 27.71

Table 5.5 (b) Systems with NaCl added (CNaCl=0, 2, 4, 6 mol•kg-1 H2O), RT, rM=1:1

-1 3 CNaCl (mol·kgH2O) E (J/cm ) Fmax (%) t (%)

0 3.24 42.82 79.16

2 2.65 41.67 63.86

4 2.68 37.99 39.64

6 3.32 32.33 16.27

Table 5.5 (c) Systems at various mass ratios of zeolite β to water (rM=1:1, 1:2, 1:4), RT,

CNaCl=0.

3 rM E (J/cm ) Fmax (%) t (%)

1:1 3.24 42.82 79.16

1:2 1.49 23.74 48.19

1:4 0.66 10.02 28.92

Due to the infiltration mechanism of zeolites, the impact can be mitigated significantly by zeolite β/water system with a rapid response. Once the impact load exceeds Pin, water molecules intrude into nanopores and impact energy is converted into

125 solid/liquid interfacial energy. This cushioning process will reduce the impact and extend the duration time of impact impulse greatly. As it’s shown in Figure 5.13(a) and Table

5.5(a), for the present impact condition on zeolite β/water system (RT, rM=1:1, CNaCl=0),

Fmax will be reduced by 42.82% and t is extended by 79.16%, which demonstrates that zeolite β/water system can work well as a cushion device for low-speed impact. It can be observed that the unloading curves present a prominent defiltration plateau, indicating that under dynamic condition, water molecules can flow out of nanopores spontaneously, therefore, reloading cycles will repeat the P-ΔV curves, and the system is reusable as impact mitigation material.

In order to give a deeper investigation on the influence of Pin and pore volume, parametric tests on rM and CNaCl are conducted. Tests on CNaCl shown in Figure 5.13(b) mainly changes Pin, and tests on rM shown in Figure 5.13(c) mainly changes gross pore volume. It’s validated that zeolite β/water system with more zeolites and less NaCl is preferable as a cushion device. It is also worth noticing that due to higher Pin and smaller pore volume, a heat treatment of 1000 ℃ leads to a poor performance, with a reduction of

16.36% in Fmax and extension of 27.71% in t.

As is shown above, zeolite β/water system can be modified by various engineering accessible methods, enabling a wide range of applications. Despite that, a lower working pressure and a larger deformability are preferable as a cushioning system, which indicates that zeolite β/water system should contain more zeolites of low

126 temperature pretreatment, with less NaCl added. Note that the above analysis is based on a given impact mass and height, the design of zeolite β/water system should be subject to its working situations. The cushioning effect may be deteriorated or suppressed by a mismatch between the system design and the practical impact. For instance, if the impact energy is too low to trigger the infiltration, the system will act as pure water and little energy can be mitigated. Meanwhile, if the impact is too intense, nanopores may be filled by water molecules before the end of impact and the entire system deforms solidly, resulting in a high peak force. Thus, zeolite /water system should be specially designed catering to specific applications to make full use of its cushioning effect.

5.4.3.2 Impact protection behavior

In order to explore the possible “dynamic effect” or “strain-rate effect” of zeolite β/water system, its quasi-static and dynamic response are compared. P-ΔV curves under impact condition are derived based on the combination of acceleration data from accelerometer and displacement data from high speed camera. Figure 5.14 shows three typical groups of curves: pure water system, zeolite β/water system without heat treatment and zeolite β/water system with treatment of 1000 ℃ (rM=1:1, and CNaCl=0).

For ease of comparison, these curves take into account the deformability of water and chamber.

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120 dash : quasi-static solid: dynamic 100

(MPa)

P 60

40 RT

Pressure, o 20 , 1000 C pure water 0 0.00 0.04 0.08 0.12 0.16 Nominal volumetric strain, V Figure 5.14 P-ΔV curves of three systems under quasi-static and dynamic condition: system composed of pure water; zeolite β without heat treatment (rM=1:1, CNaCl=0) and zeolite β with heat treatment of 1000 ℃ (rM=1:1, CNaCl=0). Firstly, for all these three systems, the bulk modulus (ΔP/ΔV) under dynamic condition is globally higher than that under quasi-static condition. It can be observed that the difference in bulk modulus is slight during the plateau, thus it mainly comes from the stain rate effect of water, instead of the infiltration process. It’s reported by plenty of studies that various materials are found to have similar performance [202, 203].

