Continuous wave, short and ultrashort pulse

International Journal of Heat and Mass Transfer 89 (2015) 866–871

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International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Photothermal response of hollow gold nanoshell to laser irradiation: Continuous wave, short and ultrashort pulse Ali Hatef a, Simon Fortin-Deschênes a, Etienne Boulais b, Frédéric Lesage c, Michel Meunier a,⇑ a

École Polytechnique de Montréal, Laser Processing and Plasmonics Laboratory, Engineering Physics Department, Montréal, Québec H3C 3A7, Canada Department of Biological Engineering, Laboratory for Computational Biology & Biophysics, Massachusetts Institute of Technology, Cambridge, MA 02139, USA c École Polytechnique de Montréal, Department of Electrical Engineering, Montréal, Québec H3C 3A7, Canada b

a r t i c l e

i n f o

Article history: Received 2 October 2014 Received in revised form 16 May 2015 Accepted 16 May 2015

Keywords: Modeling and numerical simulation Finite element method Continuous wave Short and ultra-short pulse laser Hollow gold nanoshell and plasmonic photothermal therapy

a b s t r a c t This paper is to investigate numerically the photothermal response of the most common size of gold nanoshell (AuNS) in an aqueous medium for biomedical applications. Three types of laser light irradiate the particle; a continuous-wave (CW), short (nanosecond) and ultrashort (femtosecond) pulse laser. The spatiotemporal evolution of the temperature profile inside and around the AuNS is computed using a numerical framework based on the finite element method (FEM). For CW and nanosecond (ns) pulse laser where the AuNS’s electrons and lattice are at thermal equilibrium, the ordinary heat diffusion equation is used to describe the heat transfer to the surrounding water. For femtosecond (fs) pulse laser, due to the inexistence of the thermal equilibrium, a two-temperature model (TTM) is used to describe the heat transfer processes occurring in the AuNS and the normal heat diffusion equation is used for the heat flux calculation at the particle/water interface. For each case, the influence of laser intensity on the maximum temperature reached at the particle/water interface is studied. The aim of this study is to provide a description for the fundamentals of heat release of AuNSs and useful insights for the development of these particles for biomedical applications such as drug delivery, photothermal cancer therapy and optoporation of cells. Ó 2015 Elsevier Ltd. All rights reserved.

1. Introduction Gold nanoparticles (AuNPs) are well known for their capabilities to support localized surface plasmon resonance (LSPR) due to collective and coherent oscillations of free electrons at the surface of the particle. In resonance with an external electromagnetic wave, occurring at a specific wavelength range, the AuNPs show unique optical and thermal properties [1,2]. Illumination of the AuNPs at or close to LSPR wavelength results in a near field enhancement, scattering and conversion of absorbed light energy to heat [3]. In addition, the surface of AuNPs can be routinely functionalized with active ligands, monoclonal antibodies and thiolated molecules due to the strong Au-S bond [4,5]. These novel properties of AuNPs provide a highly localized functional and multifunctional platform in biomedical applications, particularly in photothermal therapy, optoporation of cells and selective or targeted drug delivery. At low temperatures, this process can be exploited for thermally induced release of drugs attached to AuNPs, which allows precise, on-demand delivery into the intracellular environment [6–8]. However, at higher temperature, AuNPs ⇑ Corresponding author. E-mail address: [email protected] (M. Meunier). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2015.05.071 0017-9310/Ó 2015 Elsevier Ltd. All rights reserved.

temperature raises killing tumour cells that can be furfure exploited for cancer therapy [9–13]. Among all AuNPs, the ultra-thin hollow gold nanoshells (AuNSs) exhibits a unique combination of small size, strong, narrow and tunable absorption band in the near infrared (NIR) tissue window (wavelength: 700–900 nm). These particles consist of a spherical gold shell filled with its embedding aqueous medium [14]. For biomedical applications, smaller size (outer diameter, 30–50 nm) allows prolonged blood circulation time and better chance in crossing the tumour vessel wall. The strong and tunable absorption band in NIR regime enables a large penetration depth, even at low laser intensities, that ranges from a few millimeters to several centimeters depending on tissue type [15–17]. The hollow core allows higher drug loading capacity, easier synthesis, and the pure gold composition reduces toxicity [18,19]. AuNSs are usually synthesized using cobalt (Co) nanoparticles as sacrificial templates, the gold shells being grown via a galvanic reaction with Au ions [14,19–21]. Photothermal response of AuNSs strongly depends on the irradiation regime (CW, ns and fs) that can be selected based on the requirement of a specific biological application. For instance, irradiation of AuNSs by a CW laser is best suited for applications that

