Mawele Coste

Joachim Loudy

Antoine Allouche

Cecile Bousquet

Hervé Courreges

Laurent Martinez

Billon

Coste Mawele Loudy

Joachim Allouche

Antoine Bousquet

Cécile Courrèges

Hervé Martinez
email: herve.martinez@univ-pau.fr

Laurent Billon
email: laurent.billon@univ-pau.fr

Core@Corona Functional Nanoparticles-driven Rod-Coil Diblock Copolymer Self-Assembly

Keywords: click chemistry, rod-coil diblock copolymer, gold nanoparticle, self-assembly, π-π interactions

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

Future applications for photovoltaic [START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF] , microelectronic [START_REF] Rosa | Enabling Strategies in Organic Electronics Using Ordered Block Copolymer Nanostructures[END_REF][START_REF] Ball | High-Density Memory: A Switch in Time[END_REF] , or photonic [START_REF] Lopes | Hierarchical Self-Assembly of Metal Nanostructures on Diblock Copolymer Scaffolds[END_REF] will require the development of new materials with novel and complex properties that pure organic or inorganic materials, will not be able to reach. However, hybrid organic/inorganic materials are more likely to present new specificities that will meet the needs. In this context, the elaboration of new hybrid materials with fine control of their chemical composition and morphology by self-assembly, is critical to the development of next-generation materials.

Within the soft matter field, block copolymers (BCPs) is a very interesting class of materials due to their ability to self-assemble in different nano-phases dictated by the interaction between the two blocks but also easy and fast bottom-up processes. This specificity makes them promising candidates for emerging nanotechnologies such as nanotemplating [START_REF] Ruiz | Density Multiplication and Improved Lithography by Directed Block Copolymer Assembly[END_REF] , nanoporous membrane [START_REF] Phillip | Self-Assembled Block Copolymer Thin Films as Water Filtration Membranes[END_REF] or anti-reflection coating [START_REF] Joo | Block Copolymer Film with Sponge-like Nanoporous Strucutre for Antireflection Coating[END_REF] . Meanwhile, the elaboration of copolymers based on a semi-conducting block has been developed in order to better control the nano-organization of conjugated polymers, especially for photovoltaics application [START_REF] Cuendias | Conjugated Rod-Coil Block Copolymers and Optoelectronic Applications[END_REF] . Conjugated polymers are rigid molecules due to the (fused) aromatic rings making up the backbone of the chains. Three parameters influence the organization of a BCP; f the volume fraction of the blocks, χ the Flory-Huggins interaction parameter and N number of repetitive units. [START_REF] Olsen | Nonlamellar Phases in Asymmetric Rod-Coil Block Copolymers at Increased Segregation Strengths[END_REF][START_REF] Qian | Hybrid Polymer-CdSe Solar Cells with a ZnO Nanoparticle Buffer Layer for Improved Efficiency and Lifetime[END_REF] Nevertheless, for rigid rodcoil copolymers, an additional component, μ the Maier-Saupe interaction parameter, needs to be taken into consideration. [START_REF] Holyst | Correlations in a Rigid-Flexible Diblock Copolymer System[END_REF][START_REF] Müller | Ordered Phases in Rod-Coil Diblock Copolymers[END_REF] Indeed, the π-π stacking occurring in the rod-phase will largely affect the organization of the macromolecules. [START_REF] Olsen | Nonlamellar Phases in Asymmetric Rod-Coil Block Copolymers at Increased Segregation Strengths[END_REF][START_REF] Lin | Cylinder-to-Gyroid Phase Transition in a Rod-Coil Diblock Copolymer[END_REF] When the π-π interactions are strong and μ > χ, the self-assembly will be dictated by the rod block and nano-fibrils will be formed instead of the typical lamellae, cylinders or spheres. Among the semi-conducting polymers, the Poly(3hexylthiophene) (P3HT) based polymers are extensively studied for organic electronics applications. Many strategies are used to synthesize block copolymers from regioregular poly (3hexylthiophene) to produce electronical materials with variable conductivities [START_REF] Iovu | Conducting Block Copolymers of Regioregular Poly(3-Hexylthiophene) and Poly(Methacrylates): Electronic Materials with Variable Conductivities and Degrees of Interfibrillar Order[END_REF][START_REF] Stefan | Grignard Metathesis (GRIM) Polymerization for the Synthesis of Conjugated Block Copolymers Containing Regioregular Poly(3-Hexylthiophene)[END_REF] . Poly(3hexylthiophene) P3HT-based copolymers films are often composed of fibrils and long range order structuration is difficult to obtain, which is limiting their use for lithography [START_REF] Alemseghed | Amphiphilic Block Copolymers Containing Regioregular Poly(3-Hexylthiophene) and Poly(2-Ethyl-2-Oxazoline)[END_REF][START_REF] Erothu | Thermal Processing, and Thin Film Morphology of Poly(3-Hexylthiophene)-Poly(Styrenesulfonate) Block Copolymers[END_REF][START_REF] Javier | Simultaneous Electronic and Ionic Conduction in a Block Copolymer: Application in Lithium Battery Electrodes[END_REF] .

To overcome the influence of π-π stacking over the organization of P3HT based copolymer, different strategies have been followed. Lee The authors proved by atomic force microscopy (AFM) and X-ray scattering that spherical and cylindrical phases could be obtained when the P2VP block was long enough [START_REF] Lee | Self-Assembly and Phase Transformations of π-Conjugated Block Copolymers That Bend and Twist: From Rigid-Rod Nanowires to Highly Curvaceous Gyroids[END_REF][START_REF] Lee | Solution Self-Assembly and Phase Transformations of Form II Crystals in Nanoconfined Poly(3-Hexyl Thiophene) Based Rod-Coil Block Copolymers[END_REF] . On the contrary, Lin and coworkers played with the rod block chemical structure to decrease the π-π interaction. [START_REF] Lin | Rational Design of Versatile Self-Assembly Morphology of Rod-Coil Block Copolymer[END_REF] They replaced the hexyl side chain of P3HT by longer or branched alkyl group to increase the bulkiness around the aromatic backbone of the chain and hinder crystallization. With this strategy the copolymer, with poly(methylmethacrylate) as the coil block, led to films with cylindrical domains. In a recent paper, our group also reported the formation of ordered structuration of an ionizable "clicked" P3HT-b-PMMA introducing a single cationic charge at the junction of the two blocks. X-ray scattering, DSC and AFM were used to reveal the decrease of the π-π stacking together with the disappearance of the fibrils [START_REF] Ji | Self-Assembly of Ionizable "Clicked" P3HT-b-PMMA Copolymers: Ionic Bonding Group/Counterion Effects on Morphology[END_REF][START_REF] Ji | Hierarchical Honeycomb-Structured Films by Directed Self-Assembly in "Breath Figure" Templating of Ionizable "Clicked" PH3T-b-PMMA Diblock Copolymers: An Ionic Group/Counter-Ion Effect on Porous Polymer Film Morphology[END_REF] .

The incorporation of nanoparticles within block polymers BCPs has evolved into an area of considerable research [START_REF] Gaines | Nanoparticle-Regulated Phase Behavior of Ordered Block Copolymers[END_REF][START_REF] Chiu | Control of Nanoparticle Location in Block Copolymers[END_REF][START_REF] Kang | Hierarchical assembly of nanoparticle superstructures from block copolymer-nanoparticle composites[END_REF][START_REF] Chiu | Distribution of Nanoparticles in Lamellar Domains of Block Copolymers[END_REF][START_REF] Kuila | Multilayer Polymer Thin Films for Fabrication of Ordered Multifunctional Polymer Nanocomposites[END_REF][START_REF] Liao | Self-Assembly of a Silicon-Containing Side-Chain Liquid Crystalline Block Copolymer in Bulk and in Thin Films: Kinetic Pathway of a Cylinder to Sphere Transition[END_REF][START_REF] Park | High-Throughput Preparation of Complex Multi-Scale Patterns from Block Copolymer/Homopolymer Blend Films[END_REF] , and comprehensive reviews are available [START_REF] Balazs | Nanoparticle Polymer Composites: Where Two Small Worlds Meet[END_REF][START_REF] Mezzenga | Nanocomposites: Nanoparticles in the Right Place[END_REF][START_REF] Hoheisel | Block Copolymer-Nanoparticle Hybrid Self-Assembly[END_REF][START_REF] Kao | Toward Functional Nanocomposites: Taking the Best of Nanoparticles, Polymers, and Small Molecules[END_REF] . These studies have established that the spatial distribution of the nanoparticles is sensitive to factors such as selectivity [START_REF] Lin | Nanoparticle-Driven Assembly of Block Copolymers: A Simple Route to Ordered Hybrid Materials[END_REF][START_REF] Jang | Morphology Evolution of PSb -P2VP Diblock Copolymers via Supramolecular Assembly of Hydroxylated Gold Nanoparticles[END_REF][START_REF] Voet | Vinylidene Fluoride)/Nickel Nanocomposites from Semicrystalline Block Copolymer Precursors[END_REF] and size [START_REF] Bockstaller | Size-Selective Organization of Enthalpic Compatibilized Nanocrystals in Ternary Block Copolymer/Particle Mixtures[END_REF][START_REF] Spontak | Selectivity-and Size-Induced Segregation of Molecular and Nanoscale Species in Microphase-Ordered Triblock Copolymers[END_REF][START_REF] Terzić | Polymer-Based Multiferroic Nanocomposites via Directed Block Copolymer Self-Assembly[END_REF] . For example, Chiu et al. [START_REF] Chiu | Control of Nanoparticle Location in Block Copolymers[END_REF] used surface modification of gold nanoparticles to drive their assembly when dispersed on symmetric coil-coil polystyrene-blockpoly(2-vinylpyridine) PS-b-P2VP. PS-thiol coated gold nanoparticles are located near the center of the PS block phase of the lamellae structure, whereas P2VP-thiol coated gold nanoparticles were located in the P2VP domains. Particles coated with a specific polymer will lower their enthalpy by segregating into the corresponding domain of the block copolymer. When the same gold nanoparticles were grafted with a composite brush made of both PS and P2VP thiols they were found at the block interfaces in the resulting film. Yeh and coworkers showed the incorporation of acid-modified CdS nanoparticles NPs into the poly(4-vinylpyridine) P4VP block via hydrogen interaction in a PS-b-P4VP film [START_REF] Yeh | CdS Nanoparticles Induce a Morphological Transformation of Poly(Styrene-b-4-Vinylpyridine) from Hexagonally Packed Cylinders to a Lamellar Structure[END_REF] . Moreover, they proved the morphological transformation of the PS-b-P4VP self-assembly from the original hexagonal-close-packed hcp cylinders to lamellar structure when the NPs were added.

