L Berquez

J Cenes

G Teyssedre

S Le

Roy P Hondaa

V Eriksson

M Bailleul

C Moreau Summary

Implementation of space charge measurement using the Pulsed Electro-Acoustic method during ageing of HVDC model cable

Keywords: Space charge, cable aging, HVDC, pulsed electro-acoustic (PEA) method, polarity reversal

Due to high dielectric performances, cross-linked polyethylene (XLPE) is one of the preferred materials for the insulation of HVDC cables. However, polymeric insulating materials tend to store electric charges, which disturb the electric field within the material and may eventually lead to a structural modification of the polymer thus promoting its ageing. This degradation of the insulation may induce a decrease in the life expectancy of the cables. Nowadays many studies are carried out to bring knowledge on the degradation mechanisms in polyethylene. Indeed, an improved understanding of the behaviour of charges makes it possible to better correlate the measurements with the ageing of the material. However, it is often not possible to measure the dielectric characteristics (current, space charge) during ageing, and most generally this has to be done a posteriori. The objective of this research is to measure the variations of the dielectric properties of the polyethylene insulation in a model cable, either during ageing conditions, i.e. when a thermo-electric stress is applied to the cable, or a posteriori. To do so, two approaches have been developed and put into practice.

The first approach is based on the adaptation of the Pulsed Electro-Acoustic (PEA) measurement method to an already charged model cable having undergone thermo-electric ageing. In this case, the PEA measurement is not performed online, but on samples taken regularly from a long cable length under thermo-electric stress. Hence, for each measurement, a different piece of cable, already charged when received, is under study. The PEA method requires a calibration step, normally performed on a non-charged sample to obtain the response of the system. We have developed a calibration procedure on an already charged cable without removing the possible charges that are present in the insulation. In this way crucial information on the state of charge before any further electrical stressing can be analysed. The treatment of the PEA signal has been revised, and it is now possible to quantify the charge present on an already stressed cable sample prior to any measurement. The improvement of the PEA signal conditioning will be presented in the paper. Moreover, the results of space charge measurements at different ageing times will be discussed.

The second approach is focused on an online space charge measurement at laboratory scale, using the PEA method on model cables over long periods of time. One of the difficulties when measuring during a long time, all the more when the set-up is not at room temperature, is the possible drift of the system configuration, as the mechanical pressure inside the PEA cell for example may vary even slightly. It may lead to changes in the transfer function of the whole system and possibly to some mistakes on the space charge profiles. The dedicated test bench has been developed with realizing periodic calibration using the procedure described below. It allows measuring space charge during long periods of time, and moreover during grounding and during polarity inversion cycles. Space charge profiles will be presented for long measurement times (several days) where the polarity is reversed each 30 min, for a mean applied field of 60 kV/mm and under thermal gradient.

INTRODUCTION

The worldwide increasing demand for renewable energy sources to supply electricity is a new challenge to face for power networks. HVDC technology is now increasingly used to transmit electricity from offshore windfarms, for interconnection of asynchronous networks, or simply for long distance transmission. Developments have been made on the insulating material used in HVDC cables, and cross-linked polyethylene (XLPE) has several advantages over oil-impregnated paper [START_REF] Montanari | Bringing an insulation to failure: the role of space charge[END_REF]. However, one drawback when using XLPE under DC stress is the possibility for the material to store charge for a long time, disturbing the electric field distribution. This behaviour needs to be deeply understood for insulating materials able to sustain ever increasing voltage levels over 40 years or more. Ageing studies have been performed on XLPE materials, under AC [START_REF] Fothergill | Electrical, microstructural, physical and chemical characterization of HV XLPE cable peelings for an electrical aging diagnostic data base[END_REF][START_REF] He | Space charge behavior in XLPE cable insulation under ac stress and its relation to thermo-electrical aging[END_REF] and DC, but mostly over short ageing periods and for temperatures above the melting temperature with no electric stress [START_REF] Zhang | Conductivity properties of XLPE insulation used for HVDC cable after accelerated thermal ageing[END_REF] or relatively low electric stress. Some aging studies under HVDC and high temperatures have been proposed on plane parallel samples [START_REF] Hascoat | Study of dielectric properties of XLPE for HVDC cable during long-term ageing[END_REF][START_REF] Choo | Space charge accumulation under effects of temperature gradient and applied voltage reversal on solid dielectric DC cable[END_REF]. In this paper, ageing has been performed on model cables, in two different ways:

-A long term ageing over 18 months has been developed at relatively high constant temperature (100°C) but below the melting temperature [START_REF] Englund | The development route towards extra high voltage DC -materials and testing[END_REF], and at average stress of 60 kV/mm, higher than the highest electric field required during short term qualification tests for 640 kV DC cables ( [START_REF]Recommendations for testing DC extruded cable systems for power transmission at a rated voltage up to 500 kV[END_REF], extrapolated for 640 kV), and also higher than the average electric field calculated for long term qualification tests for 640 kV DC cables with polarity inversions (1.45 U DC ).

-An accelerated ageing is proposed over shorter periods (several weeks), but with a temperature gradient along the insulation radius and with regular grounding (GR) or polarity reversal (PR) periods, as polarity reversals are thought to shorten the cable lifetime [START_REF] Cavallini | A life model based on spacecharge quantities for HVDC polymeric cables subjected to voltage-polarity inversions[END_REF].

We present in this paper the challenges overcome during the method development and space charge measurements for each ageing type, the evolutions of the space charge measurement test bench and the signal treatment. We also present for the first time space charge measurement performed during 24h of polarity reversal.

MATERIALS

Model cables are used for this project, as they have the advantage to be more representative of the real full-size cable configuration than plaques, i.e.:

-a cylindrical geometry where electric field and temperature are not homogeneous over the insulation thickness, and -the presence of semiconducting screens (SC) on each side of the XLPE insulation, which can have a role on the thermal and electrical behaviour.

The model cable consists of a copper core and a three layers (SC/XLPE/SC) insulation system (Figure 1). It has been extruded on a laboratory CCV (Continuous Catenary Vulcanization) line using the material grade developed for the currently most demanding HVDC applications. Model cables were degassed for 10 days at 70°C after extrusion to remove XLPE peroxide decomposition products [START_REF] Andrew | The role of degassing in XLPE power cable manufacture[END_REF].