A. Hatef et al. / International Journal of Heat and Mass Transfer 89 (2015) 866–871

require an enduring, moderate increase in temperature, such as hyperthermia and photothermal release of molecules. In this case, AuNSs dissipate the absorbed energy into their surrounding environment without a substantial increase of their temperature [22,23]. Some applications such as photoacoustic imaging of cells and gene silencing by transfection, necessitate a much higher energy density in the vicinity of the AuNSs [24]. Further reducing of the pulse width up to fs regime enables a very high-localized temperature increase, more efficient energy deposition allowing the cleavage of bonds to link molecules to the AuNS surface [25]. In recent years, there has been few research interests to advance fundamental understanding of plasmon-assisted photothermal phenomena around AuNS [26,27]. The main objective of this paper is to investigate the spatiotemporal photothermal response of the most common size of AuNS (40 nm diameter and 3 nm shell thickness) for biomedical applications [28]. The particle is irradiated by CW, ns and fs laser pulses in water medium at a wavelength of 800 nm where scattering in biological tissue is very low. It has been found that such a AuNS around this size anneals into solid particles within hours at 523 K [29], therefore, we restrict the maximum temperature increase calculation to be in the same range. For each irradiation regime we show the maximum temperature increase dependency and rate to laser intensity. It is worth to mention here that although we performed the calculations for a particular sized AuNS, however, upon request the developed tools are capable of doing the same calculation for any metallic configuration and shape. 2. Methods The modeled system consists of AuNS with water core of radius of 17 nm and a gold layer with a thickness of 3 nm. The AuNS is immersed in water since this medium has proven to be adequate for the modeling of laser processes occurring in a cellular medium. The time-dependent distribution of the electromagnetic field and thermal response of the AuNS is modeled by a system of partial differential equations (PDE). The system is solved in three-dimensional (3D) using the finite element method (FEM) provided by the commercial software COMSOL 4.3 (www.comsol.com). 2.1. Electromagnetic field distribution Assuming time-harmonic electric field, the electric field distriEðr; tÞ is computed using the Helmholtz equation [13]: bution ~

2 ~ r ðl1 r r EÞ k0 er j

r ~ E¼0 xe0

ð1Þ

where er is relative permittivity. For gold shell this quantity is a complex, frequency dependant number and interpolated from Johnson and Christy [30]. For water er is set to be 1.77. The relative permeability lr is taken as unity and k0 is the wave number. The other parameters in Eq. (1) are given in the reference [13]. This equation is solved in a spherical domain 10 times larger than the AuNS with an outer perfectly matched layers (PML) shell and a scattering type boundary condition that emulates an infinite domain. Assuming a non-dissipative host medium, the absorbed and scattered energies by the AuNS are obtained as [31]:

Q scat ¼

Q abs ¼

1 Re 2 1 Re 2

ZZ

ZZ

~ ~scat ~ Escat H nds

ð2-aÞ

s

~ ~tot ~ Etot H nds

surface of the AuNS. The absorption, scattering and extinction cross-section are defined as rabs ¼ Q abs =I0 , rscatt ¼ Q scatt =I0 and

rext ¼ rabs þ rscatt , respectively. Here, I0 ¼ ð1=2Þe0 nw E20 represents the intensity of the incident laser beam of amplitude E0 in the surrounding medium. 2.2. Thermal evolution The equation governs the thermal evolution of the AuNS and surrounding water strongly depends on the irradiation time-regime. Comparison the pulse laser time width to the electron-lattice thermalization time 0.5–1 ps [32] plays a key role to choose thermal evolutional equations. For CW irradiation and ns pulses, the pulse width is much longer than electron-lattice thermalization time, therefore, the gold electrons and lattice are heated in relative equilibrium. In this case the AuNS and water temperature evolution are calculated from the usual heat diffusion equation [33]:

qðrÞcðrÞ

~ represent the electric and magnetic field vectors, E and H where ~ respectively. ~ n is an outward-pointing unit vector normal to the

