Department of Ecosystem Engineering, The University of Tokushima, Tokushima , Japan bs Supporting Information

Transcription

1 pubs.acs.org/jpcc Improved Working Model for Interpreting the Excitation Wavelength- and Fluence-Dependent Response in Pulsed Laser-Induced Size Reduction of Aqueous Gold Nanoparticles Daniel Werner and Shuichi Hashimoto* Department of Ecosystem Engineering, The University of Tokushima, Tokushima , Japan bs Supporting Information ABSTRACT: We propose a model better describing the pulsed laser-induced size reduction of gold nanoparticles in aqueous solution. A numerical simulation was carried out for energy deposition processes initiated by laser excitation on the basis of the two-temperature model (TTM) of electron temperature T e, lattice temperature T l, and the temperature of the medium surrounding the particle. Further improvement was made by rigorous treatments of electron-phonon dynamics, heat losses, and the optical effect of water bubbles surrounding the nanoparticles due to the temperature rise. The most striking effect was brought about through bubble formation by a nanosecond laser pulse irradiation during which a remarkable decrease in the absorption cross section of gold particles takes place, especially in the spectral region of the surface plasmon resonance band. The calculation allowed the clear classification of two mechanisms (the Coulomb explosion and photothermal mechanisms), and a guideline for examining the mechanistic aspect absent previously was provided presently. To initiate the splitting due to the Coulomb explosion, it is necessary to realize T e high enough to emit electrons thermally while on the other hand the photothermal mechanism is important when T l exceeds the boiling point of gold nanoparticles. For instance, given that the excitation is carried out by a femtosecond laser that allows T e and T l to evolve with time in strong nonequilibrium, fragmentation due to the Coulomb explosion can be observed provided that the laser energy is high enough to raise T e above 7000 K for liquid gold and above 8000 K for solid gold. In contrast, for a nanosecond laser excitation, the time evolution of T e and T l is in quasi-equilibrium during the excitation period. In effect, the photothermal melting-evaporation model prevails regardless of the laser intensity because T l increases steadily to reach the melting and boiling temperatures of gold, leaving T e insufficiently low for the Coulomb explosion to take place. Interestingly, both mechanisms are likely in picosecond laser excitation depending on the laser fluence. The clear classification of the mechanism in terms of T e and T l was made for the first time. By using our guideline, we made an assessment on previous mechanistic arguments. At the same time, excitation wavelength-dependent different fragmentation efficiency was also explained more satisfactorily than before. INTRODUCTION Pulsed laser-induced size reduction of noble metal nanoparticles (NPs) plays a central role in laser ablation-based generation of nanoparticles in solutions 1-5 and thus attracted a great deal of attention from a mechanistic point of view. Two models have been proposed to account for the mechanism of the size reduction: a Coulomb explosion model and photothermal evaporation model. The Coulomb explosion model presumes ejection of quite a number of electrons to generate multiply ionized NPs to undergo spontaneous fission because of the charge repulsion. Kamat and co-workers 6 adopted this model to interpret the 355 nm picosecond laser-induced splitting of silver NPs because they detected hydrated electrons in the transient absorption measurement. Subsequently, Mafune and co-workers observed hydrated electrons on intense nanosecond-pulsed laser excitation of gold NPs in aqueous sodium dodecyl sulfate (SDS). 7,8 Their results indicated higher size reduction efficiencies for 355 nm irradiation than for the excitation of the surface plasmon resonance (SPR) band of the gold NPs. The observed high efficiency was explained by interband electronic excitationrelaxation cycles that enable a faster absorption of a new photon than the conduction band electrons can absorb. Furthermore, they detected positively charged gold ions by applying a mass spectrometry and proposed that the thermionic emission of electrons due to interband excitation is responsible for the highly efficient splitting of gold NPs. 9,10 Meanwhile, Koda and co-workers 11 introduced the photothermal evaporation concept based on the classical thermodynamics for the observation of a size reduction of chemically Special Issue: Laser Ablation and Nanoparticle Generation in Liquids Received: September 28, 2010 Revised: November 24, 2010 Published: December 20, 2010 r 2010 American Chemical Society 5063 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

2 prepared aqueous gold NPs with sizes ranging from 19 to 47 nm diameters by exposure of the SPR band to various intensities and numbers of a 532 nm nanosecond pulsed-laser beam. In support of Koda's photothermal mechanism, Inasawa and co-workers 12 conducted further detailed research through the use of a 355 nm picosecond laser and revealed that the size reduction of average 25 nm ellipsoidal gold NPs takes place by a layer-by-layer mechanism on the basis of the observed bimodal distribution of particle sizes of slightly smaller and much smaller than the original ones. They concluded that irradiation by the picosecond laser pulses is the most efficient way to induce the size reduction over femtosecond or nanosecond pulses. Later, Pyatenko 13 made a calculation to examine the melting and size reduction of gold and silver NPs and concluded that the photothermal mechanism prevails at low laser intensities. He also drew a conclusion that the excitation of the SPR band of gold by a nanosecond laser at 532 nm is more efficient because of a greater absorption cross section C λ abs than that at other wavelengths of 1064 or 355 nm but gave no experimental proofs. More recently, Giammanco and co-workers developed a theoretical analysis based on the two temperature model (TTM) to explain the fragmentation of gold NPs by picosecond laser irradiation. 