Enzo Bertuit

Emilia Benassai

Guillaume Mériguet

Jean-Marc Greneche

Benoit Baptiste #

Sophie Neveu

Claire Wilhelm

Ali Abou-Hassan
email: ali.abou_hassan@sorbonne-universite.fr

Structure-Property-Function Relationships of Iron Oxide Multi-Core Nanoflowers in Magnetic Hyperthermia and Photothermia

Keywords: multi-core iron oxides, nanoflowers, magnetic nanoparticles, magnetic hyperthermia, photothermia, nanothermal agents, thermal therapies MAGNETIC GRAIN SIZES Powder XRD

Magnetite and maghemite multi-core nanoflowers (NFs) synthesized using the modified polyol-mediated routes are to date among the most effective nano-heaters in magnetic hyperthermia (MHT). Recently, magnetite NFs have also shown high photothermal (PT) performances in the most desired second near infra-red (NIR-II) biological window making them attractive in the field of nanoparticle-activated thermal therapies. However, what makes magnetic NFs efficient heating agents in both modalities still remain an open question. In this work, we investigate the role of many parameters of the polyol synthesis on the final NFs size, shape, chemical composition, number of cores and crystallinity. These nanofeatures are later correlated to the magnetic, optical and electronic properties of the NFs as well as their collective macroscopic thermal properties in MHT and PT to find relationships between their structure, properties and function. We evidence the critical role of iron(III) and heating ramps on the elaboration of well-defined NFs with high number of multi-cores. While MHT efficiency is found to be proportional to the average number of magnetic cores within the assemblies, the optical responses of the NFs and their collective photothermal properties depend directly on the mean volume of the NFs (as supported by optical cross sections numerical simulations) and strongly on the structural disorder in the NFs, rather than the stoichiometry. The concentration of defects in the nanostructures, evaluated by photoluminescence and Urbach energy (EU), evidences a switch in the optical behavior for a limit value of EU = 0.4 eV where a discontinuous transition from high to poor PT efficiency is also observed.

Introduction

Due to their unique physico-chemical properties, multi-core iron oxide nanoparticles (NPs) also called nanoflowers (NFs), are used as functional materials in many applications, [START_REF] Stanković | Iron Oxide Nanoflower-Based Screen Print Electrode for Enhancement Removal of Organic Dye Using Electrochemical Approach[END_REF][START_REF] Han | Construction of Magnetic Nanoflower Biocatalytic System with Enhanced Enzymatic Performance by Biomineralization and Its Application for Bisphenol A Removal[END_REF][START_REF] Moyano | Carbon-Coated Superparamagnetic Nanoflowers for Biosensors Based on Lateral Flow Immunoassays[END_REF][START_REF] Urraca | Magnetic Field-Induced Polymerization of Molecularly Imprinted Polymers[END_REF] including for diagnosis and therapy in the biomedical field. [START_REF] Pelaz | Diverse Applications[END_REF][START_REF] Ognjanović | 99m Tc-, 90 Y-, and 177 Lu-Labeled Iron Oxide Nanoflowers Designed for Potential Use in Dual Magnetic Hyperthermia/Radionuclide Cancer Therapy and Diagnosis[END_REF][START_REF] Curcio | Iron Oxide Nanoflowers @ CuS Hybrids for Cancer Tri-Therapy: Interplay of Photothermal Therapy, Magnetic Hyperthermia and Photodynamic Therapy[END_REF][START_REF] Van De Walle | Magnetic Nanoparticles in Regenerative Medicine: What of Their Fate and Impact in Stem Cells?[END_REF] NFs are efficient magnetic resonance imaging (MRI) contrast agents [START_REF] Hu | Highly Dispersible, Superparamagnetic Magnetite Nanoflowers for Magnetic Resonance Imaging[END_REF] and performant nano-heaters in magnetic hyperthermia (MHT), with specific loss powers (SLP) values amongst the highest reported ones for magnetic materials. [START_REF] Hugounenq | Iron Oxide Monocrystalline Nanoflowers for Highly Efficient Magnetic Hyperthermia[END_REF][START_REF] Espinosa | Magnetic (Hyper)Thermia or Photothermia? Progressive Comparison of Iron Oxide and Gold Nanoparticles Heating in Water, in Cells, and in Vivo[END_REF] NFs efficiencies are explained by the presence of magnetic exchange couplings within the cores forming the flower-like assemblies, endowing them with enhanced magnetic relaxivity and susceptibility. [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF] Because of a lower surface/volume ratio, NFs also present lower spin surface disorders when compared to single-core structures. [START_REF] Dutta | Size Dependence of Magnetic Parameters and Surface Disorder in Magnetite Nanoparticles[END_REF] More recently, magnetic NFs have been proved to be promising materials for photothermal therapy (PTT) thanks to their absorption in the first [START_REF] Shaw | γ-Fe2O3 Nanoflowers as Efficient Magnetic Hyperthermia and Photothermal Agent[END_REF] (around 808 nm for maghemite) and second [START_REF] Cabana | Iron Oxide Mediated Photothermal Therapy in the Second Biological Window: A Comparative Study between Magnetite/Maghemite Nanospheres and Nanoflowers[END_REF] (around 1064 nm for magnetite) infra-red biological windows. However, how the fine structure features of NFs at the nanoscale govern their properties and their collective function in MHT and PT still needs to be elucidated.

As magnetic [START_REF] Frison | Magnetite-Maghemite Nanoparticles in the 5-15 Nm Range: Correlating the Core-Shell Composition and the Surface Structure to the Magnetic Properties. A Total Scattering Study[END_REF][START_REF] Bender | Relating Magnetic Properties and High Hyperthermia Performance of Iron Oxide Nanoflowers[END_REF][START_REF] Kolhatkar | Tuning the Magnetic Properties of Nanoparticles[END_REF] and optical [START_REF] Espinosa | Influence of Nanoparticle Size on the Nonlinear Optical Properties of Magnetite Ferrofluids[END_REF] properties of NPs directly rely on their size, shape, crystallinity and chemical composition, the control over the synthesis of NFs is of primary importance. Nevertheless, the understanding of the experimental synthesis parameters enabling the control of their formation is still scarce in literature. [START_REF] Gavilán | Formation Mechanism of Maghemite Nanoflowers Synthesized by a Polyol-Mediated Process[END_REF][START_REF] Hemery | Tuning Sizes, Morphologies, and Magnetic Properties of Monocore Versus Multicore Iron Oxide Nanoparticles through the Controlled Addition of Water in the Polyol Synthesis[END_REF][START_REF] Freis | The Size, Shape, and Composition Design of Iron Oxide Nanoparticles to Combine, MRI, Magnetic Hyperthermia, and Photothermia[END_REF] To yield well-defined and monocrystalline magnetic NFs, different high temperature synthesis strategies have already been reported. For example, the so-called thermal decomposition of organometallic compounds (ACAC routes) results in the formation of hydrophobic NFs stable in diverse organic solvents. [START_REF] Zhang | Sterically Induced Shape Control of Magnetite Nanoparticles[END_REF][START_REF] Nikitin | Synthesis of Iron Oxide Nanoclusters by Thermal Decomposition[END_REF] Conversely, polyol-mediated syntheses, historically developed by Fievet, Lagier and Figlars, [START_REF] Fievet | Monodisperse Métal Powders in Micrometer and Submicrometer Sizes by the Polyol Process[END_REF]26 provide hydrophilic NFs highly stable in aqueous media. [START_REF] Maity | Polyol-Based Synthesis of Hydrophilic Magnetite Nanoparticles[END_REF][START_REF] Abbas | Modified Polyol Route for Synthesis of Fe3O4/Ag and α-Fe/Ag Nanocomposite[END_REF] To induce the formation of flower-like structures by polyol processes, surfactants can be added in the reactive media or mixtures of different polyols can be used. [START_REF] Caruntu | Reactivity of 3d Transition Metal Cations in Diethylene Glycol Solutions. Synthesis of Transition Metal Ferrites with the Structure of Discrete Nanoparticles Complexed with Long-Chain Carboxylate Anions[END_REF]30 The influence of different synthesis parameters (temperature slope and heating time, [START_REF] Hugounenq | Iron Oxide Monocrystalline Nanoflowers for Highly Efficient Magnetic Hyperthermia[END_REF] presence of water in the reaction mixture, [START_REF] Hemery | Tuning Sizes, Morphologies, and Magnetic Properties of Monocore Versus Multicore Iron Oxide Nanoparticles through the Controlled Addition of Water in the Polyol Synthesis[END_REF] nature of polyol solvents, [START_REF] Cheng | Facile Synthesis and Morphology Evolution of Magnetic Iron Oxide Nanoparticles in Different Polyol Processes[END_REF][START_REF] Roca | Design Strategies for Shape-Controlled Magnetic Iron Oxide Nanoparticles[END_REF] proportions of iron precursors [START_REF] Wetegrove | Formation of Maghemite Nanostructures in Polyol: Tuning the Particle Size via the Precursor Stoichiometry[END_REF] ) on the formation of iron oxide NFs has already been investigated but a clear overview is still missing.

Herein, in an attempt to rationalize the function of the NFs in MHT and PT and to understand the relationships between their structure at the nanoscale and their collective physical properties, we conducted a multi-scale materials science investigation ranging from a multi-parametric study of the synthesis parameters, their effect on the resulting NFs including their structure, electronic and magnetic properties to their heating function in MHT and PT as depicted in Scheme 1. First, the effect of heating conditions and iron precursor proportions on the resulting NP's characteristics including their morphology, size, stoichiometry, number and size of multi-cores, crystallinity are investigated. From the collective behavior of the resulting colloidal suspensions to the crystal defaults using the electronic structure as a fingerprint, NFs characteristics are fully analyzed at different length scales to establish correlations between the synthesis conditions responsible of their structure, their magnetic and optical properties and finally to their function in MHT and PT in order to understand what governs both modalities.