Besides, it’s demonstrated that Pin is slightly higher under dynamic condition, with its plateaus above those in quasi-static condition in Figure 8, indicating a possible strain rate strengthening effect. In dynamic loading condition, water molecules in local area at the entrance of nanopores have little time to react due to inertia effect, which results in a higher energy barrier for water molecules to leave from the bulk phase and enter nanopores. While given enough time in quasi-static cases, water molecules can

128 move into nanopores gradually and a thermodynamic equilibrium state will be constantly maintained during the infiltration process. Pin is thus relatively lower. From the perspective of interfacial energy, the local effect of water molecules under dynamic loading leads to an increase in the curvature of interface, such that higher interface energy has to be overcome prior to infiltration.

Another part of “dynamic effect” lies in the plateau length. Figure 8 exhibits that the plateau under dynamic condition is significantly shorter than the quasi-static, which is possibly related to the existence of gas phase in nanopores. Since the pores are of nanoscale, the permeability of zeolite β is very poor according to the equation

2 3/2 K=Ad (1-ρf/ρs) , where A is a constant; d is the average pore diameter; (1-ρf/ρs) is the porosity, with ρf and ρs representing the mass density of foam and monolithic material respectively [204]. Hence, gas in nanopores cannot permeate outwards in a short time under impact loading, and consequently less water molecules can penetrate into nanopores with the collision between two phases and the compression of gas phase in nanopores.

This section provides a preliminary attempt on the “dynamic effect” of zeolite

β/water system, and it can be expected that higher loading rate may contribute to more significant dynamic effect. However, further work needs to be conducted in a quantitative manner based on the results of various strain rates. The dynamic response of the system with packing materials should also be investigated to explore possible coupling effect.

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5.5 Concluding Remarks

In this paper, a nanoporous energy dissipation system is established, which composes pretreated ZSM-5 zeolite and distilled water. Quasi-static compression experiments are carried out and the infiltration, defiltration, and energy dissipation mechanisms can be read from the sorption isotherm curves. The system is reusable with an attractive index of energy dissipation density, and its performance can be fine tuned by varying a few parameters related to material preparation. Specifically, increasing the pretreatment temperature of ZSM-5, enhancing the mass ratio of zeolite to water, and using coarse particled zeolite, can promote the energy dissipation density. Quasi-static compression experiments are also carried out aiming at the key parameter, i.e., the NaCl concentration are investigated based on Laplace-Washburn equation, which presents that the system characteristic can be fine-tuned for various situations. Specifically, the infiltration pressure can be raised by increasing pretreatment temperature or adding NaCl; the outflow of water molecules can be accelerated by adding NaCl. Both advancing contact angle and receding contact angle for ZSM-5 zeolite - NaCl solution – air system are determined, indicating that these two increase with NaCl concentration. The contact angle hysteresis is also observed, which decreases with NaCl concentration. In addition, the dynamic testing based on drop hammer reveals that zeolite β/water system has a significant cushioning effect under low-speed impact. The maximum peak force is reduced and the reaction time is elongated. The “dynamic effect” of zeolite β/water

130 system shows a sharp increase in global modulus, a slight increase in infiltration pressure and a decrease in plateau.

The advantageous energy dissipation characteristics of the nanofluidic system provides an alternative solution for damping and impact protection.

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Chapter 6 Conclusions and Future Work

6.1 Concluding Remarks

In this thesis, by comprehensively investigating the mechanical behavior of nanoscale materials and structures, including water-filled CNTs, buckyballs and nanoporous/water mixture both from MD simulation and desktop experimental work, it is demonstrated that due to the unique physical properties that nanomaterial may have, the impact protection properties are of 1 or 2 orders of magnitude of current engineering materials and structures in terms of the energy dissipation or mitigation.

