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An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles

Ian McCueJonah Erlebacher

Department of Materials Science and Engineering

This work is supported by NSF DMR 1003901

Materials Research Society, November 29th, 2012

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Nanoporous Gold (NPG)

Characteristics of NPG

•bicontinuous, open porosity

•tunable pore size ~5 nm 10 microns via electrochemical processing and/or thermal annealing

•porosity is sub-grain sizeNPG is not nanoparticulate

• porosity retains a long-range single crystal networksingle-crystalline to a scale > 3 orders of magnitude larger than any pore/ligament diameter

grain boundary

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Electrochemistry of Porosity Evolution

The “critical potential” separates two potential windows: • below Ec planar, passivated morphologies• sufficiently far above Ec porosity evolution

What changes with potential?• rate of silver dissolution (fast), surface diffusivity

(slow)

Department of Materials Science and EngineeringErlebacher, J., J. Electrochem. Soc. 151 (2004), C614

A. Nucleation and growthof vacancy islands

B. Development of gold-passivated mounds

C. Evolution of gold-poor mound bases

D. Mound undercutting, nucleation of new goldmounds, and pore bifurcation

E. Evolution of gold-passivated porosity

F. Post-dealloying coarsening,and/or further dissolution

Formation Mechanism in Bulk Systems

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Kinetic Monte Carlo (KMC):A simulation tool to study coarsening

real nanoporous gold

KMC Algorithm1. Tabulate all possible transitions

2. The time for an event to occur with 100% probability is:

3. Pick an event to occur during the time interval with probability

4. Move atoms corresponding to event

5. Update neighbors, transition list, go to step 2 and repeat

simulated nanoporous metal

ik

1

lnN

ii

t k

where is a random number in

0,1

i1

1

N

i i jj

P k k

i

Rate Parameter for Surface Diffusion:

Rate Parameter for Dissolution:

1 exp Bdiff

b

nEk vk T

13 1

1 10 secv

2 exp Bdiss

b

nEk vk T

4 12 10 secv

0.15eVBE

applied potential

n coordination

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Nanoporous Nanoparticles

J. Snyder, J. Erlebacher

Initial ConditionsLooked at four different particle sizes: radii of 10, 15, 25 and 40 atomsLooked at three different compositions: 65%, 75%, and 85% AgSimulations ran for 104-105 simulated seconds, or ~ 5 x108 iterations

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Gibbs-Thomson Effects on Electrochemical Stability

L. Tang, B. Han, K. Persson, C. Friesen, T. He, K. Sieradzki, G. Ceder, J. Electrochem. Soc. 132, 596 (2010).

• Particle of radius r will have additional surface energy increase per atom by:

where is the atomic vol.

• Smaller means more unstable

• G-T effect manifests in electrochemical stability of nanoparticles

• Decrease in dissolution potential of atom by:

where n is the number of electrons given up to form metal cation

2 r

E n

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What about Binary Particles? NO!

• Does not mean Ag atoms require more energy to dissolve

• As size decreases more potential is required to form porosity

The potential we are measuring is not a certain critical current, but an intrinsic potential based on the propensity that a particle will dealloy

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Porosity Evolution in Nanoparticles

• Low-coordination surface silver sites are dissolved

• Surface gold atoms quickly passivate the surface

• Regions of bulk are exposed due to fluctuations in the outermost layer and porosity can occur

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Porosity Evolution in Nanoparticles (cont)Diffuse threshold between passivation and porosity evolution

Smaller volume corresponds to fully dealloyed particles

Larger volume corresponds to passivated particles

Define Ep as potential where the distribution area of each Gaussian was equal

Below Ep Above Ep

1:1 Ratio

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Observation on Porosity Evolution in NP

Surface Diffusion events are controlled by kink fluctuations

Ag terrace atoms are the rate limiting step in dissolution

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Kinetic Derivation

Can setup a first order rate equation for the change in the number of surface silver atoms

AgAgpercdiss kink

dNk P P Ndt

Probability Ag atom is connected to bulk Ag atoms

Equilibrium Number of Ag atoms on the surface

exp 9diss B P Bk E E k T

Probability of Au fluctuation at a kink site

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Solution to Kinetic Equation

0 119 ln ln0

AgP B b

perckink Ag

NE E k T vP P t N

• Single dissolution event at the passivated state leads to porosity evolution

• Simplest criterion for Ep is that over a time interval ∆t- the lifetime of the step edge fluctuation- is that 0 1Ag AgN t N

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Percolation Probability for Surface Ag Atoms

What does percolation probability mean: • Can we trace a path of silver atoms from one side of

the particle to the other

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Number of Ag Terrace Atoms

Ag terrace atoms distributed evenly across facets

As particle size increases:

• Facet size does not appreciably increase

• Ag atoms are found on the edges of facets

• As a result the number of Ag terrace sites scales with the radius

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Surface Diffusion

Key points:• Peak at ~10-6 corresponds to adatom fluctuations• Peak at ~101 corresponds to fluctuations at step edges• Area under kink interval curve corresponds to Pkink

Radius 40Radius 10

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Evaluation of Kinetic Expression

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Summary

• Porosity evolution in nanoparticles is dependent on a chorus of size dependent variables and exhibits rich complexity

• Gibbs-Thomson effects dictate the size dependence, but not as we initially expected

• First order rate equation gives an awesome fit to our observed results

• Major conclusion is that surface diffusion changes the critical potential

• Could potentially tailor porosity in nanoparticles adding an alloying component that will kill the formation of a passivating monolayer

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Acknowledgements

• Jonah Erlebacher• Erlebacher Research Group

• Josh Snyder• Ellen Benn

• Felicitee Kertis