AGEING SET-UP

Figure 2 presents the test bench used for accelerated ageing with a thermal gradient and under periodic grounding or polarity reversal conditions (the study also included a separate setup for long-term ageing under isothermal conditions, which is presented in [START_REF] Cènes | Implementation of space charge measurement using the Pulsed Electro-Acoustic method during ageing of HVDC model cable[END_REF]). Space charge measurements are performed online, while under voltage, and during grounding and/or polarity reversal periods. As no power supply with embedded polarity reversal function is available commercially, the voltage is applied with two high voltage power supplies of opposite polarity (+ and -100 kV), being connected to a high voltage switch. To apply a temperature gradient within the cable insulation, an AC current is injected in the cable loop using a current transformer. The control of the thermal gradient is presented in the following paragraph. The maximal applied average electric stress is 60 kV/mm (i.e. 90 kV voltage to the cable), which corresponds to a geometric electric field of around 90 kV/mm at the inner SC and around 45 kV/mm at the outer SC, following the equation:

(

) 1
where V is the applied voltage, and r is the insulation radius at which the electric field is calculated (r 2 and r 3 are defined in Figure 1a). The electric field distribution across the insulation is given in Figure 1b).

The maximal temperature at the conductor is 90°C, with a thermal gradient of 5.7 °C between the inner and the outer SC. For this short term ageing test bench, three cables are installed in parallel:

-Cable "Pulse" for applying the voltage pulse for space charge measurement by PEA; -Cable 1 for on line space charge measurements while under voltage, during grounding and PR (thermo-electric ageing). The length of this cable is 3m.

-Cable 2 for sampling and off-line characterizing of the physico-chemical behaviour of the insulation (thermo-electric ageing). The length of the cable is 25m at the beginning of ageing, and decreases of 3m each 7 days, due to sampling. Note that a second cable of 25m is aged with thermal stress only and is sampled every 7 days like for cable 2.

All three cables are connected to the high slot sphere immersed in an insulating oil bath. For each cable termination, the outer SC has been removed on a length of 30 cm, kept in oil bath, to manage sufficient creepage distance between conductor end and SC screen end. The quality of cable stripping is of utmost importance, as the ending point of the SC represents a weak point for breakdown. Sampling on cable 2 for physico-chemical measurements implies to prepare a new cable termination every 7 days.

Cable "Pulse" is dedicated to PEA pulse application. In the literature, different PEA set-ups designed for cables are available, applying the PEA pulse either via the PEA cell electrode [START_REF] Hozumi | Direct observation of time-dependent space charge profiles in XLPE cable under high electric fields[END_REF], via the cable conductor [START_REF] Wang | Space charge in XLPE power cable under dc electrical stress and heat treatment[END_REF][START_REF] Fu | Space charge measurement in polymer insulated power cables using flat ground electrode PEA system[END_REF], or via the outer screen [START_REF] Bodega | Charging and polarization phenomena in coaxial XLPE-EPR interfaces[END_REF][START_REF] Montanari | Space charge measurements and ageing evaluation in stressed cables[END_REF]. For the last case, the external SC needs to be removed over a certain length within the cable loop to form a decoupling capacitor. As the cable stripping is a sensitive operation, we decided to dedicate a specific cable loop for pulse application.

SETTING THERMAL GRADIENT

As stated before, a thermal gradient is generated in the cable insulation by Joule effect in the conductor. In steady state condition, the temperature gradient can be calculated if the temperatures at the cable core and at the outer SC are known (i.e. measured) [START_REF] Fabiani | Polymeric HVDC cable design and space charge accumulation. Part 3: Effect of temperature gradient[END_REF]. The temperature at the outer SC is relatively easy to measure, but for the one at the conductor, a dummy loop is needed.

We have estimated the temperature T C at the conductor core from the resistance per unit length of the conductor :

(

) 2
where R C20 is the resistance per unit length of the cable at 20°C, and λ 20 is a coefficient characterizing the temperature dependence of the resistivity of copper, and is taken as 3.9 10 -3 K -1 . R C20 is related to the electrical resistivity of copper ρ Cu (1. 7 10 -8 Ohm.m at 20°C):

(3)

Figure 2 : Schematics of space charge measurement using the PEA method on model cables where S is the conductor section. R C20 is theoretically 0.0117 Ω/m. This value has been determined experimentally and the mean of this value over four measurements is 0.01168 ±1 10 -4 Ω/m, which is in good agreement with the theoretical data.

can be determined on a dummy loop of length L=3m by measuring the current (I S ) and voltage (V S ) in the model cable forming the secondary winding of the current transformer: (4) I S is measured using a contactless sensor. V S is not measured directly on the model cable, but is deduced from the voltage (V P ) at the primary winding and the transformer ratio (m) which is 98.5. Measuring I S and V P allows obtaining and then T C . It is then possible to calculate the temperature everywhere inside the model cable, using: [START_REF] Hascoat | Study of dielectric properties of XLPE for HVDC cable during long-term ageing[END_REF] where T(r') is the temperature at radius r', T(r) the temperature at radius r, α is the thermal conductivity of the medium, being 0.34 W/m/K for XLPE and 0.45 W/m/K for the SC. These thermal conductivity values have been measured separately. In equation ( 5), W c is the heat flow per unit length (W/m), which is equal to: [START_REF] Choo | Space charge accumulation under effects of temperature gradient and applied voltage reversal on solid dielectric DC cable[END_REF] Using equation ( 5), one can obtain the temperature everywhere inside the cable system, composed of three layers (SC/XLPE/SC), and particularly at each interface. The thermal gradient across the insulation is given by: [START_REF] Englund | The development route towards extra high voltage DC -materials and testing[END_REF] Table 1 summarises the values used in order to have a temperature at the conductor of 90°C (fixed for the ageing protocol) and of 70°C (fixed for the model cable characterization in postageing). Temperature measurements achieved at the outer SC to check the procedure were in good agreement with those calculated, for the given injected current. However, temperature measurements performed on the surface of the outer SC inside the PEA cell were much lower than outside the cell being of the order of 30°C and 33°C respectively for a desired temperature at cable core of 70°C and 90°C. This is due to the fact that the PEA cell acts as a heat sink compared to the cable installed in air. Neglecting axial heat transfer and temperature dependence of the electrical resistivity of copper, Eq. 7 shows that the thermal gradient is unchanged in spite of different limit conditions for thermal exchange. It is therefore considered that the thermal gradient is the same inside and outside the PEA cell.

EXAMPLE OF PEA MEASUREMENT ON MODEL CABLES WITH A THERMAL GRADIENT

Before ageing, a benchmark was performed on model cables without thermal gradient, and with different thermal gradients, to characterise the unaged system. Figure 3 presents the space charge measurements for an average applied electric field of 60 kV/mm -for 4h under voltage, and 4h without voltage, -with no thermal gradient at room temperature (Figure 3a), and with a thermal gradient of 4.3°C (Figure 3b).

As stated in the previous paragraph, the temperature at the core at the measurement point is of 34.3°C for Figure 3b. The anode is the inner electrode (conductor).