We evidence the role of the synthesis conditions on the fine structure of the NFs including the number of cores and their size. We also demonstrate that the number of cores in the flower-like assemblies controls their magneto-thermal properties while the chemical stoichiometry and disorder defects govern their optical and photothermal behavior. S1). n-p) Schematic description of the morphologies (RF-NPs, NFs, IF-NPs) of the obtained NPs. Letters in brackets indicate the morphology of each sample.

Fe 3+ Fe 3+ Fe 3+ ! 0 = 1 Fe 2+ Fe 2+ Fe 2+ ! 0 = 0 Fe 3+ Fe 3+
A complete morphological study was carried out in order to determine which synthesis parameters are best suited for the production of monodisperse and well-defined iron oxide NFs. who obtained ≈20 nm NFs by applying a discontinuous multi-step heating ramp of 10°C/5min or a continuous heating of 2°C/min.

In order to investigate the effects of the chemical composition of the NPs on their magnetic and optical properties, a fraction of all samples is oxidized. TEM images of three randomly chosen samples (E, G and K; see Figure S5 for TEM micrographs and size distributions) show that morphology did not change after oxidation, while only minor size changes are observed with mean values of < Doxidation(dTEM) > = 1.7% and < Doxidation(sTEM) > = 15% before and after the oxidation step. As surface state can also affect magnetic and optical properties, [START_REF] Cotin | Unveiling the Role of Surface, Size, Shape and Defects of Iron Oxide Nanoparticles for Theranostic Applications[END_REF] the surface of the synthetized NPs is characterized by Fourier-Transform Infra-Red (FT-IR) spectroscopy on dried powders before and after oxidation for all samples. Identical spectral signatures are found for all samples with no significant changes before and after oxidation step (see Figure S6). The observed vibrations and stretching bands are in good agreement with previously reported spectra for acidic aqueous ferrofluids with NO3 - counterions (see Table S2). [START_REF] Talbot | PH-Sensitive Magnetic Alginate/γ-Fe2O3 Nanoparticles for Adsorption/Desorption of a Cationic Dye from Water[END_REF] The synthetized particles are analyzed by powder X-ray diffraction for crystalline phase identification. All samples are compatible with a spinel structure (see Figure S7a) characteristic of Fe3O4 or g-Fe2O3 crystalline phases. A very small but significant shift of D2q = 0.0152° ± 0.001° towards higher angular values, corresponding to a small decrease of the lattice parameter, is observed for the set of oxidized samples by analyzing (220), (311) and (440) peak positions (see Figure S7b). These results suggest, as already reported, a higher oxidation state meaning a lower Fe II /Fe III ratio. [START_REF] Annersten | Vacancy Distribution in Synthetic Spinels of the Series Fe304-y-Fe203[END_REF][START_REF] Gorski | Determination of Nanoparticulate Magnetite Stoichiometry by Mossbauer Spectroscopy, Acidic Dissolution, and Powder X-Ray Diffraction: A Critical Review[END_REF][START_REF] Gotić | Study of the Reduction and Reoxidation of Substoichiometric Magnetite[END_REF][START_REF] Schmidbauer | Magnetic Hysteresis Properties, Mössbauer Spectra and Structural Data of Spherical 250nm Particles of Solid Solutions[END_REF][START_REF] Voleník | A Mössbauer and X-Ray Diffraction Study of Nonstoichiometry in Magnetite[END_REF][START_REF] Yang | Magnetic and Structural Studies of the Verwey Transition in Fe3-δO4 Nanoparticles[END_REF] To quantify the stoichiometry of both non-oxidized and oxidized samples sets, XANES analyses (see Figures S8 andS9) are performed on some samples. Correction, normalization and analysis of the experimental raw data (Equations S1 to S5) are fully described in the supplementary information (see Figure S10). [START_REF] Sun | XAFS in Dilute Magnetic Semiconductors[END_REF][START_REF] Kuzmin | EXAFS and XANES Analysis of Oxides at the Nanoscale[END_REF][START_REF] Fdez-Gubieda | X-Ray Absorption Fine Structure Spectroscopy in Fe Oxides and Oxyhydroxides[END_REF][START_REF] Šutka | Study of the Structural Phase Transformation of Iron Oxide Nanoparticles from an Fe2+ Ion Source by Precipitation under Various Synthesis Parameters and Temperatures[END_REF][START_REF] Wilke | Oxidation State and Coordination of Fe in Minerals: An Fe K-XANES Spectroscopic Study[END_REF][START_REF] Petit | Determination of the Iron Oxidation State in Earth Materials Using XANES Pre-Edge Information[END_REF][START_REF] Piquer | Fe K-Edge X-Ray Absorption Spectroscopy Study of Nanosized Nominal Magnetite[END_REF][START_REF] Rubio-Zuazo | Electronic Structure of FeO, γ -Fe 2 O 3 , and Fe 3 O 4 Epitaxial Films Using High-Energy Spectroscopies[END_REF] Interestingly, the presence of iron(II) is found in the NPs even when the syntheses are carried out with iron(III) only (x0 = 1). These results strongly suggest that DEG and/or NMDEA behave as in situ reducing agents of iron(III). Such hypothesis is reinforced by the detection inside the refluxing column of an aldehyde (oxidation product of alcohols) thanks to a silver mirror Tollens test (see Figure S11). At the same time, iron(III) is found for the syntheses starting from iron(II) only (x0 = 0). No correlation is found between x0 and R values and all samples are found to be off-stoichiometric magnetite (see Table S3). All these results highlight that NPs formation and stoichiometry control are involving complex processes that still need to be clarified. Upon oxidation of the NPs, iron(II) amount decreases in the structures reaching almost zero (R ≲ 0.05) in most cases (see Table S3). To gain more insights on the distribution of magnetite and maghemite phases in the nanostructures, Mössbauer spectroscopy is performed at 77 K on representative samples C and Cox (well-defined NFs). The spectra (see Figure S12) show different hyperfine structures with fairly well-defined magnetic sextets, typical of the presence of magnetically blocked NPs. Indeed, spectra of sample Cox can be well described by means of two magnetic sextets while the one of sample C requires at least five components, in agreement with the presence of almost exclusively maghemite and a mixture of magnetite and maghemite, respectively. According to previous studies, [START_REF] Gerber | Low Oxidation State and Enhanced Magnetic Properties Induced by Raspberry Shaped Nanostructures of Iron Oxide[END_REF][START_REF] Gerber | Synthesis Engineering of Iron Oxide Raspberry-Shaped Nanostructures[END_REF] their proportions can be estimated from the mean value of the isomer shift (see Table S4), giving rise to 100 ± 1 % (sample Cox, < diso > = 0.455 mm/s) of maghemite and 40 ± 3 % (sample C, < diso > = 0.565 mm/s) of maghemite (with the presence of Fe 3+ and Fe 2+ species, as well as intermediate oxidations state [START_REF] Doriguetto | Characterization of a Natural Magnetite[END_REF] ). As shown from HR-TEM micrographs (see Figure S13), the NFs are almost perfect monocrystalline structures, with a very small angular mosaicity of 5.5 ± 0.2°. Assuming a magnetite-maghemite core-shell model [START_REF] Sharifi Dehsari | Determining Magnetite/Maghemite Composition and Core-Shell Nanostructure from Magnetization Curve for Iron Oxide Nanoparticles[END_REF] for the assembly (dTEM = 18.4 nm for sample C), the NFs consist of a magnetite core of 9.6 nm diameter and a maghemite mean shell about 4.4 nm thick. Such a mixed structure agrees quite well with that observed with the spherical NPs prepared using ammonium R4NOH alkaline agents with increasing aliphatic chain lengths (R = methyl, ethyl, propyl). [START_REF] Santoyo Salazar | Magnetic Iron Oxide Nanoparticles in 10-40 Nm Range: Composition in Terms of Magnetite/Maghemite Ratio and Effect on the Magnetic Properties[END_REF] The reduction of the thickness of the shell when compared to spherical NPs can be explained by the nature of NPs aggregated into flower-like structures. Their densification prevents from the oxidation and thus the oxidized shell is smaller. As the synthesis pathways of all NPs are comparable, we can assume that all non-oxidized samples present a core-shell structure composed of a magnetite core and a small maghemite shell, while oxidized samples are mainly composed of maghemite.

Correlating the structure of the NFs to their function in magnetic hyperthermia

It has already been reported that multi-core NPs present enhanced magnetic properties when compared to single-core NPs, as surface disorder is drastically decreased. [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF] The exchange coupling between the multi-core NPs also modifies the dynamic of the magnetic moments in a way that thermal losses are increased. As a result, saturation magnetizations and MHT efficiencies are often better for flower-like structures than for single-core NPs. [START_REF] Cabana | Iron Oxide Mediated Photothermal Therapy in the Second Biological Window: A Comparative Study between Magnetite/Maghemite Nanospheres and Nanoflowers[END_REF] The magnetic properties of all samples are investigated in solid state under static magnetic field conditions and all samples show a superparamagnetic behavior (see Figure S14). The TGA-corrected saturation magnetization values (Equations S6 and S7, see Table S5) of non-oxidized and oxidized samples range around MS = 70 + 10 emu/gmat, consistent with previous reported values of ≈75 emu/gmat 20 and ≈60 emu/g 57 and for Fe3O4/g-Fe2O3 NFs and spheres, respectively.