In the present work, we study the incorporation of functionalized gold nanoparticles (GNPs) into a diblock copolymer designed with a semi-conducting P3HT rod block and a coil poly(ethylene glycol) methyl ether methacrylate PEGMA, which presents interesting properties for bio-applications [START_REF] Lee | Antibiofouling Polymer-Coated Superparamagnetic Iron Oxide Nanoparticles as Potential Magnetic Resonance Contrast Agents for in Vivo Cancer Imaging[END_REF][START_REF] Hu; Neoh | Cellular Response to Magnetic Nanoparticles "PEGylated" via Surface-Initiated Atom Transfer Radical Polymerization[END_REF][START_REF] Bontempo | Streptavidin as a Macroinitiator for Polymerization: In Situ Protein-Polymer Conjugate Formation[END_REF] . Synthesis of the diblock copolymer and surface functionalization of NPs are thoroughly described. For the first time, the controlled localization of grafted GNPs was reported to influence the self-assembly of a rod-coil copolymer made up of a conjugated rod block and thus counteract the π-π interactions. The impact of grafted GNPs on rod-coil diblock copolymer self-assembly and the film morphology changes were characterized by AFM, TEM, DSC and surface analysis techniques. X-ray Photoelectron Spectroscopy (XPS) was used to quantify gold nanoparticles at the surface of the hybrid film (HF) and Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) allowed to precisely locate the functionalized gold nanoparticles inside the hybrid film.

Experimental section

Materials. All chemicals were purchased from Sigma Aldrich. CuBr was stirred with acetic acid during 16 hrs, washed with acetic acid, absolute ethanol, and finally diethyl ether to remove impurities. The commercial solution of 2,5-dibromo-3-hexyl thiophene in THF was stirred in a dried Schlenk and degazed for a few seconds to remove oxygen.

Characterization.

Diffusion order spectroscopy (DOSY) and [START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF] H NMR experiments were performed on a Bruker 400 MHz spectrometer in CDCl3 at 27 °C. All spectra were recorded on a Bruker AVANCE 400 MHz spectrometer. Chemical shifts are reported as ppm downfield from Tetramethyl silane (TMS).

Size exclusion chromatography (SEC) was carried out in THF with a flow rate of 1.0 mL.min -1 . One pre-column and two columns (Styragels HR 5E and 4E (7.8 ´ 300 mm)) were used for the analysis. Four detectors were combined; a UV-visible spectrophotometer (Viscotek VE 3210), Multi-Angle Light Scattering (Wyatt Heleos II), viscosimeter (Wyatt Viscostar II) and refractive index detector (Viscotek VE 3580). A Polystyrene calibration was used to calculate dispersities.

UV-Vis spectroscopy measurements were carried out in spectrum mode using a SHIMADZU UV-2450 spectrophotometer controlled by a software. The sample was solubilized before analysis in an appropriate solvent and inserted in a quartz cell having an optical path length of 1 cm. Differential scanning calorimetry (DSC) was performed using a Q100 from TA instruments under N2 atmosphere. For each sample, the temperature was increased from 40 to 240 °C with a ramp of 10 °C/min, then cooled to -65 °C at the same ramp. This was repeated during a second cycle.

XPS measurements were performed on a Thermo K-alpha spectrometer with a hemispherical analyzer and a microfocused (400 µm diameter microspot) monochromated radiation (Al Kα, 1486.6 eV) operating at 72 W under a residual pressure of 1.10 -9 mbar. The pass energy was set to 20 eV. Charge effects, currently important for hybrid sample, were compensated by the use of a dual beam charge neutralization system (low energy electrons and Ar + ions) which had the unique ability to provide consistent charge compensation. All spectra were energy calibrated by using the hydrocarbon peak at a binding energy of 285.0 eV. Spectra were mathematically fitted with Casa XPS software© using a least squares algorithm and a nonlinear Shirley-type background. The fitting peaks of the experimental curves were defined by a combination of Gaussian (70%) and Lorentzian (30%) distributions. Quantification was performed on the basis of Scofield's relative sensitivity factors [START_REF] Scofield | Hartree-Slater Subshell Photoionization Cross-Sections at 1254 and 1487 EV[END_REF] Time-of-Flight Secondary Ion Mass Spectrometry (ToF-SIMS) analyses were performed using a TRIFT V nanoToF II (Physical Electronics, US) equipped with a 30kV Au LMIG primary ion gun. All mass spectra were acquired in the positive polarity with the same experimental conditions, so that to perform semi-quantitative analysis (comparing the ratio of peaks intensities). For surface analysis, the LMIG gun was tuned to deliver Au3 ++ gold clusters primary ions with a DC current of 7 nA over a 10 µm raster size, the mass range was fixed between 0 and 1850 uma and the number of frames was set to 50 (dose: 3.7x10 11 ions/cm 2 ). Depth profile experiments (series of 20 cycles "analysis/sputtering") were carried out using Au3 ++ primary ions over 10x10µm 2 raster size for analysis and a 1 kV Ar + gas gun for etching (with a sputtering time of 20 seconds for each cycle, a DC current of 50 nA and a sputtered area of 100x100 µm 2 ). For 2D imaging, a resolution of 512x512 pixels with a time per channel of 256, over 100x100 µm 2 raster size was used. Note that dual charge (e -/Ar + ) compensation was used for all analyses and the sodium peak, which appears with a high intensity, has been blanked during the experiments so that to detect better smaller peaks. Data processing was performed using ToF-DR software provided by Physical Electronics. All positive polarity mass spectra were calibrated using CH + (m/z 13), CH2 + (m.z 14) and C2H + (m/z 25) peaks.

Atomic force microscopic (AFM) was carried out on a MultiMode® 8 Atomic Force

Microscope (AFM) from Bruker in the PeakForce Quantitative NanoMechanics mode.

Transmission Electron Microscopy images of gold nanoparticles were performed on a Philips CM 200 (200 kV) TEM microscope equipped with a LaB6 source. The particles dispersed in water or chloroform were dropped onto a carbon-coated copper grid and dried before analysis.

Transmission Electron Microscopy pictures of hybrid films were performed on a Talos F200S G2 Thermofisher -Eindhoven -Transmission Electron Microscope at 200kV, equipped with a Camera ONE VIEW -Gatan -Paris for image acquisition. Before observation, the films were dip-coated on Thermanox substrates and cross cut using a Cryo-ultramicrotome UC-7 FC7 -Leica Microsystems. The use of this substrate allows the elaboration of thin cross-section slices using an ultramicrotome. TEM images have been performed after film treatment with ruthenium tetraoxide to enhance electronic contrast. This chemical reacts with thiophene moities, colors the P3HT domains (dark zones) and thus increases the contrast with PEGMA environments (clear areas). Cross sections were performed at -90°C using a Cryo-knife 35°. Polymer's samples were contrasted with Ruthenium Tetraoxide aqueous solution (0.5%).

Synthesis

Synthesis of ethynyl-terminated P3HT. P3HT was synthesized according to the procedure described in a previous work. [START_REF] Awada | Versatile Functional Poly(3-Hexylthiophene) for Hybrid Particles Synthesis by the Grafting onto Technique: Core@shell ZnO Nanorods[END_REF] In a dried Schlenk flask, 2,5-dibromo-3-hexyl thiophene (6.13 mmol) was degazed under vacuum for 3 seconds. Then 10 mL of dried THF were introduced as the solvent. Isopropyl magnesium chloride (6.13 mmol) was added and the media was stirred for two hours at 20°C under nitrogen atmosphere. Dried THF (40 mL) containing Ni(dppp)Cl2 (0.34 mmol) was then added to the solution and reacted during ten min.

Eventually, of ethynyl magnesium chloride (1.84 mmol) was inserted in the media for an additional 2 min. The mixture was precipitated twice in methanol and the obtained polymer was characterized by SEC (Mn = 6 500 g mol -1 ; Ð = 1.3) and [START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF] H NMR (400 MHz, CDCl3): δ = 0.91

(t, 3 H), 1.34 (m, 6 H), 1.69 (t, 2 H), 2.80 (t, 2 H), 3.53 (s, 1 H), 6.97 (s, 1 H).

Synthesis of azido functionalized PEGMA (PEGMA-N3). P(EGMA-stat-MEO2MA) was

prepared by Atom Transfer Radical Polymerization initiated by 2-azidoethyl 2bromoisobutyrate. Copper bromide (26 mg, 0.18 mmol) and N,N,N′,N′′,N′′-PentaMethylDiEthyleneTriAmine (PMDETA) (62.4 mg, 0.36 mmol) were added to a Schlenk flask sealed with a septum. Next, a degassed mixture of both monomers oligo (ethylene glycol) methacrylate (0.9 g, 1.8 mmol) and 2-(2-methoxyethoxy)ethyl methacrylate (3 g, 16.2 mmol) and 3 mL of dioxane were added through the septum with a degassed syringe. The flask was put in an ice bath and purged with nitrogen for 30 minutes. Then the initiator, 2-azidoethyl 2bromoisobutyrate (14.1 mg, 0.06 mmol) was added with a microliter syringe. The mixture was heated at 75 °C in an oil bath and stopped 30 minutes later. The experiment was stopped by opening the flask to expose the catalyst to air. Dialysis was used to remove free monomers and purify the azido-terminated PEGMA-N3. The mixture was diluted with ethanol and dialyzed with deionized water using a regenerated cellulose membrane RC (weight cut off: 3.5 kDa) for one week. Water was removed by putting the polymer solution in a crystallizer glass to let water evaporate itself at room temperature for 3 days. The pure polymer appeared as a colorless viscous oil. The polymer was characterized by NMR, and SEC (Mn=18 000 g.mol -1 ; Ð = 1.2) after drying it under vacuum. [START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF]

Synthesis of P3HT-b-PEGMA copolymer (Scheme S1

). P3HT (1 eq), PEGMA-N3 (1.2 eq) and CuBr (10 eq) were dissolved in THF (40 mL) and submitted to three freeze-vacuum cycle to remove oxygen. PMDETA (10 eq) was then added and the media was stirred at 50 ºC for 2 days. The solution was then purified through a basic alumina column to remove copper bromide precipitated in methanol. The obtained polymer was washed by Soxhlet extraction with methanol, cyclohexane, and chloroform. Acetone and cyclohexane washing were performed to remove residual homo PEGMA and homo P3HT respectively.

Synthesis of gold nanoparticles and functionalization with PEG-thiol ligand.

Small citrate-capped gold nanoparticles were first synthesized according to the protocol reported by Jana and Murphy [START_REF] Jana | Seed-Mediated Growth Approach for Shape-Controlled Synthesis of Spheroidal and Rod-like Gold Nanoparticles Using a Surfactant Template[END_REF] to obtain small gold nanoparticles (3-5 nm). Briefly, HAuCl4 and trisodium citrate were solubilized in 20 mL of deionized water at a concentration of 2.5 mM for both reagents. 0.6 mL of a 0.1M NaBH4 solution was then added at once in the gold solution under a constant and strong stirring. The solution turned from yellow to a wine-red color. After 15 minutes stirring, 2.5 mM of PEG800-SH was added and the reaction was left for 4 hours to complete the exchange of ligands, stopped and dialyzed against deionized water using a regenerated cellulose membrane RC (weight cutoff: 8 kDa) for 3 days (Scheme SI2).

Film preparation

The hybrid films were prepared through a dip-coating process. Silicon wafers or Thermanox® substrates were vertically withdrawn at 10 µm/s from a 1 mL chloroform suspension of gold nanoparticles containing 3 mg of P3HT6.5-b-PEGMA18. The concentration of the gold suspension in chloroform was set so that the hybrid film will contain 0, 2, 5 or 10 vol%.