Firstly, the impact protection performance of water-filled CNTs are investigated inspired by the outstanding mechanical properties of CNTs. Water may conduct through a hydrophobic CNT which makes the water-filled CNT easy to process in application, namely, simply spread water onto the CNT forests prepared by chemical vapor deposit.

Thus, the discussion starts from the water-filled situation. The most direct step should be made towards the dynamic mechanical property. The force-displacement curve under the dynamic crushing at the speed of 10 m/s. For comparison, a hollow CNT tube with the same loading is setup. Results show that with the water molecules in, the rigidity of the tube becomes larger and water enhances the stabilization of the CNT such that the buckling force increases, leading to higher mechanical energy dissipation for the integration over the force-displacement curve, which is similar in continuum mechanics.

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Further, by varying the aspect ratio of the tubes, the mechanical behaviors are investigated. It is shown that the buckling properties of hollow CNTs strongly depend on their geometrical parameters, whereas the critical buckling load and post-buckling stress can be significantly elevated with a filament of water, leading to pronounced energy absorption densities. Additional enhancements result from CNT bundles and forests.

Secondly, the mechanical behavior of buckyball is investigated using MD simulation. With respect to different buckling characteristics, the fullerenes may be divided into three categories according to their radius-thickness ratios. The classical buckling model in continuum mechanics may perfectly describe the buckling phenomenon in nano-scale with a larger coefficient. Interestingly, upon the ricochet of the impactor, the deformation of the smaller buckyballs fully recovers whereas the inverted buckling morphology of the larger buckyballs remains. In smaller buckyballs, the buckling force is larger and the van der Waal force created by few molecules are not strong such that the ball always recover to its original shape if the maximum deformation is within the thermal stability limit. In larger buckyballs, the buckling force is much smaller and more molecules are involved to have the van der Waals force between the buckled layer and the bottom layer thus the buckyball may stay in the buckled shape even if it is unloaded. Thus, energy dissipation is more prominent in the larger fullerenes, and the percentage of dissipated energy is also larger upon higher speed impact since extra energy is stored within the strain energy.

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Further, several impact protection systems based on buckyball are designed and studied by using MD simulation. The impact mitigation characteristics of a long one dimensional buckyball chain are investigated, which can be extended to granular buckyballs of simple cubic packing. Representative small and large buckyballs, i.e. C60 and C720 under high speed impact loadings are studied. The impact energy, size and number of buckyballs, are varied in a systematic manner. With relatively small elastic deformations of C60 buckyballs during impact, a mechanical model based on Hertz contact law is proposed, with critical parameters calibrated via MD simulations for given impact loading conditions. Energy mitigation is illustrated through force impulse history difference between the impact and receiver. The stress wave propagation speed, the reduction of peak impulse force, and the impulse duration ratio are studied to reveal the dynamic response of the system. The major energy dissipation mechanism for the buckyball chain is the wave reflection among the deformation layers, covalent potential energy, van der Waals interactions as well as the atomistic kinetic energy. These terms may have higher contribution to energy dissipation in C720 system with non-recoverable morphologies. Moreover, buckyball systems are investigated under various impact speeds and impact masses. The smaller mass and higher impact speed results in a higher impulse force attenuation effect, as well as higher system stiffness and shorter wave propagation time. Over 99% and 90% of impact energy for C720 and C60 chain systems could be mitigated under particular impact conditions respectively and thus a promising buckyball

134 based stress wave mitigation system is suggested. In the meantime, considering the good energy dissipation and mitigation capability that large buckyball may possess, short one-dimensional C720 arrays (both vertical and horizontal alignments) are studied at various impact speeds. Results show that the energy absorption ability is dominated by the impact energy per buckyball and less sensitive to the number and arrangement direction of buckyballs, a piece of good news for engineering application. Pseudo 3D stacking of buckyballs in simple cubic, body-centered cubic, hexagonal, and face-centered cubic forms with different packaging densities and forms are investigated.

It is found that stacking form with higher occupation density yields higher energy absorption and proves the available buckyball in bulk is ready for impact protection.

