Interrogating Gas-Borne Nanoparticles Using Laser-Based Diagnostics and Bayesian Data Fusion

Abstract

We demonstrate how the evaporation properties of gas-borne nanoscale materials, here liquid silicon and germanium nanoparticles, can be obtained through a novel combination of in situ time-resolved laser-induced incandescence (TiRe-LII) and phase-selective laser-induced breakdown spectroscopy (PS-LIBS) based on Bayesian data fusion. This approach reduces the uncertainty in the parameters describing evaporation and condensation by more than a factor of 2 compared to the conventional path and has the capability to provide much needed particle-size-dependent information on nanomaterial phase transitions at high temperature. The inferred parameters are generally consistent with those repeated in the literature but with reduced uncertainty and an extended temperature range.

Laser-induced incandescence for non-soot nanoparticles: recent trends and current challenges

“…Furthermore, one can formally introduce and weigh prior information via Bayes equation where p ( x | b ) is the posterior, the joint probability distribution for the inferred QoI; p ( b | x ) is the likelihood, derived from the data, measurement noise, and TiRe-LII model; and p ( x ) is the prior, containing any information known prior to the measurement, such as molecular dynamics (MD)-derived TACs along with their uncertainties. This approach was introduced by Sipkens et al [ 72 ] for analyzing LII data from silicon nanoparticles and has subsequently been used for general UQ [ 61 , 75 ], to incorporate nuisance parameters [ 46 , 60 ], choose between thermophysical models [ 73 ], to combine data from multiple complementary diagnostics [ 60 , 92 ], and to visualize limitations during inference [ 46 , 60 ].

Fig.

…”

“…Likewise, both the latent heat of vaporization and vapor pressure have been inferred for metal nanoparticles [ 71 , 73 , 74 , 92 ]. Most often this is done in terms of the Clausius-Clapeyron or Antoine equation parameters.…”

“…Sipkens et al [ 73 ] applied Bayesian model selection on TiRe-LII data collected on iron nanoparticles to identify the most probable model to account for the temperature-dependence of the latent heat of vaporization of iron. Menser et al [ 92 ] carried out a combined TiRe-LII/LIBS measurement on liquid silicon nanoparticles, in which the evaporation rate was obtained directly from the intensity of an atomic emission line corresponding to evaporated silicon atoms. This measurement (discussed in greater detail in Sect.…”

“…A known portion of the evaporated atoms and molecules will therefore be electronically excited, and will spontaneously relax in the gas state according to the Einstein coefficient for a given transition. Menser et al [ 92 , 194 ] exploited this phenomenon to investigate the evaporative behavior of liquid silicon and liquid germanium nanoparticles. This was done by systematically varying the laser fluence, and measuring the corresponding peak line intensity of key transitions (e.g., 3s 2 3p 4 s 1 P ° 1 → 3s 2 3p 2 1 D 2 at 288 nm for Si [ 195 ]) using a streak camera.…”

“…( 13 )–( 15 ). Moreover, Menser et al [ 92 ] combined the peak atomic emission intensity versus fluence, peak nanoparticle temperature versus fluence, and individual temperature decay traces to develop probabilistic estimates of the Antoine parameters. Intriguingly, the detected atomic emission signal intensities showed two distinct modes: a short peak temporally aligned with the heating pulse, which corresponds to the evaporation mechanism described previously, and a second, longer lasting peak having a characteristic relaxation time on the order of microseconds.…”