Results and Discussion

Synthesis of the diblock copolymer P3HT-b-PEGMA.

A P3HT-b-PEGMA block copolymer was synthesized in 3 steps, ATRP of a mixture of MEO2MA and OEGMA monomers using 2azidoethyl-2-bromoisobutyrate as an initiator, GRIM polymerization of 3-hexylthiophene and the click reaction of both homopolymers. The purification of the ethynyl-terminated P3HT was performed as described previously in the experimental section to avoid the denaturation of the alkyne end-chain. Using the integration of the methylene proton at 2.8 ppm by [START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF] H NMR, a P3HT degree of polymerization of 35 units was estimated (Figure S1). This value was in agreement with the molecular mass determined by SEC (Mn = 6 500 g.mol -1 ). The alkyne end-chain functionalization was calculated to be efficient at 92% by integration of the signal at 3.5 ppm.

The azido end-capped PEGMA was synthesized using 2-azidoethyl-2-bromoisobutyrate as initiator to introduce an azide moiety at the end of the chains from the initiator avoiding postmodification. [START_REF] Sumerlin | Macromolecular Engineering through Click Chemistry and Other Efficient Transformations[END_REF] Due to the high molecular weight of the synthesized PEGMA-N3, we were not able to calculate the degree of polymerization by 1 H NMR since the CH2 in alpha or beta position of the azide group has the same chemical shift with the repeat units; the methylene group in alpha position of the methacrylate (4.15 ppm) (Figure S2). The molecular weight determined by SEC using PS standard is Mn = 18 000 g.mol -1 . The ratio of the integration values of the CH2 in alpha position of the methacrylate group with the other CH2 is 1.0 : 4.3 for a theoretical value of 1.0 : 4.4. The final composition of the thermo-responsive homopolymer is then 90 and 10% of MEO2MA and OEGMA, respectively.

P3HT-b-PEGMA was prepared using a click reaction between the ethynyl-P3HT and the azidoterminated PEGMA as described in Scheme SI1. Since it is easier to remove free PEGMA than to remove free P3HT due to versatile solubility, an excess of PEGMA-N3 was used to perform the click reaction with the ethynyl-P3HT. [START_REF] Sumerlin | Macromolecular Engineering through Click Chemistry and Other Efficient Transformations[END_REF] Since P3HT shows a maximum light absorption at 460 nm, we were able to control and monitor the cyclo-addition reaction via SEC using UV-visible detector (Figure S3). A shift of the molecular weight was observed compared to the homo P3HT, showing an increase of the diblock copolymer molecular weight (Figure S4). A single and narrow peak was observed with a dispersity value Ð of 1.2, confirming the successful purification of the diblock copolymer. The Diffusion Ordered SpectroscopY (DOSY) NMR analysis of the P3HT-b-PEGMA also confirmed the success of the click reaction since all 1 H signals belonged to the same macromolecule (Figure 1). The two parent homopolymers ethynyl-P3HT and PEGMA-N3 showed higher diffusion coefficients values than the one from the diblock copolymer. The ethynyl-P3HT with the smallest molecular weight of 6 500 g.mol -1 showed the highest diffusion coefficient value around 110 µm 2 /s in comparison with the lowest diffusion coefficient value of 42 µm 2 /s for the final P3HT-b-PEGMA (Mn = 24 500 g.mol -1 ).

The integration of the area under the 1 H NMR peak at 2.8 ppm corresponding to the methylene protons of the thiophene and the methylene units in alpha position of the methacrylate group, allowed to calculate a molar composition P3HT/PEGMA of 1/2 (Figure S5). Since of the P3HT block was equal to 35, the PEGMA block had a of 70, which was consistent with a molecular weight of 18 000 g.mol -1 (Table 1).

Synthesis and characterization of gold nanoparticles.

UV-Vis analyses in water of both of citrate and PEG-thiol capped nanoparticles show a red-shift of the gold nanoparticles absorption from 515 nm to 530 nm (Figure 2a) after functionalization.

This confirms the ligand exchange during the functionalization step where citrate was replaced by the PEG-thiol (Scheme SI2).

TEM image of gold nanoparticles after functionalization by the PEG-thiol ligand is shown in

Polymer

Mn a (g.mol -1 ) DPn a Mn b (g.mol -1 ) respectively. [START_REF] Mehtala | Citrate-Stabilized Gold Nanorods[END_REF][START_REF] Mikhlin | On the Nature of Citrate-Derived Surface Species on Ag Nanoparticles: Insights from X-Ray Photoelectron Spectroscopy[END_REF] The C-C and C-OH components can be attributed to alkyl and alcohol groups in citrate. On the other hand, the COO component is attributed to the carboxylate function of citrate. The intensity ratio between COO and C-OH was calculated to be 3.3, close to 3 as it is in the composition of citrate ( -OOC-CH2-C(OH)COO --CH2-COO -). The O1s spectrum of citrate-capped gold nanoparticles has been fitted in two peaks (Figure 3b). The first peak at 531.7

Ð b f c P3HT Ethynyl-P3HT 6
eV was attributed to the oxygen atoms in COO environment and the one at 536 eV to the oxygen atom of the alcohol group [START_REF] Mikhlin | On the Nature of Citrate-Derived Surface Species on Ag Nanoparticles: Insights from X-Ray Photoelectron Spectroscopy[END_REF][START_REF] Mazov | Oxidation Behavior of Multiwall Carbon Nanotubes with Different Diameters and Morphology[END_REF][START_REF] Okpalugo | High Resolution XPS Characterization of Chemical Functionalised MWCNTs and SWCNTs[END_REF][START_REF] Huang | A Morpholinium Surfactant Crystallization Induced Formation of Au Nanoparticle Sheet-like Assemblies with Uniform SERS Activity[END_REF] . The atomic ratio of oxygen between the carboxylate group and the alcohol was equal to 5.9, in agreement with the citrate formula (6.0).

The C1s spectrum of PEG-thiol-capped gold nanoparticles was similar to the C1s spectrum of the commercial PEG-thiol used for the functionalization of gold nanoparticles, only two components at 285 and 286.5 eV are observed (Figure 3c). Indeed, the contribution of carboxylate environment at higher energy (288.8 eV) has disappeared indicating the replacement of citrate ligand by PEG-thiol. In addition, the contribution at 286.5 eV can be attributed to the C-O bond from the PEG ligand and C-S bond linked to the surface of gold. The latter cannot be discriminate from the former. The component at 285 eV is from the C-C bonds. The O1s spectrum of PEG-capped nanoparticles showed only one component at 532.7 eV (Figure 3d). This is typical of the C-O environment in PEG. Most importantly, the oxygen contribution at higher energy (536 eV) from the alcohol in citrate-capped nanoparticles has completely disappeared, indicating that the citrate ligand is no longer present.

Note that for all spectra, the C1s component located at 285 eV is attributed to the C-C bonds of the molecules probed but also to adventitious carbon (C-C and C-H species), always present at the surface analyzed by XPS. eV is due to the π-π* shake-up transition in the thiophene cycle [START_REF] Lachkar | Interaction of Vapor-Deposited Cu and Ni with Poly[END_REF] . The peak at higher energy can be attributed to the COO bond from the methacrylate group.

The height and adhesion images show a random organization of nanofibrils of 10 nm in width and several hundred nanometers in length (Figure 4 b-c). This morphology is typical of rod-coil diblock copolymer when the rod block crystallization dominates over the block copolymer self-assembly. [START_REF] Lee | Self-Assembly and Phase Transformations of π-Conjugated Block Copolymers That Bend and Twist: From Rigid-Rod Nanowires to Highly Curvaceous Gyroids[END_REF] Phase diagram of coil-coil BCPs with equivalent composition, i.e. fvP3HT = 0.33 for a P3HT6.5k-b-PEGMA18k would normally lead to a structure of P3HT cylinders in a PEGMA matrix. [START_REF] Kim | Effect of Areal Chain Density on the Location of Polymer-Modified Gold Nanoparticles in a Block Copolymer Template[END_REF] In that case, BCPs self-assembly is governed by the volume fraction f of the blocks and the χN product. [START_REF] Olsen | Nonlamellar Phases in Asymmetric Rod-Coil Block Copolymers at Increased Segregation Strengths[END_REF] For the P3HT6.5k-b-PEGMA18k the rigidity and the π-π interactions coming from the P3HT aromatic structures control the macromolecular interactions, which are dominated by the strong rod regime where µ >χ.

PEG-decorated gold nanoparticles GNP@PEG were then added at 2, 3, 5 and 10 vol % to the copolymer solution and films were dip-coated onto silicon wafer. AFM images and XPS of the hybrid films are depicted in Figure 4. C1s spectra of the hybrid films obtained after the incorporation of PEG-thiol-capped gold nanoparticles show an increase of the intensity of the peak at 286.7 eV with the amount GNP@PEG added. When the amount of GNP@PEG incorporated inside the film was increased (2 v%, 5 v% and 10 v%), the intensity of the C-O component increased as well (Figure 4 d, 4g and 4j). This is increase of the intensity of the C-O peak is due to the fact that the incorporated gold nanoparticles are PEG-capped and the C-O bond from -(CH2-CH2-O)-PEG units appears at 286.5 eV [START_REF] Martin-Vosshage | X-Ray Photoelectron Spectroscopy Studies on PEOnMBr2 (M = Co, Ni, Zn) Solid Electrolytes[END_REF] . A slight decrease of the intensity of the COO peak from the methacrylate (289 eV) was observed. This is probably due to the diminution of its ratio as the global concentration of carbon increases with the amount of PEGcapped nanoparticles added.

Both height and adhesion images showed that fibrils organization gradually disappeared with the increase of the gold nanoparticles. Indeed, for the lowest volume fraction, P3HT fibrils were observed in the top surface of the thin film (Figure 4 d-f). Then for 5 vol% of GNP@PEG, the surface is equally partitioned in both nano-domains in a PEGMA matrix with the remaining presence of fibrils and new out-of-the-plane P3HT cylinders-like (Figure 4 g-i). With the introduction of 10 vol % of GNP@PEG, the fibrils are almost completely erased and the out-ofthe-plane cylindrical-like morphology is observed on the whole surface (Figure 4 j-l).

Figure 4.

C1s XPS spectra of the hybrid films with a volume fraction of 0%, 2%, 5% and 10% in gold nanoparticles for a), d), g) and j), respectively. PeakForce QNM-mode AFM images of the hybrid films with a volume fraction of 0%, 2%, 5% and 10% in gold nanoparticles b-c), e-f), h-i) and k-l), respectively.

The spatial distribution of the incorporated GNPs inside the hybrid film was then investigated by ToF-SIMS (Figure 5). First of all, pure films based P3HT or PEGMA homopolymers, P3HT-b-PEGMA copolymer or GNPs@PEG were separately analyzed in order to establish a database with the main specific peaks of each species (Table 2).

