Supporting Information. Optically Induced Structural Instability in Gold- Silica Nanostructures: A Case Study

Transcription

1 Supporting Information Optically Induced Structural Instability in Gold- Silica Nanostructures: A Case Study Rijil Thomas, Sivaramapanicker Sreejith,*, Hrishikesh Joshi, Srikanth Pedireddy, Mihaiela Corina Stuparu,, Yanli Zhao,*,, and Soh Cheong Boon*, School of Electrical and Electronic Engineering and School of Materials Science and Engineering, Nanyang Technological University, 50 Nanyang Avenue Singapore , Singapore. Division of Chemistry and Biological Chemistry, School of Physical and Mathematical Sciences Nanyang Technological University, 21 Nanyang Link, Singapore , Singapore. S1

2 S1. Temperature Dependent Variables S1.1 General Following are the possible temperature dependency of variables during 526 nm laser excitation: Figure S1. Illustration of the mutually dependent variables (each variable elaborate below). The one sided solid arrow and dotted lines denotes the cyclic negative effect and equivalence points respectively. Double sided solid arrow indicates non-monotonic relation. The first relation of temperature T with size R s (radius) is derived from temperature rise assisted thermal expansion. This increase in R s (expansion) negatively affects both heat relaxation τ r (B from eq E12, when including the effect of density change with size) and the temperature rise (eq E14) with a cyclic feedback as shown in Figure S1 and tends to attain a stable state. S2

3 The second relation comes from thermal expansion as explained in eq E16 and eq E17 which has an overall positive effect on thermal stress at the interface. Here β Au is the temperature dependent expansion coefficient of gold and ε is the thermal strain, the relative change in size of the particle. The third relation derives the temperature dependence of refractive index of silica n silica whereby the refractive index of fused silica was reported to increase with temperature. However, the expected change in refractive index of silica near 1000 K is < 1% [SR1,SR2]. Additionally, absorption coefficient α abs of AuNP for 526 nm excitation increases when a temperature dependent variation of local refractive index of silica occurs. The rise in α abs with n silica is shown in the Figure S2 which was computed using the following equation [SR3]: α p = 4π(R s + d) 3 (ε s ε m )(ε c + 2ε s )+ R s Rs+d 3 (ε c ε s )(ε m + 2ε s ) (ε s + 2ε m )(ε c + 2ε s )+ R s Rs+d 3 (ε c ε s )(2ε s 2ε m ) (E1) α abs α ext = k Im(α p ) where k = 2πn/λ (wavenumber) of the ambient medium, n is the refractive index of the ambient medium, λ = 526 nm, α ext is the extinction cross section and α p is the polarizability. ε c, ε s, ε m are the dielectric constants of gold, silica and water respectively. The values for ε c and ε s are obtained from as per reported [SR4,SR5] while R s is radius of AuNP and d is shell thickness of silica. eq E1 has been computed using a dipolar approximated simplified version of MIE theory for the Rayleigh limit where particles size is very small (radius< 20 nm) compared to the wavelength of light, which further supports the approximation α abs α ext [SR6, SR3]. S3

4 due Figure S2. Plot of change in absorption coefficient of gold ( α abs ) with n silica R to the change in temperature. Hence, effectively a thermal stress enhancement could be anticipated. Since, no previous experimental studies on refractive index of fused silica for higher temperatures have been conducted, we have omitted this effect in our studies. Additionally, analysing these values, the overall effect of change in refractive index of silica was estimated to be negligible [SR7]. The fourth relation reflects positive temperature dependence of specific heat capacity of AuNP as shown in eq E2 [SR8]: c 0 (T) = (0.128)T ( )T 2 + ( )T 3 ( )T 4 + ( )T 5 (E2) S4

