ARL Postdoc Presentation

An Investigation of Boron Nitride Nanomaterial Functionalization

At the Army Research Laboratory

by Kevin Waters

Who am I?

Computational "Physicist"
Started at Michigan Tech. in 2013
Working with Ravindra Pandey
Currently at PNNL on a Fellowship
Defending in August

Hypothesis

"We can accurately predict the interface between biological molecule and nanomaterials in physiological conditions."

Nanomaterials

Materials with at least one dimension in the sub-micron range.

Nanomaterials

Ratio of surface to bulk atoms changes
Bulk properties are not present at this scale
Adding one atom changes the properties of the material
Exhaustive searches and research must be done

Morphological Dependent Properties

Clusters
Nanoparticles
Fullerenes
Nanotubes
2D-Materials

A. K. Geim et. al Nature Materials (2007) 6: 183

Boron Nitride Nanotubes

Predicted by 1994
Synthesized in 1995
Typically considred a wide band gap semiconductor
Parameters to consider

Chirality (n,n), (n,0), (n,m)
Diameter
Layers

Boron Nitride Nanotubes

Steel, "A Primer on Carbon Nanotubes – Part 1"

Boron Nitride Nanotubes (Band Gap)

Boron Nitride Nanotubes (Strain Energy)

Rimola et. al. (2013) PCCP 15:13190

Biological Molecules

Carbohydrates
DNA (Nucleotides)
Lipids
Proteins (Amino Acids, Peptides)
etc.

Methods and Tools

Solving the system's electronic wavefunction

Schrödinger Equation $\hat{H}\Psi(\vec{r}\hspace{0.05cm})=E\Psi(\vec{r}\hspace{0.05cm})$
Density Functional Theory (DFT)
Ab Initio Molecular Dynamics (AIMD)
High Performance Computing Platform

Conjugated Boron Nitride Nanomaterials

Waters et. al. (2017) ACS Omega 2:76

Proteins

pdb : 3V03

Waters et. al. (2017) ACS Omega 2:76

Conjugated Structures

Binding Energies

BNML (eV)
		Pro.	Dep.
Trp	-1.04
Arg		-0.92	-0.96
Asp		-0.55	-0.57

BNNT
		Pro.	Dep.
Trp	-0.71
Arg		-0.85	-2.12
Asp		-0.89	-2.17

Mechanical Properties of 2D BN₂

Waters et. al. (2018) Journal of Physics: Condensed Matter 30: 13

Chemical Functionalization

Experimental Functionalization

Sainsbury et. al. (2007) JACS 111:12992

BN Electronic Structure Evolution

Coverage (%)	Band Gap (eV)	Binding Energy (eV)
0	4.25
16	3.34	-0.74
25	3.11	-0.70
50	2.25	0.72

BN₂ Monolayer

Atoms 2B + 4N
Symmetry : Amm2 (38)
Lattice Vectors
- a : 6.84 Å
- b : 2.55 Å
Bonds

N-N : 1.29 Å
B-N : 1.50 Å
N-B : 1.34 Å

BN₂ Band Structure (Orbital Projected)

BN₂ Band Structure (Atom Projected)

Hooke's Law / Elastic Tensor

$\boldsymbol{\sigma_{ij}} =\boldsymbol{C_{ijkl}\epsilon_{kl}}$

σ_ij is the stress tensor
C_ijkl is the elastic tensor
ε_kl is the stain tensor

Elastic Tensor

$C_{IJ} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & C_{14} & C_{15} & C_{16} \\ & C_{22} & C_{23} & C_{24} & C_{25} & C_{26} \\ & & C_{33} & C_{34} & C_{35} & C_{36} \\ & & & C_{44} & C_{45} & C_{46} \\ & & & & C_{55} & C_{56} \\ & & & & & C_{66} \\ \end{bmatrix}$

Orthorhombic Symmetry (Amm2)

$C_{IJ} = \begin{bmatrix} C_{11} & C_{12} & C_{13} & 0 & 0 & 0 \\ & C_{22} & C_{23} & 0 & 0 & 0 \\ & & C_{33} & 0 & 0 & 0 \\ & & & C_{44} & 0 & 0 \\ & & & & C_{55} & 0 \\ & & & & & C_{66} \\ \end{bmatrix}$

Orthorhombic Symmetry in 2D

$C_{IJ} = \begin{bmatrix} C_{11} & C_{12} & 0 \\ & C_{22} & 0 \\ & & C_{66} \\ \end{bmatrix}$