14 They excited rather small gold NPs with an average diameter of 3.5 nm stabilized with PAMAM-G5 in water. They concluded by fitting their experimental data with the theoretical analysis that the evaporation of the NPs does not play a relevant role compared to the Coulomb explosion resulting from thermionic electron emission and photoelectric effect. The photothermal and Coulomb explosion mechanisms have been investigated independently and hitherto no unified concepts have been developed to distinguish the two mechanisms. For instance, it is not clear under what conditions of pulse width and laser energy one mechanism surpasses the other. In the Coulomb explosion mechanism, the electron dynamics that govern various relaxation processes including electron emission plays a major role on electronic excitation. In contrast, in the photothermal evaporation mechanism, surface evaporation is important and determined by the thermal energy deposited into the lattice system resulting in the heating of NPs to the evaporation point depending on the evaporation pressure of the material. Until now, precise theoretical calculations were lacking in the literature to determine the thresholds for surface evaporation and Coulomb explosion, especially for nanosecond pulsed-laser excitation of NPs. Recently we have carried out the experimental study of nanosecond laser-induced transformation of aqueous 55 and 20 nm gold NPs at low laser intensities to determine the onset energy of fragmentation dependent on excitation laser wavelengths. 15 Notably, we employed pseudospherical particles with a narrow size distribution to eliminate the effect of inhomogeneous spectral broadening due to polydispersity. The narrow size distribution guarantees a feasible estimation of absorbed energies by the particles at each excitation wavelength on the basis of Mie theory calculations. 16 We observed a greater efficiency of melting and evaporation on excitation of interband transition than that observed for the excitation of SPR band or intraband transition, contrary to Pyatenko's calculation. 13 Analysis of the experimental results on the basis of a classical thermodynamic model revealed that the origin of the greater efficiency of the interband excitation is ascribed to a reduced heat capacity, C p, when the assignment was made of the observed two-step size reduction behavior to the onset of melting and evaporation of gold. But later, we realized that the model needs a few improvements such as the optical effect of vapor bubble formation due to heating-induced evaporation of water adjacent to the gold NPs and the dynamic depression of the SPR band during the excitation The present report describes an improved thermodynamic model developed on the basis of the TTM calculation. The TTM model has been applied successfully to the investigations on the electron and lattice dynamics of metal NPs in femtosecond laser spectroscopy 27,28 as well as on the T e and T l of metal plates or thin films in laser ablation. 29,30 In the model, the deposition of laser energy into the electron and lattice subsystems is described by two temperatures, electron temperature T e and lattice temperature T l, to determine the energy distribution inside the system. Previous TTM-based models have a drawback because they considered only the free electron gas (FEG) model with its parabolic electron density of states (EDOS) and replaced the T e - dependent chemical potential (μ) in the Fermi distribution by a constant value of Fermi energy (E F ). 31,32 Additionally, the value of an electron-phonon coupling term, g, was usually assumed as a constant. All these simplifications are applicable only for electron temperatures below 2500 K. 33 Above this temperature, the FEG model description deviates appreciably from realistic metals. Thus, we took care of real EDOS calculated by VASP (Vienna ab initio simulation program) and the Fermi distribution, as well as lattice expansion, phase transformation, and heat diffusion to the surrounding water with consideration of interface heat conduction from the NP surface to water. An additional point deserves commenting is the formation of vapor bubbles due to the explosive evaporation of surrounding liquid Surprisingly, the effect of bubble formation on the nanosecond pulsed laser fragmentation study of metal NPs has been totally ignored This is serious because the refractive index of the medium decreases dramatically from the value of a liquid phase depending on the temperature and pressure, affecting enormously the absorption cross section of the metal NPs within the duration of excitation pulse. This means that the absorption of the NP cannot be assumed as a constant as before but is subject to dynamic changes during the time lapse of excitation. The present result indicated that the Coulomb explosion and photothermal mechanisms in the laser-induced fragmentation of gold NPs are in most cases classified by the pulse duration and energy relative to the particle size. We gave a guideline to this classification that is applicable to previous experimental studies. Our method can be useful to predict the mechanism not only in the laser fragmentation studies but also in laser ablation-based NP production. ANALYTICAL METHOD The energy deposition process resulting from metal NP-laser interaction can be described by the following three stages. First, the laser light is absorbed by the electronic system, promoting electrons from lower-lying levels to upper levels and occasionally to the continuum state. Then, after a few hundreds of femtoseconds, a thermal equilibrium is reached obeying the Fermi distribution as a result of electron-electron scattering and then the electron energy is transferred to the lattice via electronphonon coupling. Finally, the lattice energy is given to the surrounding liquid, resulting in the cooling of the NP. The present analytical method is described in the following four parts. 1. Absorbed Laser Energy Dependent on Optical Properties of Gold NPs. A laser energy, S [W 3 m -3 ], absorbed by the unit volume of a spherical particle of radius R [m] with a Mie absorption cross section of C λ abs [m 2 ] in the medium with a 5064 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

