An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles

1. 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

2. 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

3. 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)

4. 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 bifurcation Evolution of gold-passivated porosity Post-dealloying coarsening, and/or further dissolution Erlebacher, J., J. Electrochem. Soc.151 (2004), C614

5. 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

6. 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

7. 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).

8. NO! 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

9. 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

10. 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

11. Observation on Porosity Evolution in NP Surface Diffusion events are controlled by kink fluctuations Ag terrace atoms are the rate limiting step in dissolution

12. 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

13. 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

14. 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

15. 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

16. 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

17. Evaluation of Kinetic Expression

18. 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

19. Acknowledgements • Jonah Erlebacher • Erlebacher Research Group • Josh Snyder • Ellen Benn • Felicitee Kertis