5 The increment in c 0 (T) positively affects heat relaxation τ r (B from eq E12) and the temperature rise (eq E14). The final relation of dielectric permittivity (ϵ) with temperature is primarily due to the change in size of the particle and factors such as damping as well as scattering rate among electrons and phonons. The electron density varies with respect to change in size of AuNP that alters the interaction of electrons with the incoming electromagnetic wave. Additionally, along with the change in size, an increase in temperature determines extent of collision and scattering within electrons and phonons and thus results in temperature damping. Due to these complex phenomena and temperature dependent changes, the change in absorption cross section of AuNP and the mathematical factors of the corresponding physics are further explained in the following section. S1.2 Temperature dependent dielectric constant [SR7,SR9-SR12] The dielectric function of gold can be represented as contribution from response of free conduction electrons represented by the Drude model and inter-band transition. Drude model is a good approximation for long wavelength excitation. But for visible region and lower, the effect of inter-band transition from 5d to 6sp conduction band of Au is dominant. Therefore, the dielectric function ϵ(ω, T) at excitation ω and temperature T can be expressed as: ϵ(ω, T) = ϵ D (ω, T) + ϵ IB (ω, T) (E3) where Drude term, ϵ D (ω, T, R) = 1 ω p 2 ω(ω+iγ(t,r)) (E4) where Γ(T, R) = Γ e e ph (T) + A v F R is the damping frequency, ω p = n 0 e 2 ϵ 0 m e denotes the plasma frequency, Γ e e ph (T) is the damping frequency due to electron-phonon and S5

6 electron-electrons scattering of conduction electrons, v F is the Fermi velocity, A is a proportionality constant (A = 1 for isotropic electron scattering), R = 4V S is the effective dimension of the particle or path length of the electrons, V is the particle volume, S is the particle surface area, n 0 is the electron density, e is the charge of electron, ϵ 0 is the permittivity of free space and m e is the electron mass. The inter-band term, ϵ IB (ω, T) = K y ω g ω g y 1 f(y, T) ω2 y 2 Γ2 e e (T)+i2ωΓ e e (T) ω 2 y 2 Γ2 e e (T) 2 +4ω 2 Γ2 e e (T) dy (E5) where f(y, T) = exp (E y E F k B T) is the Fermi distribution of quasiparticle states, ω g = E g ħ, EE gg is the interband gap energy of 1.8 ev at the tail, E y = yħ is the electron energy of state, E F is the Fermi energy, k B is the Boltzmann constant, Γ e e (T) is the damping frequency due to electron-electron scattering of inter-band electrons and K is a constant. The above model is tuned to fit Otter s experimental data by tuning the parameters as follows: Γ e e ph (T) = T Γ e e (T) = T K = s 3/2 E F = 2.55 ev (E6) The above parameters were tuned to fit Otter s data which was adopted from previous report [SR12]. Finally, we obtained the temperature profile T iter with maximum temperature T max of 1059 K using an analytical estimation and iterative approach in MATLAB R2014a which is S6

7 explained in S2. We have also obtained a temperature profile T sim from simulation using Finite Element Method solver COMSOL multiphysics 4.4 with maximum temperature T max of 1032 K. S2. Quasi Static Temperature of Nanoparticle under Pulsed Irradiation S2.1 Analytical estimation of quasi static temperature Due to the high conductivity of gold metal nanoparticle (AuNP), temperature at any time instant t can be assumed to be uniform T(t) throughout the sphere. The non-uniformity was found to be negligible as reported previously [SR8,SR13,SR14]. The heat equation which describes the heating of a particle with radius R s was shown to be [SR13]: ρ 0 c 0 V 0 dt dt = 1 4πR s 2 I g (t)α abs S 0 J ε S 0 (E7) 2 with initial condition T(t = 0) = T, where S 0 = 4πR s is the surface area of the particle, V 0 = 4 πr3 3 s is the volume of the particle, I g (t) is the Gaussian profile intensity profile, T is the ambient temperature K, c 0 (T) is the specific heat capacity of bulk gold [SR8] (agrees with that of the nanoparticle estimated at 532 nm excitation [SR14]), α abs is the absorption cross section of AuNP and J ε is the energy loss from the particle. J ε is composed of loss due to conduction J c and radiation cooling J r. J ε = J c + J r (E8) Since heat loss due radiation was negligible [SR13], J ε = J c = k(t) dt dr sp (E9) S7