Evolution of magnetic properties with temperature is investigated by zero field cooled and field cooled (ZFC/FC) measurements (see Figure S15) to gain information about the blocking temperature (TB) for samples with different shapes, diameters and oxidation states (D, E, Gox, Kox, M, Mox). For all samples, TB ranges between 180 K and 295 K (see Table S6) which confirms the superparamagnetic behavior of the NPs at ambient temperature. As previously reported, TB is found to be higher in the case of multi-core NFs (D, E) and multi-core RF-NPs (Gox, Kox) when compared to single-core IF-NPs (M, Mox). As diameters of investigated samples ranges between 13 and 24 nm, such a difference may not only be due to diameter differences but also to the presence of couplings between the grains in the multi-core assemblies. Before recording magnetization curves in liquid phase, the colloidal stability of all samples is evidenced by DLS and zeta potential measurements (see Table S7 and Figures S16, S17, S18). M-H curves allow the determination of the diameter of the magnetic cores [START_REF] Chen | Size Determination of Superparamagnetic Nanoparticles from Magnetization Curve[END_REF] (dm) assembled in the flower-like structures (see Figures S19, S20 and S21) thanks to a log-normal weighted Langevin law (Equations S8 to S12). In the case of RF-NPs and NFs, an average value of < dm > = 8.2 ± 1 nm (see Table S5) is found consistently with the value of 8 ± 1 nm obtained from HR-TEM micrographs, in good agreement with previously reported value of 8.4 ± 1.5 nm determined by HR-TEM by Lartigue et al. [START_REF] Lartigue | Cooperative Organization in Iron Oxide Multi-Core Nanoparticles Potentiates Their Efficiency as Heating Mediators and MRI Contrast Agents[END_REF] Subsequently, the mean number of magnetic cores (NMC) per NP is evaluated by comparing physical (dTEM) and magnetic (dm) diameters (see Tables S1 andS5). Assuming that NPs and magnetic cores are spherical, NMC can be approximated as NMC = (dTEM/dm) [START_REF] Moyano | Carbon-Coated Superparamagnetic Nanoflowers for Biosensors Based on Lateral Flow Immunoassays[END_REF] . At the same time, MHT experiments are carried out to measure the SLP of each sample (Equation S13, see Table S5) using an alternative magnetic field of H = 180 G operating at f = 471 kHz, to stay close to the safe domain of application of [START_REF] Jordan | Magnetic #uid Hyperthermia (MFH): Cancer Treatment with AC Magnetic "eld Induced Excitation of Biocompatible Superparamagnetic Nanoparticles[END_REF] As shown in Figure 2a, non-oxidized and oxidized samples present the same NMC values meaning that the oxidation process does not affect the multi-core structure. Moreover, NMC(FH) is found to be significantly S5). To the best of our knowledge, such a linear correlation between MHT efficiency and the number of cores in the flower-like assemblies has not been evidenced before. The linear correlation found here (Figure 2c) may be explained by an increase of exchange couplings between the cores. Indeed, as already reported, [START_REF] Kostopoulou | Colloidal Magnetic Nanocrystal Clusters: Variable Length-Scale Interaction Mechanisms, Synergetic Functionalities and Technological Advantages[END_REF] the coupling energy can be written as:

magnetic field (H•flim = 5•10 9 A•m -1 •s -1 , H•f = 6.7•10 9 A•m -1 •s -1 here).
E coupling =-∑ ∑ J n,k •(S n (((⃗ N MC k≠n •S k (((⃗ ) N MC n=1 =-∑ ∑ J n,k •S n N MC k≠n •S k •cos(θ n,k ) N MC n=1 (1)
where Jn,k is the coupling constant between magnetic spins of core n (Sn) and core k (Sk) and decreases with the distance between Sn and Sk, and qn,k is the angle between the two magnetic spins Sn and Sk. According to Equation 1, a minimization of the coupling energy (i.e. a maximization of the exchange couplings) is obtained by maximizing NMC and minimizing qn,k value. FFT analyses of HR-TEM micrographs show an average value of < q > ~ 5.5°. Since the NPs are almost monocrystalline, we assume that all qn,k can be approximated to < q >, so that all cos(qn,k) tend to 1. The coupling energy thus becomes a function of NMC only. Consequently, the increase of MHT efficiency can be explained by the increase in the number of magnetic cores. Such results could help to the rationalized design of NFs with higher number of cores to maximize their heating efficiency in MHT modality by the use of very slow heating ramps.

Relating the structure of the NFs to their optical properties and function in photothermia

Along with being highly efficient in MHT, we have recently shown that magnetite NFs are also performant nano-heaters in NIR-II mediated PT. [START_REF] Cabana | Iron Oxide Mediated Photothermal Therapy in the Second Biological Window: A Comparative Study between Magnetite/Maghemite Nanospheres and Nanoflowers[END_REF] However, the reasons of their photothermal efficiency remained unclear. To rationalize the experimental optical data, we start by calculating the extinction spectra of stoichiometric Fe3O4 and g-Fe2O3 NPs using an extension of the Mie theory [START_REF] Tang | Magnetite Fe 3 O 4 Nanocrystals: Spectroscopic Observation of Aqueous Oxidation Kinetics †[END_REF][START_REF] Link | Simulation of the Optical Absorption Spectra of Gold Nanorods as a Function of Their Aspect Ratio and the Effect of the Medium Dielectric Constant[END_REF] based on complex refractive index 63 values (see Figure S23 and Tables S8, S9). To do so, we assume that NFs can be approximated as perfectly spherical NPs.

Calculations are performed for mean diameters ranging from 13 nm to 24 nm (Figures 3a-3d)

to include all the experimental values listed in Table S1. The different codes used here are based on the Mie Python module developed by S. Prahl. 64 Codes are provided and fully described in the supplementary information (see Figures S24 andS25). Simulation of the scattering and the absorption parts of the extinction cross section for Fe3O4 and g-Fe2O3 are shown in Figures 3a and4b, respectively. When the diameter values are set to the extreme experimental diameters obtained by TEM (dmin = 13 nm and dmax = 24 nm), absorption is found to be the predominant phenomenon and scattering effects can be totally neglected even for the highest diameter. A different absorption signature is found for both stoichiometric magnetite (Figure 3c) and maghemite (Figure 3d) NPs, especially in the NIR-II region (1000-1400 nm) where an absorption band is evidenced for magnetite only. This absorption band can be assigned to an intervalence charge transfer (IVCT) between Fe 3+ and Fe 2+ cations which can only occur in magnetite. [START_REF] Tang | Magnetite Fe 3 O 4 Nanocrystals: Spectroscopic Observation of Aqueous Oxidation Kinetics †[END_REF][START_REF] Cooper | Insights into the Magnetic Properties of Sub-10 Nm Iron Oxide Nanocrystals through the Use of a Continuous Growth Synthesis[END_REF] We thus focus on the NIR-II region and more precisely around 1064 nm since it is a laser wavelength used in NIR-II mediated PT experiments. [START_REF] Ge | Photoacoustic Imaging and Photothermal Therapy in the Second Near-Infrared Window[END_REF] For both magnetite and maghemite, the calculated extinction cross sections at 1064 nm are found to depend linearly on dTEM 3 for a given polydispersity, and exponentially on the polydispersity for a given diameter (Figure 3e • exp ,

9 • σ TEM 2 2
in order to linearize the optical responses with the physical shape. For a fixed < V > value, the extinction cross section of magnetite at 1064 nm is ≈100 times higher than for maghemite. The experimental particular extinction coefficient eexp(NP) is deduced from the molar extinction coefficient eexp(Fe) extracted from Beer-Lambert curves at 1064 nm (see Figure S29 and Table S10), according to Equations S14 and S15. In parallel, the theoretical particular extinction coefficient etheo(NP) is deduced from the calculated extinction cross section (sext)

according to Equation S16. A comparison between etheo(NP) and eexp(NP) as a function of the mean volume < V > is shown on Figure 4a. A good agreement is observed between the experimental and theoretical extinction coefficients for the set of non-oxidized samples, even if the stoichiometry of the sample deviated from the perfect stoichiometry considered in the simulations including low values around R = 0.16 (sample E). In the case of oxidized samples, experimental values deviate from the theoretical ones while their stoichiometry approaches the one of pure maghemite. The observed divergences may be due to intrinsic features of the NPs unrelated to stoichiometry and size which are not considered in the simulations. Indeed, factors such as shape imperfections, stoichiometry deviations or defects (vacancies and/or crystalline flaws) [START_REF] Belin | Influence of Grain Size, Oxygen Stoichiometry, and Synthesis Conditions on the γ-Fe2O3 Vacancies Ordering and Lattice Parameters[END_REF] may alter the electronic band structure of the NPs which in turn modify macroscopic material characteristics such as their optical properties. [START_REF] Sadat | Photoluminescence and Photothermal Effect of Fe 3 O 4 Nanoparticles for Medical Imaging and Therapy[END_REF] As both non-oxidized and oxidized NPs present comparable flower-like structures, the observed deviations from simulations for the oxidized samples may not be attributed to the spherical shape assumed in the calculations.

Similarly, both non-oxidized and oxidized samples are found to be off-stoichiometric with R non-ox ≠ R Fe 3 O 4 = 0.5 and R ox ≠ R Fe 2 O 3 = 0 (Table S3). So, the disagreement between the experimental and theoretical data cannot be attributed to stoichiometric deviations either.

Finally, the only remaining hypothesis for experimental deviations from calculations is the presence of intrinsic disorder in the NPs which influence the band structure of oxidized nanocrystals. To gain information about the semi-conductor band structure of the NPs, bandgap (Eg, see Figure S30 and Table S10) and Urbach (EU, see Figure S31 and Table S10) energies are deduced from UV-Vis-NIR spectra according to Equations S17-S18 and S19, respectively.

