Boshen Fu and Nitin P. Daphalapurkar

School of Mechanical and Aerospace EngineeringOklahoma State University

Stillwater, OK, U.S.A.

Simulation of Microstructural Evolution of A Crosslinked Templated Silica-aerogel in

Compression

Polymer Mechanics Laboratory

Very lightweight glass-like materials, but extremely fragileAt best:•1.5 mg/cc, Guinness World Records•99.8% porosity •1000 times less dense than glass•about 40 times better thermal insulators than the best fiberglass

JPL Website, Stardust Program

Invented by S. S. Kistler (Stanford U.) in 1931lengthy process,

first major breakthrough: supercritical drying of wet gels retaining volume of the gel

“Forgotten” for almost 30 years

“Re-invented” in the 1960’s in France second major breakthrough: sol-gel process

cutting Kistler’s method from weeks to hours

Aerogels

Aerogels have been considered for:- thermal insulation (architectural, automotive industrial

applications);- acoustic insulation (buildings, automobiles, aircraft);- dielectrics (for fast electronics);

- supports for catalysts; and,- hosts of functional guests for chemical,

electronic and optical applications.

Silica aerogels have been actually used:- as Cerenkov radiation detectors

- aboard spacecraft:o as collectors of cosmic particles

(Stardust Program)

o for thermal insulation (e.g., Sojourner Rover - 1997)

Commercialization has been slow, because silica aerogels are:- fragile;- hygroscopic; and,- require supercritical fluid (SCF) extraction

Current and Projected Use for Aerogels

nonporous primary particles (<1 nm; dense silica)

mesopores

channels to micropores

porous secondary particles (density ~ 1/2 silica)

~5-10 nm

Crosslinking aerogels — Microscopically, nanocast conformal polymer coating on the silica nanoparticles

conformal polymer coating

Micropores are blocked

thicker necks increase strength of material

Leventis, et al, Nano Letters, 2002

Specific Energy Absorption (X-aerogel): 197 J/g in compression.Spider Dragline Silk: 165 J/g in tension.

Compressive Stress-Strain Curves for Templated Aerogels

conformal polymer coating

Leventis (2007), Luo, Lu and Leventis (2003)

• Lightweight thermal insulation• Acoustic Insulation • Catalytic reformers and converters• Dielectrics• Ballistic materials • Filtration membranes• Membranes for fuel cells• Optical sensors• Aircraft structural components

Cross-linked silica aerogel

Pontential Applications for Crosslinked Aerogels

Native Cross-linkedSection of

Cross-linked

Secondary particles

Polymer coating

Bending stresses at necks responsible

for low failure strain leading to fragility in

native silica aerogels

Bending stress contours from FEM

Increase in the cross-linked aerogel stiffness with the amount of polymer

addition

Bulk density ratio (XSA/Native)

Ben

din

gst

iffn

ess

ratio

(XS

A/N

ativ

e)

1 1.5 2 2.5 31

1.2

1.4

1.6

1.8

2

2.2

2.40.27740.33640.3992

Simulation of Two-spheres Model for TwoSecondary Particles Connected to Each Other

SEM of Crosslinked Templated Aerogels(X-MP4-T045)

TransmittedX-ray Image

CC

D f

Incident X-rayBeam

X-rays

* Low depth of field, reject scattered light photons.

CCDOpticalLens*

Thin Single Crystal Scintillator Sample

X-raysLightLight

I oI

Nano-Computed Tomography (nano-CT)

3D discretized MPM simulation model

110 pixels along the length

nano-CT structure for X-MP4-T045

Pixel size =480 nm/voxel;

Average pore size 6−7μm

Crosslinked Silica Aerogel – MPM Simulation

0% 2% 4% 6% 8% 10% 12% 14% 16% 18% 20%0

10

20

30

40

50

60

Representative volume element (RVE) 4X6X7X

Strain

Stre

ss (

MPa

)

Crosslinked Silica Aerogel – MPM SimulationFlexural Modulus Estimation

Weight ratio( Polymer: Silica)=70%: 30%Density of polymer = 1.2 g/ccDensity of silica = 2.6 g/ccModulus of polymer = 2 GpaModulus of silica =70 Gpa

The volume ratio( Polymer: Silica) ≈5:1The dimensionless radius of the model R=6

Based on the bending equation for the composite material

The silica-aerogel modulus is about 3.889 Gpa

Simulation Results

Microstructural evolution under compression Microstructure deformation characteristic (comparison with

rohacell foam)

Dynamic equilibrium Dynamic stress equilibrium; velocity loading history

Compressive stress-strain curve Typical silica-aerogel material stress-strain relation

Effect of porosity on the material properties Gibson & Ashby beam structure analog for the honeycomb

structure material; response for the different porosity silica-aerogel models

Microstructural Evolution

Microstructural Evolution

Cell buckling is not a primary deformation mechanism.

Shear bandDaphalapurkar et al, Mech. Adv. Mater. & Struc.,2008

Dynamic Stress Equilibrium

0% 1% 2% 3% 4% 5% 6%0

5

10

15

20

25

30

Bottom face (Fixed)

Top face (Moving)

Exp. results

Strain

Stre

ss (M

Pa)

0.00E+00 2.50E-06 5.00E-06 7.50E-06 1.00E-05 1.25E-050

0.2

0.4

0.6

0.8

1

1.2Velocity history of loading

Time (Second)

Am

plit

ude

Compressive stress-strain curves indicating the dynamic stress equilibrium.Time step in simulation is 0.0442 nanoseconds

Stress-Strain Curve

0% 10% 20% 30% 40% 50% 60% 70% 80%0

200

400

600

800

1000

1200

1400

Strain

Stre

ss (

MPa

)

Compressive Stress-strain curve for 3D model

0% 10% 20% 30% 40% 50% 60% 70% 80% 90%0

200

400

600

800

1000

1200

Compressive stress-strain curve for 2D model

Strain

Stre

ss(M

Pa)

2D simulation does not appear to be able to capture the initial elastic region accurately for an irregular porous structure.

0% 1% 2% 3% 4% 5% 6%05

1015202530

Effect of Porosity

30 40 50 60 70 80 9030%

35%

40%

45%

50%

55%

60%

65%

70%Cutoff Grayscale Vs Porosity

100*100*100

200*200*200

Cutoff Grayscale

Poro

sity

45% porosity, cutoff grayscale 53 50% porosity, cutoff grayscale 58

55% porosity, cutoff grayscale 64

Effect of Porosity

Gibson & Ashby, Cellular Solids 1997

Effect of Porosity

0% 5% 10% 15% 20% 25% 30% 35% 40%0

50

100

150

200

250Effect of Porosity

45% porosity

50% porosity

55% porosity

Strain

Stre

ss (

MPa

)

Gibson & Ashby, Cellular Solids 1997

0% 5% 10% 15% 20% 25% 30% 35% 40%0

50

100

150

200

250

45% porosity

Predicted 45% porosity based on 50%

Predicted 45% porosity based on 55%

50% porosity

Predicted 50% porosity based on 55%

55% porosity

Strain

Stre

ss (M

Pa)

Conclusion

MPM simulation indicates the dynamic stress equilibrium condition has been reached. The stress-strain relation agrees with the experimental results in the elastic region and yielding region.

The simulation shows the potential to simulate the nanostructure property relationship of the crosslinked templated aerogels.

The simulation can capture the elastic, compaction and densification behavior of the silica-aerogel.

The mechanical behavior of silica-aerogel follows a cubic power relation when the pores are not fully compacted. The relation does not hold when the pores are all closed.