Evaluation of temperature history of a spherical nanosystem irradiated with various short-pulse laser sources

Spatiotemporal thermal response and characteristics of net entropy production rate of a gold nanosphere (radius: 50–200 nm), subjected to a short-pulse, femtosecond laser is reported. In order to correctly illustrate the temperature history of laser-metal interaction(s) at picoseconds transient with a comprehensive single temperature definition in macroscale and to further understand how the thermophysical response of the single-phase lag (SPL) and dual-phase lag (DPL) frameworks (with various lag-ratios’) differs, governing energy equations derived from these benchmark non-Fourier frameworks are numerically solved and thermodynamic assessment under both the classical irreversible thermodynamics (CIT) as well as extended irreversible thermodynamics (EIT) frameworks is subsequently carried out. Under the frameworks of SPL and DPL with small lag ratio, thermophysical anomalies such as temperature overshooting characterized by adverse temperature gradient is observed to violate the local thermodynamic equilibrium (LTE) hypothesis. The EIT framework, however, justifies the compatibility of overshooting of temperature with the second law of thermodynamics under a nonequilibrium paradigm. The DPL framework with higher lag ratio was however observed to remain free from temperature overshooting and finds suitable consistency with LTE hypothesis. In order to solve the dimensional non-Fourier governing energy equation with volumetric laser-irradiation source term(s), the lattice Boltzmann method (LBM) is extended and a three-time level, fully implicit, second order accurate finite difference method (FDM) is illustrated. For all situations under observation, the LBM scheme is featured to be computationally superior to remaining FDM schemes. With detailed prediction of maximum temperature rise and the corresponding peaking time by all the numerical schemes, effects of the change of radius of the gold nanosphere, the magnitude of fluence of laser, and laser irradiation with multiple pulses on thermal energy transport and lagging behavior (if any) are further elucidated at different radial locations of the gold nanosphere. Last, efforts are further made to address the thermophysical characteristics when effective thermal conductivity (with temporal and size effects) is considered instead of the usual bulk thermal conductivity.

Figure 1

Physical representation of the problem.

Figure 2

Temporal intensity distribution of (a) one Gaussian pulse, series of (b) two, (c) three Gaussian laser pulses, and (d) Gaussian laser pulse train.

Figure 3

Schematic of D1Q3 lattice of LBM formulation for concentric spherical coordinate geometry with implementation of boundary conditions.

Figure 4

(a)–(c) Distribution of $T$ vs $r$ at $t=0.1$, 0.2, and 0.5 and (d)–(f) relative error, ${\xi }_1$ vs $t$ plot for $N=100$, $N=200$, and $N=400$.

Figure 5

Grid convergence history $\left({\xi }_{\infty }\le {10}^{-3}\right)$ for (a) FDM1, (b) FDM2, (c) FDM3 [15], and (d) LBM with numbers of lattice or control volumes.

Figure 6

Temporal temperature rise and heat flux distribution of a 100-nm GNS irradiated with one laser pulse under DPL framework by all the numerical schemes.

Figure 7

Temporal temperature rise and heat flux distribution for a 100-nm GNS irradiated with one laser pulse under SPL framework by all the numerical schemes.

Figure 8

Normalized temperature change at the surface of a 100-nm GNS irradiated with one laser pulse under the frameworks of DPL, SPL, and classical diffusion.

Figure 9

Net entropy production rate distribution in 100-nm GNS irradiated with one laser pulse under DPL and SPL frameworks at (a) 0.4, (b) 0.7, (c) 1.0, (d) 10.0, (e) 15.0, (f) 20.0 ps.

Figure 10

Absolute difference between equilibrium and nonequilibrium absolute temperature at the interior of 100-nm GNS irradiated with one laser pulse under SPL framework.

Figure 11

Effect of lag ratio on (a) temperature rise, (b) heat flux, (c) equilibrium, and (d) non equilibrium entropy production rate, (e) absolute equilibrium and non equilibrium temperature difference.

Figure 12

Temporal temperature rise and heat flux distribution of a 100-nm GNS irradiated with series of (a),(b) two, (c),(d) three, and (e),(f) pulse train under DPL framework respectively by all the numerical schemes.

Figure 13

Temperature rise at various interiors $\left(\frac{r}{L}=0.0,0.25,0.50,0.75,1.0\right)$ of 100-nm GNS vs laser fluence for (a) one, series of (b) two, (c) three laser pulses, and (d) laser pulse train under DPL framework.

Figure 14

Normalized temperature change at various interiors $\left(\frac{r}{L}=0.0,0.25,0.50,0.75,1.0\right)$ of (a) 50-nm, (b) 100-nm, (c) 150-nm, (d) 200-nm GNS irradiated with one laser pulse.

Figure 15

Normalized temperature change at various interiors $\left(\frac{r}{L}=0.0,0.25,0.50,0.75,1.0\right)$ of (a) 50-nm, (b) 100-nm, (c) 150-nm, (d) 200-nm GNS irradiated with series of two laser pulses.

Figure 16

Normalized temperature change at various interiors $\left(\frac{r}{L}=0.0,0.25,0.50,0.75,1.0\right)$ of (a) 50-nm, (b) 100-nm, (c) 150-nm, (d) 200-nm GNS irradiated with series of three laser pulses.

Figure 17

Normalized temperature change at various interiors $\left(\frac{r}{L}=0.0,0.25,0.50,0.75,1.0\right)$ of (a) 50-nm, (b) 100-nm, (c) 150-nm, (d) 200-nm GNS irradiated with laser pulse train.

Figure 18

Normalized temperature change and temporal variation of effective thermal conductivity at surface and center of (a),(b) 50-nm, (c),(d) 100-nm, (e),(f) 150 nm, and (g),(h) 200-nm GNS respectively: the role of effective thermal conductivity.

Figure 19

(a) Convergence history with physical time, (b) CPU time vs physical time under DPL framework for all the numerical schemes.