Both non-oxidized and oxidized samples present the same band-gap of < E g non-ox > = 3.5 ± 0.2 eV and < E g ox > = 3.4 ± 0.2 eV, which is close to the value of 3.1 eV reported by Fontjin et al. 63 As shown on Figure 4b, for the two sets of samples, ln[eexp(Fe)] linearly depends to 1/EU as predicted by the Urbach theory (Equation S20). Interestingly, oxidized samples exhibit lower EU values when compared to non-oxidized ones. The intensity of the IVCT is thus found to highly depend on the crystal defects: the higher the EU, the higher the extinction coefficient at 1064 nm. As already reported, small EU values correspond to high-defect systems [START_REF] Sadat | Photoluminescence and Photothermal Effect of Fe 3 O 4 Nanoparticles for Medical Imaging and Therapy[END_REF][START_REF] Akshay | Visible Range Optical Absorption, Urbach Energy Estimation and Paramagnetic Response in Cr-Doped TiO 2 Nanocrystals Derived by a Sol-Gel Method[END_REF][START_REF] Hassanien | Effect of Se Addition on Optical and Electrical Properties of Chalcogenide CdSSe Thin Films[END_REF][START_REF] Wasim | Effect of Structural Disorder on the Urbach Energy in Cu Ternaries[END_REF][START_REF] Ghandoor | Synthesis and Some Physical Properties of Magnetite (Fe3O4) Nanoparticles[END_REF][START_REF]Absorption Edge, Urbach Rule, Exciton (Electron)-Phonon Interaction, Disordering[END_REF] meaning that the conduction band shape of the oxidized samples is far from an ideal band. Consequently, differences between simulated and experimental data are explained by the presence of defaults in oxidized samples that are not considered in the calculations: defaults have a strong impact on the optical properties prevailing on stoichiometry. Focusing on non-oxidized NFs only, it is ). The light-to-heat efficiency extracted from this data analysis is equal to h = 29%, which is in perfect agreement with the previously reported value of 30% for Fe3O4 materials. [START_REF] Sangnier | Targeted Thermal Therapy with Genetically Engineered Magnetite Magnetosomes@RGD: Photothermia Is Far More Efficient Than Magnetic Hyperthermia[END_REF] The same adjustment is achieved for the oxidized samples but using < eexp(Fe) > = 12 L•molFe

Relating the structural defects of NPs to Urbach energy and photothermia

As established previously, structural defects have a direct impact on the optical properties of NPs and their function in PT, as translated by Urbach energy. In order to identify the nature of the defects and their proportions in the NPs, a complete photoluminescence study is carried out.

The fluorescence emission spectra (Figure 5a) of all investigated samples show two different emission bands located around 525 nm and 590 nm for an excitation at 232 nm. The green emission at 525 nm can be ascribed to the presence of oxygen vacancies [START_REF] Maibam | Photoluminescence and Intrinsic Ferromagnetism of Fe Doped Zinc Oxide[END_REF] within the spinel structures. Under irradiation of 232 nm, the created photo-excited holes (h * ) can combine with electrons trapped in singly-ionized (OO x ~ VO + + e -trapped) or uncharged (OO 2-~ VO x + 2e -trapped)

oxygen vacancies, respectively called F + -centers and F-centers. The subsequent deexcitation of electron-hole combinations gives rise to the emission of different photons according to the following reactions:

OO x + hvabs(232 nm) → VO + + e -trapped + h * + ½O2 → OO x + hvem(F + -centers) (2)
OO 2-+ hvabs(232 nm) → VO x + 2e -trapped + 2h * + ½O2 → OO 2-+ hvem(F-centers) (3)
where the Kröger-Vink 76 notation for defects is used and hv represents an absorbed (abs) or emitted (em) photon. The green emission is expected to be composed of two different contributions if both F and F + centers are present in the nanomaterial. The yellowish emission around 590 nm is usually ascribed to the presence of interstitial oxygen defects. [START_REF] Vijaya | Effect of Cu2+ Doping on Structural, Morphological, Optical and Magnetic Properties of MnFe2O4 Particles/Sheets/Flakes-Like Nanostructures[END_REF] To gain insights on the nature of defects present in the NPs, fluorescence emission spectra are modeled by the convolution of several gaussian functions (see Figure S33). In all cases, three distinct components centered around 520 nm, 532 ± 2 nm and 590 nm are found. According to previous works, [START_REF] Maibam | Photoluminescence and Intrinsic Ferromagnetism of Fe Doped Zinc Oxide[END_REF][START_REF] Vijaya | Effect of Cu2+ Doping on Structural, Morphological, Optical and Magnetic Properties of MnFe2O4 Particles/Sheets/Flakes-Like Nanostructures[END_REF] these contributions can be ascribed to F + -centers (Equation 2), F-centers (Equation 3) and interstitial oxygen defects, respectively. The proportions of each defect within the nanostructures are estimated thanks to the area of each gaussian function (see Table S14). [START_REF] Choudhury | Oxygen Defect Dependent Variation of Band Gap, Urbach Energy and Luminescence Property of Anatase, Anatase-Rutile Mixed Phase and of Rutile Phases of TiO2 Nanoparticles[END_REF] Briefly, the amount of interstitial oxygen defects is found to be constant in the investigated samples with a mean percentage of 23 ± 2 %. The relative proportion of the two types of Fcenters (F/F + ratio) ranges between 1.5 and 3.1 depending on the sample, for which synthesis conditions are not identical (variation of heating ramps or iron precursor proportions). Such results are consistent with the fact that the proportion and nature of F-centers highly depend on the history of the materials. [START_REF] Ghamnia | Luminescent Centres F and F+ in α-Alumina Detected by Cathodoluminescence Technique[END_REF] Time-resolved photoluminescence spectroscopy is carried out for an excitation at 232 nm. Emission wavelengths of 525 nm and 590 nm are investigated to obtain fluorescence lifetimes of the different excited states. For all samples, the decay at 525 nm (Figure 5b) are modeled by a bi-exponential function (Equation S22) suggesting two different modes of deexcitation which are heterogeneously distributed. [START_REF] Shaw | γ-Fe2O3 Nanoflowers as Efficient Magnetic Hyperthermia and Photothermal Agent[END_REF] Such results are consistent with the previously evidenced presence of both F and F + -centers. Mean values of t1 = 29 ± 2 µs and t2 = 4.6 ± 0.5 µs with relative proportions (Equation S23) 80 of 64 ± 5 % and 36 ± 5 % are found. As evidenced by emission spectra, F-centers are more abundant so one can assume that t1 = tF-centers and t2 = tF+-centers. All results are listed in Table S15 and are consistent with previously reported values in the microseconds range for spinel nanomaterials. [START_REF] Pathak | An Insight into the Various Defects-Induced Emission in MgAl 2 O 4 and Their Tunability with Phase Behavior: Combined Experimental and Theoretical Approach[END_REF] Fluorescence decays at 590 nm (Figure 5c) also present two exponential contributions (t1 = 14 ± 1 µs, t2 = 1.9 ± 0.3 µs) suggesting the presence of two types of interstitial oxygen defects. As surface excited states are known to present very fast decays and NFs present low surface/volume ratios, the relative proportion of the lifetimes (68 ± 5 % for t1 and 32 ± 5 % for t2) and the fastness of the second component allow to ascribe the deexcitations to core (t1 = tcore) and surface (t2 = tsurf) oxygen defects respectively. Finally, the integrated fluorescence intensity is plotted against the characteristic defect value 1/EU (Figure 5d). A good correlation between the concentration of emitting defects and 1/EU values is observed. The experimental points are modeled by a power law evidencing a linear dependence of the fluorescence with EU 4 (Figure 5d, inset) which means that defect concentration strongly enhances the fluorescence intensity.

A linear increase of integrated fluorescence with 1/EU is evidenced at small values followed by a plateau at 1/EU = 2.5 eV -1 (EU = 0.4 eV). Such limit corresponds to the previously determined Urbach limit value for absorption and PT efficiency (e and h, respectively) which means that NPs presenting high level of fluorescence are less efficient in PT. It has already been proved that electronic hoping along the Fe III -O-Fe II chain is decreased by high concentrations of oxygen vacancies. [START_REF] Wang | Role of Oxygen Vacancy in Metal Oxide Based Photoelectrochemical Water Splitting[END_REF][START_REF] Liao | Electron Transport in Pure and Doped Hematite[END_REF] So, the decrease of PT efficiency in the case of highly fluorescent samples may be explained by a diminution of the electron transfer between Fe II and Fe III (IVCT) when oxygen vacancies are abundant, giving rise preferentially to phonon-mediated nonradiative deexcitations.

.

Conclusions

In this work, we investigated the effects of polyol synthesis parameters such as heating ramps, iron precursor molar ratios and oxidation step on flower-like multi-core NPs (NFs) in terms of size, shape, chemical composition and crystallinity. We then correlated their nanostructure characteristics to both magnetic and optical properties, including magnetic hyperthermia (MHT) and photothermia (PT), the leading NPs-based modalities for thermal therapy of cancer. Firstly, we established that iron(III) is a crucial actor for the formation of well-defined NFs in the polyol process while iron(II) is not necessary. The experimental heating conditions are found to control the morphology of the resulting NPs with fast ramps yield smaller, more polydisperse and poorly defined flower-like NPs, while slow ramps produce larger and well-defined NFs. Comparing SH and DH ramps, we point out that the mean heating ramp between 120°C and 220°C was the key parameter that govern the flower-like structure formation. A linear correlation was then established between MHT efficiencies and the number of magnetic cores composing the flower-like assemblies. Such linear relationship must be attributed to an increase of exchange coupling between the cores. Conversely, the optical properties are found to depend linearly on the mean volume of the NPs and strongly on the crystal defects rather than the stoichiometry. When focusing on EU values, it was evidenced that iron(III)-based syntheses yield less disordered structures when compared to the iron(II,III)based syntheses. Moreover, a switch in the optical behavior is observed for the limit value of EU = 0.4 eV independently from stoichiometry, explaining the differences of optical properties between the samples. The same limit value of EU is observed for PT efficiencies when comparing SLP between the different sets of samples. Such a EU limit value was also confirmed by fluorescence measurements establishing the crucial role of defects on the optical properties of NPs and their efficiency in PT. These results suggest that optimal MHT and PT efficiency can be reached for large volume NFs composed of a high number of cores having low concentration of defects. Such nanostructures can be obtained with the modified polyol route by the use of iron(III) only (decrease of defects) and very slow temperature ramps (increase of the number of cores). To date available literature on iron oxide clusters have mainly focused on understanding the magnetic properties of NFs from the side of magnetism or more recently by structural analysis (using high resolution TEM techniques) but at the level of one single NP. In addition, and to the best of our knowledge, the photothermal properties rationalization and correlation at multiple bottom-up levels was never attempted. Taken together, these results will help rationalizing the design of efficient nano-heaters for thermal therapies. 4) of the boiling oxidation agent solution is then added on the precipitated NPs to respect a constant ratio b equal to 3 (Equation 5).