@Tðr; tÞ ¼ r ðkðrÞrTðr; tÞÞ þ Q ðr; tÞ; @t

ð3Þ

in above equation, T(r, t) is the local temperature, r is the position with the origin fixed at the particle center and t is the time. Three material parameters: cðrÞ; qðrÞ and kðrÞ are the heat capacity, mass density and thermal conductivity, respectively. jðr; tÞ ~ Q ðr; tÞ ¼ h~ Eðr; tÞi is the local heat generation density resultt

jðr; tÞ in the shell. In the case ing from the electric current density ~ of pulse laser, the local field intensity calculated in Eq. (1) is modulated by the Gaussian time profile of the incident laser pulse. The intensity of the ns and fs pulse lasers are modeled by a Gaussian curve, as following:

FL ½t t 0 2 IðtÞ ¼ pffiffiffiffiffiffiffi exp 2t 2r 2pt r

! ð4Þ

pffiffiffiffiffiffiffiffiffiffiffiffi in the above equation, t r ¼ t l =2 2 ln 2 is the pulse width, where tl is the laser pulse width defined as the full with at half maximum of the Gaussian temporal profile, t0 is the position of the center of the peak and FL is the incident laser energy density (fluence). Absorption of radiation in the core and in the surrounding medium is neglected. In our calculations, the following thermal characteristics of water and gold are used: cw = 4182 J kg1 K1, qw = 103 kg m3, kw = 0.6 W K1 m1, cAu = 130 J kg1 K1, qAu = 19.3 103 kg m3 and kAu = 300 W K1 m1. To study fs pulsed laser and AuNS interaction mechanisms, we consider the case where tl is much smaller than the characteristic time constants of the transient non-equilibrium photothermal effects. These characters are electron–lattice interactions and phonon–phonon interactions at the surface of the particle. For this time regime the TTM can be used in which the electrons and lattice remain at different temperatures (Te and Tl). This is due to the fact that the heat conduction in the lattice is small compared to that in the electrons. Also the electron relaxation time is shorter than tens of fs for gold. In the water, considering laser fluences well below the optical breakdown, direct absorption is neglected and the usual one temperature heat diffusion equation applies. However, because of the phonon mismatch factor, discontinuity between the water and shell temperature appears at the interface. We solve the following set of thermal evolutional equations for the electrons and the lattice for AuNS and water [34]:

ð2-bÞ

s

867

C e ðT e Þ

@T e ðr; tÞ ¼ r ðke rTðr; tÞÞ G ½T e ðr; tÞ T l ðr; tÞ þ SðtÞ @t ð5-aÞ

868


C l ðT l Þ

@T l ðr; tÞ ¼ r ðkl rT l ðr; tÞÞ þ G ½T e ðr; tÞ T l ðr; tÞ F @t

2

ð5-cÞ

in above equations, Te, Tl and Tm are the time dependent temperatures of the electrons, lattice and surrounding medium, respectively. c is the heat capacity (ce, electronic; cl, lattice and cm, medium heat capacity) and k is the thermal conductivity. The second term on the right hand side in (5-a) and (5-b) describes the energy exchange from the electrons to the lattice via electron–phonon coupling with a coefficient G. The thermal conductance G = 2 1016 W/m3K [32] relates the temperature drop at an interface to the heat flux crossing the interface and constitutes the coupling parameter between a particle and surrounding medium energy equations. The term S(t) in Eq. (5-a) is the absorbed laser energy. Also, the F term in Eqs. (5-b) and (5-c) describes the heat transfer across the interface between AuNS and surrounding which is defined as [34]: 3