8 where k(t) = k T T a is the temperature dependent coefficient of thermal conductivity of surrounding medium where a denotes material dependent constant. For temperature independent case, a = 0 and thus k(t) = k. Then the heat flux for quasi-stationary scenario was described by [SR13]: J ε = J c = k T T a+1 1 (a + 1)R s T = k T T 1 R s T (E10) Substituting eq E10 in eq E7 and with rearrangement of terms delivers: dt dt + 4πk R s T = I g(t)α abs + 4πk R s T ρ 0 c 0 V 0 ρ 0 c 0 V 0 ρ 0 c 0 V 0 Or dt 0 dt + C 1T 0 = C 2 I g (t) + C 1 T (E11) where C 1 = 4πk R s ρ 0 c 0 V 0 and C 2 = α abs ρ 0 c 0 V 0 substitutions are made assuming all parameters involved in C 1 and C 2 are constants. eq E11 is a linear first-order ordinary differential equation with a solution: T(t) = T + Ae Bt t I g (x)e Bx dx 0 (E12) where A = (3α abs )/(4πR s 3 c 0 ρ 0 ) and B = (3k )/(c 0 ρ 0 R s 2 ) indicates the inverse of the characteristic relaxation time τ r. I g is the gaussian laser input intensity given as: S8

9 I g (t) = 4 E 4 log(2) (t t0 )2 p t2 πb2 e p d t p (E13) where E p is the pulse energy, t p is the pulse duration at full width half maximum (fwhm), B d is the laser beam diameter and t 0 is a time offset used before starting the irradiation in simulation in COMSOL Multiphysics 4.4. Also an estimate for maximum temperature was given in a previous literature [SR3] as: T max_rise = max{i g} α abs 4πR s k (E14) where max I g = maximum intensity I gmax. Here temperature of gold nanoparticle was estimated assuming with a matrix of silica surrounding. Additionally, the temperature profile T(t) estimated in eq E12 assumed some parameters to be constant for solving the differential equation. Therefore, the mutual dependency of variables explained in supporting information S1 are ignored. To solve this, the analytically estimated T(t) is subjected to a more comprehensive iterative algorithm to incorporate those effects. S2.2 Iterative algorithm for quasi static temperature (MATLAB R2014a) Algorithm steps proceeds as follows: 1. Set the initial conditions particle dimensions (core radius R s, core volume V p ), core density (ρ 0 ), and particle temperature T. 2. Set T i = T and change in temperature dt = T i 0 where i = Find absorption cross section α abs using eq E1. 4. Evaluate T i+1 = T(t n ) using eq E12. S9

10 5. Update dt = T i+1 T i. 6. Find β Au (T i+1 ) using eq E Estimate change in volume dv p =3 β Au (T i+1 ) V p (T i+1 T i ). 8. Update V p = V p + dv p. 9. Update R s from new volume V p. 10. Update ρ 0 from new volume V p. 11. Find c 0 (T i+1 ) using eq E Update ϵ(ω, T) using Equations E3, E4, E5, E Repeat steps 3 to 12 until convergence of temperature is attained, which we defined as T/T < 0.1%. 14. Assign T iter (t n ) = T i Repeat steps from 1 to 13 for each time instant t n. Steps 1 and 2 initialize all the variables which are expected convergence owing to mutual dependency. Steps 3 to 12 define iteration and run through temperature convergence as defined in Step 13. Step 3 covers the temperature dependency of α abs. Step 4 address the temperature dependency of τ r and T mmmmmm. Step 6 covers the temperature dependency of β Au and ε. Step 12 covers the temperature dependency of ϵ(ω, T). Thus obtained T iter. Assumptions and approximations for theoretical calculation: S10

11 Heat loss due to radiation is neglected and effect of silica thickness was not taken into account. S2.3 Finite Element Method simulation (COMSOL Multiphysics 4.4) The methodology for COMSOL simulation was taken from literature [SR15]. First a gold nanosphere with silica coating in water as medium was geometrically modeled and meshed accordingly. For simulation of the physics in COMSOL we made use of 1) electromagnetic wave and 2) heat transfer inbuilt modules. Electromagnetic wave: The source laser was modeled as a linearly polarized plane wave of required wavelength (526 nm). The module uses the Helmholtz equation to estimate the electric field distribution inside and outside the structure. The energy absorbed by the particle is calculated as the resistive heating in AuNP. Using the required pulse duration and obtained values, average power absorbed can be estimated supported by suitable laser pulse (Gaussian pulse) of designed duration can be created. This laser pulse is used in the next heat transfer module. Heat transfer: Heat diffusion equation is accounted with heat source as energy absorbed (resistive heating) from the aforementioned module and the temperature profile ( T sim ) in AuNP is estimated. Assumptions and approximations for FEM: Due to the inability to couple frequency domain module electromagnetic wave and time domain module heat transfer, the temperature dependency in optical property (here dielectric permittivity of gold) is omitted. S2.4 Results S11