Methods

V oxi = [Fe] FF • V FF 3 • [oxi] (4)
β = n oxi (Fe) n FF (Fe) ≡ 3 (5)
The resulting solution is magnetically stirred and maintained at 75°C for 30 minutes before being allowed to cool down to room temperature. The classical washing procedure described before is finally followed to obtain an oxidized aqueous ferrofluid.

Characterizations

Scheme 1 .

 1 Scheme 1. Diagram summarizing the multi-scale materials-science approach used in this

FeFigure 1 .

 1 Photon scattering

[

  figure (see TableS1). n-p) Schematic description of the morphologies (RF-NPs, NFs, IF-NPs)

Figure 1

 1 Figure1shows representative TEM micrographs (see FigureS1for size distribution

  different (highly significative p-values < 0.001) from NMC(SH) and NMC(DH), which exhibit comparable results (non-significative p-value >> 0.05). Briefly, FH ramps yield RF-NPs with a lower NMC when compared to the NFs obtained with SH and DH ramps. More precisely, mean values of < N MC FH > ≈ 5 and < N MC SH > ≈ < N MC DH > ≈ 13 are obtained for the three different heating conditions (SH, FH and DH). The number of magnetic cores is also determined for VFH (sample N) and RDH (sample O) conditions (see Figure S3) and yield N MC VFH = 1.8 and N MC RDH = 23. Figure 2b shows the dependence of NMC value with the mean heating ramp. The number of magnetic cores is found to be inversely proportional to the mean ramp, which indicates that aggregation into flower-like structure is strongly favored by slow heating. NMC values are finally plotted, for each sample, against the SLP obtained in MHT modality (Figure 2c). Two different regimes can be observed, characterized by SLP < 150 W/gFe for RF-NPs and SLP > 200 W/gFe for NFs. All SLP values are consistent with previously reported values for both NFs and RF-NPs when converted to field-and frequency-independent intrinsic loss power (ILP) values (see Figure S22 and Table

Figure 2 .

 2 Figure 2. a) Number of magnetic cores for each type of heating condition before (blue) and

3 > = d TEM 3

 33 and 3f, respectively). The same behavior is observed for all the simulations independently from {dTEM, sTEM} values (see FiguresS26, S27 and S28). These results demonstrate that optical responses are proportional to the mean volume (<V>) of a log-normal distribution of NPs. We thus define a morphological parameter corresponding to the third moment of a log-normal distribution < V > = < d TEM

7 - 3 Polydispersity

 73 Fe 3 O 4 -g-Fe 2 O

25 d TEM 3 [nm 3 ]Figure 3 .

 25333 Figure 3. Simulated cross sections s (extinction: points, absorption: solid lines, scattering:

found that x0 = 1

 1 syntheses (samples C, D, E) yield higher EU values when compared to x0 = 0.67 syntheses (samples H, I, J) with mean values of < EU(C,D,E) > = 1.0 ± 0.2 eV and < EU(H,I,J) > = 0.6 ± 0.1 eV. It can thus be assumed that the use of iron(II) in the reactive medium generates less ordered structures than those obtained by an in situ polyol-mediated reduction of iron(III). Figure4balso evidences two distinct areas separated from a limit value of EU = 0.4 eV. Interestingly, when plotting eexp and EU values of samples Kox and Mox (red stars) on Figures4a and 4bthey appear to belong to the region of the non-oxidized samples (blue areas) despite a low stoichiometry of R ≈ 0.16. Independently from stoichiometry, a switch in the optical behavior is observed for the limit value of EU = 0.4 eV.

Figure 4c finally provides

  Figure4cfinally provides the PT efficiency at 1064 nm (see also FigureS32) through

Fe 3 Fe 3 Fe 3 Fe 3 Fe 3 Fe 3

 333333 -1 •cm -1 at 1064 nm and results in a smaller value of hox = 11%. Samples for which h = 29% are characterized by an average value of < EU > = 0.7 ± 0.2 eV while samples for which h = 11% present an average < EU > = 0.27 ± 0.4 eV. Consequently, one can deduce an EU limit between 0.3 and 0.5 eV in agreement with the value of 0.4 eV extracted from Figure 4b. O 4 simulation g-Fe 2 O 3 simulation Linear 1/E U [eV -1 ] O 4 simulation g-Fe 2 O 3 simulation Linear 1/E U [eV -1 ] O 4 simulation g-Fe 2 O 3 simulation Linear 1/E U [eV -1 ] mM] η = 0.29 ± 0.02 η ox = 0.11 ± 0.01 SLP [W/g Fe ] 1064 nm @ 0.28 W/cm 2 O 4 simulation g-Fe 2 O 3 simulation Linear 1/E U [eV -1 ] mM] η = 0.29 ± 0.02 η ox = 0.11 ± 0.01 SLP [W/g Fe ] 1064 nm @ 0.28 W/cm 2 O 4 simulation g-Fe 2 O 3 simulation Linear 1/E U [eV -1 ] O 4 simulation g-Fe 2 O 3 simulation Linear

Figure 4 .

 4 Figure 4. a) Comparison between experimental and theoretical NPs extinction coefficients at

Figure 5 .

 5 Figure 5. a) Fluorescence emission spectra recorded for an excitation wavelength of 232 nm.

Fluoresencel

  U [eV -1 ] Integrated Fluorescence Spectra [a.u.] exc = 232 nm l em = 590 nm Exp. ◼ Fit ---•

.

  The morphology of the NPs is imaged using a JEOL-1011 transmission electron microscope operating at 100 kV. Size distributions are determined thanks to Image J software by measuring manually 300 NPs on at least three different images. The resulting histograms are modelized by a log-normal law using Igor Pro 7 software to determine the mean physical diameter (dTEM) and the polydispersity (sTEM) of each sample. High-resolution TEM (HR-TEM) is performed on a JEOL 2010 operating at 200 kV. The total iron concentrations of NPs suspensions are measured by atomic absorption spectroscopy (AAS, PinAAcle 500, Perkin Elmer) and/or induced-coupled plasma atomic emission spectroscopy (ICP-AES, iCAP 6500, Thermo) by degrading the samples in concentrated HCl (37%) before a dilution in HNO3 (2%).Dynamic light scattering and zeta potential measurements are performed on a Malvern Zetasizer Nano-ZS. Samples are studied in water at room temperature using a back-scattering angle of 173°. Fourier-Transform Infra-Red (FT-IR) spectroscopy is performed on a Bruker TENSOR 27 spectrophotometer with a resolution of 4 cm -1 between 400 cm -1 and 4000 cm -1 on dried powders diluted in solid KBr. Magnetization hysteresis loops in liquid phase are measured using a home-made vibrating sample magnetometer in the range -9 kOe to +9 kOe. Zero field cooled and field cooled measurements (ZFC/FC) are performed on frozen colloidal suspensions between 10 K and 275 K with an applied field of 50 Oe on a Quantum Design PPMS equipped with a VSM module. Magnetization curves in solid phase (powder) are measured on a MPMS-XL7 Quantum Design SQUID in the range 0 Oe to 25 kOe. Thermogravimetric analyses (TGA) are performed on a TA TGA550 Discovery series operating in high-resolution mode with a heating speed of 20°C/min in the range 20°C-600°C. MHT experiments are carried out using 0.5 mL Eppendorf® containing 50 µL of the NPs suspensions excited for 600 seconds by an alternating magnetic field generator device (DM3, NanoScale Biomagnetics) operating at 180 Gauss with a frequency of 471 kHz (temperature increase is measured by an infrared camera FLIR SC7000). X-Ray powder diffraction measurements are carried out at the XRD platform of the IMPMC (Paris, France) on a Rigaku MM007HF diffractometer equipped with a Mo rotating anode source (λKα1 = 0.709319 Å, λKα2 = 0.713609 Å), Varimax focusing optics and a RAXIS4++ image plate detector. The detector is installed at a distance of 200 mm and the beam size fixed to 100 µm. From samples in 0.3 mm borosilicate capillaries, the XRD powder patterns are collected from 2θ = 2° to 2θ = 45° during 30 min at 20°C. LaB6 standard sample is measured in the same experimental conditions to calibrate the FIT2D program, the image processing software used to integrate the intensities around the Debye-Scherrer rings and to get the 1D patterns. The crystal structure refinements are carried out using the Rietveld method as implemented in the FullProf software (Rodriguez-Carvajal, 1993). Starting from the known cell parameters of maghemite, the refinements converge rapidly. The peak widths are significantly larger than the instrumental resolution (2θ ~ 0.15°). Starting from the instrumental resolution function, anisotropic size parameters are refined. It improves significantly the fits and allows to extract the size of meancoherent domains which are found to be almost spherical. X-ray absorption spectroscopy at Fe K-edge is performed at Synchtoron SOLEIL on the ROCK line in 1 mm diameter glass capillary, using a Si(111) monochromator.[START_REF] Goya | Static and Dynamic Magnetic Properties of Spherical Magnetite Nanoparticles[END_REF] Fe transmission Mössbauer spectra are obtained using a conventional constant acceleration transducer and a[START_REF] Goya | Static and Dynamic Magnetic Properties of Spherical Magnetite Nanoparticles[END_REF] Co source diffused into a Rh matrix. The experiments are performed at 77 K using a bath cryostat on samples resulting from frozen solutions containing approximately 3 mgFe/cm 2 . The spectra are analyzed using a leastsquares fitting method involving Lorentzian functions while the values of isomer shift are referred to that of a-Fe at 300 K. UV-Vis-NIR spectra (400-1100 nm) are recorded at room temperature in a 1 cm quartz cuvette using an Avantes spectrophotometric set-up composed of an AvaLight-DHc lamp connected by optical fibers to a StarLine AvaSpec UV/Vis detector and to a NIRLine AvaSpec-NIR256-1.7 NIR detector. Infrared PT experiments are carried out using 0.5 mL Eppendorf ® containing 50 µL of the NPs suspensions excited for 300 seconds by a NIR laser (1064 nm, 0.28 W/cm 2 ) coupled to an optical fiber from Laser Components SAS (temperature increase was measured by an infrared camera FLIR SC7000). Fluorescence emission spectra are recorded on a Cary VARIAN Eclipse fluorescence spectrophotometer in 1 cm quartz cuvette with a excitation wavelength of 232 nm, a resolution of 1 nm/s and slits of 20 nm for both emission and excitation. Time-resolved fluorescence spectroscopy measurements are obtained using a Jobin-Yvon Fluorolog 3 Fluorometer equipped with a UV-Xenon flash tube. Excitation is set at 232 nm with 14 nm slits in both emission and excitation. Sample window and initial delay are set to 0.05 and 0.01, respectively. Two emission wavelengths (525 and 590 nm) are investigated with increments of 0.005 (525 nm) and 0.001 (590 nm).Plénet for X-ray absorption measurements at Synchrotron SOLEIL. We acknowledge SOLEIL for provision of synchrotron radiation facilities and we would like to thank Valérie Briois for assistance in using beamline ROCK. The authors thank Dr. Hélène Brault (IMJR, Université de Nantes) and Dr. Nicolas Menguy (IMPMC, Sorbonne Université) for their assistance during time-resolved fluorescence and HR-TEM measurements. The authors also thank Aude Michel-Tourgis, Delphine Talbot (PHENIX, Sorbonne Université) and Laure Cordier (IPGP, Université de Paris) for iron concentration measurements by AAS or ICP-AES.