Table 2. Main secondary ions detected by ToF-SIMS for P3HT, PEGMA, P3HT-b-PEGMA, GNPs@PEG and P3HT-b-PEGMA + GNPs@PEG films over a 0-200 mass range in the positive polarity. Characteristic peaks of the PEGMA methacrylate polymer backbone [START_REF] Hearn | Analysis of Polymer Surfaces by SIMS. 12. On the Fragmentation of Acrylic and Methacrylic Homopolymers and the Interpretation of Their Positive and Negative Ion Spectra[END_REF][START_REF] Hearn | SIMS and XPS Studies of Polyurethane Surfaces. 1. Preliminary Studies[END_REF] homopolymer are detected at m/z =139 (C7H7O3 + ), 141 (C7H9O3 + ) and 143 (C7H11O3 + ), as well as a fragment characteristic of the sulfur containing ring of P3HT block at m/z = 81 (C4HS + ), and the Au + peak at m/z=197 specific of GNPs. Moreover, polymer structure patterns, composed of a main peak surrounded by smaller peaks resulting of the loss or the gain of 2 protons, are also detected at bigger masses: from m/z = 313 to m/z =319, from m/z = 371 to m/z =377 or from m/z = 429 to m/z =435 (Figure 5a bottom spectrum). Note that the fragmentation patterns of the two homopolymers appear to be slightly different after their incorporation in the block copolymer macromolecular structure with and without GNPs (see Table 2). For example, for the P3HT homopolymer, the positive ion peaks at m/z=147 and m/z=149 attributed to C9H7S + and C9H9S + respectively are not detected anymore for the block copolymer. The 2D chemical mapping of C7H7O3 + ions (characteristics of the copolymer, in green) and Au + ions (characteristics of GNPs, in red) over a 100x100µm field of view in positive polarity (Figure 5b) shows a homogeneous distribution of GNPs at the surface of the hybrid film. Moreover, richer areas of the copolymer fragment (in bright green) are distinguishable, maybe due to topography effects. In order to obtain information about the GNPs spatial distribution more deeply in the copolymer bulk material, ToF-SIMS depth profile experiments (series of 20 cycles "analysis/sputtering") were performed on the hybrid film containing 10 vol% of GNPs. Figure 5c presents the concentration depth profiles of C7H7O3 + (representing the copolymer, in green), Au + (specific to GNPs, in yellow) and total secondary ions detected (in blue) obtained in the positive polarity over 380 seconds of etching. Concerning C7H7O3 + and Au + profiles, they remain constant from 25s to the end of the sputtering. A 3D image has been reconstructed from the depth-profiles where the signal intensities of C7H7O3 + (in green) and Au + (in yellow) are plotted over the analyzed area (10µmx10µm = x and y dimensions) versus the etching time (the z axis, 280s); for a better visibility, the z axis is over-dimensioned compared to the other two axes. Note that it is difficult to determine precisely the sputtered depth due to the unknown sputtering ion yield of the hybrid organic-inorganic material. However, it is reasonable to say that only few tens of nanometers have been removed, regarding the very smooth etching conditions used (1kV, 50nA). The 3D image clearly shows that the spatial distribution of GNPs follows the one of the copolymer in the analyzed volume. The two species are well connected and they are homogenously present in the bulk of the material due the strong interaction of the GNPs@PEG with the PEGMA domains.

Samples m/z Ions

This ToF-SIMS study confirms that the self-assembly of the hybrid film occurs without any macro segregation between the gold functionalized GNPs and the diblock copolymer. The role of GNPs in the structural modification from fibrils to cylinder like morphology was then investigated. First, TEM experiment was performed on cross-section transversal slices of hybrid films dip-coated on a polymer substrate (Thermanox®) to study the location of the GNPs within the films. TEM images of the hybrid film showed a clear segregation between the two polymer areas, pictured by light and dark grey domains corresponding to PEGMA and P3HT domains, respectively (Figure 6a). As it can be clearly observed on the high magnification picture (Figure 6b), GNPs (black spots) are preferentially localized in the light grey PEGMA domains, due to their functionalization with PEG ligand and their hydrophilic affinity. Additional image where GNPs are clearly visible inside the block copolymer film is available in supporting information (SI7).

As a consequence of the GNP@PEG insertion in the PEGMA block, the volume fraction of the corresponding phase increases and then influences the diblock copolymer self-assembly. In the literature, other strategies were followed to reduce the predominance of π-π interactions over the morphology of P3HT-based copolymer films. Lee et al. [START_REF] Lee | Self-Assembly and Phase Transformations of π-Conjugated Block Copolymers That Bend and Twist: From Rigid-Rod Nanowires to Highly Curvaceous Gyroids[END_REF] perfomed the synthesis of various P3HT-b-P2VP copolymers in which the P2VP degree of polymerization was changed. Fibrils were obtained for coil block fraction under 68 vol%. When the coil fraction was further increased, cylindrical and spherical phases were observed by AFM. The authors attributed such a variation to the chain twist generated for the bulkiness of the coil block which impeded π-π stacking. Herein, the copolymer has P3HT and PEGMA volume fraction of 0.33 and 0.67 respectively. After the addition of 10 vol% of GNP@PEG, the resulting P3HT volume fraction dropped at a maximum of 0.3. Although the difference in the P3HT content seems low, it is high enough to break the fibrils diblock copolymer self-assembly. To follow this trend, we investigated the morphology of a P3HT-b-PEGMA/PEGMA homopolymer blend with a volume ratio of 90/10 to reach a P3HT volume fraction of 0.3. AFM images show that the surface is composed of randomly aligned nano-fibrils without neither in-the-plane nor out-the-plane cylindrical morphologies (Figure S6). It is worth noting that we observed an increase of the volume fraction of the PEGMA matrix, in which P3HT fibrils appeared more diluted.

Therefore, the increase in the volume fraction is not the only factor leading to the morphology transformation. Indeed the rigidity caused by the incorporation of hard metallic nanoparticles in the PEGMA phase could also impede the creation of π-π stacking and therefore the crystallization of the P3HT. DSC of the composite blend (90/10 copolymer/particle in volume) was performed and compared to the pure diblock copolymer and to the parent P3HT homopolymer to check the influence of the NPs addition on the P3HT block crystallization.

P3HT exhibited an endothermic peak at 210 °C corresponding to P3HT crystals melting temperature Tm (Figure 7a). This value is almost the same in P3HT-b-PEGMA thermogram, i.e. Tm = 220 °C, but with a weaker intensity due to the decrease of P3HT content and a possible decrease of the crystallization rate. Since PEGMA glass transition temperature is below -50°C, the crystallization of P3HT blocks is more affected by the size of the PEGMA block than by its rigidity. The heating scan of the blend containing gold nanoparticles present a lower endothermic peak at 195 °C with a weak intensity. This behavior may mean a significant reduction in the crystallinity of P3HT leading to the cylindrical microstructures observed by AFM.

In the cooling ramp, a similar trend was observed in the crystallization temperature Tc of the P3HT, P3HT-b-PEGMA and the hybrid blend, at 160, 125 and 95 °C respectively. This behavior indicates that the crystallization of the P3HT moieties is hindered by the addition of, first a large volume fraction of soft PEGMA, and then a small addition of hard nanoparticles.

This kind of behavior has already been described by Dai et al. [START_REF] Dai | Facile Synthesis of Well-Defined Block Copolymers Containing Regioregular Poly(3-Hexyl Thiophene) via Anionic Macroinitiation Method and Their Self-Assembly Behavior[END_REF] Thus, a morphological transition from P3HT fibrils into out-of-the-plane cylinders-like can be driven by introducing GNP@PEG during the nanophase segregation of the P3HT-b-PEGMA by self-assembly.

Conclusion

Herein is described the change of a diblock rod-coil copolymer film morphology driven by the addition of metallic nanoparticles NPs. The precise location of a small amount of gold NPS in the coil phase hindered the crystallization of the rod block. AFM images of the diblock copolymer shows the transition from a random organization of P3HT nanofibrils, as a typical organization of rod-coil block copolymers, where the crystallization of the rod block takes over the block copolymer self-assembly. From such a behavior, out-of-the-plane rod polymer cylinders-like in a coil polymer matrix are then observed. TEM of film cross sections shows the GNP@PEG embedded in the PEGMA regions thanks to the physical affinity brought by their surface functionalization with PEG chain corona. DSC revealed that the thermal transitions pertaining to the P3HT rod crystals disappeared after the addition of the GNPs. Such a morphological change triggers by the elaboration of a hybrid composite is of great interest for many applications. In this specific case, the use of a thermosensitive block PEGMA in which lower critical solubility temperature was tuned to be 37°C (Figure S8) by the introduction of a precise ratio of both OE2MA and OEGMA monomers, [START_REF] Lutz | Polymerization of Oligo(Ethylene Glycol) (Meth)Acrylates: Toward New Generations of Smart Biocompatible Materials[END_REF][START_REF] Lutz | About the Phase Transitions in Aqueous Solutions of Thermoresponsive Copolymers and Hydrogels Based on 2-(2-Methoxyethoxy)Ethyl Methacrylate and Oligo(Ethylene Glycol) Methacrylate[END_REF] can allow very interesting biological

  et al. have synthesized several poly(3hexyl thiophene-b-vinylpyridine) (P3HT-b-P2VP) copolymers to vary the size of the coil block.

Figure 1 .

 1 Figure 1. DOSY NMR of the P3HT-b-PEGMA copolymer and its building blocks.

Figure 2b .

 2b Figure 2b. The TEM photo exhibits spherical NPs with an average diameter around 5 nm without aggregation indicating their efficient stabilization by PEG corona.

Figure 2 .

 2 Figure 2. UV spectra of gold nanoparticles before and after ligands exchange with PEO (a) and TEM micrograph of the synthesized PEO800-capped gold nanoparticles (b).

Figure 3 .

 3 Figure 3. C1s XPS spectra of citrate-capped GNPs (a) and PEG800-capped GNPs (c). b) and d) are O1s spectra of citrate-capped GNPs and PEG800-capped GNPs respectively.

Figure 5a presents the

  Figure 5a presents the positive ion mass spectra of P3HT-b-PEGMA + 10 vol% GNPs@PEG hybrid film over m/z 50-250 (top spectrum) and m/z 280-440 (bottom spectrum) mass ranges.

Figure 5 .

 5 Figure 5. a) TOF-SIMS positive ion mass spectra of P3HT-b-PEGMA + GNPs (10 v%) hybrid film over m/z 50-250 (top spectrum) and m/z 280-440 (bottom spectrum) mass ranges, b) TOF-SIMS 2D chemical mapping of C7H7O3 + and Au + ions over a 100x100µm field of view in positive polarity c) TOF-SIMS depth-profile experiment over 380s etching time of C7H7O3 + (green) and Au + (yellow) ions in positive polarity and 3D image reconstruction from the depthprofile showing the spatial distribution over 10x10µm 2 raster size and 380s etching time of C7H7O3 + (green) and Au + (yellow) ions at the surface of P3HT-b-PEGMA + GNPs (10 v%) hybrid film. For a better visibility, the z axis is over-dimensioned compared to the other axes.

Figure 6 .

 6 Figure 6. (a) TEM micrographs of a cross section the diblock copolymer-GNP@PEG (5 vol%) hybrid film contrasted with ruthenium oxide RuO4 for 90 min. (b) is the magnification picture of (a).

  when they studied the transition temperatures of different P3HT-b-P2VP with several coil block lengths. Indeed, the melting temperature Tc decreases from 200°C to 140°C with the decrease of the volume fraction of the P2VP block from 0.29 to 0.57. Above a volume fraction of 0.57 in the coil polymer, no crystallization was observed.

