An inverse gibbs thomson effect in nanoporous nanoparticles
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An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles. Ian McCue Jonah Erlebacher Department of Materials Science and Engineering. Materials Research Society, November 29th, 2012. This work is supported by NSF DMR 1003901 . Nanoporous Gold (NPG). Characteristics of NPG

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An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles

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An inverse gibbs thomson effect in nanoporous nanoparticles

An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles

Ian McCue

Jonah Erlebacher

Department of Materials Science and Engineering

Materials Research Society, November 29th, 2012

This work is supported by

NSF DMR 1003901

Nanoporous gold npg

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 size

    • NPG is not nanoparticulate

  • porosity retains a long-range single crystal network

    • single-crystalline to a scale > 3 orders of magnitude larger than any pore/ligament diameter

grain boundary

Electrochemistry of porosity evolution

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)

Formation mechanism in bulk systems

Formation Mechanism in Bulk Systems

Nucleation and growth

of vacancy islands

Development of

gold-passivated mounds

Evolution of gold-poor

mound bases

Mound undercutting,

nucleation of new gold

mounds, and pore


Evolution of

gold-passivated porosity

Post-dealloying coarsening,

and/or further dissolution

Erlebacher, J., J. Electrochem. Soc.151 (2004), C614

Kinetic monte carlo kmc a simulation tool to study coarsening

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

KMC Algorithm

  • simulatednanoporous metal

Tabulate all possible transitions

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

Pick an event to occur during the time interval with probability

Move atoms corresponding to event

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

  • realnanoporous gold

where is a random number in

Rate Parameter for Surface Diffusion:

Rate Parameter for Dissolution:

applied potential

Nanoporous nanoparticles

Nanoporous Nanoparticles

J. Snyder, J. Erlebacher

Initial Conditions

Looked at four different particle sizes: radii of 10, 15, 25 and 40 atoms

Looked at three different compositions: 65%, 75%, and 85% Ag

Simulations ran for 104-105 simulated seconds, or ~ 5 x108 iterations

Gibbs thomson effects on electrochemical stability

Gibbs-Thomson Effects on Electrochemical Stability

  • 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

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

What about binary particles


What about Binary Particles?

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

  • Does not mean Ag atoms require more energy to dissolve

  • As size decreases more potential is required to form porosity

Porosity evolution in nanoparticles

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

Porosity evolution in nanoparticles cont

Porosity Evolution in Nanoparticles (cont)

Below Ep

Diffuse threshold between passivation and porosity evolution

Above Ep

Smaller volume corresponds to fully dealloyed particles

1:1 Ratio

Larger volume corresponds to passivated particles

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

Observation on porosity evolution in np

Observation on Porosity Evolution in NP

Surface Diffusion events are controlled by kink fluctuations

Ag terrace atoms are the rate limiting step in dissolution

Kinetic derivation

Kinetic Derivation

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

Probability of Au fluctuation at a kink site

Probability Ag atom is connected to bulk Ag atoms

Equilibrium Number of Ag atoms on the surface

Solution to kinetic equation

Solution to Kinetic Equation

  • 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

Percolation probability for surface ag atoms

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

Number of ag terrace atoms

Number of Ag Terrace Atoms

  • 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

Ag terrace atoms distributed evenly across facets

Surface diffusion

Surface Diffusion

Radius 10

Radius 40

  • 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

Evaluation of kinetic expression

Evaluation of Kinetic Expression



  • 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



  • Jonah Erlebacher

  • Erlebacher Research Group

    • Josh Snyder

    • Ellen Benn

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