Deformation Matrices

$\boldsymbol{F_{11}} = \left[ \begin{array}{*4{C{1em}}} \lambda_{11} & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{array} \right] \\$	$\boldsymbol{F_{22}} = \left[ \begin{array}{*4{C{1em}}} 1 & 0 & 0 \\ 0 &\lambda_{22} & 0 \\ 0 & 0 & 1 \\ \end{array} \right]\\$
$\boldsymbol{F_{66}} = \left[ \begin{array}{*4{C{1em}}} \lambda_{66} & 0 & 0 \\ 0 & \lambda_{66} & 0 \\ 0 & 0 & 1 \\ \end{array} \right]\\$	$\boldsymbol{F_{12}} = \left[ \begin{array}{*4{C{1em}}} 1 & \epsilon_{12} & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{array}\right]\\$

Workflow

-2% to 2% in steps of 0.2%
Generate optimized structure
Apply deformation matrix to optimized structure
Optimized atoms with modified unit cell
Extract Cauchy stress data (σ_ij)
Calculate mechanical properties of interest

Properties Derived from Elastic Constants

$E_{arm} = \frac{C_{11}C_{22} - C_{12}C_{12}}{C_{11}} \\ E_{zig} = \frac{C_{11}C_{22} - C_{12}C_{12}}{C_{22}}$

Results

N/m	Graphene¹	This Work	BN²	This Work	BN₂
C₁₁	358.1	353.7	293.2	290.5	368.8
C₁₂	60.4	61.7	66.1	64.4	47.2
C₂₂					153.3
C₆₆		144.9		113.1	58.7

Mechanical Properties of Crystalline Poly Ether Ether Ketone (PEEK)

Pisani et. al. (2018) In Prepartation

US-COMP

The Institute for Ultra-Strong Composites by Computational Design
NASA Space Technology Research Institute
Computationally-driven development of CNT-based ultra high strength lightweight structural materials
Project lead by Dr. Odegard at Michigan Tech.

PEEK

Polyether ether ketone
Investigating properties of the polymer future applications
ReaxxFF force field testing and validation
Comparing crystalline classical MD with DFT calculations
Challenging to model Amorphous PEEK with electron approach

PEEK Structure

O₁₂C₄₈H₇₈
Symmetry : Pbcn (60)
Lattice Vectors
- a : 7.38 Å
- b : 5.92 Å
- c : 30.09 Å

Orthorhombic Symmetry (Pbcn)

PEEK Elastic Constants

$C_{IJ} = \begin{bmatrix} 133.3 & 15.3 & 2.6 & 0 & 0 & 0 \\ 11.0 & 15.5 & 6.1 & 0 & 0 & 0 \\ 1.7 & 12.7 & 15.3 & 0 & 0 & 0 \\ & & & 14.0 & 0 & 0 \\ & & & & 9.0 & 0 \\ & & & & & 4.8 \\ \end{bmatrix}$

Elastic Constants

(GPa)	MD	DFT
C₁₁	140.5 ± 7.31	133.3
C₂₂	4.87 ± 1.56	15.5
C₃₃	7.18 ± 1.34	24
C₄₄	0.24 ± 0.16	14.0
C₅₅	3.79 ± 3.00	9.0
C₆₆	3.37 ± 0.36	4.8

Poisson's Ratio

	MD	DFT
ν₁₂	0.88 ± 0.24	0.38
ν₁₃	-0.01 ± 0.58	-0.33
ν₂₃	0.50 ± 0.12	0.38

Gold Deposition Boron Nitride Nanomaterials

Waters et. al. (2018) In Prepartation

Gold Quantum Dots on Boron Nitride

Boron Nitride Nanotubes Functionalized with Gold Quantum Dots

Gold Flakes on Boron Nitride

Unpublished work from Bhandari et. al.

Gold Cluster Structures

2D	3D

Unpublished work from Waters et. al.

L. Xiao et al. (2004) Chemical Physics Letters 392, 452

L. Xiao et al. (2006) The Journal of Chemical Physics 114309

G. Chen et. al. (2010) The Journal of Chemical Physics 194306

Gold Clusters Structural Parameters

	2D Cluster
Structure	Avg. Bond (Å)	Bonds (#)	Symmetry
Au₆	2.69	9	D_3h
Au₁₀	2.71	19	D_2h
Au₁₂	2.71	24	D_3h
Au₁₄	2.71	29	D_2h
Au₁₆	2.72	34	C_s

	3D Cluster
Structure	Avg. Bond (Å)	Bonds (#)	Symmetry
Au₆	2.73	10	C_s
Au₁₀	2.72	23	C_2v
Au₁₂	2.75	26	C_2v
Au₁₄	2.74	33	C_s
Au₁₆	2.73	36	T_d

Gold Cluster Cohesive Energy

Gold Clusters on BN

Gold/BN Clusters Parameters

	2D Cluster
Structure	Avg. Bond (Å)	Bonds (#)	Symmetry
Au₆	2.69 (2.70)	9 (9)	D_3h (D_3h)
Au₁₀	2.71 (2.72)	19 (19)	D_2h (D_2h)
Au₁₂	2.71 (2.72)	24 (24)	D_3h (D_3h)
Au₁₄	2.71 (2.72)	29 (29)	D_2h (D_2h)
Au₁₆	2.72 (2.72)	34 (34)	C_s (C_s)