When no thermal gradient is applied (Figure 3a), there is first a front of negative charges, coming from the outer electrode, with an apparent transit time of around 2 hours. Once these charges have reached the inner electrode, there is an injection of positive charges from the inner electrode. These positive charges completely mask the previous negative charges.

During short-circuit, only positive charges are measured, with the same position as at the end of the phase under voltage.

When a thermal gradient is present (Figure 3b), the negative charge front tends to disappear.

It is only visible in the first minutes of the measurement. Positive charges are rapidly dominating the space charge pattern. This is not surprising as the thermal gradient drives the charges from the inner electrode to the outer electrode [START_REF] Cenes | Assessment of ageing in the insulation of HVDC model cables under thermoelectric stress[END_REF]. However, the accumulation of positive charges at the outer electrode is not predicted by the thermal gradient, and is due to other physical processes. Negative charges seem however present, during short-circuit, they seem to appear next to the inner electrode. Imposing a thermal gradient has a significant impact on the space charge pattern. This shows the interest of using a thermal gradient when ageing the material.

SETTING POLARITY REVERSALS

Polarity reversals have been proposed in the ageing protocols, as they are thought to have an adverse effect on the lifetime, compared to continuous DC application or periodic grounding [START_REF] Cavallini | A life model based on spacecharge quantities for HVDC polymeric cables subjected to voltage-polarity inversions[END_REF][START_REF] Fabiani | HVDC aging modelling for polymeric cable: an overview[END_REF]: the higher the frequency of inversion, the shorter the lifetime. Accelerating the ageing of model cable using PR or GR implies setting several parameters related to the ageing protocol. In this paragraph, only PR will be presented, as the GR protocol is based on the PR one. The thermal and electrical constraints have already been discussed previously. The methodology proposed for ageing under PR consists of applying cycles of 24hours each with the following sequence: +U 0 , PR, -U 0 , PR (Figure 4a). This sequence is repeated during several weeks, with a sampling each week for current measurement, and physico-chemical characterizations. Polarity reversal takes 2 min, following the CIGRE recommendation TB496 a) b) Figure 3. Space charge cartography on a model cable stressed at an average electric field of 60 kV/mm, where a) there is no thermal gradient, T=25°C, and b) the thermal gradient across the insulation is 4.3 °C. The colour scale refers to charge density, in C/m 3 .

[8]. During each PR, a waiting time of 1 min at 0V is applied. Hence, for an inversion from positive to negative applied voltage, the voltage decrease from 90 kV to 0V takes 30s, and the decrease to -90 kV also takes 30s. The frequency of PR is set to two per hour (Figure 4b).

During this accelerated ageing, PEA measurements are performed online, with the possibility to probe the space charge behaviour during PR. Figure 5 shows a cartography of charges measured on a model cable during short term ageing, at E average = 60 kV/mm, and ΔT=5.7°C, after 24hours of DC polarization at +90 kV. We observe clearly the repetition of negative charges injection at the inner SC, and phases during the ageing where the charge density in the bulk is higher. These patterns will require a more detailed analysis. However, the purpose here is mainly to show the feasibility of achieving on-line measurement during PR.

PEA MEASUREMENTS ON AGED CABLES

Space charge measurement by the PEA method requires a calibration step necessary to identify the transfer function of the PEA cell. This step consists of applying a relatively low electric field in order not to inject charges into the cable and to consider that the output signal of PEA cell is the response of capacitive charges at the interfaces between the insulation and the internal and external SC. In the case of a pre-stressed cable, the presence of space charge within the insulation makes the hypothesis of the sole presence of capacitive charges invalid, and the calibration step must be adapted accordingly.

In order to identify the transfer function of the PEA cell for aged cables, two measurements are performed (Figure 6a) as proposed previously in the case of flat samples [START_REF] Chen | A novel calibration method in the presence of space charge in dielectric materials using the pulsed electroacoustic technique[END_REF]:

-A first measurement without applying voltage in order to measure the signal coming only from the internal space charge and the corresponding image charges; -A second measurement where a DC voltage is applied to measure a composite signal due to the internal space charge, the image charges and the capacitive charges. A first treatment consists of making the difference between the two measurements in order to obtain the signal only related to capacitive charges, which will then be used to identify the transfer function of the system. The second treatment is the classic deconvolution used to identify the transfer function of the system constituted by the PEA cell and the cable in a cylindrical geometry [START_REF] Vissouvanadin | Deconvolution techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF]:

-Identification of the response of the measuring cell from the response of capacitive charges on the external electrode -Identification of the cable transfer function taking into account the attenuation and dispersion of acoustic waves from the responses of capacitive charges on the internal and external electrodes. The synoptic of the signal conditioning scheme is shown in Figure 7 [START_REF] Vu | Space charge measurement by electroacoustic method: impact of acoustic properties of materials on the response for different geometries[END_REF]; details of the mathematical treatment are given in [START_REF] Vissouvanadin | Deconvolution techniques for space charge recovery using pulsed electroacoustic method in coaxial geometry[END_REF]. Note that in the present treatment, we do not account for the gradient in acoustic properties along the cable radius. Once the overall frequency response of the PEA cell and cable is identified, the electric field and the space charge density distribution in a previously charged cable and the evolution when a protocol is applied can be obtained. Figure 6b shows the residual space charge profiles corresponding to pre-charged cables during the long term ageing protocol, for different ageing times. The amount of stored charge increases with ageing time and the charge is positive, as was the polarity of the conductor [START_REF] Cènes | Implementation of space charge measurement using the Pulsed Electro-Acoustic method during ageing of HVDC model cable[END_REF]. During ageing, for sampling, the cable was cooled to room temperature with the voltage still applied, in a way that the accumulated space charges were "frozen".

LONG-TERM ON-LINE MEASUREMENTS BY PEA

An advantage of the test bench developed above is the possibility to measure space charges all along the ageing, in principle for days. Aside from the question of available data storage space that should be resolved (the frequency of data acquisition is 1 profile every 3 minutes), the main difficulty that came is a slow change in the shape of the acoustic signals being recorded which is not due solely to the evolution of the space charge density. After deconvolution, an overestimate of the charge density was obtained. This drift in the acoustic response resulted from different sources:

-The mechanical pressure imposed to the cable for acoustic signal detection could evolve in time at the scale of days due to mechanical creeping of the material. This may also result in a change in cable shape. Figure 7: Synoptic of deconvolution method on PEA signal from cable [START_REF] Vu | Space charge measurement by electroacoustic method: impact of acoustic properties of materials on the response for different geometries[END_REF].

-The temperature of the test cell could evolve slightly.