50 nm 50 nm 50 nm 50 nm 50 nm c d h i l 50 nm 50 nm 50 nm 50 nm 50 nm

  pure water are added and the resulting solution is then heated at 220°C (reflux) thanks to a silicon oil bath. The solution is finally allowed to cool down to room temperature. The black suspensions are diluted in ethanol to be magnetically separated and washed as follow: one time in diluted HNO3 (10%) for ten minutes, two times in acetone and two times in Et2O.

	Fe(NO3)3•9H2O (oxi) are dissolved in 800 mL of ultra-pure water under magnetic stirring and
	heated until ebullition. In parallel, a volume VFF of ferrofluid is precipitated in a volume 3VFF
	of HNO3 (10%) on a permanent magnet to remove the supernatant. A precise volume Voxi
	(Equation
	The black solid is then re-dispersed in a minimum of ultra-pure water to obtain a stable aqueous
	ferrofluid. Iron(III)-based syntheses (x 0 = 1): iron(II) precursor is replaced by iron(III) precursor
	(1.62 g, 6 mmol). The dissolution of iron(III) salts into polyols takes place in half an hour
	instead of one night for the iron(II,III) mixture and the same procedure described before is
	/Experimental Chemicals. N-methyldiethanolamine (NMDEA, >99%), diethylene glycol (DEG, >99%), iron(III) chloride hexahydrate (FeCl3•6H2O, 99%) and iron(II) chloride tetrahydrate (FeCl2•4H2O, 99%) are purchased from Merck. Sodium hydroxide pellets (NaOH, 99%), hydrochloric acid (HCl, 37%), iron(III) nitrate nonahydrate (Fe(NO3)3•9H2O, >96%), ethanol performed under oxic conditions. Iron(II)-based syntheses (x connected (EL-USB-TC-LCD, Thermocouple Data Logger) thermometer. Briefly, heating
	(96%), nitric acid (HNO3, 68%), acetone (>99%), diethyl ether (Et2O, 100%) and silicon oil speeds of 480°C/h and 120°C/h are set to carry out the fast heating ramp (FH) conditions of
	(47-V-350) are purchased from VWR International. All chemicals are used without further 8°C/min and the slow heating ramp (SH) conditions of 2°C/min, respectively. Once the
	purification. temperature reaches ≈220°C, it is hold stable for durations of 1 hour and 2 hours. In the case
	of double heating ramp (DH) conditions, the first heating speed is set at 480°C/h until the
	Synthesis procedures. Iron(II,III)-based syntheses (x 0 = 0.67): in a typical experiment,
	temperature reaches 200°C (plateau of 50 min) and switched to 120°C/h to go from 200°C to
	FeCl3•6H2O (1.08 g, 4 mmol, 2 eq.) and FeCl2•4H2O (0.39 g, 2 mmol, 1 eq.) are dissolved
	220°C (plateau of 60 min). In the case of reverse double heating (RDH), the first heating speed
	overnight in a mixture of DEG (40 mL) and NMDEA (40 mL) under N2 inert atmosphere. At
	is set at 120°C/h until the temperature reaches 200°C (plateau of 50 min) and switched to
	the same time, NaOH pellets (0.64 g, 16 mmol, 8 eq.) are grinded and dissolved overnight in a
	480°C/h to go from 200°C to 220°C (plateau of 60 min). Very fast heating (VFH) ramp of
	16.5°C/min is obtained by setting the speed to 1000°C/h until the temperature of 220°C is
	reached (plateau of 60 min). Oxidation step (Fe3O4 → g-Fe2O3): 323 g of the oxidation agent

mixture of DEG

(20 mL)

and NMDEA (20 mL). After 30 min under N2 inert atmosphere, the two solutions are mixed by magnetic stirring for 1 hour still under N2 inert atmosphere. 500 µL of ultra-0 = 0): iron(III) precursor is replaced by iron(II) precursor (1.19 g, 6 mmol) and the same procedure as iron(II,III)-based syntheses is performed. Heating conditions: different heating conditions are investigated for each x 0 value thanks to a silicon oil bath placed on a Cat MCS 77 heating plate equipped with a thermocouple, allowing a precise control of the temperature over time. The temperature variations inside the reactive medium are recorded as a function of reaction time using an USB-

Acknowledgments

E. Bertuit and A. Abou-Hassan acknowledge the doctoral school ED388 for funding. We acknowledge the support of the French Agence Nationale de la Recherche (ANR) under reference ANR-18-CE09-0004 (MicroNanoCell project). The authors acknowledge the staff of the MPBT (physical properties -low temperature) platform of Sorbonne Université for their support. The authors would also like to thank Dr. Anne-Laure Rollet and Dr. Juliette Sirieix-

Associated content

Supporting Information

The supporting Information is available free of charge via the Internet at: Theoretical basis and equations, additional figures including TEM and HR-TEM, size distributions histograms, powder XRD diffraction data and Rietveld refinements, XANES data, [START_REF] Goya | Static and Dynamic Magnetic Properties of Spherical Magnetite Nanoparticles[END_REF] Fe Mössbauer spectra, SQUID, TGA, ZFC/FC measurements and DLS measurements, ILP values, Python codes, Beer-Lambert plots at 1064 nm, Urbach and Tauc plots, MHT and PT measurements, fluorescence emission spectra and additional tables.

Author Information

Corresponding Author

Ali Abou-Hassan Sorbonne Université, CNRS, PHysico-chimie des Électrolytes et Nanosystèmes InterfaciauX (PHENIX), F-75005 Paris, France. ali.abou_hassan@sorbonneuniversite.fr

Author contributions

The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.


Ibtissem Zaatouri
email: ibtissem.zaatouri@hotmail.com

Francoise Sailhan

Stephane Rovedakis

Awatef Guiloufi
email: awatef@yahoo.fr

Nouha Alyaoui

Abdennaceur Kachouri
email: abdennaceur.kachouri@enis.rnu.tn

Performance Evaluation of Mobility-Aware Routing Protocol for Low power and Lossy Networks

Keywords: IoT, RPL, Mobility

Wireless Sensor Networks (WSNs) is a class of low power and Lossy networks (LLN) which are useful to monitor a physical/environmental phenomenon. The Routing Protocol for Low Power and lossy networks (RPL) is a standardized protocol specifically designed to route the data over LLN networks. In particular, to take into account the specific features of LLN the RPL protocol computes the best routes following one or several metrics (e.g., the residual energy of nodes or the link quality) based on the state of the nodes (a.k.a sensors) or links. Nevertheless, RPL was originally designed to handle static networks ; when node(s) move(s), the performances of RPL drop down. This issue has motivated a great deal of interest in ensuring that sensors may route the sensing data even thought they move from place to place, establishing new links and moving away from the previously established links. In this paper, we present RPL and the solutions that permit to deal with mobile nodes. We introduce a simulation-based evaluation of these solutions, which is focused on the energy consumption and the packet losses. The comparison between RPL and MRPL shows that RPL consumes less energy due to many packet losses. In counterpart, RPL does not provide a continuous connectivity to mobile sensor contrary to MRPL that keeps connection.