Figure 7 .

 7 Figure 7. Thermogramms of the heating a) and the cooling of P3HT, P3HT-b-PEGMA and the hybrid film with 10 v % in gold nanoparticles b).

  H NMR (400 MHz, CDCl3): δ ppm = 0.83 (s, 3 H), 1.81 (m, 2 H), 3.46 (t, 2 H), 3.59 (m, 3 H), 3.76 (m, 3 H), 4.11 (m, 2 H).

Table 1 .

 1 Summary of the polymers' characteristics.

a calculated by

[START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF]

H NMR b Calculated from SEC via PS calibration. c The P3HT volume fraction was calculated by using Mn provided by

[START_REF] Huynh | Hybrid Nanorod-Polymer Solar Cells[END_REF]

H NMR and the polymer densities: ρP3HT = 1.11 g/mL and ρPEGMA = 1.19 g/mL

ACKNOWLEDGMENT

TEM Imaging of the hybrid film was performed at the Bordeaux Imaging Center, member of the FranceBioImaging national infrastructure (ANR-10-INBS-04). We thank S. Lacomme for her work on this project. Dr. A. Khoukh and J.B. Ledeuil are acknowledged for fruitful discussion on NMR and XPS analysis. We thank F. Portail, C. Bessibes, and F. Casbas of Arkema Industry for the TEM analysis realized on PEO-capped gold nanoparticles.

applications in the field of cellular culture and bioelectronic especially. [START_REF] Aguirre | Dual-Responsive Biocompatible Microgels as High Loaded Cargo: Understanding of Encapsulation/Release Driving Forces by NMR NOESY[END_REF][START_REF] Aguirre | Smart Self-Assembled Microgel Films as Encapsulating Carriers for UV-Absorbing Molecules[END_REF][START_REF] Aguirre | Versatile Oligo(Ethylene Glycol)-Based Biocompatible Microgels for Loading/Release of Active Bio(Macro)Molecules[END_REF] Further applicative works are in progress with these films using the light absorbing properties of both P3HT and GNPs into a thermosensitive biocompatible PEGMA matrix.

Supporting Information.

The supporting information provides synthetic scheme and chemical characterization (SEC, NMR) of the materials used in this study. Moreover, additional microscopy images can be found in the file.

AUTHOR INFORMATION

Corresponding Authors e-mail: herve.martinez@univ-pau.fr; laurent.billon@univ-pau.fr;

Funding Sources


Denis Fougerouse

Christopher Kirkland

David Saxey

Anne-Magali Seydoux- Guillaume

Matthew R Rowles

William D A Rickard

Steven M Reddy

Nanoscale isotopic dating of monazite

Monazite U-Th-Pb geochronology is widely used for dating geological processes, but current analytical techniques are limited to grains greater than 5 μm in diameter. This limitation precludes the analysis of both micrometre-scale discrete monazite grains and fine textures within monazite crystals that are commonly found. Here, we analyse reference materials by atom probe tomography and develop a protocol for 208 Pb/ 232 Th dating of nanoscale domains of monazite (0.0007 μm 3 analytical volume). The results indicates that the 208 Pb ++ / 232 ThO ++ are higher than the true values. Such fractionation can be corrected using a linear regression between 208 Pb ++ / 232 ThO ++ and the M/ΔM10 peak shape parameter, where M is the position of the O2 + peak and ΔM10 the full-width-tenth-maximum for the same peak. This correction results in 15 to 20 % analytical uncertainty on the corrected 208 Pb/ 232 Th age. Nonetheless, this approach opens the possibility of obtaining 208 Pb/ 232 Th ages with sufficient precision to address geological questions on an unprecedented small scale. To illustrate the approach, atom probe geochronology of a small monazite grain from the contact aureole of the Fanad pluton (Ireland) yielded a 208 Pb/ 232 Th atom probe age of 420 ± 60 Ma (2σ) and is consistent with the known metamorphism in the region.

Introduction

The light rare earth element phosphate (LREEPO4) monazite is used widely to establish the timing of rock formation, metamorphism, hydrothermal alteration, and deformation [START_REF] Parrish | U-Pb dating of monazite and its application to geological problems[END_REF][START_REF] Janots | Constraints on fluid evolution during metamorphism from U-Th-Pb systematics in Alpine hydrothermal monazite[END_REF][START_REF] Seydoux-Guillaume | Low-temperature alteration of monazite: Fluid mediated coupled dissolution-precipitation, irradiation damage, and disturbance of the U-Pb and Th-Pb chronometers[END_REF][START_REF] Wawrzenitz | Dating rock deformation with monazite: The impact of dissolution precipitation creep[END_REF][START_REF] Erickson | Deformed monazite yields high-temperature tectonic ages[END_REF][START_REF] Laurent | Two successive phases of ultrahigh temperature metamorphism in Rogaland, S. Norway: Evidence from Y-in-monazite thermometry[END_REF]. In particular, monazite may dissolve and regrow in entirety or partially during fluid-rock interaction, providing a high-fidelity temporal record of this process [START_REF] Poitrasson | Electron microprobe and LA-ICP-MS study of monazite hydrothermal alteration:: Implications for U-Th-Pb geochronology and nuclear ceramics[END_REF][START_REF] Janots | Prograde metamorphic sequence of REE minerals in pelitic rocks of the Central Alps: implications for allanite-monazite-xenotime phase relations from 250 to 610 C[END_REF][START_REF] Kirkland | Fluid-assisted zircon and monazite growth within a shear zone: a case study from Finnmark, Arctic Norway[END_REF][START_REF] Allaz | Microprobe analysis and dating of monazite from the Potsdam Formation, New York: A progressive record of chemical reaction and fluid interaction[END_REF].

During crystallisation, monazite may incorporate several 1000s ppm of U and up to 25% Th which will undergo radioactive decay to Pb at a rate appropriate for geological studies [START_REF] Parrish | U-Pb dating of monazite and its application to geological problems[END_REF]. In situ radiometric dating of monazite thus can be performed using a number of analytical techniques, including laser ablation inductively coupled plasma mass spectrometry (LA-ICPMS) and secondary ionization mass spectrometry (SIMS). However, each isotopic measurement technique has an associated analytical volume (Fig. 1). The techniques attaining the smallest analytical volume can reach down to ~9 μm 3 for NanoSIMS [START_REF] Yang | Precise micrometresized Pb-Pb and U-Pb dating with NanoSIMS[END_REF] and 2.5 μm 3 for SIMS depth profiling [START_REF] Grove | Monazite Th-Pb age depth profiling[END_REF]. However, such analytical volumes are too large to effectively date micrometre to sub-micrometre monazites and their associated textures. As a result, the geological record contained within small monazites and their fine textural domains is unexplored. Nanoscale analyses of monazites have also revealed 10-20 nm Pb-rich clusters and partial replacement reactions [START_REF] Seydoux-Guillaume | Transmission electron microscope study of polyphase and discordant monazites: Site-specific specimen preparation using the focused ion beam technique[END_REF][START_REF] Grand'homme | Partial resetting of the U-Th-Pb systems in experimentally altered monazite: Nanoscale evidence of incomplete replacement[END_REF]. Atom Probe Tomography (APT) is capable of measuring the isotopic compositions of minerals at the nanoscale for volumes <0.0007 μm 3 , four to six order of magnitude smaller than other high spatial resolution techniques [START_REF] Reddy | Atom Probe Tomography: Development and Application to the Geosciences. Geostandards and Geoanalytical Research[END_REF]. The APT analytical approach has been shown to be important in refining our understanding of other accessory mineral geochronometers including zircon [START_REF] Valley | Hadean age for a post-magmaocean zircon confirmed by atom-probe tomography[END_REF][START_REF] Valley | Presidential Address. Nano-and micro-geochronology in Hadean and Archean zircons by atom-probe tomography and SIMS: New tools for old minerals[END_REF][START_REF] Peterman | Nanogeochronology of discordant zircon measured by atom probe microscopy of Pb-enriched dislocation loops[END_REF], Baddeleyite [START_REF] White | Atomic-scale age resolution of planetary events[END_REF], and titanite [START_REF] Kirkland | Assessing the mechanisms of common Pb incorporation into titanite[END_REF], but the potential that nanogeochronology has to unlock otherwise untraceable information remains largely unexplored.

Previous APT analyses of monazite has revealed heterogeneous nanoscale distribution of Pb that has the potential to be used to trace the geological history of the mineral (Fougerouse et al., 2018;[START_REF] Seydoux-Guillaume | Nanoscale resetting of the Th/Pb system in an isotopically-closed monazite grain: A combined atom probe and transmission electron microscopy study[END_REF]. However, 208 Pb/ 232 Th ages extracted from these analyses were inaccurate. These previous studies systematically overestimated the 208 Pb/ 232 Th ratio; however, the reasons for overestimation remained unclear in that work. Nonetheless, the overestimation was hypothesized to result from geological processes leading to unsupported Pb or missing Th from the atom probe mass spectra [START_REF] Fougerouse | Nanoscale distribution of Pb in monazite revealed by atom probe microscopy[END_REF]. In order to better understand the 208 Pb/ 232 Th age inaccuracy of APT data, and any instrumental effects, we have analysed five monazite reference materials of varying composition and age.

Samples

Five monazite reference materials were selected for this study; C-83-32 (2,685 ± 2 Ma; [START_REF] Corfu | Differential response of U-Pb systems in coexisting accessory minerals, Winnipeg River Subprovince, Canadian Shield: implications for Archean crustal growth and stabilization[END_REF][START_REF] Kirkland | Fluid-assisted zircon and monazite growth within a shear zone: a case study from Finnmark, Arctic Norway[END_REF]), DIG19 (1928 ± 2 Ma; [START_REF] Schärer | Isotope systematics and shock-wave metamorphism: II. U-Pb and Rb-Sr in naturally shocked rocks; the Haughton Impact Structure, Canada[END_REF])), B0109G (1137 ± 1 Ma; [START_REF] Bingen | Geochronology of high-grade metamorphism in the Sveconorwegian belt, S. Norway: U-Pb, Th-Pb and Re-Os data[END_REF]), Manangotry (555 ± 2 Ma; [START_REF] Paquette | High resolution (5 μm) U-Th-Pb isotope dating of monazite with excimer laser ablation (ELA)-ICPMS[END_REF][START_REF] Montel | The giant monazite crystals from Manangotry (Madagascar)[END_REF]) and Moacyr (504.3 ± 0.2 Ma;[START_REF] Seydoux-Guillaume | Experimental resetting of the U-Th-Pb systems in monazite[END_REF][START_REF] Fletcher | Matrix effects and calibration limitations in ion probe U-Pb and Th-Pb dating of monazite[END_REF][START_REF] Gasquet | Miocene to Messinian deformation and hydrothermal activity in a pre-Alpine basement massif of the French western Alps: new U-Th-Pb and argon ages from the Lauzière massif[END_REF]). We analysed one specimen from C-83-32 (M1), two specimens from B0109G (M2 and M3), one from Moacyr (M4), two from DIG19 (M5 and M6) and three specimens from Manangotry (M7, M8 and M9). The composition of the different reference materials varies from 3.01 to 13.25 wt.% ThO2, 0.085 to 0.45 wt.% UO2 and 0.16 to 0.9 wt.% PbO and summarized in Table 1. The Th/U ratio varies from 10 to 66. When possible the standard was selected to ensure concordance and avoid decoupling of the parent-daughter radioactive pair [START_REF] Seydoux-Guillaume | Nanoscale resetting of the Th/Pb system in an isotopically-closed monazite grain: A combined atom probe and transmission electron microscopy study[END_REF].