-The periodic (weekly) sampling of the cable imposed to stop application of high voltage, and reducing the length of one cable (for sampling and preparing terminations) changed the capacitance of the load viewed by the pulse generator. -In the event of breakdown or incident on the test bench, the cable heating had to be stopped which could change the thermo-mechanical stress on the sample.

All these possibilities produce a drift in the transfer function of the system and prevent reliable analysis of the data over a long period. Figure 8 shows examples of rough calibration signals obtained at the beginning of the ageing protocol with PR, and after 7 weeks of ageing. The position of the peaks has evolved along with the delay between the responses from the two interfaces. Space charge profile accumulated during the ageing). As an indication, PEA measurements can be reasonably done for a few days without calibrationbut this may depend on the temperature. Tighter control of the geometry of the cable, of pressure exerted on it and keeping the environment unchanged are ways to improve the reliability of the long term measurements.

CONCLUSION

We have presented the implementation of a test bench for simultaneous ageing and space charge characterization of model cables for HVDC applications, the ageing cycle combining voltage application, grounding, and/or polarity reversal steps. This short-term ageing is achieved with a thermal gradient applied to the cable. We have shown the feasibility of realizing continuous measurement of space charges during ageing for several weeks using the pulsed electroacoustic method. The temperature gradient in the aged cable loop is controlled by the AC current injected in the conductor through a current transformer and by the surface temperature. Custom DC voltage cycles up to +/-100kV can be defined and applied using two HVDC supplies and a high voltage switch. The PEA hardware is the one developed for model cables where the pulse is applied through a separate cable loop. In this way, higher fields could be applied as the weak points in cable samples were moved to cable terminations. Two main bottlenecks were encountered. The first one is the temperature gradient control at the measurement point for space charge. As the PEA cell acts as a heat sink, the temperature is lower than it is in the rest of the cable loop outside of the cell. A way to fix this while keeping online space charge monitoring, could be to control temperature of the PEA cell by means of a heating system. The second challenge resorts to the drift of the transfer function of the PEA test cell as a function of ageing time. This drift can be due to an evolution of the test object and / or of the mechanical stress. A procedure for calibration of the PEA on a pre-charged cable was implemented. An update of the calibration then becomes possible during the ageing, limiting the impact of the transfer function drift. Using the same test bench, it is possible to probe space charges in cable sections aged under thermoelectric stress in separate conditions, the procedure for calibration on pre-charged cable sections being necessary for such case.

BIBLIOGRAPHY

Figure 1

 1 Figure 1. a) Model cable geometry, b) electric field distribution for the model cable when the applied voltage is 90kV.

Figure 5 .

 5 Figure 5. Space charge cartography measured on a model cable stressed during 24 hours with PR. The colour scale refers to charge density, in C/m 3 .

Figure 4 .

 4 Schematic representation of a) the sequences of applied voltage and polarity reversal, and b) detail of voltage variation during two periods of PR.

  a) PEA signal of an aged cable: before calibration, during calibration (with 15kV applied DC voltage), and calibration signal of an aged cable used for identification of the cell transfer function; The peak to the left corresponds to the response at the outer screen/XLPE interface. b) Measured charge density profiles on as received aged cables at different ageing times.

Figure 8 :

 8 Figure 8: Rough PEA (calibration) signals obtained with 15kV DC voltage, at the beginning of the ageing under PR and after 7 weeks.

Table 1 -

 1 Relation between interface temperatures and injected current in model cables.

	See


A Mazzanti

Z Yang

M G Silva

N Yang

G Rizza

P E Coulon

C Manzoni

A M De Paula

G Cerullo

G Della Valle

M P Pileni

Light-Heat Conversion: Tracking Photothermal Energy Flow in Highly Diversified Water-Dispersed Hydrophobic Nanocrystal Assemblies

Keywords:

Significant

The last decade has witnessed an explosive growth of interest in the photothermal properties of nanostructures, for both fundamental and applied aspects (e.g., ref. [START_REF] Govorov | Generating heat with metal nanoparticles[END_REF] and references therein). A striking application is photothermal therapy for cancer, in which light, following irradiation of nanocrystals (NCs), is converted to cytotoxic heat to selec-tively kill cancer cells and minimize the invasive injury to normal tissues [START_REF] Hirsch | Nanoshell-mediated near-infrared thermal therapy of tumors under magnetic resonance guidance[END_REF][START_REF] Park | Cooperative nanomaterial system to sensitize, target, and treat tumors[END_REF][START_REF] Huschka | Visualizing light-triggered release of molecules inside living cells[END_REF][START_REF] Huang | Biodegradable gold nanovesicles with an ultrastrong plasmonic coupling effect for photoacoustic imaging and photothermal therapy[END_REF][START_REF] Zhihong | Near-infrared light-responsive inorganic nanomaterials for photothermal therapy[END_REF][START_REF] Jaqued | Nanoparticlesforphotothermaltherapies[END_REF]. Another notable example of the high impact of nanoparticles' photothermal properties is repre-sented by the demonstration of novel solar photodevices for water vapor generation [START_REF] Neumann | Compact solar autoclave based on steam genera-tion using broadband light-harvesting nanoparticles[END_REF][START_REF] Ghasemi | Solar steam generation by heat localization[END_REF] and direct sunlight-driven desali-nation [START_REF] Dongare | Nanophotonics-enabled solar membrane distillation for off-grid water purification[END_REF].

Most of the studies in the field deal with Au nanoparticles. The development of novel and possibly more effective photothermal agents requires the understanding of the energy flow upon opti-cal excitation of the nanostructure. For plasmonic NCs, this is well known to be governed by a cascade of dynamic relaxation processes, namely electron-electron scattering, electron-phonon scattering (and subsequent dephasing of acoustic vibrations), and phonon-phonon scattering, the latter culminating in the heat transfer from each nanoparticle to its microenvironment [START_REF] Hartland | Optical studies of dynamics in noble metal nanostructures[END_REF]. However, unexpected and novel reactions of the medium upon light irradiation and subsequent electron relaxation have been observed in more complex systems [START_REF] Hogan | Nanoparticles heat through light localization[END_REF][START_REF] Neumann | Nanoparticle-mediated, light-induced phase separations[END_REF][START_REF] Mukherjee | Hot-electron-induced dissociation of H2 on gold nanoparticles supported on SiO2[END_REF]: The combination of multiple scattering processes induces formation of either steam or a liquid vapor phase within a reduced volume even when the temperature of the bulk fluid volume remains far below its boiling point. Furthermore, hot-electron-induced photodissoci-ation of H 2 was demonstrated by Au nanoparticles supported on SiO 2 . These recent data clearly indicate that the heat release mechanisms in composite nanomaterials are far from being fully understood and several open questions remain. This is partic-ularly true for NC assemblies, as the interaction between NCs and the heat transfer through molecular linkers can, in principle, strongly change the thermal properties of these nanostructures and, subsequently, the dynamics of the photothermal energy conversion [START_REF] Govorov | Generating heat with metal nanoparticles[END_REF].