I. INTRODUCTION

Nowadays, Wireless Sensor Networks (WSNs) are used by many applications pertaining e.g. to the industrial or military domains [START_REF] Stankovic | Realistic applications for wireless sensor networks[END_REF]. The specific features of WSNs (wireless communication, small size, low price) stimulate their deployment everywhere. However, sensors are characterized by a relatively limited capacity expressed in terms of energy, memory, computing power and throughput. These distinctive features require to design a routing protocol that is adapted to WSN [START_REF] Carels | Rpl mobility support for point-to-point traffic flows towards mobile nodes[END_REF]. In particular, RPL [START_REF] Winter | Rpl: Ipv6 routing protocol for low-power and lossy networks[END_REF] (Routing Protocol for Low Power and Lossy networks) is one of the best candidates that was proposed by IETF ROLL (Routing Over Low Power and Lossy Network) working group. RPL was originally designed to support data collection in static networks (i.e., without any consideration for mobility). Nevertheless, new trend seeks to handle more complex applications that involve mobile users equipped with sensors. In this paper, we present the versions of RPL that accommodate mobility. We further compare RPL with one version of RPL, which is adapted for mobility and is called MRPL [START_REF] Fotouhi | mrpl: Boosting mobility in the internet of things[END_REF].

The rest of the paper is organized as follows: Section II provides an overview of RPL with regards to mobility, followed in Section III by the related work. Then, Section IV introduces a comparison between RPL and MRPL. Finally, a synthesis is presented in the conclusion with a description of the future works.

II. OVERVIEW OF RPL

RPL [START_REF] Oliveira | Low-power and lossy networks under mobility: A survey[END_REF] is a proactive and distance-vector protocol that aims at building a DODAG (Destination Oriented Directed Acyclic Graph), which is further used to disseminate data packets. A DODAG is a directed acyclic graph rooted at a particular node, called sink or root. RPL supports three types of traffic: point-tomultipoint a.k.a from sink to all nodes, multipoint-topoint a.k.a from all nodes to sink and point-to-point a.k.a from node to node. RPL attempts to deal with sensors having either sufficient or insufficient storage. In the former case (versus later case), routing information are stored (versus not stored) by the intermediate sensors. During the construction of the DODAG, each node identifies a set of parents so that a path towards the DODAG root (also called a upward path) can be established. This selection is operated based on a predefined Objective Function (OF) that implements one or a combination of metrics. Establishment of upward route-In order to build the DODAG (see Figure 1), the sink periodically sends a so-called DIO message (DODAG Information Object) to its neighbors, which includes the following parameters: a rank1 corresponds to the position of the node in the DODAG, a routing metric is used to determine the best path to the sink, as defined by the OF, a DODAG id, and a path cost (associated to a path toward the sink, as given by the OF). Based on these parameters, the sink neighbors establish the sink as parent and join the DODAG. Each node belonging to a DODAG sends a DIO to its neighbours. In order to join a DODAG, each node has to select as parent one of its neighbors that belongs to the DODAG. Such a parent selection is governed by an Objective Function (OF), which relies on the routing metric(s). This selection is periodically repeated so that each node includes in its routing table its (actual) parent(s) and its relative position (i.e., rank and path cost). In order to keep to a minimum the amount of DIO messages that are exchanged so as to maintain and update the DODAG, RPL relies on the Trickle algorithm [START_REF] Oliveira | Low-power and lossy networks under mobility: A survey[END_REF] which tunes the time period between the emission of two consecutive DIO messages. This algorithm increases (versus decreases) this time period when the network remains stable (versus when changes are detected). Rather than waiting for a DIO message, any node may also request a DIO message by sending a DIS (DODAG Information Solicitation) message to its neighbours.

Once the DODAG is established (using DIO and/or DIS messages), any data packet can be routed, hop-byhop, towards the sink: this constitutes a multipoint-topoint intraction pattern. In order to support a pointto-multipoint interaction pattern wherein the sink can send data packets to the sensors, downward routes are computed. Establishment of Downward Route -In order to establish the downward route, a DAO (Destination Advertisement Object) message is propagated from the leafs towards the sink. This DAO message contains the network prefix so that the sink can further establish which network (and which constituting sensors) is under its responsibility.

RPL relies on a Neighbor Discovery mechanism [START_REF] Narten | Neighbor discovery for ip version 6 (ipv6). Technical report[END_REF] so as to discover new/unavailable neighbors. This mechanism uses the following ICMPv6 control messages:

• Neighbor Solicitation checks if a neighbor is still accessible. • Neighbor Advertisement is sent periodically to announce link changes. • Router Solicitation requests the neighbours of a node. • Router Advertisement corresponds to a response to a route solicitation. It includes link information. On one hand, sending the above messages very frequently involves a high responsiveness given topology changes, but induces a high overhead; on the other hand, sending less frequently these messages implies a low responsiveness and a reduced traffic.

RPL shortcomings -RPL was originally designed to handle static sensors that communicate using a wireless and low data rate network, which may be subject to high loss rates and instabilities. Thus, RPL assumes that topological changes are mostly due to sensors disconnections and to wireless instabilities. In order to detect sensors disconnections and link instablities, DIO messages are periodically sent. The periodicity is defined by the Trickle algorithm [START_REF] Vuini | Trickle-d: high fairness and low transmission load with dynamic redundancy[END_REF], which is tuned based on the number of consistent DIO messages received: if there are no update, the periodicity is increased, otherwise active dissemination is performed by setting this period to the minimum value. With the Trickle algorithm, the time is divided into intervals of size (with 0 . Any node listens during the first half of the I interval and then transmits during the second half. The transmission takes place if the number of inconsistent messages received is less than a given threshold. If the message cannot be sent within I, then this interval I is doubled (until I max is reached) and the node sends again the message. But, when an inconsistent message is detected, Trickle sets I to its minimum value. The Trickle algorithm presents two major shortcomings. First, the listen period increases the transmission delay and henceforth the convergence time of RPL. Consequently, the time induced to detect inconsistency [START_REF] Ghaleb | E-trickle: Enhanced trickle algorithm for low-power and lossy networks[END_REF] is increased. When nodes are mobile, Trickle also delays the selection of a new parent for mobile nodes, which results in high packet loss, energy consumption and end-to-end latency. Thus, the trickle algorithm and the RPL protocol should be adapted to accommodate mobile nodes.

III. RELATED WORK: TOWARDS MOBILE-AWARE RPL

Dealing with the node mobility involves performing the three following tasks:

• Detection of the node mobility consists in determining whether a node is mobile. There are three options to detect the mobility. First, a mobile node may simply announce its mobility (Reverse Trickle [START_REF] Cobarzan | Analysis and performance evaluation of rpl under mobility[END_REF]). Second, the mobility can be established/anticipated based on the node history (ME-RPL [START_REF] Cobarzan | Analysis and performance evaluation of rpl under mobility[END_REF]). Third, the network is monitored so as to determine whether a node is mobile and if the disconnection with parent will take place. For this purpose, different parameters can be used.

For instance, the jitter between two DIO messages can be analyzed by the mobile node (MRPL [START_REF] Fotouhi | mrpl: Boosting mobility in the internet of things[END_REF]).

The RSSI can also be analyzed by the mobile node (MRPL, Mod-RPL [START_REF] Gara | An adaptive timer for rpl to handle mobility in wireless sensor networks[END_REF]) or by the parent (EC-MRPL [START_REF] Bouaziz | Ec-mrpl: An energyefficient and mobility support routing protocol for internet of mobile things[END_REF]) so as to determine when the mobile node will get out of range. In these cases, the nodes need to overhear. When the presence of a mobile node is detected, the periodicity of the DIO messages (CO-RPL, Mod-RPL) and DIS messages (CO-RPL, ME-RPL) is increased so as to maintain the connectivity with the mobile node. • Forwarding the data traffic to the newly selected parent -while the node is connected to another parent, the data traffic should be forwarded by the previous parent to the new parent (EC-MRPL, MRPL+).

In the following, we detail the solutions that have been proposed so that RPL supports mobile sensors. With the CO-RPL protocol [START_REF] Gaddour | CO-RPL: RPL routing for mobile low power wireless sensor networks using corona mechanism[END_REF], the network is divided into some circular regions, named coronas, which are characterized by a certain radius (corresponding typically to the maximum transmission range) and which are centered around the DODAG root. Each corona is identified by a corona ID. This corona ID presents the distance from mobile node to the sink. Each node belongs to one corona. This notion of corona permits to select the parents among the closest sensors (i.e., on same corona id). In practice, the node selects as the best parent, the candidate that has the lowest corona id, and if the potential candidates have the same corona id, then the one having the best link quality is selected. In order to deal with the sensor mobility without flooding the network with DIO messages, CO-RPL adapts the transmission rate of DIO messages according to the sensor speed. In addition, a mobile node that joins the DODAG immediately broadcasts a new DIO message, ignoring the Trickle timer. CO-RPL prevents packet loss by (i) quickly detecting sensor disconnection and (ii) searching for an alternative path: when a node does not receive a DIO message from its parent, it sends DIS messages to inform its children, in order to stop forwarding data packets until an alternative parent is found. This protocol is evaluated using the Cooja [START_REF] Osterlind | Cross-level sensor network simulation with cooja[END_REF] simulator. All the nodes follow a random mobility model (except the sink which is static): the destination, the speed and the direction of each mobile node is chosen independently and randomly. Thus, CO-RPL induces (i) a significant communication overhead due to the high-periodical broadcast rate associated with DIO messages, (ii) congestion and (iii) an increase of the energy consumption.