12 Figure S3 shows the absorbed power intensity profile P abs = I g α abs, iteratively estimated T iter and simulated value of temperature profile as T sim. Figure S3. Intensity profile of power absorbed P abs (black line) by the hybrid (silica coated AuNP). Theoretically obtained temperature profile T iter (dotted blue line) and simulated temperature profile T sim (solid blue line). Inset graph: Comparison between the simulated and theoretically obtained temperature profile. The maximum temperature estimated using eq E14 was ~1054 K. After subjecting T(t) (eq E12) to iterative method we got T iter whose maximum was ~1059 K. At the same time the simulation results a maximum temperature ~1032 K. The simulated temperature attained a S12

13 maximum whose value is different than theoretical T max _rise, T iter due to the assumptions and approximations mentioned above. The theoretical value had a deviation ~2.6% from the simulated value. S3. Thermal Stress Analysis at Gold-Silica Interface In this study, due to silica coating on Au cored nanostructure ( 40 nm) the possibility of supplementary phenomena such as surface evaporation and light intensity modulation effect is eliminated [SR16]. Light intensity modulation effect occurs strongly upon interference of the incident light with scattered or reflected light from the particle. An eventual strong enhancement of the electromagnetic field in interference points resulting in damage of silica lattice pattern. However, considering the case of nanosized AuNP (radius < 40nm), the effect of this field intensity modulation is insignificant [SR16]. Next, surface evaporation is another possible phenomenon that reduces the size of a bare nanoparticle by evaporation due to heat deposition on the lattice attainable near boiling point of the nanoparticle and this size reduction might change its optical as well as thermal coefficients. Coulomb explosion of AuNP upon interaction with pulsed laser excitation is an extreme condition which might occur with a femtosecond regime [SR17]. Coulomb explosion happens when ejection of a batch of electrons due to the absorbed heat and charge repulsion to generate multiple ionized nanoparticles to undergo spontaneous fission [SR17]. This is mainly due to the high power from short duration pulse which rapidly raises the temperature of electron gas leading to ultra-slow heat damping and thus attain an equilibrium with lattice by electron-phonon scattering. Additional possibility of laser force induced elongation and change in shape of AuNP is a process to be considered only near the melting point of gold in the hybrid nanostructure S13

14 [SR18, SR19]. Thus, for a nanosecond pulse that generates AuNP core temperature less than the melting point of gold, the sole reason for interface stress remains thermal expansion. Therefore, the analysis of stress due to thermal expansion is as follows: Linear thermal expansion coefficient of gold β Au = K 1 Linear thermal expansion coefficient of silica β silica = K 1 Thermal stress was calculated using: σ = ε B M (E15) where B M = 180 GPa is the bulk modulus of gold, ε = β Au (T)(T(t) T ) is thermal strain and β Au (T) is the temperature dependent expansion coefficient of gold [SR8] given by: β Au (T) = ( ) + ( )T + ( )T 2 + ( )T 3 (E16) Using maximum temperature T max = max {T sim } in thermal expansion coefficient in eq E16, the maximum expected strain for gold nanosphere: ε Au = 3β Au (T sim )(T sim T ) ε Aumax = 3β Au (T max )(T max T ) = ( ) = (E17) S14

15 The expansion of silica was calculated using the silica temperature of immediate surrounding at the interface. Assuming continuity in temperature at interface, the maximum expected strain for hollow sphere: ε silica = 3β silica (T max T ) = ( ) = (E18) From eq E17 and eq E18, the ratio r of maximum expected expansion: r = ε Au ε silica = (E19) When we use theoretical T iter instead of simulated T sim in eq E17, eq E18 and eq E19, we will get ratio r = Thus expansion of silica is 35 less than gold and neglected to calculate thermal stress using eq E15. Then, for simulated T sim the maximum expected thermal stress at maximum temperature was calculated using eq E15 as: σ = ε B M σ max = ε Aumax B M = GPa = GPa (E20) S15