In addition, desktop experiments also serves as an important part of this thesis research. To quantitatively study the governing factors of impact protection of the nanoporous/water mixture system, a nanoporous energy dissipation system composed of a mixture of zeolite ZSM-5 and water is established and studied experimentally. Firstly, quasi-static compression experiments are carried out to analyze the pressure–volume curve and reveal the energy dissipation mechanism. Afterwards, a parametric study is conducted to explore the effects of three parameters, the pretreatment temperature of zeolite ZSM-5 (600~1100 ℃), mass ratio of ZSM-5 to water (1:5~6:5), average zeolite particle size (2.145~5.251 mm before heated or 6.104~9.557 mm after heated) and the concentration of NaCl (0~2 mol/kg H2O). Results show that in order to obtain optimum

135 energy absorption performance, the pretreatment temperature of about 1000 ℃, and higher ratio of ZSM-5 with larger particle size are desired. Also, it is concluded that both pretreatment temperature and NaCl concentration raise the infiltration pressure and NaCl can also promote defiltration. The advancing contact and receding contact angle of zeolite-NaCl-air system increase with both pretreatment temperature and NaCl concentration, and the contact angle hysteresis decreases with NaCl concentration.

Finally, dynamic impact tests based on drop weight device are conducted to demonstrate the cushioning effect of zeolite β/water system under low-speed impact. It shows that the peak force can be decreased by 42.82% and reaction duration time t can be extended by

79.16%, a promising candidate for energy absorption/mitigation under dynamic loadings.

6.2 Recommendations for Future Work

Nanoscale materials and structures truly provide a new solution to the science and engineering of impact protection with the highly interdisciplinaried background and knowledge, as well as the promising rich research innovations. The outstanding mechanical properties of nanomaterials and structures, i.e. tough, strong and lightweight, along with the unique behavior of the liquid in the confined nanochannel has paved a new road for impact protection system design. However, triggered by this research, there two questions remain unsolved in general, i.e. one is that the full mechanisms of the nanostructure mechanical behavior with the consideration of multi-physical fields, such as force field, chemical reaction kinetics field and electric field is unclear so far; the other

136 one is the more sophiscated system design for multi-level energy dissipation and mitigation. The following sections will discuss these two questions in detail.

6.2.1 Nanomaterial behaviors in multi-physical fields

Graphenes, CNTs and buckyballs are representatives of nanomaterials with origination from the carbon family, without any electric charges. In the MD simulations in chapters 2, 3 and 4, the bond breakage and fusion (coalesce) effect is not considered which will not influence the buckling behavior but may not be able to depict the material behaviors at large deformation where near or beyond the boundary of the bond breakage or fusion, limiting the application of the impact protection. Currently, the most widely accepted force-field is ReaxFF potential to describe reactive carbon-carbon interactions

[205-208]. By considering the distance-dependent bond-order functions to describe the contributions of chemical bonding to the potential energy may illuminate and extend the system application to a more severe or high-energy impact scenarios. Fundamentally, the science to understand the system failure/cracking mechanism may bring in multidisplinary knowledge to push forward the cutting-edge theories in mechanics.

Another important factor is the electric field, especially for nanofluidics system.

Water molecules are polar such that they are responsive to external electric field. Many interesting phenomena have been discovered for electric field driven water molecules in transportation [209-211]. It is also expected that by taking advantage of unique water molecule transportation properties within electric field, the impact protection effect may

137 be strengthened and if one digs further, many new questions may raise. Can large water-filled in buckyballs recover to the original shapes after unloading if they stay within the electric field such that the system is able to sustain multi-hit? How the water molecules transport within the buckyball during the impact process? What’s the electrolyte behavior in the electric field added in the nanoporous material/water mixture?

These works are critical building blocks for the science of nanoporous flow dynamics and are extremely useful to apply in the micro/nanodevice fields.

In addition, the thermal problem is also an important issue for nanoscale materials and structures, especially for protective layers subject to impact [212]. During an adiabat process, the thermal energy has nowhere to release but heat the entire system.

