Chemically-Controlled Ultrafast Photothermal Response in Plasmonic Nanostructured Assemblies

Plasmonic nanoparticles are renowned as efficient heaters due to their capability to resonantly absorb and concentrate electromagnetic radiation, trigger excitation of highly energetic (hot) carriers, and locally convert their excess energy into heat via ultrafast nonradiative relaxation processes. Furthermore, in assembly configurations (i.e., suprastructures), collective effects can even enhance the heating performance. Here, we report on the dynamics of photothermal conversion and the related nonlinear optical response from water-soluble nanoeggs consisting of a Au nanocrystal assembly trapped in a water-soluble shell of ferrite nanocrystals (also called colloidosome) of ∼250–300 nm in size. This nanoegg configuration of the plasmonic assembly enables control of the size of the gold suprastructure core by changing the Au concentration in the chemical synthesis. Different metal concentrations are analyzed by means of ultrafast pump–probe spectroscopy and semiclassical modeling of photothermal dynamics from the onset of hot-carrier photogeneration (few picosecond time scale) to the heating of the matrix ligands in the suprastructure core (hundreds of nanoseconds). Results show the possibility to design and tailor the photothermal properties of the nanoeggs by acting on the core size and indicate superior performances (both in terms of peak temperatures and thermalization speed) compared to conventional (unstructured) nanoheaters of comparable size and chemical composition.


S1. Reduced 2D geometry to model plasmonic nanoeggs
To simulate the complex geometry of the experimental nanoegg samples, featuring a metallic nanostructured core embedded in an organic matrix and surrounded by a ferrite colloidosome, a reduced two-dimensional (2D) model has been developed using a nite element method (FEM)-based commercial software (COMSOL Multiphysics 5.6). In this framework, Au nanocrystals (NCs) composing the plasmonic assembly have been simulated as circles (modelling spheres in 3D) of radius r = 2.5 nm arranged in a hexagonal lattice with an interparticle distance of 2 nm. The number n 2D of NCs in the assembly is then xed by the Au:Fe 3 O 4 concentration ratio and ranges between 37 and the 207 from the lowest to the highest concentration of metal. Similarly, the radius of the organic ligand matrix R y , determining the size of the nanoegg core, is evaluated starting from the Au:Fe 3 O 4 relative concentration, its estimated value varying between 25 and 55 nm. Therefore, the resulting volume of the Au phase can be estimated as V Au = N 3D V i , with V i = 4πr 3  As an example, Figure S1 shows the 2D model geometry and the mesh built in the FEMbased software for the case c r = 1. As noted in the main text, our reduced model describes NCs as nanowires innitely extended in the out-of-plane direction. Although introducing a substantial geometrical dierence in the modelled structure, such an approximation does not prevent us from capturing the most fundamental processes of light-matter interaction S2 produced by illuminating the nanoeggs, which are preserved regardless of the dimensionality of the system (as it also happens e.g. with dielectric waveguides, 1 photonic crystals 2 and metamaterials 3,4 ). in bulk gold. 6 The polymeric organic matrix has instead been treated as a dispersionless dielectric material with a purely real refractive index n O = 1.359, slightly varied with respect to values reported for dodecanethiol, 7 and the refractive index of water has been set to 1.33.
Finally, the optical properties of ferrite has been described in terms of a complex-valued weakly-dispersed refractive index. 8 Note that, although Fe 3 O 4 exhibits a non-zero imaginary part of refractive index, its contribution to the sample absorption and corresponding dynamical modulation has been disregarded, the optical extinction of the nanoeggs in the considered wavelength range being dominated by the plasmonic response of the suprastructure core.
From the numerical solution retrieved for the scattered electric E s and magnetic H s elds as a function of wavelength λ, we estimated the absorption and scattering cross-section spectra, σ a (λ) and σ s (λ) respectively, of the structure. 9,10 The former is written as a 2D integral of the electromagnetic power loss density over the whole Au-NC assembly (a surface where c is the speed of light in vacuum, ε 0 the vacuum permittivity, I 0 the intensity of the incident wave (in W/m, the model being in 2D), and E = E s + E 0 the total electric eld, sum of the scattered and the incident ones. The scattering cross-section is similarly written S4 as an integral computed along a closed line Σ surrounding the scatterer: where n denotes the outward pointing normal vector of the domain Σ. The 3D cross-sections of the structure have been estimated from the above 2D cross-sections as σ 3D = πσ 2D R y /2.
The transmission of the sample is then determined according to Lambert-Beer's law as and referred to as a four-temperature model (4TM) has been employed. 11 The numerical solution of the system of four coupled ordinary dierential equations provides the dynamical evolution of the structure internal degrees of freedom, namely the excess energy associated to a non-thermalised portion of hot carriers in the plasmonic structures, N , together with the temperatures of metal electrons, Θ E , metal lattice, Θ L , and of the organic matrix Θ O .
Regarding the quantities appearing in the 4TM (Eqs. (1)-(4) of the main text), the drive S5 term of the photoexcitation, directly coupled to non-thermalised carriers, is p a (t), namely the electromagnetic power density absorbed by the plasmonic system, which reads: Finally, based on the dynamical evolution of the permittivity across the hybrid metallicorganic system, the transient transmittance of the structure is computed as a function of wavelength and time delay, to determine the simulated dierential transmittance ∆T /T (λ, t), to compare with pump-probe measurements. To do so, as mentioned in the main text, a perturbative approach is implemented. In particular, the numerical relative transmittance variation is written as a linear combination of the complex permittivity modulation terms ∆ε Au and ∆ε O previously calculated. Its expression reads: where the four c i (λ) functions are real-valued spectral coecients calculated by FEM analysis. For instance, by considering c 1 (λ) (the algorithm is identical for the three others), the same electromagnetic problem discussed above is solved rst in unperturbed conditions, then by applying a ctive real permittivity modication ∆ε Au , set equal to 0.1 as a good estimation of the order of magnitude of the modulation retrieved by the 4TM. The former provides then the static transmittance T (λ), while the latter gives a perturbed transmittance S7 T (λ). The corresponding nonlinear spectral coecient can thus be evaluated as: An equivalent procedure enables us to estimate the remaining coecients and to build a 2D map of the transient broadband pump-probe spectroscopy signal to be compared with measurements.