3 Figure 1. Absorption cross section curves as a function of wavelength for a 55 nm diameter gold NP in water of various phases: liquid, vapor, and the critical state. Vertical lines in the figure represent the excitation wavelengths of a nanosecond Nd:YAG laser: dashed-dotted line, 532 nm; dashed line, 355 nm; solid line, 266 nm. refractive index of n m is defined by eq 1. SðtÞ ¼ Cλ abs ðn m;rþ 3 PðtÞ V p ðt l Þ ð1þ In this equation, P [W 3 m -2 ] is the laser power dependent on time, t, at the maximum of the spatial Gaussian profile described in eq 2. The volume V p depends on the lattice temperature T l,becauseof the volume expansion in both solid and liquid phases, and C λ abs strongly depends on the refractive index of surrounding medium n m, exciting the laser wavelength and the size of the NPs. The assumption was made because a spatial Gaussian profile for beam diameters of micrometer to millimeter at fwhm is invariant within the absorbing area of a NP. For a pulsed laser, the time profile of the laser power is also described by Gaussian given in eq PðtÞ ¼ 8 3 E pffiffiffiffiffiffiffi! p 3 ln 2 pffiffiffi π 3 3 d 2 3 τ 3 exp 4ðln 2Þt2 - ð2þ p τ 2 p Here, E p is the laser pulse energy [J], d the spatial beam diameter [m], and τ p the pulse duration [s]. In modeling, we employed a numerical code of FORTRAN given by Bohren and Huffmann 16 to calculate the absorption cross section C λ abs, with a modified dielectric function of the metal (see Supporting Information, eq 3), the radius of NP, and the wavelength dependent refractive index of the surrounding liquid as input parameters. The intrinsic size effect 35 that was not considered by Bohren and Huffmann was also included. A calculated extinction spectrum for a 55 nm gold particle applying the Mie theory is in satisfactory agreement with an experimental one not only in the region of the SPR band but also in the wavelength range from 200 to 400 nm corresponding to the interband transition (Supporting Information, Figure S2). The value of C λ abs strongly depends on the refractive index of the surrounding medium and thus can easily undergo alterations as a result of the evaporation of solvents induced by temperature rise within the laser pulse duration. Figure 1 shows the absorption cross section, C λ abs of a 55 nm diameter gold NP as a function of light wavelength in water that is subject to phase changes due to temperature rise. Given that the spectral variation is caused by the change in the physical state of water as depicted in Figure 1, the timedependent change in the solvent state has to be considered in the modeling especially for long laser pulse durations such as Figure 2. Absorption cross section for a 55 nm diameter gold NP as a function of the refractive index of aqueous medium at the laser excitation wavelengths of 532, 355, and 266 nm. The assumption was made that the refractive index of water surrounding the NP is subject to change as a result of phase transformation. nanoseconds during which heating of the solvent takes place. For convenience, the absorption cross section at three excitation wavelengths was plotted as a function of the refractive index of the surrounding medium as given in Figure 2. Inspection of Figure 2 reveals that, at 355 and 532 nm, C λ abs increases with increasing refractive index, while at 266 nm, the absorption cross section stays nearly constant regardless of the refractive index changes. The refractive index of water and water vapor dependent on pressure and temperature has been investigated extensively by Thormaehlen and Schiebener. 36,37 With the increase of temperature and pressure, the refractive index depression takes place from 1.33 of liquid water to 1.07 at the critical point of water (647 K, 22.1 MPa) resulting from the explosive evaporation. For pulse durations longer than the cooling time constant of NP due to the heat transfer to the surrounding water, i.e., several nanoseconds, water molecules surrounding the NP evaporate within the pulse duration. This causes the reduction in the refractive index of the NP, leading to a change in the absorption cross-section C λ abs of the NP (see Figure 1 and Figure 2). This effect has to be taken into consideration in eq 1. The mathematical description for the modified refractive index, n m, due to the phase transformation is given by eq n m ¼ Hn vapor þð1-hþn liquid ð7þ Here, n vapor denotes the refractive index of the vapor, n liquid the refractive index of liquid water, and H the Heaviside step function that varies from 0 to 1 during the evaporation of water in the close vicinity of the NP. 2. Two Temperature Model-Based Description. The laser energy deposited into the metal NP is eventually transformed into heat, leading to a rise of T e, T l, and the temperature of the surrounding medium, T m. The TTM model gives a set of three coupled differential heat equations given in eq 8: C e ðt e Þ T e ¼ k e ðt e ;T l ÞΔT e - gðt e Þ t 3 ½T e - T l ŠþSðtÞ ð8aþ C l ðt l Þ T l t ¼ k l ðt l ÞΔT l þ gðt e Þ 3 ½T e - T l Š - F ð8bþ C m ðt m Þ T m ¼ k m ðt m ÞΔT m þ F ð8cþ t in which C stands for the heat capacity (C e, electronic heat capacity; C l, lattice heat capacity; C m, heat capacity of the medium), k is the 5065 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

4 thermal conductivity, and Δ represents the Laplace operator in the spherical coordinate system as given in eq 8d, ΔT ¼ 1 r 2 r 2 T þ 1 T 1 2 T r r r 2 sin ϑ þ sin ϑ ϑ ϑ r 2 sin 2 ϑ φ 2 ð8dþ In eqs 8a-8c, the basic concept of equation is represented by the heat equation for the electron system (a), lattice system (b), and surroundingmedium(c)ifthetermsafterthefirsttermontherighthand side (RHS) are neglected. The second term on the RHS in (a) and (b) describe the energy exchange from the electron to the lattice system via the electron-phonon coupling with a coefficient, g. Additionally, the term S(t) is the absorbed laser energy given in eq 1, and F stands for an interface energy transfer between the NP and the liquid. For convenience, a couple of simplifications were made. The energy loss through thermal radiation defined by the Stefan- Boltzmann law was neglected in eq 8, because of the very small surface area, A P of the NP and negligible emissivity E M of about 0.1 for pure gold. Thus, the thermal radiation is about times smaller in energy than the heat diffusion to the surrounding water. The NP can be treated as a point absorber where the temperature distribution in space at various times is constant for the entire particle volume. It follows that the approximations, k l (T l )ΔT l 0, and k e (T e,t l )ΔT e 0, are made. Additionally, we can assume that the NP and the surrounding medium is isotropic and thus in eq 8d, the spherical Laplace operator, reduces to ΔT =(1/r 2 )( / r)- (r 2 T/ r). Thus, eq 8 reduces to C e ðt e Þ dt eðtþ ¼ - gðt e Þ dt 3 ½T e - T l ŠþSðtÞ ð9aþ C l ðt l Þ dt lðtþ dt C m T m ðr;tþ t ¼ gðt e Þ 3 ½T e - T l Š - F ¼ k m 1 r 2 r r 2 T mðr;tþ r þ F ð9bþ ð9cþ The heat loss term F has been experimentally determined by Plech and co-workers, 39 and Juve and co-workers. 