NC assemblies have attracted increasing interest in the past few years (see, e.g., ref. [START_REF] Boles | Self-assembly of colloidal nanocrystals: From intricate structures to functional materials[END_REF] for an overview). Advances in colloidal synthesis have enabled the manufacturing of NCs with uniform size, shape, chemical composition, and crystallinity, which in turn allowed their selfassembly in 3D ordered structures. Such assemblies, with a well-defined lattice configuration [e.g., face-centered cubic (fcc), body-centered cubic (bcc), etc.], are similar to atoms in crystals and are thus referred to as supracrystals [START_REF] Courty | How to control the crystalline structure of supracrystals of 5-nm Ag nanocrystals[END_REF]. Depending on the experimental conditions, amorphous 3D aggregates can also be produced [START_REF] Wan | Hierarchy in Au nanocrystal ordering in supracrystals: A potential approach to detect new physical properties[END_REF]. The growth mech-anism of these assemblies involves several factors [START_REF] Thanh | Mechanisms of nucleation and growth of nanoparticles in solution[END_REF] leading to a complex and hard to predict behavior in the formation of shaped supracrystals that depends on the affinity between the solvent and the coating agents [START_REF] Talapin | A new approach to crystallization of CdSe nanoparticles into ordered three-dimensional superlattices[END_REF][START_REF] Kalsin | Electrostatic self-assembly of binary nanoparticle crystals with a diamond-like lattice[END_REF]. Being difficult to sta-bilize in aqueous solution, supracrystals are typically available and widely investigated in dried configurations, i.e., supported on a substrate. This poses a severe limitation on the develop ment of real-world photothermal agents based on supracrystals, to be operated in vivo.

Very recently, some of the authors created hybrid structures, freely diffusing in water. They consist of hydrophobic inorganic NCs that selfassemble in either disordered or ordered structures due to the presence of hydrophilic organic materials (vesicles, surfactants, colloids). The synthesis of these structures exploits two basic concepts: (i) NCs standing at the interface between two immiscible liquids are highly mobile and can rapidly reach equilibrium through assembling. This enabled the demonstration of ferrite colloidosomes, i.e., shells of ferrite NCs, spherical fcc supracrystals, and egg structures, i.e., a supracrystal trapped in a colloidosome [START_REF] Yang | Supracrystalline colloidal eggs: Epitaxial growth and freestand-ing three-dimensional supracrystals in nanoscaled colloidosome[END_REF]. (ii) The packing is governed by interdigitation processes in the organic chains of the matrix ligands. This led to the first demonstration of thermodynamically stable supra self-assemblies, i.e., supraaggregates [START_REF] Lisiecki | Mesostructured fluids. 1. Cu(AOT) 2 -H 2 O-isooctane in oil rich regions[END_REF][START_REF] Lisiecki | Mesostructured fluids. 2. Microstructure and supra-aggregation[END_REF][START_REF] Kranenburg | Phase behavior and induced interdigita-tion in bilayers studied with dissipative particle dynamics[END_REF], and water-dispersed clustered structures of hydrophobic NCs and organic molecules [START_REF] Yang | Dispersion of hydrophobic Co supracrystal in aqueous solution[END_REF][START_REF] Yang | Water-dispersed hydrophobic Au nanocrystal assemblies with a plasmon fingerprint[END_REF].

To the best of our knowledge, the energy flow upon optical excitation in water-soluble assemblies of hydrophobic NCs is largely unexplored.

Here we study the specific heat release properties of 100-nm-size Au clustered structures, fer-rite (Fe 3 O 4 ) supraparticles (spherical fcc supracrystals), and Au/ferrite eggs, i.e., (Fe 3 O 4 )Au 13 assemblies trapped in ferrite colloidosomes. Our results indicate that the light-heat conversion in these kinds of nanomaterials is governed by a specific mechanism that relies on the intrinsic hybrid composition of the assembly involving optically active inorganic NCs and a matrix of organic ligands with relatively high heat capacity, embedded in a water environment. electron microscopy (TEM) image of individual assemblies shown in Fig. 1 B-D indicates a local ordering of the NCs. This is confirmed by the TEM image obtained after deposi-tion of a drop of the colloidal solution (Fig. 1E), which shows that the Au NCs are well ordered in a compact hexagonal network.

Results and Discussion

Spherical assemblies of Au NCs with ⇠ 5.5-nm diameter embed-ded in a matrix of 1-octadecane-thiol (C 18 H 37 SH) were syn-thesized (Materials and Methods). The average diameter of the assemblies was measured to be 160 ± 50 nm (Fig. 1A). The fast Fourier transform (FFT) pattern of the transmission electron microscopy (TEM) image of individual assemblies shown in Fig. 1 B-D indicates a local ordering of the NCs. This is confirmed by the TEM image obtained after deposi-tion of a drop of the colloidal solution (Fig. 1E), which shows that the Au NCs are well ordered in a compact hexagonal network.