16 Similarly, applying eq E20 using theoretical temperature profile T iter, we get σ max = GPa shows a deviation of ~3.6% from the simulated value. S4. Experimental Section S4.1 General Transmission electron microscopy (TEM) analyses were performed on a FEG-TEM (JEM-2100F, JEOL, Japan) operated at 200 kv. Field emission scanning electron microscope images were taken using JEM-2100F, JEOL, Japan operated at 5.0 kv. Gold nanoparticles (radius cccc. 10 nm) and tetraethyl orthosilicate (TEOS) were purchased from sigma Aldrich and used without further purification. S4.2 Experimental procedure The silica coated gold nanoparticles were prepared by a process developed, based on the Stöber method involving tetraethyl orthosilicate (TEOS). [SR20] In a typical synthesis, AuNP solution (3 ml) was concentrated by centrifugation at 6000 rpm for 15 min. The concentrated AuNPs were then dispersed in ultrapure water (0.5 ml) followed by addition of isopropyl alcohol (2.5 ml) containing 4-mercaptobenzoic acid (5 mm, 5 ml) under vigorous vortexing. After incubating under room temperature without stirring for 30 min, triethylorthosilicate (TEOS, 1.2 ml) and ammonia solution (90 ml) were added for condensation. After 15 min, APTES (0.5 ml) was added into the solution and then the mixture solution was incubated at room temperature overnight in order to ensure complete encapsulation. Further purification was carried out before using AuNP@SiO 2 for the next step. The amount of APTES was varied to S16

17 obtain different shell thicknesses of silica 2-30 nm and 2-15 nm). The as-synthesized hybrids were taken in aqueous solution which had a measured optical density (OD) of 10 cm 1 and particle density of particles/ml. The metal volume fraction (p) was tuned to ~0.0025%( ~13%) which minimized the interaction between metal spheres and thus provided a solution which was similar to an isolated single structure system, as assumed in the computational analysis [SR21]. The solution was irradiated with single laser pulse with fluence of 0.2 J/cm 2 and a pulse duration of 9 ns at a wavelength of 526 nm. To monitor the changes in the morphology several electron microscopic images were captured at two stages, before and after the irradiation. S5. Results: Electron Microscopy Images and Spectroscopic Analysis S17

18 Figure S4. TEM images of a) gold nanoparticles (AuNPs), radius cccc. 10 nm, b) silica coated AuNPs with overall radius cccc. 40 nm before irradiation. SEM images of silica coated AuNPs c) before irradiation and d) after irradiation. Fluence for the irradiation was 0.2 J/cm 2 with pulse duration of 9 ns and wavelength of 526 nm. S18

19 Figure S5. UV/Vis absorption spectra of silica coated AuNPs in water (0.5 mg/ml) with overall silica thickness of cccc. 30 nm before and after exposed to laser pulse. S19

20 Figure S6. TEM images of a) silica coated AuNPs with overall silica thickness of cccc. 15 nm, b) a single particle before irradiation. (c, d) Morphology changes observed after irradiation. Fluence for the irradiation was 0.2 J/cm 2 with pulse duration of 9 ns and wavelength of 526 nm. S20

21 Figure S7. UV/Vis absorption spectra of silica coated AuNPs in water (0.2 mg/ml) with overall silica thickness of cccc. 15 nm before and after exposed to laser pulse. REFERENCES SR1) Leviton, D. B.; Frey, B. J. Temperature-Dependent Absolute Refractive Index Measurements of Synthetic Fused Silica. arxiv: , ID: SR2) Guo, Y.; Wang, Z.-Y.; Qiu, Q.; Su, J.; Wang, Y.; Shi, S.; Yu, Z. Theoretical and Experimental Investigations on the Temperature Dependence of the Refractive Index of Amorphous Silica. J. Non-Cryst. Solids 2015, 429, S21