In [START_REF] Bouaziz | Ec-mrpl: An energyefficient and mobility support routing protocol for internet of mobile things[END_REF], the authors propose a new proactive protocol named EC-MRPL, which prevents mobile sensor from acting as RPL routers: only static nodes should act as parents so as to guarantee the stability of the core RPL DODAG. The parent of a mobile node is responsible for monitoring the connection with the mobile node and for choosing an alternative parent if necessary. EC-MRPL enhances the routes stability by using mobile sensors only as leaf nodes. However, the failure of the parent causes a loss of connection in the network. This protocol is tested with the Cooja simulator with a static sink and a single mobile sensor that follows a random walk model with horizontal moves from the one corner to the other with a constant speed (v=2 m/s).

In [START_REF] Fotouhi | mrpl: Boosting mobility in the internet of things[END_REF], authors introduce the MRPL protocol wherein mobile sensors use the DIO messages to monitor (i) the link quality with its parent and (ii) the jitter to establish that the mobile sensor moves away. In such a case, the mobile sensor triggers a hard hand-off which consists in choosing as parent the node having the highest RSSI. This hard hand-off mechanism consists of the two following phases:

• Monitoring phase during which the mobile node monitors the quality of link with its parents. The quality is determined when the mobile node receives packet emitted by its parent. If the Received Signal Strength Indicator (RSSI) value is lower than a given threshold, the next phase starts. • Parent selection phase -the mobile node selects as parent the node characterised by the highest RSSI value.

Unfortunately, in order to establish the RSSI, many DIO message should be frequently sent. With EC-MRPL and MRPL, mobile sensors act only as leaf nodes to reduce instabilities and path changes. Simulations and real experiments are performed. During simulations, one mobile node travels 15 times between the left and bottom corner and the right bottom corner with a constant speed of 2 m/s in a row in first scenario and in two parallel rows in the second. Real experiments are achieved with one person equipped with a sensor. MRPL+ [START_REF] Fotouhi | mrpl+: A mobility management framework in rpl/6lowpan[END_REF] supports both a hard and soft hand-off. The hard hand-off takes place when a sensor does not receive a DIO message from its parent within a given time period or when the sensor observes a low amount of data traffic. In such a case, the connection between the mobile node and the preferred parent is canceled and then a new connection is established (see MRPL for detail). With soft hand-off, the connection between the mobile node and the new parent is activated before the current link is dropped so as to avoid loosing data traffic. The soft hand-off, which constitutes the default option, necessitates a overhearing mechanism so that mobile node monitors the link with its parent and measures RSSI. A mobile node is defined as mobile (i) if the link with the parent is inactive during a given period of time and/or (ii) the RSSI strength varies. The mobile node is placed in an overhearing state to monitor the link quality and to discover potential alternative parents. Such an overhearing process is especially energy-consuming. MRPL+ introduces the soft hand-off that enables continuous connection between the mobile node and its parents. This reduces the packet loss in comparison to EC-MRPL.

With ME-RPL (Mobility Enhanced RPL) [START_REF] Korbi | Mobility enhanced rpl for wireless sensor networks[END_REF], mobile nodes announce their mobility by adding a mobile flag to the DIO message. Thus, sensors do not monitor the link state to determine that a node is mobile. Only static nodes can be parent. Authors suppose that the mobility of the node in the near future can be established based on its past mobility. So, if a node has been stable (versus instable) for a while, the DIS interval increases (versus decreases). Overall, DIS messages are used to add nodes to a DODAG and to refresh the connection to a preferred parent ; the frequency of DIS messages is regulated following the history of the mobile nodes. This protocol is tested based on the Cooja simulator with a static sink and one mobile node that moves depending on linear and grid topologies. However, the variation of the DIS interval implies that the disconnection of the mobile nodes is not rapidly detected.

Mod-RPL [START_REF] Gara | An adaptive timer for rpl to handle mobility in wireless sensor networks[END_REF] customizes the trickle timer to accommodate mobility. As a first step upon that goal, any mobile node relies on the RSSI so as to determine when it gets out of communication range from its preferred parent. Based on this estimation, the mobile node adjusts the DIO interval. This protocol is tested with Cooja simulator considering a static sink, 10 senders and a varying number of mobile nodes (ranging from 20 to 100). The velocity of mobile nodes varies from 0 to 10 m/s. This protocol reduces overhead but it is tricky to determine when a mobile node is out of range of the parent when the parent is also mobile.

In [START_REF] Cobarzan | Analysis and performance evaluation of rpl under mobility[END_REF], the authors introduce the Reverse Trickle timer to deal with mobile nodes. As with ME-RPL [START_REF] Korbi | Mobility enhanced rpl for wireless sensor networks[END_REF], mobile nodes advertise the fact that they are mobile. But in this case a mobile node can only act as a leaf node. This work supposes that the more the mobile node remains connected to the same parent, the more it is likely to move outside the coverage of the parent. Therefore, if a node advertises its mobility, its parent reduces drastically the (Reverse) Trickle timer. In a nutshell, this timer starts with the maximum allowed value and is halved when a DIO message is received. Once the minimum value is reached, the Reverse Trickle timer is reset (i.e., is given the maximum value). Simulations have been performed using the WSNet simulator by considering a scenario with only one mobile node moving along a linear trajectory with a constant speed of 2 m/s. Moreover, real experiment has been performed with 100 static nodes and 10 mobile nodes moving randomly inside the area covered by the fixed nodes. The DODAG root is located in the middle of the network area. This protocol reduces the packet loss, but the mobile node stability does not always decrease over the time since it is deeply related to the model of mobility.

Table 1 summarizes the characteristics of the aforementioned works that accommodate mobility.

IV. COMPARISON BETWEEN RPL AND MRPL

Our objective is to compare RPL and MRPL with regards to mobility. We performed 1-hour simulations with the Cooja network simulator. We consider two scenarios (Figures 2 and3) in which 12 sensors are static (including the sink) and one is mobile. Sensors correspond to Tmote Sky motes [START_REF] Po | On design and deployment of fuzzy-based metric for routing in low-power and lossy networks[END_REF] that run Contiki 2.7 OS and move following the random way point mobility model. The nodes move: (i) horizontally at 2 m/s, from the left and bottom corner to the right bottom corner, and then, returns to the original position in the first scenario, and (ii) from the bottom to the top corner and then returns to its original position in the second scenario. The comparison between RPL and MRPL is performed according to the following two criteria: • packet loss is defined as the number of dropped packets during the simulation. • energy consumption (E i ) is calculated as follows:

Ei = (T CP U × I CP U + T RX × I RX + T T X × I T X ) × V f (1)
where I CP U , I T X , I RX represent respectively the energy consumed during the time during which the CPU runs (T CP U ), the sensor transmits (T T X ), the sensor listens (T RX ). V represents the initial battery voltage level and f represents the number of ticks per second. In practice, I CP U =1.8 mA, I T X = 19.5 mA, I RX = 21.8 mA, V =3.6V, f = 32 768 Hz.

We present in Figures 4 and5 the results with regards to the two scenarios, considering a ratio of 6 data packets or 12 data packets per minute for each sensor.

Energy consumption -Figures 4(a) and 5(a) present the energy consumption of RPL and MRPL under Scenario (i) and (ii) respectively. As expected, both RPL and MRPL consume more energy when the packet transmission rate increases. The increase is explained by the additional amount of data packets transmitted. RPL is characterized by the lowest energy consumption because RPL induces less control messages. In counterpart, RPL does not provide a continuous connectivity to mobile sensor(s): this is suggested by the high rate of lost packets of RPL. MRPL is characterized by a significant energy consumption because a mobile node overhears so as to receive any packet sent by the neighbors and detect any change in the topology. In order to detect any topology changes, the mobile node sends many control messages (i.e., DIS and DIO messages). With Scenario (i), RPL and MRPL consume more energy compared to Scenario (ii). This result can be explained by the fact that in Scenario (i), nodes move horizontally keeping almost the same distance to the sink (3 hops), while in Scenario (ii), the nodes move vertically and hence approaches the sink (the number of hops decreases and therefore the energy consumption decreases)

Packet loss -Figures 4(b) and 5(b) present the packet loss under Scenarios (i) and (ii) respectively. The packet loss ratio increases with the packet transmission rate due to the saturation of the wireless medium. However, the packet loss decreases over time, especially for RPL. RPL is characterized by the highest packet loss because RPL is characterized by a low responsiveness to topology changes: mobile sensors receive infrequent control messages and are often not connected to any parent. In the contrary, with MRPL, the mobile sensor sends data to the previous parent during the discovery of a new parent, which allows to maintain a higher delivery ratio. The packet loss ratio for RPL and MRPL in Scenario (i) is more important than in Scenario (ii) since the mobile node is located near the sink in Scenario (ii).

V. CONCLUSION

This paper reviews recent advances that support sensor mobility with regards to the RPL routing protocol. This work presents a description of the challenges encountered by RPL and the recent mechanisms proposed in the state of the art to enhance RPL for mobility. A performance evaluation of RPL and MRPL has been undertaken under two particular node mobility scenarios with respect to two parameters: packet loss and energy consumption. MRPL successfully deals with packet loss but is characterized by a high energy consumption compared to RPL. This can be explained by the fact that MRPL sends (and overhear) more control messages to detect network changes. However, MRPL is characterized by a low packet loss ratio because MRPL performs a soft hand-off: when a new parent need to be selected, data are forwarded to the previous parent.

Fig. 1 .

 1 Fig. 1. DAG composed of a single DODAG.

Fig. 2 .

 2 Fig. 2. Scenario i -Simulation Environment

Fig. 4 .

 4 Fig. 4. Impact of the data transmission rate on the energy consumption (a) and packet loss (b) for RPL and MRPL under Scenario (i).

Fig. 5 .

 5 Fig. 5. Impact of the data transmission rate on the energy consumption (a) and packet loss (b) for RPL and MRPL under Scenario (ii).

A rank is a strictly increasing value in the downward direction of the DODAG