40 In Plech's work, spherical gold NPs with an average diameter of 100 nm dispersed in aqueous solutions were subjected to excitation with femtosecond pulses and the time dependent volume expansion and contraction were measured with a X-ray scattering technique during the cooling of the NPs through heat loss to the surroundings. They found that the time-dependent cooling curve displays stretched exponential behavior that was interpreted as a discontinued heat transfer at the NP-water interface, in agreement with Hartland's previous work. 41 Moreover, Plech's group introduced a thermal conductance, h, asa fitting parameter for the cooling process of gold NPs in aqueous solutions and obtained a value of Wm -2 K -1,whichis applicable to our gold nanoparticle solutions. 39 It has also been recognized that the cooling time shows parabolic behavior dependent on the particle radius, R. Consequently, eq 10 describes an empirically found energy loss term employed in our thermodynamic model. 39 F ¼ 3h RðT l Þ ½T l - T m ðrþš ð10þ Here, T m (R) describes the maximum water temperature at the NPwater interface. Note, however, that T m (R) does not necessarily mean thewatertemperatureonthenpsurfacebecausethedescriptionof the temperature based upon the classical thermodynamics is difficult in the molecular dimensions. Instead, it is considered that the NPwater interface builds a layer of a few nanometers surrounding the NP surface with an average temperature defined by T m (R). Depending on the distance, r, from the NP-water interface, the surrounding water medium gives a temperature distribution according to eq 9c. Such an example is given in the Supporting Information, Figure S11. Plech 42 and co-workers also investigated experimentally the formation of vapor bubbles by probing the environmental water and its structural change with X-rays after the explosive phase transformation and estimated an evaporation temperature that is slightly dependent on the gold NP size but is approximately equal to the critical point of water. Furthermore, they measured the heat diffusion after the bubble formation and found that heat losses are negligibly small. Another important point included in our model is the volume expansion in the solid and liquid phase of gold NPs, due to lattice temperature (T l ) rise. The parameters used for water and gold are given in the Supporting Information, Table S1. We should stress that the electronic heat capacity, C e, and the electron-phonon coupling coefficient, g, need more careful treatments. In previous publications, 13,27,28,43 C e and g were calculated on the basis of the FEG model that gives a linear relationship between C e and T e with a constant value for the electron-phonon coupling coefficient, g, as given in eq C e ¼ γt e γ ¼ 1 3 π2 DðE F Þk B 2 ð11aþ g ¼ π2 m e C s 2 n e ð11bþ 6τ e- ph ðt e ÞT e D(E F ) denotes the FEG density of states at the Fermi level, which is defined by 3n e /2E F, with n e being the electron concentration at the Fermi level and E F the Fermi energy. The parameters, k B, m e *, C s,andτ e-ph are the Boltzmann constant, the effective mass of electron, the sound velocity, and the electron-phonon relaxation time. Lin and co-workers 33 made calculations for C e and g using the real EDOS of several bulk metals by applying eqs 12a and 12b, and compared it with the result of FEG model given in eq 11. Z C e ðt e Þ¼ E f ðe;μðt eþ;t e Þ EDOSðEÞ de ð12aþ T e 0 Z gðt e Þ¼ πpk BλÆω 2 æ EDOSðE F Þ EDOS 2 ðeþ 0 - f ðe;μðt eþ;t e Þ de E ð12bþ where E represents the electronic state energy above the Fermi level, f the Fermi distribution dependent on the chemical potential μ, λ the electron-phonon mass enhancement parameter, and Æω 2 æ the second momentum of the phonon spectrum. Lin's group obtained a nonlinear dependence of C e and g on the electron temperature T e for gold with positively deviated values at temperatures above 2500 K from those obtained by the FEG model. In normal heating processes of metals, temperatures rarely exceed 2500 K and the FEG model usually gives a good agreement with experiments. For pulsed-laser excitation, on the other hand, the heating process of the electrons with a time scale of femtoseconds to picoseconds gives rise to the electron temperatures T e of several thousand Kelvin. Thus, it is important to use the values of C e and g using the equations given by Lin and 5066 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

5 is described by the liquid drop model 7,8,47,48 and depends on the ratio of the square of the number of ejected electrons, N 2 ε, to the total number of free electrons, N e, and the physical properties of the NP material, as given in eq 14. X ¼ N ε 2 N e! = 16πr ws 3 3 σ e 2! ð14þ Figure 3. EDOS of bulk gold (black solid curve on the left) and Fermi distributions (colored curves) at various temperatures: 6000 K (green curve), 8000 K (red curve), K (blue curve) dependent on the energy state of the electron system. The dashed curve shows the Fermi distribution at 0 K as a reference. co-workers. 33 The EDOS of bulk gold and the Fermi distribution at three different temperatures are shown in Figure 3. At 0 K, the Fermi distribution exhibits a sharp edge, where all electronic states below the Fermi level are occupied. If the electron temperature increases to several thousand Kelvin, the Fermi edge is smeared out because electrons below the Fermi energy can occupy levels above E F with lower lying levels with vacancy. 