The linear optical response of Au clustered structures dispersed in aqueous solution was characterized by extinction measurements with a standard spectrophotometer. The measured absorbance (Fig. 1F) exhibits a pronounced peak around 600 nm, which, according to a previous study [START_REF] Yang | Water-dispersed hydrophobic Au nanocrystal assemblies with a plasmon fingerprint[END_REF], is ascribable to a pho-tonic (i.e., collective) mode of the assembly, since its spectral position scales linearly with supracrystal size. To investigate the energy flow upon light irradiation, we per-formed pump-probe experiments with ultrashort laser pulses. A 100-fs pump pulse at 400-nm wavelength, generated by fre-quency doubling the output of an amplified Ti:sapphire laser system [START_REF] Pollid | High-time-resolutionpump-probesystemwithbroadband detection for the study of time-domain vibrational dynamics[END_REF], is used to excite the sample. A broad-band laser pulse focused on the sample at a given time delay t with respect to the pump pulse is used to dynamically probe the transient optical response. The differential transmission (T/T) spec-tra are recorded as a function of t and the probe wavelength . The results are shown in Fig. 2 A and B for visible and near-infrared probing, respectively. On the initial timescale of 10 ps, the transient signal resembles the typical T/T map recorded for plasmonic nanoparticles [spheres [START_REF] Brown | Experimental and ab initio ultrafast carrier dynamics in plasmonic nanoparticles[END_REF] or rods [START_REF] Wang | Broadband spectral signature of the ultrafast transient optical response of gold nanorods[END_REF][START_REF] Silva | Universal saturation behavior in the transient optical response of plasmonic structures[END_REF], for example]. In particular, the map crosssections at early time delays (black and red traces in Fig. 2A, Bottom) show the characteristic transient spectra of isolated NCs which are dom-inated by shift and broadening of the plasmonic resonances [START_REF] Silva | Universal saturation behavior in the transient optical response of plasmonic structures[END_REF]. Moreover, these spectra exhibit a decay constant of a few picoseconds (Fig. 2A) that is the timescale of electron-phonon scattering in noble metals [START_REF] Sun | Femtosecond-tunablemea-surement of electron thermalization in gold[END_REF]. See also Fig. 3A for the dynam-ics at selected probe wavelengths for delay times up to 10 ps. This demonstrates that in the ultrafast optical response the Au assemblies keep the fingerprint of their building blocks [START_REF] Yang | Water-dispersed hydrophobic Au nanocrystal assemblies with a plasmon fingerprint[END_REF]. However, on the longer timescales, the T /T of Au clustered structures exhibits very distinct features which, to the best of our knowledge, have not been reported in any metallic nanostruc-ture: Instead of a monotonic decrease over time, we observe the buildup of a positive signal which is red shifted by about 100 nm (blue and magenta traces in Fig. 2 A and B, Bottom) com-pared with the early spectra. The temporal dynamics at selected probe wavelengths, reported in Fig. 3B, detail the onset of this broadband transient signal within about 100-150 ps. To ascer-tain that the observed buildup is a phenomenon that cannot be ascribed to mechanical oscillations [which, in Au NCs, are well known to have a strong impact on the ultrafast optical response on this timescale [START_REF] Hartland | Optical studies of dynamics in noble metal nanostructures[END_REF]], we performed pump-probe measure-ments on the nanosecond timescale. The results, reported in Fig. 3C, confirm that after the buildup the signal remains con-stant on the nanosecond timescale. However, we see a clear-cut fingerprint of mechanical oscillations with an oscillation period T osc ⇠ 300 ps. We assign that oscillation to a breathing mode of the whole assembly by assuming an average speed of sound v s of the order of 1 km/s (i.e., T osc ' 2D/v s , with D = 160 nm), which makes sense considering the hybrid metal-organic com-position (v s in bulk gold being about 3.2 km/s).

Finally, note that this transient signal was not observed in dry Co assem-blies deposited on highly oriented pyrolytic graphite (HOPG) substrate [START_REF] Lisiecki | Coherent longitudinal acoustic phonons in three-dimensional supracrystals of cobalt nanocrystals[END_REF].

To understand the origin of the observed optical features and, in particular, of the unexpected transient optical response on the 100-ps timescale, we developed a model to simulate the opti-cal experiments. A 2D model of the supracrystal, based on the morphology detailed in Fig. 1A, is reported in Fig. 4A. Finite-element method (FEM) electromagnetic simulations retrieve the same wavelength position as in the experiment for the extinction peak in the simulated absorbance (black curve in Fig. 1G). Note that, different from the effective index approximation of ref. [START_REF] Yang | Water-dispersed hydrophobic Au nanocrystal assemblies with a plasmon fingerprint[END_REF], the present model fully mimics (even though in 2D) the nano-structuring of the assembly: A square lattice arrangement of Au NCs is embedded in the C 18 H 37 SH matrix and surrounded by a thin (3-nm) layer of dipalmitoylphosphatidylcholine (DPPC) (Fig. 4A). For comparison, we also performed numerical simula-tions of a triangular arrangement of NCs with the same density (SI Appendix). The static optical response turned out to be similar to that retrieved from the square lattice configuration (compare solid curves with dashed-dotted curves in Fig. 1G). This result indicates that our assemblies behave as metaparti-cles, rather than finite arrays of NCs, as the collective effects are not dominated by Bragg scattering mechanisms, but rather by the onset of an effective medium, in agreement with the approxima-tions made in ref. [START_REF] Yang | Water-dispersed hydrophobic Au nanocrystal assemblies with a plasmon fingerprint[END_REF]. Interestingly, despite the thickness of the assembly, the power absorbed per unit volume ⇢ at the 400nm excitation wavelength (Fig. 4B) is more uniform compared with that in a Au nanosphere of the same diameter. This is due to the higher penetration depth of light in the supracrystal struc-ture (about 60 nm, which is almost four times larger than in bulk Au at the same wavelength) in view of the dilution of the metallic phase. If and how the organic phase in the assembly contributes to the energy flow dynamics and thus to the performance of the supracrystal as a nanoheater is the main subject of the study detailed below. In the spirit of the semiclassical models reported for plasmonic nanomaterials [noble metals [START_REF] Zavelani-Rossi | Transient optical response of a single gold nanoantenna: The role of plasmon detuning[END_REF] and heavily doped [START_REF] Valle | Ultrafast optical mapping of nonlinear plasmon dynamics in Cu 2x Se nanoparticles[END_REF] and even all-dielectric [START_REF] Gaspari | Quasi-static resonances in the visible spectrum from all-dielectric intermediate band semiconductor nanocrystals[END_REF] semiconductors] a set of dynamical variables (usually temperatures) describing the different energy degrees of freedom is introduced and coupled together in a system of rate equations. For the hybrid metal-organic structure of Au assemblies we adopted the following four-temperature model (4TM): N = p a (t)-aN, [START_REF] Govorov | Generating heat with metal nanoparticles[END_REF] gqEq'E = aN -g ( qE -qL) [2] cLq'L =g( qE -qL) -g0( qL -qO)

[3] fcOq'O = g0( qL -qO) [START_REF] Huschka | Visualizing light-triggered release of molecules inside living cells[END_REF] In Eqs. 1-4, the dot indicates the first derivative with respect to time, and N, qE, qL,and qO respectively are the energy density of the out-ofequilibrium electrons in the metal, the temperature of thermalized electrons in the metal, the temperature of the metal lattice, and the temperature of the organic subsystem (C 18 H 37 SH) embedding the NCs. the electron-phonon cou-pling constant, and a = 15 THz the hot electrons' heating rate at 400-nm pumping [START_REF] Zavelani-Rossi | Transient optical response of a single gold nanoantenna: The role of plasmon detuning[END_REF]. The 3TM of gold is then coupled to a fourth equation, Eq. 4, that models the energy dynamics of the organic matrix of lattice heat capacity c O =1.917⇥10 ), with g O the coupling rate between gold phonons and the phonons of the organic matrix (to be fitted on the experimental data). In Eq. 4, f = V O /V Au ± 2 is the ratio between the volume of the organic matrix V O and the volume of the metallic phase V Au = nV i , with n being the estimated number of NCs in the assembly (SI Appendix), with V i =(4/3)pr 3 , i.e., the average volume of each NC. With the numerical solution of Eqs. 1-4 at hand (Fig. 4 D and E), the permittivity change of the metallic and of the organic phases of the assembly is then computed as a function of the probe wavelength and time delay. In brief, N (t ) and ( qE(t ) are responsible for a modulation of the interband transitions in gold, which is dominated by the Fermi-smearing mechanism due to the hot electrons at temperature ⇥ E (t)>>300 K; qL(t) accounts for a variation of the Drude permittivity belonging to gold free electrons, whose scattering rate with phonons linearly increases with the lattice temperature; and finally, qO(t) translates into a variation of the refractive index n O of the C 18 H 37 SH matrix due to the thermo-optical effect.

