Nanoparticle–laser interaction: computation of size reduction and thermal conductance at solid–vapor interface

Hadi Movahedinejad; Hamid Nadjari; A. H. Farahbod

doi:10.1364/JOSAB.378973

Journal of the Optical Society of America B
Vol. 37,
Issue 2,
pp. 412-419
(2020)
•https://doi.org/10.1364/JOSAB.378973

Nanoparticle–laser interaction: computation of size reduction and thermal conductance at solid–vapor interface

Hadi Movahedinejad, Hamid Nadjari, and A. H. Farahbod

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Hadi Movahedinejad, Hamid Nadjari, and A. H. Farahbod, "Nanoparticle–laser interaction: computation of size reduction and thermal conductance at solid–vapor interface," J. Opt. Soc. Am. B 37, 412-419 (2020)

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Abstract

Laser interaction with a water-immersed metal nanoparticle can bring about a condition such that a bubble is generated and the nanoparticle is evaporated. This phenomenon is strongly dependent on the laser parameters and the nanoparticle size. In this study, we simulate the behavior of a gold nanoparticle and its surrounding medium during interaction with a nanosecond-pulsed laser by considering nanoparticle size reduction, variations in the nanoparticle absorption cross section, and variations in thermal conductance at the nanoparticle–bubble interface. Results show that the bubble dynamics under a low-energy and long-pulse-width laser (so that it does not cause evaporation) strongly depends on the nanoparticle temperature behavior, while under higher laser energy, it is dependent on the amount of nanoparticle size reduction. Moreover, by comparing the nanoparticle thermal behavior with experimental data, we are able to estimate the thermal conductance at the nanoparticle–bubble interface. This simulation not only leads to nanoparticle size control but also helps in understanding the heat transfer processes at nanoscale.

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Laser Fluence	Pressure	Temperature	Moment of Bubble Formation	Reduced NP Size
( ${J m}^{- 2}$ )	(MPa)	(K)	(ns)	(nm)
1 ns pulse width
80	16.8.5	606.025	0.202	80
150	19.280	621.634	0.121	79.686
500	22.055	647.030	0.005	72.615
5 ns pulse width
80	12.107	573	1.502	80
150	13.078	580.594	0.710	80
500	16.619	606.799	0.195	76.966
10 ns pulse width
80	11	565.216	5.606	80
150	11.711	570.476	2.110	80
500	14.014	587.520	0.423	77.429

Laser Parameters	Symbol	Value
Laser fluence ( $J \cdot m^{- 2}$ )	$F$	Input data
Pulse duration (s)	$τ$	Input data
Gold NP Parameters
Radius (m)	$R_{n p}$	Input data and Eq. (12)
Temperature (K)	$T_{n p}$	Eq. (2)
Density ( $K g \cdot m^{- 3}$ )	$ρ_{n p}$	19320
Specific heat capacity ( $J \cdot {K g}^{- 1} \cdot K^{- 1}$ )	$c_{n p}$	129
Latent heat of fusion ( $J \cdot {K g}^{- 1}$ )	$L_{f}$	63000
Latent heat of vaporization ( $J \cdot {K g}^{- 1}$ )	$L_{n p}$	1577000
Melting point (K)	$T_{m . p}$	1337
Boiling point (K)	$T_{b . p}$	Eq. (11)
Thermal conductance at the gold–water interface ( $M W \cdot m^{- 2} \cdot K^{- 1}$ )	$G_{n p - w}$	105 [31]
Thermal conductance at the gold–vapor interface ( $M W \cdot m^{- 2} \cdot K^{- 1}$ )	$G_{n p - b}$	Eq. (8)
Absorption cross section ( $m^{2}$ )	$C_{a b s}$	$f R_{n p}, R_{b}, n_{r e f}$

Water Parameters	Symbol	Value
Temperature (K)	$T_{w}$	Eq. (3)
Density ( $K g \cdot m^{- 3}$ )	$ρ_{w}$	$f T_{w}$ [32]
Specific heat capacity ( $J \cdot {K g}^{- 1} \cdot K^{- 1}$ )	$c_{w}$	$f T_{w}$ [32]
Thermal conductivity ( $W \cdot K^{- 1}$ )	$k_{w}$	$f T_{w}$ [32]
Pressure far away from the bubble (Pa)	$P_{\infty}$	10000
Water density far away from the bubble ( $K g \cdot m^{- 3}$ )	$ρ_{\infty}$	1000
Molar mass of water ( $K g \cdot {m o l}^{- 1}$ )	$M$	0.018
Refractive index	$n_{r e f}$	$f T_{w}$ [32]