F¼

3hr 2 ½T l ðr; tÞ T m ðr; tÞ r31 Þ

ðr32

Cross section (nm2×104)

ð5-bÞ @T ðr; tÞ qm ðrÞcm ðrÞ m ¼ r ðkm rT m ðr; tÞÞ þ F; @t

Absorption Scattering Extiction

1.8 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 600

650

700 750 Wavelength (nm)

800

850

Fig. 1. FEM calculation of scattering, absorption and extinction cross sections for a 40 nm diameter AuNS with a 3 nm thick shell as a function of the incident laser wavelength. The maximum energy absorption occurs at kmax = 715 nm. Inset shows cross-section of the near-field enhancement distribution in and around an AuNS at off-resonance wavelength k = 800 nm. The color legend on the right shows the magnitude of the field enhancement.

ð6Þ

here, h is called interfacial thermal conductance and is the fitting parameter for the cooling process of AuNS in aqueous solutions. Its value is 105 106 Wm2K1 [35]. Here kl = 0.001 kAu, ke = kAu, ce = 70 Te and cl = 3 106 J m3 K1 [36]. r2 and r1 are the outer and inner shell radius, respectively. It is worth to mention that in the previous studies on fs laser-AuNP interaction [37], AuNP is treated as a point absorber by considering kl DTl 0 and ke DTe 0 in Eqs. (5-a) and (5-b). Neglecting these two terms causes a nonuniform temperature distribution at the surface of the AuNP. However, in our calculations, we considered these two terms and removed this approximation. This study focuses on irradiation conditions leading to moderate temperature increase of the medium surrounding the particle. This regime corresponds to temperature increases that lead to significant cell membrane damage (55 K) [38]. Being significantly lower than the annealing temperature of AuNS into solid AuNPs (523 K [29]), evaporation or fragmentation of the AuNS is very unlikely and is neglected in the modeling. In addition, temperature reached in the aqueous medium remains well below the water critical temperature (647 K). Hence cavitation resulting from phase explosion or explosive boiling is neglected. 3. Results and discussion Fig. 1 shows the AuNS absorption, extinction and scattering cross-sections as a function of wavelength. Absorption is dominant, with a maximum value (rabs = 1.53 104 nm2) occurring at the resonance wavelength of 715 nm (kmax). The off resonant wavelength (k = 800 nm) lies on the middle of minimum absorption window in water where the penetration depth of the incident laser field is at its maximum value. Therefore, our results can be more useful especially for biological application where one can consider the biological tissue and environment as water [39]. Please note that for off resonant wavelength the AuNS absorption cross section (rabs = 1.53 104 nm2) is around 24 times less than the on resonant wavelength case (rabs = 6.4 102 nm2 at k = 715 nm). In result irradiating the AuNS at this off resonant wavelength avoids overheating and damaging the particle. Also the thermal energy deposition in AuNS is a linear process, therefore one can easily use the results here in the case of off resonant wavelength as well. From practical point of view this wavelength is one of the most common and stable one

for Ti:sapphire femtosecond laser. The inset in Fig. 1 shows near-field enhancement when a linearly polarized laser irradiates the particle. The color legend on the right shows the magnitude of the field enhancement (|E|/|E0|). As shown in the inset, although the incident laser field has an off-resonance wavelength, near-field enhancement still occurs in a region 20 nm wide around the structure and a significant portion of the electromagnetic energy is absorbed in the gold shell.