3. Thermionic Emission of Electrons and Rayleigh Instability. The number of electrons, n ε, that exceeds the work function per atom at an electron temperature of T e can be calculated by eq ,32 Z nε ¼ ε EDOSðEÞ f ðe;μðt e Þ;T e Þ de ð13þ where ε donates the energy required to take out electrons from the NP surface, defined by ε = E F þ W, with W the work function of a metal. In the first approximation, photoelectric ejection, where the energy to eject electrons is defined as ε = E F þ W - hυ, is neglected because the probability of the direct electron ejection is difficult to estimate. Grua and co-workers 43 have developed a kinetic model based on electron-phonon and electron-electron collision operators to describe the rate of electron ejection from gold NPs due to the photoelectric and thermionic effects. They found that the probability of photoelectric ejection of hot electrons by excitation with a laser wavelength of 351 nm is negligibly small. Furthermore, it is known that hot electrons cause a depression of the absorption band (SPR band) of the NPs ,27 In other words, hot electrons are blind to incoming photons and thus the direct photoelectric ejection of hot electrons is less likely compared to electrons in their ground state. In reality, the main outcome of the interaction of pulsed-laser with metal NPs is heat generation under the condition of laser power <10 15 W 3 cm -2. At such low laser powers, the occurrence of nonlinear optical (NLO) effects such as multiphoton excitation and self-focusing is unlikely, instead, thermionic emission of electrons takes place. Then, the total number of such electrons are given by N ε = n ε a with a the total atom number in one NP. Given that the energy of the electron system above the Fermi level is high enough to eject a sufficient number of electrons thermally, the NP can be destabilized. The instability of a particle In eq 14, r ws is the Wigner-Seitz radius, σ the surface tension, and e the elementary electric charge. For gold, we obtain a Rayleigh instability factor of X = 0.9(N 2 ε /N e ) in the solid phase and X = 6.8(N 2 ε /N e ) at 1337 K for a liquid drop. Obviously, liquid gold is less stable. This is because the surface tension σ of liquid gold at 1337 K is approximately 7 times smaller than that of the solid. Assuming the fcc (face-centered cubic) structure in which a unit cell contains 4 atoms, the total number of atoms, a, per NP is given by eq 15. a ¼ V p a ð15þ fcc Here, V p is the volume of NP and a fcc is the basic length of the unit cell. For gold, a is equal to N e, because one atom possesses only one valence electron. According to the literature, 31 the free electron density n e is estimated as m -3. More or less the same total atom number is obtained by multiplying n e by V p. It was derived that Rayleigh instability and thus the possibility of NP fragmentation occurs at X values of for metals. 7,8,49 This means that for a 55 nm gold particle, electron temperature T frag e estimated for fragmentation in the liquid phase is 7300 and 8200 K in the solid one. 4. Simulation Procedure. The details of the simulation procedure are given in the Supporting Information. All the simulations were carried out for a 55 nm gold sphere dispersed in water excited by femto-, pico-, and nanosecond laser pulses to distinguish the Coulomb explosion from the surface-evaporation size reduction mechanism dependent on the pulse duration and laser fluence. The simulations have been carried out for single pulse events, because the pulse repetition rate of the lasers applied in our previous experiments is 10 Hz (pulse-to-pulse time duration: 100 ms). We can safely assume that the time required for gold NP to cool to room temperature is much shorter than 100 ms. The primary goal of the simulation is to give an explanation satisfactory for our previous experiments 15 that determined the fragmentation thresholds for 54 ( 7nmdiameter gold NPs by exposing to a nanosecond pulsed laser excitation dependent on both excitation wavelength and laser intensity. Additional examinations were made on previous experiments by other investigators who applied either the melting-evaporation mechanism 11,12,50 or the Coulomb explosion model 8-10 for the interpretation of their results. These comparisons may serve as a check for the validity of our simulation. RESULTS AND DISCUSSION Simulation-Based Prediction of Splitting Mechanism. Figure 4 illustrates the simulated time-dependent curves of T e, T l, and T m for a gold sphere exposed to a 300 fs (fs) laser pulse with a wavelength of 400 nm and a laser fluence of 10 mj 3 cm Inspection of Figure 4 reveals that T e rises instantaneously reaching a maximum value of 8750 K at a time delay of 300 fs relative to the position of the maximum intensity of the Gaussian 5067 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

6 Figure 4. Time dependent temperature evolution of electrons, T e (red dashed curve); lattice, T l (black solid curve); and maximum water temperature T m, at the NP-water interface, (blue dashed-dotted curve) for a 55 nm gold sphere absorbing a laser pulse of 300 fs (fwhm of the Gaussian time profile) at 400 nm and a laser fluence of 10 mj cm -2 (P max = 31.3 GW cm -2 ). The small step in the lattice temperature curve indicates the consumption of the melting enthalpy. Horizontal lines in the figure represent temperatures at which important events take place: T ce (liquid), threshold for the Coulomb explosion in liquid; T bp, boiling point of bulk gold; T mp, melting point of bulk gold; T cp, critical point of water. pulse time profile. Subsequently, the energy deposited into the electronic system is transferred via electron-phonon coupling to the lattice system, leading to a rise of T l up to its maximum of 1770 K within 24 ps. Then, at approximately 50 ps, T e and T l reach their thermal equilibrium and the gold NP starts to cool down in several hundreds of picoseconds through heat dissipation to the surrounding water. The simulation also suggests that the water does not evaporate even after 100 ps because of a slow heating process. Most importantly, the Coulomb explosion mechanism is highly likely when the condition of T e > K is met, because the lattice temperature can never exceed the boiling point of the gold NP at all. On the other hand, the simulation of nanosecond pulsed laser heating of gold NPs results in a quasi-equilibrium between the electron (T e ) and lattice (T l ) temperatures. Figure 5 depicts the time evolution of three temperatures for a 5 ns pulse with a wavelength of 355 nm at a notably different fluence of 28 mj cm -2 (a) and 52 J cm -2 (b). Here, we see the remarkable effect of pulse duration to the temperature dynamics. Both T e and T l increase almost synchronously. For a large particle such as 55 nm diameter gold NP, a weak nonequilibrium occurs between T l and T m due to the long heat dissipation time constant of about 500 ps according to the previous Hartland study. 41 Our calculation predicts that, at delay times of approximately 7 ns at 28 mj cm -2 (a) and 2.4 ns at 52 J cm -2 (b), the water at the NP-water interface is transformed explosively into vapor. Subsequently, the vapor layer expands rapidly to the surroundings and forms a vapor bubble. As a result, the refractive index of water may undergo a jump from the value of the liquid to the vapor value, causing a large reduction in the absorption intensity of the NP (see Figure 1) under the condition of negligible NP cooling. 