S4. Model of the nanoegg thermal response
To estimate the temporal dynamics of the thermal response of the suprastructures, the 2D thermal model briey discussed in the main text has been dened. Numerical simulations, performed on the reduced 2D geometry introduced in Section S1, implement the standard Fourier equation for heat diusion: ρC p ∂Θ ∂t −κ∇ 2 Θ = Q(t), solved for the temperature eld Θ dened across the whole simulation domain (therefore Θ = Θ L in Au volumes, Θ = Θ O in the organic matrix, Θ = Θ S in the surrounding environment). In the equation, ρ, C p and κ are respectively the density, heat capacity and thermal conductivity of the considered material, while Q(t) is the time-dependent light-induced heat source. Its expression has been written 15 τepV Au e −t/τep , with F p the pump pulse uence, σ a is the absorption cross-section evaluated at the pump wavelength λ from electromagnetic simulation results, V Au is the volume of gold, xed by the concentration of the analysed sample. Temporal evolution of the employed heat source is governed by the electron-phonon scattering rate τ ep , here set equal to 3 ps as an estimation of the characteristic time of energy transfer from electrons towards the Au lattice, which in turns becomes the heat source for the organic matrix embedding the nanoassembly, and eventually for the surrounding aqueous environment. Concerning the parameters detailing the thermal properties of materials, Au has been described 16,17 by a ρ = 19320 kg/m 3 , C p = 129 J · K −1 · kg −1 , κ = 317 W · K −1 · m −1 , while for the organic S8 matrix ρ = 845 kg/m 3 , C p = 2187 J · K −1 · kg −1 as in Ref. 13, and κ ∼ 0.04 W · K −1 · m −1 as a reasonable estimation of the order of magnitude of thermal conductivity in similar polymers, 18 and providing consistent dynamics of the matrix temperature from optical and thermal simulations. The ferrite NCs, forming the shell of the nanoeggs, have instead been considered as passive elements (their contribution to the heating process being substantially negligible), with 19 ρ = 4962 kg/m 3 , C p = 0.89 J · K −1 · kg −1 and κ = 4.9 W · K −1 · m −1 .
For water instead, ρ = 1000 kg/m 3 , C p = 4186 J · K −1 · kg −1 , κ = 0.6 W · K −1 · m −1 . 20 Thermal simulations are performed for the three dierent metal concentration congurations, by varying the volume of water so to keep constant the ratio between Au and water volumes.
Innite Elements (IEs) are set at the boundaries of the domain, numerically treated as innitely extended, and boundary conditions imposing the temperature to its equilibrium value are dened beyond IEs. S5. Organic matrix temperature relaxation By tting the relaxation dynamics of the organic matrix temperature increase ∆Θ O with a negative exponential, a characteristic decay time of the cooling rate can be extracted.
Such decay time serves as a temporal estimation of the rate at which the organic matrix cools down by varying the features of the nano-heater used, i.e. suprastructure versus coated nanoparticle and by varying the Au relative concentration. Table S1: Decay times of the temperature increase across the organic matrix (curves in Fig. 4 Table S1 reports such decay times for the six scenarios detailed in Fig. 4 of the main text.
Results of the tting procedure show the advantages of using suprastructures in terms of cooling rate, as mentioned in the main text. Such decay times tend to increase with c r in both congurations, although they remain faster by a factor of 2 when nanostructured heaters are employed. S10