Additionally, a sample with unknown age from the Fanad contact metamorphic aureole in Ireland was investigated (specimen M10, M11 and M12; see section 5). The grain size distribution of the monazites in the Fanad sample was measured using a Tescan TIMA automated mineralogy Scanning Electron Microscope (SEM) in bright-phase search mode.

The bright-phase mode uses backscattered electron images to calculate the monazite grain size. Operating conditions were set at 25 kV and 6 nA, using a spot size of 50 nm with a working distance of 15 mm. The pixel resolution was 1 μm.

Method

Samples preparation

Needle-shaped atom probe specimens were prepared by the lift-out method from the surface of one inch polished resin mounts using a Tescan Lyra3 Ga + focused ion beam mounted on a scanning electron microscope (FIB-SEM) located in the John de Laeter Centre at Curtin University [START_REF] Rickard | Novel Applications of FIB-based Techniques in Atom Probe Tomography Workflows[END_REF]. The ion beam was operated at an accelerating voltage of 30 kV during the manufacturing of the atom probe specimens, with a final polishing stage at 2 kV to remove any surface layer affected by high-energy Ga ion implantation. The final specimen shape was approximately 50 to 100 nm in diameter at the apex of the needle and approximately 300 nm in diameter at 1 μm depth (Fig. 2). Due to the manual manufacturing of the atom probe specimens, each specimen has a slightly different shape.

Atom probe tomography

Atom probe tomography is a technique that provides chemical and isotopic information at sub-nanometre resolution in 3-dimensions [START_REF] Larson | Local electrode atom probe tomography[END_REF]. Atoms are positively ionised and evaporated from the apex of needle-shaped specimens under a high electric field. For non-conductive materials, including most geological minerals, a laser pulse is focussed at the apex of the specimen to trigger the field-induced evaporation of an atom. In ideal cases, atoms are evaporated one at a time. Once evaporated, the ions traverse the ion optics and impact on a position-sensitive detector (detection event) that provides information on the lateral position (X-Y) position of the atoms in the specimen. The sequence of detection events is used to establish the location of each ion along the specimen axis (Z). The identification of ions is determined by their time-of-flight between the laser pulse and the detection event. The timeof-flight of an individual ion is characteristic of its mass and charge state, and the combination of all detected ions form a mass/charge ratio spectrum (Da; Fig. 3). During APT analysis, the voltage (V) evolves proportionally to the tip radius at the specimen apex (R). During APT analysis, the voltage (V) is increased in approximate proportion to the radius at the specimen apex (R) in order to maintain a constant rate of ion detection. This corresponds to an approximately constant electric field (E) required for ion evaporation, following equation (1):

E= V kR (eq. 1)
with a geometrical factor, k, assumed to be constant and equal to 3.3 for this study. Commonly, the FIB-prepared specimens are conical in shape with the tip radius increasing during APT analysis. As a result, the voltage increases gradually during acquisition (Fig. 2). The size of an atom probe dataset is typically between a few million and one hundred million ions, but can be larger. The shape of the analysed volume is dependent on the original specimen shape but typically has a diameter of 50 to 150 nm and a length of up to 1 μm.

In this study, we have used the Cameca Local Electrode Atom Probe (LEAP 4000X HR) housed within the Geoscience Atom Probe facility at Curtin University. The instrument is equipped with a UV laser (λ = 355 nm) and a curved ion flight path (reflectron) in order to increase the mass resolving power and reduce background noise. For all analyses, the specimens were maintained at 60 K, the detection rate at an average of one detected event per 100 laser pulses and the laser was pulsed at 125 kHz. A total of 19 datasets from five different monazite reference standards are reported in this study (Table 2). The raw data was reconstructed using the IVAS software package from Cameca Instruments, version 3.8.2. Corrections to the raw time-of-flight data were made using the default settings for both voltage and flight-path ('bowl') corrections. The O2 + peak at 32 Da was selected for the time-of-flight corrections, using a 'next to leading order' fit for the voltage correction, and a maximum of 4 subdivisions in the piece-wise two-dimensional bowl correction [START_REF] Larson | Local electrode atom probe tomography[END_REF]. The software found the same solution (FWHM value) for every range width selection for the O2 + peak. The mass-to-charge ratio spectra was calibrated using the O + , O2 + , PO2 + , PO3 + , ThO ++ and ThP2O6 ++ peaks.

To investigate the role of laser energy on atom probe data, two specimens (M1 -C-83-32; and M2 -B0109G) were analysed over a range of laser energies between 20 and 500 pJ (Table 2).

Seven datasets where acquired for each of these specimens (M1-1 to M1-7 and M2-1 to M2-7). Such sequential analyses allows investigation of the effect of specific instrument running parameters and permits the separation of the effects of external variables such as differences in needle shape (Table 2). For M1, the laser energy started at 20 pJ (M1-1) and increased to 50 pJ (M1-2), 100 pJ (M1-3), 200 pJ (M1-4), 300 pJ (M1-5), 400 pJ (M1-6) and then decreased to 300 pJ (M1-7). For M2, the laser energy increased from 50 pJ (M2-1), then 100 pJ (M2-2), 200 pJ (M2-3), 300 pJ (M2-4), 400 pJ (M2-5), 500 pJ (M2-6) and then decreased to 300 pJ (M2-7).

Five million atoms were acquired for each dataset with the specimen voltage increasing during each acquisition to compensate for the increasing tip radius of the specimen.

Isotopic quantification

The quantification procedure for isotopes used in this work differs slightly from that applied in previous studies of monazite [START_REF] Fougerouse | Nanoscale distribution of Pb in monazite revealed by atom probe microscopy[END_REF]. Due to the variable U content of the selected standards, 238 U was not always present above the mass spectrum background, and therefore the 208 Pb/ 232 Th isotopic system was used for this study. The quantification of 232 Th was limited to the major Th ionic species ThO ++ . Due to the interference of REEP5O5 +++ molecules (from 124.25 Da) on the thermal tail of the ThO ++ peak (124.02 Da), the full ThO ++ peak cannot be accurately measured. Instead, a narrow range (0.1 Da) was used to measure the counts under the centre of the peak only (Fig. 3 inset). The same narrow range was used to measure the 208 Pb counts using only the 208 Pb ++ peak (103.99 Da). Counts for ThO ++ and 208 Pb ++ were quantified by subtracting the estimated background counts from each peak. The local background level was measured from the counts in a wide 'peak-free' range of 1 Da at ~100 Da for 208 Pb ++ and of 2 Da at ~130 Da for ThO ++ (Fig. S1). These background counts were subsequently normalised to the width of the range used for quantification (0.1 Da).

Uncertainties for each background-corrected isotopic species were estimated from counting statistics for each isotope peak and its correction. The isotopic ratio uncertainties are derived from the uncertainty of each species used for calculating the ratio and reported at 95% confidence (2 sigma) (Table 2).

The instrumental 208 Pb/ 232 Th fractionation parameter (F) is defined by the percentage departure of the APT measured 208 Pb ++ / 232 Th 16 O ++ ratio from the reference material true 208 Pb/ 232 Th ratio, as independently determined, following equation ( 2):

F = � ( Pb 208 Th) 232 � True ( Pb ++ 208 ThO ++ ) 232 � Measured x 100� -100 (eq. 2)
Negative values indicate an overestimation of the 208 Pb/ 232 Th ratio and positive values an underestimation of the ratio. In this study, we have used a half-life of 1.405×10 10 years for 232 Th [START_REF] Audi | The NUBASE evaluation of nuclear and decay properties[END_REF].

Peak shape quantification

When considering probable causes of inaccuracy in 208 Pb/ 232 Th ratios in APT measurements, one of the major influences is likely to be peak-shape variability. Typical mass peak shapes in APT spectra are asymmetric, with an extended tail at the high-mass end due to slow cooling of the specimen tip following the laser pulse. However, the precise shape can vary between acquisitions, depending on materials property and specimen shape, and may also vary between mass peaks within a single dataset, particularly between different elemental/molecular ions and charge states.

To completely correct for the full array of influences on quantification due to peak shape variations is a complex problem. However, a robust and quantifiable measure of 'peak shape' can be sought that may provide sufficient quantification of peak shape effects to be useful in correcting any resulting fractionation. In this work, the mass resolving power, measured as the width at one-tenth of maximum peak height (M/ΔM10) was selected as a metric for quantifying the peak shape. In this expression, M is the position of the maximum peak intensity and ΔM10 the full-width at tenth-maximum.

A method was developed to quantify M/ΔM10, as a proxy for the peak shape. The detailed peak shape quantification is given in the supplementary material. A model curve to a selected peak was fitted using the software package Topas (version 5) [START_REF] Coelho | TOPAS and TOPAS-Academic: an optimization program integrating computer algebra and crystallographic objects written in C++[END_REF]. The largest peak in the monazite spectra (O2 + ; Fig. 3) was selected in order to increase the signal to noise ratio and maximise counting statistics. Data was imported into Topas as mass vs intensity, and the O2 + (31.99 Da) peak was fitted with a split Pearson VII peak shape and a constant background between 31.6 and 32.6 Da in order to avoid the small peaks at mass 33 and 34 Da (Fig. 4). This model was weighted based on counting statistics. Once the peak fitting model had converged, the peak M/ΔM10 at 95% confidence (2 sigma) was calculated.

Results

Chemical and physical parameter variation with laser energy

All datasets investigated appeared homogeneous at the nanoscale and no clusters were observed in the studied standards. Therefore, no emphasis was placed on the effect of clusters as observed in granulite facies monazite grains of the Sandmata complex (India; [START_REF] Fougerouse | Nanoscale distribution of Pb in monazite revealed by atom probe microscopy[END_REF]) and the rogaland complex (Norway; [START_REF] Seydoux-Guillaume | Nanoscale resetting of the Th/Pb system in an isotopically-closed monazite grain: A combined atom probe and transmission electron microscopy study[END_REF]).

The sequential analysis of specimen M1 and M2 (M1-1 to M1-7 and M2-1 to M2-7) reveals the effect of laser energy on various measurement parameters (Fig. 5). The proportion of two charge states of an ion can be used as a proxy measurement of the electric field during analysis.

For individual specimen, the La +++ /La ++ ratio is similar at same laser energies but different voltages (M1: 6.1 kV and 6.8 kV at 300 pJ; M2: 6.5 kV and 7.5 kV at 300 pJ) suggesting a small influence of the voltage on the electric field. However, the La +++ /La ++ ratio is negatively correlated with the laser energy for both M1 and M2 and indicates that the field is weaker at stronger laser energies. The 208 Pb ++ counts decrease at higher laser power in specimen M1, however such decrease is not observed for specimen M2. The decrease in 208 Pb ++ counts in M1

is correlated with the increase of 208 Pb + counts, which is consistent with a weaker field at high laser energies. In opposition, the ThO ++ counts are correlated with increasing laser energy for M1 and M2. The M/ΔM10 value also increases with higher laser energies indicating that the peak is narrower at higher laser energy. These experiments indicate a positive correlation, and a possibly useful relationship, between the measured ThO ++ counts and M/ΔM10.