42 Because of the effect of a bubble surrounding the NP, our calculation suggests a steep rise in T l at the onset of bubble generation. Additionally, the two steps observed in Figure 5 indicate the transformation of the gold NP from solid to liquid and later from liquid to vapor phase, during which no temperature rise occurs while consuming the Figure 5. Temperature versus time curves for electron, T e (red dashed curve), lattice, T l (black solid curve), and maximum water temperature T m at the NP-water interface (blue dashed-dotted curve) for a 55 nm diameter gold particle interacting with a 5 ns laser pulse (fwhm of the Gaussian time profile) at 355 nm, 28 mj cm -2 (P max = 5.26 MW cm -2 ) (a) and 52 J cm -2 (P max = 9.77 GW cm -2 ) (b). The red explosion symbol describes the initiation of vaporization of the surrounding water at the NP-water interface. See the caption of Figure 4 for symbols T bp, T mp, T cp. melting or evaporation enthalpy. Most significantly, electron temperatures of about 7300 to 8200 K to exceed the Rayleigh instability can never be reached before the melting or evaporation of the NP occurs. Consequently, the fragmentation due to the Coulomb explosion is unlikely in the nanosecond laser excitation. In contrast to the above two cases of femtosecond and nanosecond excitation, where a single but different fragmentation mechanism applies, it turned out that a size reduction through both mechanisms is possible depending on the laser fluence in picosecond pulsed-laser heating of gold NPs. Figure 6 shows the evolution of T e, T l, and T m at 18 mj cm -2 (a) and 52 mj cm -2 (b) for the excitation wavelength of 355 nm with a typical pulse duration of 30 ps. In this case, thermal nonequilibrium exists between the maximum T e and T l but to a smaller extent than that observed for femtosecond laser excitation. At a fluence of 18 mj cm -2, the boiling temperature of bulk gold is reached after 96 ps, but the fragmentation temperature T e frag of 7300 K that exceeds the Rayleigh instability limit is not reached. Thus, the evaporation as the possible size reduction mechanism is favored here. By increasing the laser fluence to 52 mj cm -2, T e frag for 55 nm gold particles is exceeded at a delay time of 54 ps, where the lattice temperature is still only about 1900 K. This value is much lower than the evaporation temperature of the gold NP. Accordingly, the fragmentation through the Coulomb explosion is possible, because the Rayleigh instability threshold is reached earlier in 5068 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

7 Figure 6. Temperature curves as a function of time for a 30 ps (fwhm of the Gaussian time profile) pulsed-laser excitation of a 55 nm diameter gold sphere at 355 nm with a laser fluence of 18 mj cm -2 (P max = 0.56 GW cm -2 ) (a) and 52 mj cm -2 (P max = 1.63 GW cm -2 ) (b). The vertical dashed-dotted line shows the time at which the fragmentation temperature, T e frag of 7300 K in liquid phase of the gold NP is reached. See the caption of Figure 4 for symbols T ce, T bp, T mp, T cp. time than the evaporation threshold is reached. In both cases, the water surrounding the NP is still in the liquid phase at the event of fragmentation and no water bubbles are formed. Our simulation-based approach to the pulsed laser heating processes exemplified three typical time scales for the pulse duration of laser τ P, the electron-phonon relaxation time τ e-ph and the phonon-phonon relaxation time τ ph-ph corresponding to the cooling time constant of the lattice to the surrounding medium. The electron-phonon relaxation time τ e-ph of gold NPs is 2-3 ps 20,21 and the phonon-phonon relaxation time constant τ ph-ph has been measured as ps 41 depending on the NP diameter, d (τ ph-ph µ d 2 ). Chichkov and co-workers 29 investigated the heat dissipation and its consequences by pulsed laser ablation of metal surfaces by applying the TTM for the three different pulse durations: τ P, τ e-ph, τ ph-ph (femtosecond pulse), τ e-ph, τ P, τ ph-ph (picosecond pulse), and τ e-ph, τ ph-ph, τ P (nanosecond pulse). Interestingly, these three regimes can be applied to the pulsed laser heating of NPs and thus explain possible fragmentation mechanisms depending on the pulse duration. For femtosecond pulsed-laser excitations in which the condition of τ P < τ e-ph, τ ph-ph is met, the total pulse energy is deposited into the electron system within 300 fs before the electron relaxation takes place through the electronphonon coupling allowing for heating up the lattice. 23 In this instance, the Coulomb explosion is feasible because T e can surpass the fragmentation temperature, T e frag while T l is still below the boiling point of the NP (Figure 4). For picosecond pulsed-laser excitations, τ P is longer than τ e-ph but shorter than τ ph-ph. In this case, energy transfer to the lattice system takes place simultaneously with the absorption of the pulse energy by the electron system. This reduces the total accumulated energy inside the electron system and increases the reservoir of the lattice system. Here, both fragmentation mechanisms are possible depending on the pulse energy, i.e., depending on which of the boiling temperature and T e frag of the gold NP exceeds the threshold earlier in time. Finally, for the pulse durations of several nanoseconds, the condition of τ e-ph, τ ph-ph < τ P is satisfied and a quasi-thermal equilibrium of T e and T l is attained (Figure 5). Under the circumstances, the size reduction of NP through the evaporation mechanism is favored, because the boiling temperature is easily reached while a fragmentation temperature that exceeds the Rayleigh instability limit can never be reached. Applicability to the Previous Experiments. Our previous work experimentally determined the surface melting and evaporation thresholds of aqueous gold NPs of 54 ( 7 nm diameter by applying in situ spectroscopy assisted by TEM measurements. 