To maintain the system temperature at the largest extent, the impact energy should better be converted into other forms of energy, such as strain energy, van der Waals energy, and interfacial energy (e.g. similar as the working mechanism in nanoporous material/water mixture) and among others. Alternatively, the quick and intense impact energy should be captured momentarily, and then released in a much milder way (e.g. the way buckyball-based system works). Once the electric field is involved, the thermal issue becomes complicated and needs to be solved.

6.2.2 Hierarchical impact protection system

In this thesis, several new types of impact protection working mechanisms are discovered and explored with satisfactory results, compared to traditional engineering

138 materials and designs. However, it is still different to move one step further to enhance the protection capability. Recently, in composite material research field, hierarchical materials are built by taking advantage of various size scales, such as celluar ceramic composites [213, 214], microlattic structure [215, 216] and bioceramic armor [217]. In essence, these materials and structure triggering multiple energy dissipation mechanisms during impact by an elegant way due to its intrinsic structure in the characteristic size.

Likewise, it is expected to have tremendous improvement on those nanomaterials and structures with hierarchical function such that the impact stress wave could be absorbed and mitigated “layer by layer”. In solids, the most common and efficient energy dissipation way is the deformation while in fluids, the shear stress between the liquid and wall, as well as within the liquid itself is the general way to deal with the impact protection. By smartly combining the solids and liquid together, infiltration, transport and the liquid head loss effect may emerge, bringing many new scientific problems worth solving. To reach the hierarchical function, the protective system should possess multiple energy dissipation mechanisms and these mechanisms should work in a time series way such that a decent impact protection goal may be reached. There are several advantages of this conceptual idea: firstly, the stress wave mitigation effect is magnified after several steps; secondly, one mechanism is not interfered or weakened by another one; last but not the least, the system would be more recoverable or usable if the impact energy is not large enough to trigger all these mechanisms.

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Finally, I’d like to point out that the interactions between nanoscale and bulk material, and between solid and liquid offer us incomparable and surprising impact protection capability. As a platform for multi-disciplinary science, impact protection research topic has unprecedented opportunities for scientists and engineers to undermine the fundamental mechanisms thus promote the current theories and engineering applications.

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Publications Related to This Thesis

[1] J Xu, Y Li, Y Xiang*, X Chen*. A Super Energy Mitigation Nanostructure at High Impact Speed Based on Buckyball System. PLOS One 8 (5), e64697 (2013)

* * [2] J Xu, Y Li, Y Xiang , X Chen . Energy absorption ability of buckyball C720 at low impact speed: a numerical study based on molecular dynamics. Nanoscale research letters 8 (1), 51 (2013) [3] J Xu, Y Sun, B Wang, Y Li, Y Xiang, X Chen*. Molecular dynamics simulation of impact response of buckyballs. Mechanics Research Communications, 3(2013)

[4] J Xu, B Xu, Y Sun, Y Li, X Chen. Mechanical Energy Absorption Characteristics of Hollow and Water-Filled Carbon Nanotubes upon Low-Speed Crushing. Journal of Nanomechanics and Micromechanics 2 (4), 65-70 2 (2012) [5] Y Sun, J Xu*, Y Li, B Liu, Y Wang, C Liu, X Chen*. Experimental Study on Energy Dissipation Characteristics of ZSM-5 Zeolite/Water System. Advanced Engineering Materials vol. 15 pp.740-746, 2013 (2013) [6] Y. Sun, J. Xu*, Y. Li, X. Xu, C. Liu and X. Chen*. Mechanism of Water Infiltration and Defiltration Through ZSM-5 Zeolite: Heating and Sodium Chloride Concentration Effect. Journal of Nanomaterials, vol. 2013 pp. 249369, (2013) [7] Yueting Sun, Ziyan Guo, Jun Xu*, Xiaoqing Xu, Cheng Liu, Yibing Li. A Candidate of Mechanical Energy Mitigation System: Dynamic and Quasi-static Behaviors and Mechanisms of Zeolite β/Water System. Materials and Designs (Accepted) [8] Jun Xu and Xi Chen. Energy mitigation capability of multi-sized nanoporous material/water system (in preparation)

Note: “*” represent for corresponding authors

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