3.1. Continuous wave laser illumination The most trivial phenomenon occurs following the CW laser irradiation is the heating of the AuNS and the subsequent heat transfer to the water by a simple conduction process at the surface. For this case, the time taken by the system to reach equilibrium depends on the thermal conductivity and the thermal capacity of the surrounding medium. However, for AuNS in water, the thermal energy generated inside the particle dissipates through the water within several nanoseconds [22]. We also performed calculations on the time evolution of the temperature increase of the AuNS and the dependency of the evolution on the incident CW laser beam intensity. The results show that for all intensities, the time required to reach 90% of maximum temperature increase is about 100 ns. In Fig. 2 we show maximum temperature increase at the AuNS/water interface as a function of laser intensity. The rate of this maximum temperature increase is 32.5 K cm2/MW. The inset shows the steady-state radial temperature increase in and around the AuNS. Knowledge of the heat affected zone and space-dependent temperature increase is important because in practice the AuNSs are functionalized by chemical or biochemical materials (e.g. antibody, antigen or ligand) and they may not be attached directly to the biological systems like cell membrane, and temperature reached inside the AuNS alone might not be relevant [40]. The temperature inside the AuNS is spatially uniform due to the high thermal conductivity of gold and small shell volume. The maximal temperature increase varies linearly with the field intensity. Typically, the temperature increase is shown to drop to 10% of its maximum value at 200 nm from the AuNS center, enabling possible long-range interactions inside biological systems.

869


250

200

180 160 140 120 100 80 60 40 20 0

temperature varies linearly with the fluence, with a slope of 3.4 K cm2/mJ. The upper inset shows the time evolution of the temperature increase on the shell’s outer surface when irradiated with a single pulse with FL = 20 mJ/cm2. The laser peak intensity is I = 3.75 MW/cm2. The maximum temperature increase DTmax = 68 K is shown to occur 1 ns after the peak intensity.

I = 5 MW/cm2

0

50

100

150

200

3.3. Femtosecond pulse laser illumination

Distance (nm)

150

100

Slope=32.5 Kcm2/MW

50

0 0

1

2

3

4

5

6

7

8

9

Laser Intensity (MW/cm2) Fig. 2. Maximum temperatures increase at the surface of AuNS embedded in water versus CW incident laser intensity. Inset shows the steady-state distribution of temperature increase as a function of the distance from the AuNS center for intensity of I = 5 MW/cm2.

In this section we study the thermodynamic response of the AuNS to a fs laser pulse. Fig. 4 illustrates the evolution of Te, Tl, and Tm, for a AuNS excited by a 100 fs laser pulse at a wavelength of 800 nm and a laser fluence of 2 mJ/cm2. As mentioned in the method section, the TTM is used to describe the thermal evolution of the system, which neglects the initial nonthermal electron distribution. Due to the smaller electron heat capacity and electron– electron scattering time, the conduction electrons in the shell first absorb the laser energy through the excitation of a plasmon that decays rapidly, leading to a highly energetic electron population. Therefore, Te rises very rapidly and reaches a maximum value

10000

2

(a)

1.8

Te (Electron temperature)

60

3

40

2

20

1

0

0 0

10

20 30 Time (ns)

40

1000

Temperature increase (K)

200

4

50 70

150


Max. temperature increase (K)

250

80

Intensity (MW/cm2)


300

100

50

60

1.4 100

1.2 Tl (Lattice temperature)

1

10

0.8 0.6

50

1

40

0.4

Tm (Medium temperature)

30

0.2

20

8 ns

10

10 ns

0.1

0

Slope=3.4

1.6

Intensity ×104 (MW/cm2)

Temperature Increase (K)

Max. temperature increase (K)

300

0

Kcm2/mJ

10

20

30 40 50 60 Distance (nm)

70

0.1

80

1

10

100

1000

0 10000

Time (ps)

0 40

60

80

100

Laser fluence (mJ/cm2) Fig. 3. Maximum temperature increases variation on the surface of AuNS embedded in water irradiated by a 5 ns laser pulse at 800 nm versus laser fluence. In upper inset the solid and dashed line shows the temperature increase evolution and the pulse intensity, respectively. In lower inset the solid and dashed line shows the temperature increase profile as a function of the radial distance from the particle center on the pulse peak time (8 ns) and 10 ns. For both insets the fluence is 20 mJ/ cm2.