15 The result indicated a strong photothermal effect on excitation of the interband transition at 266 and 355 nm by a nanosecond pulsed-laser irradiation. For instance, the evaporation onset on irradiation of 266 and 355 nm was derived to be as low as near the melting point of Au of 1337 K when a simple light to heat energy conversion model that assumes the direct conversion of the absorbed laser energy Q given by Q = C λ absi/fv P (C λ abs, absorption cross section at wavelength λ; I, laser fluence; F, the density of bulk gold; V P, particle volume) is applied. Here, the assumption was made that electron-phonon dynamics, heat dissipation to the surrounding water, and C λ abs changes due to bubble formation are all negligible. Also, a Gaussian laser pulse profile was replaced by a square pulse for simplicity. In contrast to the interband excitation, the excitation of the intraband at 532 nm allowed the observation that the NPs start to evaporate at approximately the boiling point of bulk gold. To provide more insight into the discussion of our previous result by resolving the discrepancy of excitation wavelength-dependent thresholds, 52 we applied the present numerical simulation by calculating the maximum electron and lattice temperatures, T e and T l on nanosecond laser excitation. Figure 7 shows the calculated laser fluence-dependent maximum temperatures as a function of laser fluence together with the experimental plots of ΔA, the change of SPR band peak intensity after shots. 15 The latter curves gives the measure of surface melting and evaporation thresholds at three different excitation wavelengths, 532 nm (a), 355 nm (b), and 266 nm (c). TEM observation (Figure 7 in ref 15) clearly demonstrated that concept of the surface melting and evaporation is applicable regardless of the excitation wavelengths. A few TEM images related to Figure 7a are given in the Supporting Information, Figure S10. In the calculation of temperature curves, the refractive index n m change from 1.33 to 1.07 was assumed to take place after the vapor bubble is formed due to explosive boiling at the critical point during the excitation pulse duration. Although a straight temperature rise is expected in the absence of the heat loss to the surrounding water below the melting point, the present calculation gave a nonlinear temperature rise with a small step. The explanation for this is as follows. At the initial low laser intensities, the temperature of water cannot reach the explosive evaporation point to form cavities around the gold NPs within the pulse duration of 5 ns. With increasing laser intensity, the heat losses to the surroundings become more and 5069 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

8 Figure 7. Laser fluence dependent temperature evolution of T e (red dashed line) and T l (black solid line) for a 55 nm aqueous gold NP (scale on the right side) together with the experimental plots of ΔA, the change of SPR band peak intensity after shots vs laser fluence (scale on the left side) on excitation at 532 nm (a), 355 nm (b), and 266 nm (c) (ΔA data from ref 15). The refractive index of the environmental water was assumed to undergo change to n = 1.07 (at the critical point of water) due to explosive bubble formation during the 5 ns laser pulse. The vertical dashed-dotted lines indicate the experimentally determined surface melting and NP fragmentation thresholds. In (b), the dashed-dotted line for surface melting is missing, because of insufficient data points at small laser fluences. The two steps within the temperature curves of the lattice T l (black solid line) show the mp (1337 K) and bp (3129 K) of bulk gold. The temperatures remain constant while the enthalpies are consumed. more negligible because of the bubble formation during the pulse and the temperature rise is greater than that of the initial part until reaching the melting point. The calculation also suggests that T e and T l are in quasi-thermal equilibrium, and the surface evaporation mechanism is more favored than the Coulomb explosion. On excitation at 266 and 355 nm, the experimental size reduction threshold takes place at about K, which is below the boiling point. This suggests the occurrence of a surface evaporation of the NPs. Given that gold atoms on the surface have binding energies smaller than those inside the particle, the melting and evaporation of the surface atoms can take place at temperatures lower than those of bulk gold. Additionally, the vapor pressure of NPs should be increased due to curvature effect according to the Kelvin equation, which leads also to a surface evaporation slightly below the boiling point. On the other hand, on excitation at 532 nm, experimentally determined melting and evaporation thresholds of the gold NPs are both above the boiling point of bulk gold. The difference from the 266 and 355 nm results can be explained by the SPR bleaching dependent on the electron temperature T e At this moment, we cannot take this effect into our model because of a difficulty in deriving equations. If we take this additional reduction of the C λ abs at 532 nm into consideration, we expect that the melting and evaporation thresholds are similar to those for excitation at 266 and 355 nm. Furthermore, comparison of Figure 7a-c reveals that the laser fluence necessary for melting and evaporation of the gold NPs is smaller at 266 and 355 nm than at 532 nm. This has no correlation with the absorption cross section of gold NP in water assumed in previous calculations. 13,15 Alternatively, the higher size reduction efficiency can now be clearly explained by the strong reduction of the absorption intensity of the SPR band due to a decreased refractive index induced by bubble formation (see Figures 1 and 2). Additionally, good agreement was obtained for the estimation of the evaporation threshold for 20 nm gold particles (see Supporting Information, Figure S7). As a next step, we examined the temperature evolution of laser splitting for two cases to test the applicability of our simulation method further. One is by Mafune's group who discussed their experimental observation 7-10 in favor of the Coulomb explosion mechanism, and the other is by Inasawa and co-workers who made an analysis assuming a photothermal surface evaporation model for fragmentation. 50 The result of our calculation for Mafune group's 10 nm diameter Au particles on irradiation of a 355 nm pulse with a 10 ns pulse duration at 283 J cm -2 (P max = 26.6 GW cm -2 ), assuming a focal point of 150 μm, was given in the Supporting Information, Figure S3. The time evolution of T e, T l, and T m displayed a trend similar to that already shown in Figure 5b in spite of a different pulse width and particle diameter. Inspection of Figure S3 (Supporting Information) reveals that 5070 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,