22 SR3) Dijk, M. A. V. Nonlinear Optical Studies of Single Gold Nanoparticles. Ph. D. thesis, Leiden University, SR4) Johnson, P. B.; Christy, R. W. Optical Constants of the Noble Metals. Phys. Rev. B 1972, 6, SR5 Malitson, I. H. Interspecimen Comparison of the Refractive Index of Fused Silica. J. Opt. Soc. Am. 1965, 55, SR6) Feis, A.; Gellini, C.; Salvi, P. R.; Becucci, M. Photoacoustic Excitation Profiles of Gold Nanoparticles. Photoacoustics 2014, 2, SR7) Yeshchenko, O. A.; Bondarchuk, I. S.; Gurin, V. S.; Dmitruk, I. M.; Kotko, A. V. Temperature Dependence of the Surface Plasmon Resonance in Gold Nanoparticles. Surf. Sci. 2013, 608, SR8) Ekici, O.; Harrison, R.; Durr, N.; Eversole, D.; Lee, M.; Yakar, A. B. Thermal Analysis of Gold Nanorods Heated with Femtosecond Laser Pulses. J. Phys. D Appl. Phys. 2008, 41, SR9) Nozières, P; and Pines, D. The Theory of Quantum Liquids; Perseus, SR10) Bigot, J. Y.; Merle, J. Y.; Cregut, O.; Daunois, A. Electron Dynamics in Copper Metallic Nanoparticles Probed with Femtosecond Optical Pulses. Phys. Rev. Lett. 1995, 75, SR11) Grua P.; Bercegol, H. Dynamics of Electrons in Metallic Nanoinclusions Interacting with an Intense Laser Beam. Proc. SPIE 2001, 4347, SR12) Setoura, K.; Werner, D.; Hashimoto, S. Optical Scattering Spectral Thermometry and Refractometry of a Single Gold Nanoparticle under CW Laser Excitation. J. Phys. Chem. C 2012, 116, S22

23 SR13) Pustovalov, V. K. Theoretical Study of Heating of Spherical Nanoparticle in Media by Short Laser Pulses. Chem. Phys. 2005, 308, SR14) Werner, D.; Hashimoto, S.; Uwada, T. Remarkable Photothermal Effect of Interband Excitation on Nanosecond Laser-Induced Reshaping and Size Reduction of Pseudospherical Gold Nanoparticles in Aqueous Solution. Langmuir 2010, 26, SR15) Hatef, A.; Darvish, B.; Dagallier, A.; Davletshin, Y. R.; Johnston, W.; Kumaradas, J. C.; Rioux, D.; Meunier, M. Analysis of Photoacoustic Response from Gold Silver Alloy Nanoparticles Irradiated by Short Pulsed Laser in Water. J. Phys. Chem. C 2015, 119, SR16) Tian, R.; Qiu, R.; Jiang, Y.; Wang, J. In Study on laser intensity modulation by spherical inclusion in silica subsurface, Proc. SPIE 9449, The International Conference on Photonics and Optical Engineering; DOI: / SR17) Werner, D.; Hashimoto, S. Improved Working Model for Interpreting the Excitation Wavelength- and Fluence-Dependent Response in Pulsed Laser-Induced Size Reduction of Aqueous Gold Nanoparticles. J. Phys. Chem. C 2010, 115, SR18) Kuhlicke, A.; Schietinger, S.; Matyssek, C.; Busch, K.; Benson, O. In Situ Observation of Plasmon Tuning in a Single Gold Nanoparticle during Controlled Melting. Nano Lett. 2013, 13, SR19) Link, S.; Burda, C.; Nikoobakht, B.; El-Sayed, M. A. Laser-Induced Shape Changes of Colloidal Gold Nanorods Using Femtosecond and Nanosecond Laser Pulses. J. Phys. Chem. B 2000, 104, S23

24 SR20) Stöber, W.; Fink, A.; Bohn, E. Controlled Growth of Monodisperse Silica Spheres in the Micron Size Range. J. Colloid Interface Sci. 1968, 26, SR21) Palpant, B.; Guillet, Y.; Rashidi-Huyeh, M.; Prot, D. Gold Nanoparticle Assemblies: Thermal Behaviour under Optical Excitation. Gold Bull. 2008, 41, S24