During these experiments, the same specimen at the same laser energy, but different voltages, did not provide comparable results. For example at a constant 300 pJ laser energy but higher average voltage, the ThO ++ counts change by +2.2% between M1-5 and M1-7, and -2.2% between M2-4 and M2-7.

Molecular fractionation and peak shape

To test the relationship between fractionation and peak shape, we have used all of the data and have selected a subset of the large datasets in order to have comparable dataset sizes. To crop the large datasets, we selected a 40 nm slice (~ 5 million ions) at approximately equidistance from the top and bottom of the reconstructed volume. Using all standards, irrespective of age or Th content, a correlation is apparent between the 208 Pb/ 232 Th fractionation and M/ΔM10 parameter (Fig. 6). A linear regression through these variables yields y = 0.381(±0.048)x -255(±26) with a coefficient of determination (R 2 ) of 0.761. A prediction interval is an estimate of an interval in which a future observation will fall, with a 95% probability [START_REF] Geisser | Predictive Inference[END_REF]. For any value within the range of M/ΔM10 measured, it is possible to calculate the 95% prediction interval for the mean value of y (ŷ) using equation (3):

ŷ ± t α/2 .SE.�1+ 1 n + (x-x̄) 2
(n-1).S x 2 (eq. 3)

With tα/2 the t-statistic parameter for 95% confidence, SE the standard error, n the number of observations, x� and S x 2 the mean and sample variance of all standards M/ΔM10 values, respectively.

Peak shape variation with voltage

To investigate the effect that voltage has on the measured peak shape and fractionation, one large dataset was studied in detail (100 million atoms; specimen M4 -Moacyr). The dataset was cropped using the voltage evolution curve in five even sections of 20 million ions and each section was reconstructed independently (Fig. 7A&B). Finally, an additional five subset were cropped using a 50 nm wide region of interest from the reconstructed atom map at various voltages across the dataset (Fig. 7A). The voltage range was estimated by subtracting the lowest voltage value from the highest value for each subset (delta voltage). The voltage range decreased progressively within the subset succession. The smallest range were measured for the 50 nm subsets (Fig 7C). The M/ΔM10 values for each subset are anticorrelated with the voltage range (Fig. 7C) with the M/ΔM10 parameter decreasing with an increasing voltage range. This correlation is expected because the post-acquisition calibration of the data correct first-order variability in time-of-flight (and thus mass-to-charge state ratios) due to changes in voltage [START_REF] Sebastian | New method for the calibration of three-dimensional atom-probe mass spectra[END_REF]. The variation of the M/ΔM10 parameter with voltage range is also apparent when plotted against fractionation with higher voltage range values resulting in higher dispersion from the 208 Pb/ 232 Th fractionation and M/ΔM10 correlation line (Fig. 7D).

The average voltage dependence on the M/ΔM10 parameter and fractionation is however less clear. In exception of the lowest voltage subset that has a large voltage range (white box on values are also similar at different voltages (Fig. 7D).

Discussion

Effect of instrument parameters on data quality

The ratio of two different charge states of one ionic species is commonly used as a proxy for the strength of the electric field during atom probe analysis [START_REF] Kingham | The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states[END_REF]. In monazite, the La +++ /La ++ ratio decreases with increasing laser energy (Fig. 5). This relationship is interpreted to be the result of lower field strength occurring at higher laser energy. In geological materials, similar observations have been made for zircon [START_REF] Fontaine | Laser-Assisted Atom Probe Tomography of Deformed Minerals: A Zircon Case Study[END_REF][START_REF] Saxey | The Optimization of Zircon Analyses by Laser-Assisted Atom Probe Microscopy: Insights from the 91500 Zircon Standard[END_REF], however the opposite relationships have been observed for rutile [START_REF] Verberne | Analysis of Natural Rutile (TiO 2) by Laser-assisted Atom Probe Tomography[END_REF] and magnetite [START_REF] Schreiber | Applicability of postionization theory to laser-assisted field evaporation of magnetite[END_REF].

The weaker field with increasing laser energy also affects the 208 Pb ++ and ThO ++ counts. With lower field, the 208 Pb ++ counts significantly decrease for specimen M1 (C-83-32). However, 208 Pb ++ counts remained relatively constant for specimen M2 (B0109G; Fig. 5). Two possible scenarios can explain this observation. The first scenario is that the field varied in smaller amounts in specimen 2 than in specimen 1. This seems unlikely because the La +++ /La ++ ratio varies in a similar fashion for both specimens. Alternatively, the compositional difference between the two standards may influence the ionic evaporation of Pb. However, this theory needs further testing with additional analyses.

In contrast, the ThO ++ counts increases by up to 40% for M1 (M1-1 to M1-7) and 20% for M2 (M2-1 to M2-7; Fig. 5), indicating that higher laser energy and lower field has a strong effect on ThO ++ counts. Molecular ion formation is generally prevalent in lower fields [START_REF] Kirchhofer | Thermal effects on mass and spatial resolution during laser pulse atom probe tomography of cerium oxide[END_REF], suggesting that ThO can be more affected by the field conditions than Pb in monazite. Several Th-bearing ionic species have been identified in the mass spectra of monazite (ThO ++ , ThPO3 +++ , ThPO4 ++ , ThP2O6 +++ ; [START_REF] Fougerouse | Nanoscale distribution of Pb in monazite revealed by atom probe microscopy[END_REF]). However, when encompassing all identified peaks at a given laser energy, the Th content remains largely underestimated [START_REF] Fougerouse | Nanoscale distribution of Pb in monazite revealed by atom probe microscopy[END_REF][START_REF] Seydoux-Guillaume | Nanoscale resetting of the Th/Pb system in an isotopically-closed monazite grain: A combined atom probe and transmission electron microscopy study[END_REF]. A missing Th ionic molecule could cause this underestimation. Given the complexity of the monazite mass spectra (Fig. 3), it is likely that an unidentified Th-bearing species could be overlapping with another major molecular species. The observation that ThO ++ increases with a decreasing field suggests that the missing molecule could be triply-charged. Doubly-charged molecules would preferentially form at the detriment of triply-charged molecules in lower field conditions [START_REF] Kingham | The post-ionization of field evaporated ions: A theoretical explanation of multiple charge states[END_REF]. A potential candidate is ThPO4 +++ overlapping with LaPO3 ++ at ~109 Da.

The various plots in figure 5 show the effect of some analysis parameters on the measured chemical makers. The voltage range experiment (Fig. 7) indicates that the specimen voltage and therefore specimen shape, only play a minor role in the measured 208 Pb ++ and ThO ++ counts. At fixed laser energy, but different voltage, the ThO ++ counts varied by +2.2% and -2.2% in the two specimens investigated (Fig. 5).

Another factor responsible for the ThO ++ increase is higher mass resolution. The methodology to quantify the ThO ++ counts rely on measuring the counts within a narrow range (0.1 Da), below the centre of the peak, at its maximum height. A higher mass resolving power (M/ΔM10)

indicates that the peak is narrower and therefore higher at equal signal. The observation that M/ΔM10 increases with higher laser energy suggests that the ThO ++ counts will increase in proportion to the laser energy. However, the increase in the M/ΔM10 is unlikely sufficient to account for the 40% increase in ThO ++ counts on its own. Hence, it is likely that the observation of increasing ThO ++ counts at higher laser energy is due to the combined effect of preferential ThO ++ formation to detriment of other triply-charged molecules and higher mass resolving power (M/ΔM10) values.

In our data, the M/ΔM10 peak parameter increases with laser energy. This trend is opposite to the trend observed in Zircon and Rutile [START_REF] Saxey | The Optimization of Zircon Analyses by Laser-Assisted Atom Probe Microscopy: Insights from the 91500 Zircon Standard[END_REF][START_REF] Verberne | Analysis of Natural Rutile (TiO 2) by Laser-assisted Atom Probe Tomography[END_REF] but is similar to what is observed in tungsten carbide [START_REF] Peng | Evaluation of analysis conditions for laserpulsed atom probe tomography: example of cemented tungsten carbide[END_REF] although it is unclear what effects the laser stepping protocol may have on peak shape. In monazite, we demonstrated that at higher laser power, the field at the apex of the specimen is reduced, suggesting that less spontaneous evaporation would occur between pulses and this could be the explanation for the narrower peaks.

Monazite 208 Pb/ 232 Th geochronology by atom probe tomography

The radioactive decay of a radionuclide is characterised by its half-life constant. Such a characteristic is based on a probability function and the half-life of a radioactive element is therefore most accurate for an infinite number of atoms. In the case of 208 Pb/ 232 Th nanogeochronology described here, we have used volumes that encompass between 15,000 and 100,000 232 Th atoms, in which volume half-life is still a viable concept.

Using the linear correlation between the 208 Pb/ 232 Th fractionation coefficient and the M/ΔM10 peak parameter, it is possible to use atom probe tomography to measure unknown monazites and derive a 208 Pb/ 232 Th age. The M/ΔM10 value (x) measured for any atom probe data can be used to predict a 208 Pb/ 232 Th fractionation factor (y) using y = 0.381(±0.048)x -255(±26). The error propagation of the prediction is given by the uncertainty of the M/ΔM10 value, the uncertainty of the measured 208 Pb/ 232 ThO ratio and the 95% prediction band of the calibration defined by equation ( 3).

In atom probe data, the uncertainty on 208 Pb/ 232 Th age is limited by counting statistics, and background and fractionation corrections. The counting statistics and background correction indicates that the maximum precision attainable for a dataset larger than 5 million atoms is 1.5 to 2% (2 σ) on individual analyses. To test the effect of the fractionation correction on the 208 Pb/ 232 Th age precision and accuracy, the methodology has been applied on the same datasets used for this study. For dataset M9 (Manangotry 555 ± 2 Ma; [START_REF] Paquette | High resolution (5 μm) U-Th-Pb isotope dating of monazite with excimer laser ablation (ELA)-ICPMS[END_REF]), an arbitrary 50 nm slice in the middle of the dataset was cropped from the reconstructed 3d atom map (Fig. 7). The M/ΔM10 parameter is 554.2 ± 1.8, yielding a predicted 208 Pb/ 232 Th fractionation coefficient of -43.3 ± 6.7 %. Using the measured 208 Pb/ 232 ThO ratio of 0.0486 ± 0.0017, a fractionation corrected 208 Pb/ 232 Th ratio of 0.0276 ± 0.004 is calculated for an age of 550 ± 86 Ma

(2 sigma). The predicted age is in good agreement with the published age of 555 ± 2 Ma [START_REF] Paquette | U-Pb, single zircon Pbevaporation, and Sm-Nd isotopic study of a granulite domain in SE Madagascar[END_REF], with uncertainties on the order of 16% at 2 sigma for a for a subset of an atom probe data set having a volume of approximately 0.0007 μm 3 . By comparison, monazite SIMS analyses have typically uncertainties in the order of 1 to 2% for a volume of <10 μm 3 . Calculating weighted mean average fractionation corrected 208 Pb/ 232 Th ages for each standard (Fig. 8; one data point per atom probe analysis), yields 551 ± 51 Ma (n = 3; MSWD = 0.046; probability = 0.95) for Manangotry (555 ± 2 Ma [START_REF] Paquette | U-Pb, single zircon Pbevaporation, and Sm-Nd isotopic study of a granulite domain in SE Madagascar[END_REF]), 1136 ± 74 Ma (n = 8; MSWD = 0.32; probability = 0.94) for B0109G (1137 ± 1 Ma; [START_REF] Bingen | Geochronology of high-grade metamorphism in the Sveconorwegian belt, S. Norway: U-Pb, Th-Pb and Re-Os data[END_REF]) and 2707 ± 150 Ma (n = 7; MSWD = 0.55; probability = 0.77) for C-83-32 (2,685 ± 2 Ma; [START_REF] Corfu | Differential response of U-Pb systems in coexisting accessory minerals, Winnipeg River Subprovince, Canadian Shield: implications for Archean crustal growth and stabilization[END_REF]). No weighted mean average is calculated for DIG19 and Moacyr as only two and one dataset for each standard was acquired, respectively.