Note that

6 J•m 3 •K 1 ( 36
The corresponding DeN, DeE, and DeL are retrieved by following the same approach detailed in previous papers on the 3TM of gold (e.g., ref.

33 and refer-ences therein). Regarding the permittivity variation induced in the organic matrix, this is computed as DeO = 2n Oh D qO , with h =dn O /dqO being a negative thermo-optics coefficient, of the order of 10 the good agreement with the experimental maps in Fig. 2 A and B. In particular, the model is capable of reproducing both the derivative behavior of the early spectra (on the first few picoseconds timescale) and the onset of the long-lived broadband positive signal on the 100-ps timescale. It should be noted that in the numerical simulations we assumed a much lower pump fluence, F ≠ 0.3 mJ/cm 2 , compared with the experimental value of 2.75 mJ/cm 2 . We believe that this discrepancy is mostly due to the simplification introduced with our 2D model of the supracrystal, which cannot achieve a quantitative match with the measurements, in terms of absorption and extinction cross-sections.

However, the spectral (Fig. 2 C and D, Bottom) and temporal (Fig. 3 D-F) cross-sections of the simulated maps further confirm the capability of the model to reproduce the dynamics of the transient optical response on the various time scales and on the very broad range of wavelengths explored in our experiments. In particular, the key role of the organic matrix is ascertained and its thermo-optical response turned out to be crucial to provide a consistent interpretation of the nonlinear response of the Au clustered structures. Neglect of this contribution results in a poor agreement with the experiments, both for the spectra (dotted magenta curve in Fig. 2 C andD) and for the dynamics (dotted curves in Fig. 3 E andF), as the model is unable to reproduce the rise of the signal observed on the 100-ps timescale. Note that its prominent contribution to the DT /T is a clear-cut indication of the high temperature increase, of about 15 K according to our simulations (Fig. 4E), attained after the absorption of a single pump pulse at a moderate fluence (2.75 mJ/cm 2 ). This is made possible by the specific collective regime of photo-temperature generation exploited in the assembly, in agreement with what is reported in a pioneering work by Govorov et al. [START_REF] Govorov | Gold nanoparticle ensembles as heaters and actuators: Melting and collective plasmon resonances[END_REF], where it has been theoretically shown that for clusters the photo-temperature is expected to increase fast with the number of NCs. On the contrary, the lattice arrangement seems to play no role, since the simulated traces of the T /T map retrieved by a triangular configuration (dashed-dotted curves in Figs. According to our model, the delayed buildup of the T/T signal on the few hundred picoseconds timescale is the sig-nature of the final step in the light-heat conversion process that ultimately results in the heating of the matrix of organic ligands. As such, this dynamical feature in the transient opti-cal response is expected to be an intrinsic property of any hybrid assembly of hydrophobic NCs, regardless of the pecu-liar nature (i.e., plasmonic or not) of their building blocks. To test this hypothesis we considered two other kinds of water-dispersed assemblies, namely ferrite supraparticles and eggs of Au/ferrite [START_REF] Yang | Dispersion of hydrophobic Co supracrystal in aqueous solution[END_REF]. As shown in Fig. 5A, spherical assemblies of ferrite NCs with an average size in the range of 200 nm are produced. The small-angle X-ray diffraction pattern (Fig. 5A, Inset) confirms the ordering of ferrite NCs in fcc supracrystals. These struc-tures exhibit a pronounced extinction peak at around 400 nm (Fig. 5B) which is mostly ascribable to absorption from ferrite NCs. The differential transmission maps are reported in Fig. 5C, with map cross-sections at selected probe wavelengths shown in Fig. 5D. Note that after the exhaustion of the initial dynamics that comprise both positive and negative signals (depending on wavelength) within the first 10 ps, the longer timescale exhibits a DT /T that monotonically increases and reaches its maximum within a few hundred picoseconds. These are precisely the same dynamics observed in Au clustered structures (Fig. 3), the differ-ences in the spectral profiles being related to the different kinds of resonances that dominate the linear extinction of the two kinds of assemblies.

A further evidence of the peculiarity of this mechanism is provided by Au/ferrite eggs. A TEM image of the sam-ple (Fig. 5E) shows formation of binary core (Fe 3 O 4 )Au 13 supracrystals trapped into a ferrite colloidosome. The linear extinction spectrum (Fig. 5F) is characterized by a shallow peak at around 580 nm, ascribable to the plasmonic resonance of the Au NCs. Actually, the DT /T map (Fig. 5G) resembles the one reported for Au clustered structures, both on the short timescale and on the long one (Fig. 2A), indicating that the plasmonic reso-nance from the metallic phase dominates on the absorption from the semiconducting nanostructures. Also for this structure we observe that the heating of the assembly takes place on the few hundred picoseconds timescale (Fig. 5H).

Conclusions and Perspectives

In this paper we have investigated the photothermal properties of water-soluble hybrid nanoassemblies: Au clustered structures, ferrite supracrystals, and Au/ferrite eggs. An extensive exper-imental and theoretical investigation of the transient optical response of these assemblies was performed with the aim of tracking the energy flow in these kinds of nanomaterials fol-lowing photoexcitation. Our results indicate that Au clustered structures exhibit very peculiar features, never observed in Au NCs or even larger (polycrystalline) gold nanoparticles or Co assemblies deposited on HOPG substrate [START_REF] Lisiecki | Coherent longitudinal acoustic phonons in three-dimensional supracrystals of cobalt nanocrystals[END_REF]. In particular we show that (i) due to the dilution of the metallic phase, the penetration depth of visible light is much greater than in homo-geneous metallic nanoparticles of similar size, thus enabling a high average thermal load in the whole assembly; (ii) the organic matrix, even though not directly absorbing, acts as an inter-nal reservoir for efficient accumulation of energy within few hundred picoseconds; (iii) for moderate excitation fluences we estimated a temperature increase in the assemblies that is fully compatible with hyperthermia [START_REF] Jaqued | Nanoparticlesforphotothermaltherapies[END_REF]; and (iv) the above features are due to the collective regime of photo-temperature genera-tion enabled by the assembling, since even though our model was validated on Au clustered structures, a similar behavior was experimentally observed with both Fe 3 O 4 NCs self-assembled in fcc spherical supracrystals (called supraparticles) and binary supracrystals [(Fe 3 O 4 )Au 13 ] trapped in colloidosomes. These results provide a clear-cut indication that such hybrid nano-structures can be operated as very efficient nanoheaters, with enhanced biocompatibility due to their larger size, high stability in water, and all of the fingerprints belonging to the NCs used as building blocks.

