Explosive, oscillatory, and Leidenfrost boiling at the nanoscale

We investigate the different boiling regimes around a single continuously laser-heated 80 nm gold nanoparticle and draw parallels to the classical picture of boiling. Initially, nanoscale boiling takes the form of transient, inertia-driven, unsustainable boiling events characteristic of a nanoscale boiling crisis. At higher heating power, nanoscale boiling is continuous, with a vapor film being sustained during heating for at least up to $20\mu \mathrm{s}$. Only at high heating powers does a substantial stable vapor nanobubble form. At intermediate heating powers, unstable boiling sometimes takes the form of remarkably stable nanobubble oscillations with frequencies between 40 MHz and 60 MHz, frequencies that are consistent with the relevant size scales according to the Rayleigh-Plesset model of bubble oscillation, though how applicable that model is to plasmonic vapor nanobubbles is not clear.

Figure 1

The well-known traditional boiling curve of macroscopic pools of water at atmospheric pressure with sketches of the different boiling regimes. Curve data adapted from Ref. [4].

Figure 2

Layered-sphere Mie theory calculation [22] with an 80 nm diameter gold core and a vacuum shell (bubble, $n=1$) of varying thickness $d_{\mathrm{vap}}$ in a medium with refractive index $n=1.33$. (a) Absorption of ${\lambda }_{\mathrm{vac}}=532\mathrm{nm}$ and (b) scattering of ${\lambda }_{\mathrm{vac}}=815\mathrm{nm}$, both shown as a function of bubble thickness. (c) Absorption spectra of 80 nm AuNPs, when in $n$-pentane as compared to vacuum. See also Appendix pp1.

Figure 3

Single-shot scattering time traces of the same 80 nm Au sphere. Black: scattering in the detector's units; red: heating intensity in the back focal plane. Four principal regimes of heated AuNP behavior are observed: (I) below boiling threshold, small thermal lensing effect. (II) Near boiling threshold, repeated short-lived vapor nanobubble formation. (III) Above boiling threshold, unstable vapor nanobubble for the duration of heating. (IV) Far above threshold, relatively stable nanobubble, probable damage to AuNP. See also Fig. 4.

Figure 4

Dependence of vapor nanobubble behavior on laser power, based on 8050 single-shot time traces measured at one nanoparticle, like those shown in Fig. 3. (a) Number of spikes (extrema $d\tilde{u}/dt=0$ where $d^2\tilde{u}/d{t}^2<0$ is below a heuristically chosen threshold, $\tilde{u}\left(t\right)$ being the signal smoothed with a 30 ns Hann filter) in the signal. (b) Mean scattering signal during heating. (c) RMS power of the frequency components between 10 MHz and 80 MHz.

Figure 5

Nanobubble oscillations; (a) Single-shot nanobubble timetrace with clearly visible oscillations. (b) Fourier transforms of 50 subsequent such time traces of the same AuNP subject to an unchanging heating profile. White arrows highlight some points with particularly clear frequency splitting. (c) Average of the time traces in panel (d), synchronized on the initial rising edge. (d) Fifty time traces used in panels (b) and (c). In panels (b) and (d), the lines marked with an asterisk correspond to panel (a).

Figure 6

Resonance frequencies for vapor nanobubbles in pentane, according to the Rayleigh-Plesset and Minnaert models, with and without considering the temperature dependence of the surface tension $\gamma$ and the density $\varrho$.

Figure 7

Example series of oscillating-bubble event Fourier transforms, all for the same nanoparticle, in the same form as Fig. 5.

Figure 8

Change of the apparent oscillation frequency with heating power for different AuNPs. This figure shows the location of peaks in the fast Fourier transforms of individual time traces such as those shown in Fig. 5. Only measurements showing good oscillations are shown: those with $Q>10$, where the quality factor $Q=f_{\max }/\mathrm{FWHM}$ is calculated from the FFT. “Particle 4” refers to the set of measurements used in Figs. 5, 7, and 10.

Figure 9

Anharmonicity of the Rayleigh-Plesset equation for a freely oscillating bubble, with the viscosity set to zero. Calculated by direct numerical (Runge-Kutta) integration with $\mathrm{\Delta }t=10\mathrm{ps}$ using the parameters for saturated pentane. (a) Example time traces of a bubble with $R_0=120\mathrm{nm}$ oscillating at two different amplitudes. The bottom of the curve, especially at larger amplitude, is noticeably more “pointed,” and the oscillation period is clearly different. (b) Calculated oscillation periods $\tau$ with different equilibrium radii $R_0$ and oscillation amplitudes $\delta R$, relative to the corresponding period ${\tau }_{\mathrm{harm}}$ in the harmonic approximation.

Figure 10

(a) Series of oscillating-bubble event Fourier transforms [same data as Fig. 7, smoothed with a 6 MHz Hann filter] showing, faintly, the second harmonic. (b) Mean of the Fourier transforms shown, calculated after rescaling the frequency axis of each to put the maximum at unity, showing clearly the second harmonic. Note that the upper cutoff frequency of our detector is 80 MHz, which reduces the apparent prominence of the second harmonic, and completely obscures higher harmonics.