	3D Cluster
Structure	Avg. Bond (Å)	Bonds (#)	Symmetry
Au₆	2.73 (2.74)	10 (10)	C_s (C_s)
Au₁₀	2.72 (2.72)	23 (18)	C_2v (C_s)
Au₁₂	2.75 (2.76)	26 (24)	C_2v (C_2v)
Au₁₄	2.74 (2.74)	33 (29)	C_s (C₁)
Au₁₆	2.73 (2.72)	36 (32)	T_d (C₁)

Gold Clusters

	2D Cluster Band Gap (eV)
Structure	Ref ¹	Isolated	Cluster/BN
Au₆	2.06	1.76 (2.76)	1.73
Au₁₀	1.28	0.96 (1.47)	0.81
Au₁₂	0.97	0.65 (1.47)	0.63
Au₁₄	0.19	0.00 (0.35)	0.00
Au₁₆		0.24 (0.95)	0.18

L. Xiao et al. (2004) Chemical Physics Letters 392, 452

Gold Clusters

	3D Cluster Band Gap (eV)
Structure	Ref ^1,2	Isolated	Cluster/BN
Au₆	1.75	1.22 (1.91)	1.53
Au₁₀	0.91	0.29 (0.72)	0.45
Au₁₂	0.95	0.92 (1.43)	0.72
Au₁₄	0.44	0.35 (0.53)	0.18
Au₁₆		0.24 (0.95)	0.54

L. Xiao et al. (2004) Chemical Physics Letters 392, 452

L. Xiao et al. (2006) The Journal of Chemical Physics 114309

Gold Cluster Electronic Gap

Conjugated Gold Cluster Electronic Gap

Current/Future Work

Improve accuracy for the exact exchange integral in PBC (NWChem)
AIMD studies on the peptide/BNNTs interface in a solvated environment
Test plane-wave AIMD simulations with O(N) DFT methods

Challenges

Computation power (Hardware/Software)
Scaling of theories (CCSD vs. DFT vs. MD)
Choosing the "right" theory
Inclusion of all releveant paramters (ions, solution, pH)
Asking the right questions

Conclusion

Layed the foundation for protein BNNT simulations
Started to investigate functionalized structurs
Building framework for future large scale applications
Flexibility to look a similar structures (e.g. Polymers)

Acknowledgements

Ravindra Pandey
Eric Bylasksa
Gregory Odegard
Nabanita Saikia
Max Seel
Wil Slough
Yoke Khin Yap

An Investigation of Boron Nitride Nanomaterial Functionalization

Who am I?

Hypothesis

Nanomaterials

Nanomaterials

Morphological Dependent Properties

Boron Nitride Nanotubes

Boron Nitride Nanotubes

Boron Nitride Nanotubes (Band Gap)

Boron Nitride Nanotubes (Strain Energy)

Biological Molecules

Methods and Tools

Conjugated Boron Nitride Nanomaterials

Proteins

Conjugated Structures

Binding Energies

Binding Energies

Mechanical Properties of 2D BN2

Chemical Functionalization

Experimental Functionalization

BN Electronic Structure Evolution

BN2 Monolayer

BN2 Band Structure (Orbital Projected)

BN2 Band Structure (Atom Projected)

Hooke's Law / Elastic Tensor

\boldsymbol{\sigma_{ij}} =\boldsymbol{C_{ijkl}\epsilon_{kl}}

Elastic Tensor

Orthorhombic Symmetry (Amm2)

Orthorhombic Symmetry in 2D

Deformation Matrices

Workflow

Properties Derived from Elastic Constants

Results

Mechanical Properties of Crystalline Poly Ether Ether Ketone (PEEK)

US-COMP

PEEK

PEEK Structure

Orthorhombic Symmetry (Pbcn)

PEEK Elastic Constants

Elastic Constants

Poisson's Ratio

Gold Deposition Boron Nitride Nanomaterials

Gold Quantum Dots on Boron Nitride

Boron Nitride Nanotubes Functionalized with Gold Quantum Dots

Gold Flakes on Boron Nitride

Gold Flakes on Boron Nitride

Gold Cluster Structures

Gold Clusters Structural Parameters

Gold Cluster Cohesive Energy

Gold Clusters on BN

Gold/BN Clusters Parameters

Gold Clusters

Gold Clusters

Gold Cluster Electronic Gap

Conjugated Gold Cluster Electronic Gap

Current/Future Work

Challenges

Conclusion

Acknowledgements

Questions

Mechanical Properties of 2D BN₂

BN₂ Monolayer

BN₂ Band Structure (Orbital Projected)

BN₂ Band Structure (Atom Projected)

$\boldsymbol{\sigma_{ij}} =\boldsymbol{C_{ijkl}\epsilon_{kl}}$