Materials and Methods

The synthesis of clustered structures has been published recently [START_REF] Yang | Dispersion of hydrophobic Co supracrystal in aqueous solution[END_REF][START_REF] Yang | Water-dispersed hydrophobic Au nanocrystal assemblies with a plasmon fingerprint[END_REF]. In brief, Au NCs with r ' 2.75 nm radius coated with C 18 H 37 SH and 5% size distribution are well dispersed in toluene. To produce shaped Au assemblies, we controlled the supracrystal growth process by subjecting the colloidal solution to a bad solvent for the alkyl chains [START_REF] Goubet | Which forces do control the supracrystal nucleation in organic media?[END_REF]. For a nucleation and growth process time of t 1 = 10 h and t 2 = 8 min, respectively, we obtained spherical assemblies with an average diameter of 160 ± 50 nm. Kranenburg et al. [START_REF] Kranenburg | Phase behavior and induced interdigita-tion in bilayers studied with dissipative particle dynamics[END_REF] demonstrated that the best interdigitation process is obtained with long-tail surfactant molecules and large head group sur-face area. Here the best interdigitation is obtained by using C 18 alkyl chains as a coating agent of Au NCs and DPPC characterized by two C 16 chains (SI Appendix). The synthesis of

Fig. 1 .

 1 Fig. 1. (A) TEM image of Au NC assemblies produced with 10 h nucleation ime and 8 min growth process time. (B-D) Samples of the FFT pattern of individual assemblies, corresponding to the areas highlighted in A. (E) TEM image of a drop of the colloidal solution of Au NCs. (F and G) Measured (F) and simulated (G) absorbance of the sample. G also shows the calculated absorption and scattering efficiencies from (solid lines) the square lattice model in Fig. 4A and (dashed-dotted lines) a triangular lattice model with the same density of NCs.

Fig. 2 .

 2 Fig. 2. Measured (A and B) and simulated (C and D) differential transmission maps T/T (Top) and map cross-sections at selected time delays (Bottom) for the water-dispersed Au clustered structures. The dotted curve in C and D is the result of a simulation which does not take into account the thermo-optical effect in the organic matrix. The dashed-dotted curves in C and D are calculated from a triangular lattice model with the same density of NCs as in the square lattice in Fig. 4A.

Fig. 3 .

 3 Fig. 3. Measured (A-C) and simulated (D-F) dynamics of the T/T sig-nal at selected probe wavelengths, on the three different timescales of energy flow in the Au clustered structures. The dotted curve in E and F is retrieved without taking into account the thermo-optical effect in the organic matrix, whereas the dashed-dotted curve in F is calculated from a triangular lattice model with the same density of NCs as in the square lattice in Fig. 4A.

Eqs. 1 - 3

 13 basically represent the three-temperature model (3TM) which successfully describes the relaxation dynamics of Au NCs,

  (to be fitted on the experimental data), and D qO being the increase of the matrix temperature. Starting from the total permittivity change in the metal, DAu = DeE + DeN + DeE, and DeL, and in the organic matrix, Deo , induced by the pump pulse, the variation of the sample transmittance is retrieved perturbatively by FEM numerical analysis (SI Appendix).

Fig. 4 .

 4 Fig. 4. (A) Model geometry and mesh structure used in the 2D numerical simulations. Inset shows a zoom-in of the mesh to highlight the individ-ual Au domains. (B) Simulated power density (normalized to the peak value in the map) after the absorption of a pump pulse at 400 nm wave-length. (C) Cartoon of the two-phase assembly, made of metallic NCs (green) and organic matrix (cyan), and rationale of the 4TM used to simulate the pump-probe experiment, with each of the four dynamical variables giv-ing rise to a separate contribution to the permittivity of the two phases. (D and E) Numerical solution of the 4TM (N normalized to the peak of ⇥ E for better reading) on (D) the short timescale and (E) the long timescale.

2 C

 2 and D and 3F) are almost superposed to the corresponding traces computed from the square configuration (solid curves in Figs. 2 C and D and 3F).

Fg. 5 .

 5 (A) TEM image of ferrite supraparticles. Inset shows the X-ray diffraction spectrum. (B) Linear extinction spectrum of the sample. (C) Measured differential transmission maps T/T. (D) Map cross-sections at selected probe wavelengths (pump fluence of about 10 mJ/cm 2 at 400-nm wavelength). (E-H) Same as A-D but for Au/ferrite eggs. E, Inset details the structure of the core with (Left) the enlargement of the TEM image in E and (Right) the FFT pattern and a sketch of the binary core (Fe 3 O 4 )Au 13 supracrystal.

Fe 3 O

 3 [START_REF] Huschka | Visualizing light-triggered release of molecules inside living cells[END_REF] supraparticles was already reported[START_REF] Yang | Dispersion of hydrophobic Co supracrystal in aqueous solution[END_REF], and Au/ferrite eggs are obtained by revisiting the synthesis of ferrite supraparticles. Here 6.5nm Fe 3 O 4 NCs coated with oleic acid and 3.5-nm Au NCs coated with dodecanthiol are dispersed in chloroform containing octadecene, whereas the remaining procedure is unchanged. At the end of the synthesis, the colloidal solution is dispersed in water. See SI Appendix for further details. ACKNOWLEDGMENTS. This work was supported by the advanced grant of the European Research Council (Contract 267129). M.G.S. and A.M.d.P. acknowledge financial support from the Brazilian funding agencies Co-ordenac ̧a ̃o de Aperfeicoamento de Pessoal de Nı ́vel Superior, Fundac ̧a ̃o de Amparo a` Pesquisa do Estado de Minas Gerais, and Conselho Nacional de Desenvolvimento Cientı ́fico e Tecnolo ́gico. G.D.V. acknowledges the project Ministero dell'Istruzione dell'Universita` e della Ricerca -Progetti di Rilevante Interesse Nazionale 2015 Grant 2015WTW7J3 (Hot-electrons in self-organised plasmonic metasurfaces coupled to semiconducting MoS 2 nanosheets) for financial support.