Bubble Parameters	Symbol	Value
Radius (m)	$R_{b}$	Eq. (5)
Density inside the bubble ( $K g \cdot m^{- 3}$ )	$ρ_{b}$	$f (d n, R_{b})$
Temperature (K)	$T_{b}$	$\frac{Δ E_{b}}{m_{b} c_{b}}$
Energy (J)	$E_{b}$	Eq. (6)
Thermal conductivity ( $W \cdot K^{- 1}$ )	$k_{b}$	0.62
Specific heat capacity ( $J \cdot {K g}^{- 1} \cdot K^{- 1}$ )	$c_{b}$	2000
Bubble Wall Parameters
Pressure (Pa)	$P_{w a l l}$	$P_{b} - \frac{2 σ}{R_{b}} - \frac{4 μ}{R_{b}} \frac{d R_{b}}{d t}$
Temperature (K)	$T_{w a l l}$	Eq. (10)
Latent heat of vaporization at the bubble wall ( $J \cdot {m o l}^{- 1}$ )	$Δ H_{e v a p}$	$f T_{w a l l}$ [32]
Viscosity at the bubble wall ( $P a \cdot s$ )	$μ$	$f T_{w a l l}$ [32]
Flux of vapor inside the bubble	$d n$	[18]
Surface tension ( $N \cdot m^{- 1}$ )	$σ$	$f T_{w a l l}$ [32]
Van der Waals equation of state parameters
Pressure inside the bubble (Pa)	$P_{b}$	$\frac{ρ_{b} K_{B} T_{b}}{1 - ρ_{b} b} - a ρ_{b}^{2}$
Critical pressure (MPa)	$\frac{a}{27 b^{2}}$	22
Critical density ( $K g \cdot m^{- 3}$ )	$\frac{1}{3 b}$	322
Critical temperature (K)	$\frac{8 a}{27 b K_{B}}$	647.3
Equations for the Exchange of Mass and Energy Inside the Bubble (J)
Energy flux caused by mass transfer	$Q_{m a s s}$	$Δ H_{e v a p} d n M$
Heat transfer at the particle interface	$Q_{n p}$	$4 π R_{n p}^{2} G_{n p - b} T_{n p} - T_{b}$
Work of pressure	$Q_{w o r k}$	$- 4 π R_{b}^{2} \frac{d R_{b}}{d t} P_{w a l l}$ [11]
Work of surface tension	$Q_{t e n}$	$- 4 π R_{b}^{2} \frac{d R_{b}}{d t} α σ$ [11]
Viscous losses	$Q_{v i s}$	$- 4 π R_{b}^{2} \frac{d R_{b}}{d t} β μ$ [11]
Heat flux at the bubble wall	$Q_{i n t e r}$	$- 4 π R_{b}^{2} k_{b} \frac{T_{b} - T_{w a l l}}{d r}$
Constants
	$α$	1.96 [11]
	$β$	1.96 [11]
Gas constant ( $J \cdot {m o l}^{- 1} \cdot K^{- 1}$ )	$R_{c o n s}$	8.314
Boiling point at atmospheric pressure (K)	$T_{a t m}$	3129
Atmospheric pressure (MPa)	$P_{a t m}$	0.1
Avogadro’s number	$N_{A}$	$6.0221409 \times 10^{23}$

Laser Fluence	Pressure	Temperature	Moment of Bubble Formation	Reduced NP Size
( ${J m}^{- 2}$ )	(MPa)	(K)	(ns)	(nm)
1 ns pulse width
80	16.8.5	606.025	0.202	80
150	19.280	621.634	0.121	79.686
500	22.055	647.030	0.005	72.615
5 ns pulse width
80	12.107	573	1.502	80
150	13.078	580.594	0.710	80
500	16.619	606.799	0.195	76.966
10 ns pulse width
80	11	565.216	5.606	80
150	11.711	570.476	2.110	80
500	14.014	587.520	0.423	77.429

Abstract

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Tables (4)

Equations (15)

Journal of the Optical Society of America B