Recommendations

To obtain reliable isotopic information from atom probe measurements of monazite, several parameters can be optimised, in particular for 208 Pb/ 232 Th chronology. ThO ++ counts increase with laser energy, in contrast 208 Pb ++ counts decrease with laser energy. However, the uncertainty on the counting statistics of the 208 Pb/ThO ++ ratio improve at higher laser energy.

In contrast, the uncertainties characterizing the M/ΔM10 peak parameter, which is used to correct the molecular fractionation, is not systematically affected by laser energy. These relationships indicate that laser energy in the 200 to 400 pJ range is optimal. Monazites with low 208 Pb content (young or low-Th crystals) may require further optimization of running conditions in order to maximise the 208 Pb ++ peak. In the latter case, low laser power in the 50 to 100 pJ range may be more appropriate.

Holding laser energy constant, the voltage applied to the atom probe needle affects the M/ΔM10 fractionation parameter. A smaller range of voltage results in a more reliable peak shape quantification and we recommend use of a subsection of any atom probe dataset where the voltage range is limited to ensure reproducibility. We have found that a 40 to 50 nm portion of the entire dataset, or a 5 million ion subset, to work well in 208 Pb/ 232 Th geochronology of monazite. Also, to minimize the voltage change during data acquisition, specimens may be prepared with low shank angles, and data collected only after the initial shaping of the tip has completed and the voltage is increasing more slowly (Fig 7).

Datasets presenting Pb-rich cluster can also be investigated [START_REF] Fougerouse | Nanoscale distribution of Pb in monazite revealed by atom probe microscopy[END_REF][START_REF] Seydoux-Guillaume | Nanoscale resetting of the Th/Pb system in an isotopically-closed monazite grain: A combined atom probe and transmission electron microscopy study[END_REF]. From the same subset, as defined above, the age of clusters and matrix can be measured together, or the matrix can be sub-sampled and measured separately. This approach can potentially provide additional information about the history of the crystal and mechanisms for Pb mobility [START_REF] Fougerouse | Time-resolved, defect-hosted, trace element mobility in deformed Witwatersrand pyrite[END_REF].

The derivation of a physically realistic model of the peak shape and associated background would allow for the modelling of entire sections of a spectrum and potentially would allow for a more precise extractions of isotopic abundances.

As shown in our data, the fractionation correction protocol defined in this study can be applied over a range of monazite composition, specimen shape (no dependence on voltage) and laser energy. Such benefits are desirable for APT in order to adjust the acquisition parameters based on the data quality for individual samples.

Case study: dating the contact metamorphism of the Fanad granite, Ireland

The granites of the Donegal region in the North of Ireland represent a classic example of a range of granite emplacement mechanisms [START_REF] Pitcher | The geology of Donegal: a study of granite emplacement and unroofing[END_REF]. These intrusions formed during the Early Devonian, at the close of the Caledonian Orogeny between c. 418 to 397 Ma, and were in the main emplaced into a major SW-NE trending sinistral shear zone system [START_REF] Kirkland | The brittle evolution of a major strike-slip fault associated with granite emplacement: a case study of the Leannan Fault, NW Ireland[END_REF]. The Fanad pluton is an important constituent of the Donegal granites that has yielded a Rb-Sr isochron age of 402 ± 10 Ma, interpreted as the magmatic crystallization age [START_REF] O'connor | Rb-Sr whole-rock isochron studies of the Barnesmore and Fanad plutons, Donegal, Ireland[END_REF]. Petrographically the granite is mainly coarse grained and sometimes porphyritic granodiorite, but it ranges to monzogranite, monzonite and monzodiorite. [START_REF] Pitcher | The geology of Donegal: a study of granite emplacement and unroofing[END_REF] indicate that the Fanad pluton was emplaced into metasediments of the Ards Quartzite Formation, Neoproterozoic Dalradian Supergroup [START_REF] Berger | The structural setting of the Main Donegal Granite; comments on a recent interpretation[END_REF]. The country rock consists of well-bedded and massive feldspathic quartzites and pelites (Fig 9A). In pelites close to the batholith, numerous small monazite grains are present, often developed as inclusions within prograde metamorphic biotite crystals. We interpret these textural relationships as consistent with crystallisation of monazite during contact metamorphism associated with emplacement of the Fanad granite.

To determine an age on these minute monazite crystals a 6x2 μm grain was analysed by atom probe. The investigated monazite sits as an inclusion within a biotite grain (Fig. 9B), some 990 metres from the intrusion contact with pelites as measured from the present day land surface.

This monazite was selected because it was possible to prepare three atom probe specimens from it, although smaller grains could have also been analysed (Fig. 9C).

Conclusion

In this study we define a protocol to correct fractionation in atom probe analysis between [START_REF] Seydoux-Guillaume | Experimental resetting of the U-Th-Pb systems in monazite[END_REF]2: Seydoux-Guillaume et al., 2004;3: Paquette et al., 1994;4: Schärer and Deutsch, 1990;5: Corfu, 1988;6: Didier, 2013;7: Bingen et al., 2008;8: Kirkland et al., 2009. Table 2: Standard description, APT analytical parameters and results. The bin size is 1 μm; D) Raw data (squares) and corrected (circles) 208 Pb/ 232 Th ages. The 420 ±

Fig

  Fig 7A), the other 50 nm subregions cluster at similar M/ΔM10 values and no systematic relationship between M/ΔM10 values and voltage is apparent. The measured fractionation

Figure 1 :

 1 Figure 1: Comparative analysis volumes for selected dating techniques. ID-TIMS: Isotopic Dilution -Thermal Ionization Mass Spectrometry; LA-ICPMS: Laser Ablation -Inductively Coupled Plasma Mass Spectrometry; SIMS: Secondary Ion Mass Spectrometry; EPMA: Electron Probe Microanalyser. Left side panel: each volumes are represented on a schematic monazite grain (diagram to scale).

Figure 2 :

 2 Figure 2: A) SEM image of a monazite atom probe specimen; B) 3-D APT atom map. Only 232 ThO ++ and 208 Pb ++ atoms are displayed; C) Voltage evolution curve during APT analysis. The voltage increases to compensate for the specimen radius increase.

Figure 3 :

 3 Figure 3: A) APT Mass-to-charge spectra of monazite. Close up for 208 Pb ++ (B) and 232 ThO ++ (C).

Figure 4 :

 4 Figure4: Example of the peak fitting result of the O2 + peak for one dataset. The black line is the experimental data and the red line is the fit. The M/ΔM10 is given by the position of the O2 + peak divided by the full-width-at-tenth-maximum (FWTM).

Figure 5 :

 5 Figure 5: Sequential analysis of specimen M1 (C-83-32; blue) and M2 (B0109G; yellow). The voltage value is the average voltage between the start and the end of the analysis. Error bars are smaller than the symbols. A) 208 Pb ++ counts normalised to 1 million atoms; B) La +++ /La ++ ratio for each analysis; C) 232 ThO ++ counts normalised to 1 million atoms; D) M/ΔM10 peak shape parameter for each analysis.

Figure 6 :

 6 Figure 6: M/ΔM10 peak shape parameter in function of 232 ThO/ 208 Pb fractionation (%) for all standards. The data are correlated and is defined by y = 0.381(±0.048)x -255(±26) with a coefficient of determination (R 2 ) of 0.761. The dark grey area represents the 95% confidence band and the light grey area the 95% prediction band.

Figure 7 :

 7 Figure 7: Effect of voltage on data quality for specimen M4 (Moacyr). A and B) Sequential reconstruction by 20 million ions subsets (colour coded) and 50 nm subregions (grayscale coded). The subsets on A and B are colour coded for C and D; C) Voltage range (delta voltage)

Figure 8 :

 8 Figure 8: Raw data (squares) and corrected (circles) 208 Pb/ 232 Th ages for (A) Manangotry, (B) B0109G and (C) C-83-32. The uncertainties are given at 2 sigma. The weighted mean average ages are in good agreement with the published standard ages.

Figure 9 :

 9 Figure 9: A) Simplified geological map of the Fanad granite and host metasediments (Donegal region, Ireland). The sample location from the pelites is indicated with a star; B) Micrograph of the monazite grain selected for this study. Three atom probe specimen were prepared from the 6x2 μm grain; C) Monazite grain size (diameter) distribution in the thin section studied.

Table 1 :

 1 232 ThO++ and 208 Pb ++ in monazite crystals with sample volumes <0.0007 μm 3 . The methodology we have developed is by far the highest spatial resolution technique for isotope geochronology of monazite. The M/ΔM10 peak shape parameter appears to adequately characterise the degree of molecular fractionation to allow results that can address a range of geologically pertinent questions. The uncertainties calculated on ages using this method take into account counting statistics, background correction, and fractionation effects. The uncertainty on the fractionation corrected 208 Pb/ 232 Th ratio is currently between 15 and 20 % (2 σ). Instrument running parameters can be optimised for nanogeochronology of monazite with the laser energy in the range 200 to 400 pJ and limiting large datasets to c. 50 nm wide crops to curtail the range of voltages applied to the specimen during analysis. This new technique opens up the potential to date small monazite grains and grain domains which have hitherto been vastly below the spatial resolution of geochronology. Table1: Reference material composition and age in wt.%; 1: Seydoux-Guillaume et

	Resource Sciences Precinct (NRSP) -a collaboration between CSIRO, Curtin University and
	The University of Western Australia -is supported by the Science and Industry Endowment
	Fund (SIEF RI13-01). The authors gratefully acknowledge support of Curtin University's
	Microscopy & Microanalysis Facility and the John de Laeter Centre, whose instrumentation
	has been supported by University, State and Commonwealth Government funding. DF
	acknowledges ARC funding DE190101307.
	Figure captions:

Acknowledgments

The Australian Resource Characterisation Facility (ARCF), under the auspices of the National

Availability of data

The data that support the findings of this study are available on request from the corresponding author. The data are not publicly available due to privacy or ethical restrictions.