3.2. Nanosecond pulse laser illumination In this case we study the AuNS thermodynamic response when the particle is irradiated by a Gaussian ns laser pulse with a duration tl = 5 ns, centered at time t0 = 8 ns. This pulse width is much longer than the characteristic time constants of the transient non-equilibrium photothermal effects. To calculate the temperature evolution of the particle during and after the interaction with the laser pulse, we numerically solve the heat transfer Eq. (3) [41,42]. Fig. 3 shows how the maximum temperature at the AuNS/water interface varies with the fluence of the incident ns laser pulse. Increasing the energy density of the laser pulse is shown to have no effect on the time required for the particle to reach its maximum temperature. Interestingly, the maximum

350

6000

(b) 300

5000

250

Te (Max. Electron temperature) Slope=1500 Kcm2/mJ

4000

200 3000

Tl (Max. Lattice temperature) Slope=113 Kcm2/mJ

150

2000 100 Tm (Max. Medium temperature) Slope=20 Kcm2/mJ

50

1000

Maximum electron temperature increase (K)

20

Maximum lattice & medium temperature increase (K)

0

0

0 0

0.5

1

1.5

2

2.5

3

Laser fluence (mJ/cm2) Fig. 4. (a) Time dependent temperature evolution of electrons, Te, lattice Tl and water temperature Tm, at the AuNS–water interface, for a laser pulse of 100 fs at wavelength k = 800 nm with a fluence of 2 mJ/cm2. The dotted curve shows the Gaussian intensity profile of the pulse. (b) The maximum temperature increase of (star markers) electrons (Te), (circle markers) lattice (Tl), and (square markers) water (Tm) at the AuNS/water interface for different fluences.

870


Table 1 Comparison the rate of maximum temperature increase in AuNS for CW, ns and fs pulsed laser irradiance. Laser irradiance

Rate

CW Ns pulsed laser Fs pulsed laser

32.5 K cm2/MW 3.4 K cm2/mJ 113 K cm2/mJ

4360 K that happens 325 fs after the pulse peak. Subsequently, the energy deposited into the electronic system is transferred via electron–lattice coupling to the lattice, increasing Tl up to 384 K within 16 ps. Finally, by lattice–lattice interactions, the thermal energy is transferred to the environment as the AuNS and medium reach their equilibrium temperature. Here, Te and Tl reach thermal equilibrium within 20 ps and the AuNS transfers its energy to its surrounding environment within several hundreds of picoseconds (4 ns). Our results show that the time taken by the shell’s electrons and lattice to reach their respective maximal temperature is weakly dependent on the incident fluence, while it remain fixed at Dt = 86 ps in the case of the surrounding water. Fig. 4(b) shows the maximal lattice, electron and water temperature increase as a function of laser fluence. As shown in this figure, the maximum temperature increases linearly with the laser fluence, with slopes Te,max, Tl,max and Tm,max being 1500, 113 and 20 K cm2/mJ, respectively. Note that Te, Tl and Tm reach thermal equilibrium after 4 ns. Here, the fluence required to reach a certain temperature is shown to be significantly lower for fs pulses than for ns laser irradiation. This can be of crucial importance in some biomedical applications, where high laser power can damage living tissues.

4. Conclusion In this paper we presented a numerical framework to study thermodynamic response of hollow gold nanoshells (AuNSs) to a continuous wave (CW), short (ns) and ultra-short (fs) pulse laser irradiation. The AuNSs have a diameter of 40 nm with 3 nm shell thicknesses that is the most common and appropriate size for biomedical applications [28]. Experimentally it has been shown that for such a small size AuNS, if the gold lattice temperature increase is more than 523 K, the particle most probably collapse to a solid particle. Therefore, for all cases we restricted our parameters to avoid over heating the AuNP causing particle fragmentation. In order to respect this restriction, we set an off resonance laser wavelengths for all cases at k = 800 nm. For all cases, we have developed a computational platform based on finite element method for modeling transient and steady state temperature of the nanoshell-environment for different laser parameters. These parameters were the intensity for CW laser and the laser fluence in the case of ns and fs laser pulses. Table 1 compares the rate of maximum temperature increase in AuNS for CW, ns and fs pulsed laser irradiance.

Conflict of interest None declared. Acknowledgment The authors would like to thank Mrs. Alexandra Thibeault-Eybalin for her insights and editing the manuscript, Le Groupe de recherche en sciences et technologies biomédicales

(GRSTB) and Unité de participation et d’initiation à la recherche (UPIR) for financial support.

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