9 lattice temperature T l reaches its maximum value at a delay of 84 ps, well before the explosive evaporation of the surrounding water takes place (see Supporting Information, Figure S4). Figure 8. ΔA peak (black solid circles) at 635 nm as a function of laser fluence according to Inasawa group's data (ref 50) and temperature curves calculated by us for T e (red dashed curve) and T l (black solid curve) under their experimental conditions. The horizontal dasheddotted line shows the electron temperature of 7300 K where the Coulomb explosion can take place and the vertical dotted line indicates the laser fluence at which the lattice temperature T l reaches the boiling point (3129 K) of bulk gold. The two steps in the temperature curves of the lattice T l (black solid line) show the mp (1337 K) and bp (3129 K) of bulk gold. temperatures T e, T l, and T m exhibit quasi-thermal equilibrium, as shown in Figure 5. According to our simulations for nanosecond pulsed lasers, we can conclude that no fragmentation due to the Coulomb explosion is observable. The total number of electrons ejected only through thermionic emission in this case is calculated to be 2-3, which is significantly smaller than the total number of ejected electrons, q cr,of37-67 necessary for exceeding the Rayleigh instability in 10 nm liquid gold NPs. This is because the maximum electron temperature attained in the calculation is insufficiently low to release an adequate number of electrons. On the other hand, the maximum pulse power P max applied in their experiment might already reach the threshold of two-photon processes for 10 nm gold particles and thus a direct electron ejection through the photoelectric effect could emit electrons enough to exceed Rayleigh instability before the temperature of the NP reaches the evaporation point. For Inasawa group's experiments, our simulation gave a result that is in support of their layer-by-layer surface evaporation mechanism. 50 They excited 36 nm gold NPs in aqueous solution with a single pulse (30 ps, 355 nm) and detected the change of the absorbance ΔA at two different wavelengths (488, 635 nm) with nanosecond time resolution. Dependent on the pulse energy, two different signals have been observed, a strong spike-like positive peak ΔA peak with a lifetime of less than 10 ns and a reduced signal ΔA base that did not recover to the zero absorption level after 300 ns. Figure 8 shows the plots of laser fluence dependent ΔA peak signals measured by Inasawa and co-workers 50 along with T e and T l calculated with our model. The rise in the ΔA peak signal was observed at a laser fluence of 18.5 mj cm -2 (P max = 0.57 GW cm -2 ) that gives a calculated maximum lattice temperature T l equivalent to the boiling point of bulk gold (3129 K). TEM observation showed the initiation of size reduction at laser fluences >18.5 mj cm -2. The temperature curves show that a thermal nonequilibrium exists between the maximum T e and T l. The maximum electron temperature T e at the expected fragmentation threshold is about 6000 K, which is 1300 K smaller than the estimated fragmentation temperature T e frag and the surface evaporation mechanism is favored. Vapor bubble formation has no influence on this process because the CONCLUSION In this study, we developed an improved thermodynamic model for interpreting the size reduction of gold NPs by taking the following physical processes: heat dissipation, bubble formation, and electron-phonon dynamics into simulation. Our model calculation is powerful enough to distinguish the Coulomb explosion and photothermal evaporation mechanisms. Previously, these two mechanisms were developed without unified concept to distinguish. The present calculation for pulsed-laser excitation of 55 nm gold particles in aqueous solution demonstrated that the fragmentation mechanism strongly depends on the pulse duration. For femtosecond laser excitation at 400 nm, the fragmentation mechanism is totally explained by the Coulomb explosion while, in marked contrast, 355 nm nanosecond pulsed laser heating of gold NPs results in entirely photothermal evaporation mechanism. Interestingly, both mechanisms can take place in picosecond laser excitation depending on the laser fluence. This clear classification was made for the first time. Another important issue, a clue to which was found in this study, is the excitation wavelength dependent efficiency of size reduction by the nanosecond pulsed-laser irradiation. A higher size reduction efficiency observed by the interband excitation of gold NPs in our previous work 15 can now be explained by the strong reduction in the absorption efficiency of the SPR band. While the interband absorption intensity remains almost constant for the 55 nm particles, the refractive index change causes a significant reduction of the absorption cross section C λ abs for the SPR band due to the bubble formation. The remarkable effect of bubble formation on the absorption behavior has not been considered in laser-induced size reduction experiments until now. Previously, it was thought that nanosecond pulsed laser fragmentation of gold NPs at 532 nm exciting the SPR band is the most efficient way because of a high absorption cross section C λ abs. 13 This is actually not true. Our results demonstrated that the previous simple light to heat energy conversion model to estimate the NP temperature fails to explain gold NP heating by the nanosecond pulsed laser excitation of inter- and intraband transitions. Finally, we made an assessment on previous mechanistic arguments. Our model is in good agreement with a conclusion of the photothermal mechanism drawn by Inasawa's group 12,50 to interpret their experiment by applying a picosecond UV pulsed laser as well as with Koda group's previous investigation 11 on 532 nm nanosecond pulsed laser size reduction of gold NPs (Supporting Information, Figure S5). On the other hand, our conclusion of the photothermal mechanism regardless of pulse energy for the nanosecond excitation is in conflict with a view given by Mafune's group who concluded that their nanosecond results are explainable by applying the Coulomb explosion mechanism through thermionic emission of electrons. 9,10 ASSOCIATED CONTENT b S Supporting Information. Description of optical properties of gold nanoparticles, numerical simulation method, figures showing UV-vis spectrum of 55 nm diameter aqueous gold particles in comparison with the calculated spectrum by Mie 5071 dx.doi.org/ /jp109255g J. Phys. Chem. C 2011, 115,