Mechanism of Hollow Nanoparticle Formation Due to Shape Fluctuations

Shape fluctuations in nanoparticles strongly influence their stability. Here, we introduce a quantitative model of such shape fluctuations and apply this model to the important case of Pt-shell/transition metal-core nanoparticles. By using a Gibbs distribution for the initial shapes, we find that there is typically enough thermal energy at room temperature to excite random shape fluctuations in core-shell nanoparticles, whose amplitudes are sufficiently high that the cores of such particles are transiently exposed to the surrounding environment. If this environment is acidic and dissolves away the core, then a hollow shell containing a pinhole is formed; however, this pinhole quickly closes, leaving a hollow nanoparticle. These results favorably compare to experiment, much more so than competing models based on the room-temperature Kirkendall effect.

Figure 1

Stages in the surface-diffusion driven formation of hollow nanoparticles. (i) A core-shell nanoparticle of radius $R_0$ and shell thickness $h$; (ii) shape fluctuations in the outer surface expose the core, allowing it to be dissolved away; (iii) a pinhole of radius $r$ exists in the shell, but quickly closes up because of a diffusional flux from the convex outer surface $A$ through the pinhole edge $B$ and into the inner concave surface $C$. (iv) When the radius of curvature of the pinhole edge $a$ becomes sufficiently large, the net flux at the pinhole edge $J^{+}-J^{-}$ is positive, closing the pinhole and leaving a hollow nanoparticle.

Figure 2

(solid lines; left vertical axis): Pinhole formation probability $F_l$ associated with generating a fluctuation with peak-to-valley length greater than threshold $2C_{*}$, vs fluctuation mode $l$. (dashed lines; right vertical axis): Fluctuation lifetime ${\tau }_l$ vs fluctuation mode $l$. Results are shown for Pt- and PtO-terminated surfaces, with shells of 0.5 and 4.0 nm thickness and core radius $R_0=6.5\mathrm{nm}$; in all cases, fluctuations are highly probable and possess lifetimes long enough to allow attack of the core by an external electrolyte.

Figure 3

Pinhole closure time $t_c$ vs initial pinhole radius $r_0$ for different values of the pinhole edge radius of curvature $a$. PtO-terminated surfaces: thick lines; Pt-terminated surfaces: thin dashed lines.